One of our regular readers, who is a member of a college mathematics faculty, sent this following comment about the state of math education today:

“I teach at a small four year college in NY. We administer a mathematics placement test to all incoming freshmen. The test we use was created in house and covers basic skills from algebra, trigonometry, and pre calculus. Questions are asked in a straightforward manner (unlike the current NYS common core based regents exams).

“Any student may take a statistics class (taught outside the mathematics department), regardless of placement score. However, we use the results of the placement test, high school coursework and individual discussions with the students to place students appropriately in the remedial algebra, college algebra, pre calculus, calculus sequence.

That said, fully 25% of our incoming freshmen place into remedial algebra–some should probably be placed lower than

remedial algebra, but we do not offer such a course. These students truly need the remedial work.

“The reasons why these students place low are varied. Some have not taken math courses for two years and have become rusty. Some students never really learned the material (the percentage of points required to pass the NYS regents exams is quite low and the tests are so poorly designed that scores are meaningless).

“I am continually bombarded by emails from companies who want to sell textbooks that combine remedial coursework with college credit coursework. Perhaps in some non STEM fields this approach works, but you cannot teach calculus to students who haven’t learned how to add fractions or who don’t understand basic laws of exponents.

“I do not blame their teachers. I blame a state system that shoves a scientific calculator in the hands of every fourth grader–before they’ve learned their multiplication tables, before they’ve learned how to add fractions, and before they’ve gained any practical sense of how numbers work, because apparently solving convoluted word problems is more important than understanding how numbers work. (Some never learn these basic skills–I have students in my classes who need a calculator to multiply 2 times 3).

“This same state system requires every student in algebra to have access to a graphing calculator with equally disastrous results. Calculator overuse is only a small part of the problem. The insistence that all students follow what used to be considered a college prep track and the subsequent rewriting of standards into a bizarre jumble of topics in which necessary skills and techniques are deemphasized in favor of solving pseudo “real world” applications are certainly major contributors.

“The regents exams have become a weird mishmash of questions with teachers left trying to guess all the permutations of how a question about a concept could be asked. I am afraid I have wandered off topic a bit. Anyway, many students truly do need remedial work that cannot be accomplished as part of another course. We do our best to get them through it and get them where they need to be mathematically. We are not 100% successful. Some simply do not have the ability, some do not make the effort, and saddest of all, some are just too far behind.”

Any comments from math teachers?

Ouch, time to get back to the basics! NYS take notice.

I was a public school teacher in California for thirty years (1975 – 2005), and I seldom read or hear anyone mention the children who make no effort to learn for whatever reason.

There are children that don’t cooperate in class.

There are children that don’t do the classwork.

There are children that don’t do the homework.

There are children that don’t read books, magazines, newspapers, etc.

There are children that do not come to class with paper, pen, pencil or textbook and some of them refuse to take a pencil and sheet of paper paid for by me, the teacher.

There are children that refused to open a textbook when me the teacher provided a copy from my class set.

When I started teaching in the late 1970s, more than half of the children I taught turned in homework and most, but not all, paid attention in class and focused on class work.

When I left teaching for a CalSTRS retirement check (a monthly retirement check I earned because 8% of my gross pay was deducted from my pay for 30 years in addition to an additional 8.25 percent the school district contributed), I still took a 40-percent pay cut and left with no medical coverage, only 5=percent of my students turned in homework and many more did not bother to cooperate and/or do the classwork.

Lloyd,

I totally agree. And to add insult to injury are those who think that teachers must somehow “motivate” students with games and fun and bells and whistles. If your students aren’t happy and perky and loving every minute of you and your wonderful, exciting class, well, then there’s something wrong with YOU, the teacher! Motivation is not something a teacher can make kids “have.” Motivation is self directed. As a teacher, I can do my best to make the subject interesting, etc. but that doesn’t mean that all students will be on board. I definitely think that the responsibility of the student is one of the least discussed issues in education. 🙂

I remember talking to a fellow teacher who made the mistake of starting her class by telling them that they were going to have fun (high school history). After a month or two one of her students asked when they were going to start having fun!

@Mamie Krupczak

We had an interesting variation of this at my school a few years ago when one of our administrators tried to push the idea that kids were skipping class because “you teachers aren’t being interesting enough.” That comment met with some very harsh push-back.

Every time one of these idiots (reformers or clueless local administrators) open their mouth, another angel gets punched in the crotch.

Lloyd, I have seen the same phenomenon, and am leaving next year. You can not teach the unwilling. I have some measure of satisfaction teaching adult education classes at night, many former students show up and tell me they are sorry and wish they had paid attention in class. Now, in Nevada, their lack of effort is somehow my fault.

It’s almost as if they didn’t like being locked up all day and treated like sub-humans by authority figures.

🙂

1st – a classroom is not the same as being locked up in a prison or jail. If my brother was still alive, I’d tell you to talk to him. He hated school and then because of his rebellious nature in his youth he spent 15 years of his life in prison. As an adult in his forties, he went back to adult night school on his own and put up with those alleged “authority figures” in a last attempt to learn to read.

If children become avid readers, critical thinkers, problem solvers, and life-long learners, that’s like insurance that they will be free. I prefer that over working for some authoritarian corporate ass hole like the malignant narcissist in the White House. Learning does not take place in a fun zone where everyone is doing what they want with no direction.

2nd – There are always authority figures in life unless you live in a libertarian fantasy land, but there has never been a libertarian country because when there are no authority figures, it’s anarchy, and anarchy means rape, murder, robbery, etc. This is what happened in China during Mao’s Cultural Revolution, and the Chinese that lived through that insanity do not want that back.

Details Lloyd.

The article was written by a Professor at a 4 yr private institution in NY

Only 25 % of his students required remedial help . So one has to question the demographic /economic make up of that freshman class.

Assuming that it was a private college there are no small 4yr state schools in NY ( the smallest Geneseo is a rather elite college, perhaps the toughest entrance requirements in the system ) leads me to believe several things are possible .

1)The economic privilege of his students is far above the median .

2) The entrance requirements may be tailored to buying oneself into a

4 year school . These are students who likely would have wound up

in a community college ,vocational training programs or work if not

not for their wealth.

3) Comparing the children of privilege to your students is a totally

false comparison.

4) The authors complaint is about the fundamental way math is

taught not the Teachers or the students , In short the standards.

Including “College and Carrier Ready ” requirements .

Complaining that calculators have been shoved into children’s

hands before they can add ,

In short Lloyd take a chill on this one. I think we are talking apples and oranges and although I suspect that some of what you describe may be applicable to what he is talking about .The 75% of his students that do not need remedial help did not learn the material by osmosis . They did their work.

This non teacher who comes to the defense of teachers all the time is not prepared to blame your students for their failure. There was a fundamental argument in the social sciences one that had been settled

in the 60’s but the right has brought back to life, in their attempt to portray failure as individual and justify inequality .

Economics determine ethos not the other way around !

The failures of your students reflect a lot of things few of them will be solved in the school.

I understand.

“This non-teacher who comes to the defense of teachers all the time is not prepared to blame your students for their failure … The failures of your students reflect a lot of things few of them will be solved in the school.”

I don’t blame those children, that I struggled to teach, who made little or no effort to learn. I blame the ravages and/or effects caused by the poverty in an area dominated by violent multigenerational street gangs, and a top-down micromanaged education system that starts in the White House to state legislatures and governors, and is supported by billionaire oligarchs like Besty DeVos, Bill Gates, Suckerberg, etc.

Most if not all of these billionaire autocrats, these want-to-be clueless future fascists, and misguided fools, were born into wealth and went to elite private schools. Their flawed and wrong assumptions are making a difficult situation impossible.

Those children and their teachers have been forced into a closing vice. One side of the vice is represented by the privileged autocrats and the other by poverty and street gangs.

As the vice closes and the children and teachers start to bleed, the blood that escapes and drops from the vice comes from dedicated teachers losing their jobs, the community-based, democratic public schools being closed and sold or given away, and the children that are being tossed aside because they don’t fit into the autocratic, often inferior and fraudulent, often child abusive corporate charter schools.

Lloyd Lofthouse

So we agree .

The answer to economic inequality is not through education although some individuals will escape poverty through education. The experience of our college educated millennial’s deeply indebted and earning less than their parents argues otherwise. As we educate more and more to be college ready that will worsen . The majority of jobs we are creating are in low wage not high wage sectors of the economy.

So educate yes and I have no problem with free higher education for all . But to solve the problems of poverty and thus education, requires solving the problems of inequality. That requires empowering workers as was done in the thirties. That in turn will correct the imbalances in the distribution of goods and services , wealth .

Further there are no hard fast laws of economics that dictate the way our economy functions and is structured . It is structured by the elites so that we have that inequality, with all wealth flowing to the top.

As Baker argues in “Rigged”

Germany for instance has a well paid thriving manufacturing sector in spite of investing multiples of what we do in robotics( at the expense of the EU). Detroit would not be gutted if the South had not been Right to Work . Those 22 + transplant auto assembly plants all in Right to Work states did not arrive in the country due to production considerations. it was a deal that Reagan made in exchange for higher import quotas . Trade agreements are structured not for the people of any Nation but for the elites who control multi national corporations . Making people in India pay for patent protected drugs does not advance the interest of Indians or Americans. And on and on …

Yes, we agree.

If i learned anything form 25 years of teaching and blogs like this one, nothing will change until the conversations about education drop the term “failing schools” and replace it with “failing students”. When that happens it may be possible for society to place the focus where it belongs such as the home and surrounding environment of students that encourage/discourage academic excellence. The continued use of “failing schools” has played right into the hands of the “reformers” seeking to enrich themselves.

In the faux “reform” movement, failing students only exist in charter schools where it is ALWAYS the fault of the violent 5 year old student (of which they have huge numbers!) that forces the school to give her an out of school suspension. Or flunk her. Or humiliate her. The kids are no good and they are to blame when they aren’t achieving in those charter schools that pretend to be working miracles with all kids except the blameworthy ones who just “got to go”.

But there are NO failing students in publics schools. There, it is all the fault of the teachers! In fact, a charter can rid themselves of a “failing” student by sending him back to a public school and then the student is no longer failing anymore! Then all the blame goes to the public schools.

Students who can’t cut it will always be at fault if they go to charters and always be absolved of blame if they attend publics where the reformers want to blame teachers.

The ideal solution from these reformers is to concentrate the good students in private charters and corral the “bad” ones in underfunded public schools. That provides the ideal comparison for charters whose billionaire supporters pay some of the most morally corrupt academics to do the kind of studies that would be laughed out of the scientific community! I’m going to compare this “random” group of kids — minus all the kids that are drummed out of the group because they have academic issues — with this other “random” group of kids — which includes all the students drummed out of group one! The two groups are exactly the same! Just like one of those drug studies where one group of “randomly” selected patients — minus all the patients who don’t do well on the drug — are compared with another group of “randomly” selected patients that include all the rejected patients from the other group!

You won’t be surprised to learn that the drug taken by the group of patients where all patients who did poorly when they took the drug is now claiming 100% success! And that the other drug, where the control group could not weed out patients AND had to accept the patients drummed out of the miracle drug group, was a failure in comparison.

That’s the kind of “science” purchased by the reform movement. Willing to hurt countless patients by misleading people and pretending a drug has a 100% success rate when their “studies” drum out each and every patient who isn’t successful.

Agree!

Michael I agree about “failing schools”. I have a problem with raising standards, making students accountable, and increasing graduation rates. How would all three occur? What miracle will occur in the area of instructional practice? Looks like the latest recipe for snake oil.

Oh I get it… it failed to occur so the school is failing.

“I blame a state system that shoves a scientific calculator in the hands of every fourth grader–before they’ve learned their multiplication tables…”

This started years ago. In the early 70s when I was in elementary school, students were just starting to be required to use calculators. My father went in to the teacher and said that I would NOT be using a calculator until I learned to do math by memorization and on paper. My dad hated the “new math” of the early 70s and complained to teachers that the textbooks were wrong. My dad really taught me math. I can’t say I recall learning anything from math teachers. He taught me to make pictures to represent math problems and to think in terms of money (because nobody wants to get cheated on that!). Math was so hard for me – truly a language I had a lot of difficulty understanding. A few years ago, when trying to figure out whether a new TV set would fit in my old armoire, I remembered somewhere in the cobwebs of my mind, there was something called a “hypotenuse” and that helped me (somewhat tangentially) to figure out if the tv would fit. 🙂 I can say with certitude that, as an adult, I’ve never had to figure out any math problem that started with, “A train leaves the station at 8:00am….” Most of the math we learn in high school is just brain exercises – which is fine. But most people won’t have to work with advanced math all their lives. So, is it REALLY that BAD if students don’t know it? Of course, if they are going into a field that requires a lot of math, it would be a problem. I wish the majority of people felt that it was important that everyone spoke French. It would sure making finding a job a lot easier! 🙂 🙂

“But most people won’t have to work with advanced math all their lives. So, is it REALLY that BAD if students don’t know it?”

Someone on this blog, I think, answered that perennial question, “When are we going to use this?” with s/he didn’t know, but they sure would know that they didn’t know it if they needed it in the future. We really can’t predict what knowledge will be useful to each individual. How many of us really knew what s/he was going to do with his/her liife and what would be necessary to know in advance? How many of us dismissed certain life or career endeavors because we knew or felt we were not well enough prepared to even pursue more education in that area? That being said, as a special educator who spent a lot of time trying to teach middle school students basic math, I cursed the calculator that allowed teachers to move ahead when these students had no clue about the what or why of performing certain operations. My sister, who was a high school math teacher, taught both remedial and advanced math classes. She would agree with you that many students will have little use for advanced math concepts. Perhaps it is time to have math teachers sit down together and hash out what is appropriate for whom and when. As far as I can tell, they did a pretty good job of it before the business community and policy wonks decided they were much more able to direct school curriculum than the educators responsible for teaching it.

“We really can’t predict what knowledge will be useful to each individual.”

That argument can be made about any subject though. Who’s to say we won’t need music – should every kid be required to learn a musical instrument? Why shouldn’t every kid learn engine repair or West African civilization or Tagalog? What if a kid grows up and realizes she really wants to be a Broadway performer, but never took dance or voice lessons?

It isn’t what the children learn. It isn’t what they remembered from what they were taught. What counts is children who are avid readers, problem solvers, and critically thinkers who then become life-long learners.

Us humans have a faulty and/or complicated memory process. We don’t remember everything we see, hear and experience. We don’t remember everything we are taught. There is short-term memory and then long-term memory and the transfer of short term memory to long term while we sleep. What happens to something a child learned in class one day that is deleted that night during the sorting process while sleeping?

Heck, many of my students forget all about the homework that was assigned during class and repeated by me at the beginning and at the end as a reminder. The next day many students accused me of not telling them about the homework even though I wrote the assignment on the board and used a yard stick to point it out as I read it to my classes more than once each period.

Standardized tests do not create avid readers, problem solvers and critical thinkers and life-long learners. Standardized tests cause most if not all children to hate school, to hate learning, to resent teachers.

HI Lloyd,

Agreed again. My mother used to say that what we learn in school is just the jumping off point and that we can learn anything if we learn HOW to learn! I always tried to impress that on my students and help them discover how they learn best. Also, over 25 years, I’ve seen a real decline (generally) in students inquisitiveness. There’s more to be excited about these days including snapchat, texting friends, playing games on their phones, etc.

Spedukatr,

I have shared before what I told students who would question learning “Why should I learn Spanish, I’ll never use it?”

My response was this: “I’ll tell you what, when you turn 21, please look me up and we’ll go to the boats (casinos in Missouri have to “be on water, a joke in itself). I’ll supply the cash and since you can see into the future, we’ll be able to get rich knowing ahead of time what is happening at the tables. We’ll have a lot of fun and then I can retire and not have to teach students who don’t want to learn.” It always brought a howl of laughter from the class.

Good thing no adminimals ever heard me tell a student that as I surely would have been written up-but then again, that wouldn’t have been anything new either.

Much better way of expressing my thoughts. It always made sense to me that maybe the teacher(s) who taught a subject were probably better prepared to decide what should be included or not. I retained more in those classes that really interested me, but I learned something about the subject and how to think even in those that didn’t always float my boat.

” What if a kid grows up and realizes she really wants to be a Broadway performer, but never took dance or voice lessons?”

Seriously? Then if she wants to go for it she will have to work damned hard and most likely will not make it. I am assuming that this individual spent some time singing and dancing on their own.

In any case, you ignored the part of my comment where I suggested that maybe those who are educators in their field are more likely to know what should be included in a course of study and what we want our children to at least be exposed to. We can’t make anyone learn anything. That requires some effort from the learner. We as a community/society may require our children to take certain subjects/courses that we feel will help them lead productive adult lives. What they actually end up using,…who knows. We cannot possibly prepare each individual for every contingency that might affect their future lives beyond trying to give them some foundational knowledge and skills.

“We can’t make anyone learn anything.”

It’s the old saying “You can lead a horse to water but you can’t make it drink.”

To which a country boy through and through biology teacher added this corollary when the adminimals would try to blame teachers for a student not learning “Yep, and I’m not sucking on the back end to make it”.

Oh, Duane! It took this basically suburban girl (even though I had uncles who farmed) a few minutes to process your “country boy” comment. Like!

As a parent of two autistic kids, ages twenty-one and seventeen, I can tell you that both my children had difficulties in math because of the way they were taught math. Forcing elementary school kids to learn both basic AND higher-level math at the same time did nothing but confuse my kids and frustrate them. You have to learn to walk before you can run.

Teaching LITTLE KIDS pre-algebra and geometry is a fat waste of time! It’s not remotely age-appropriate for kids in the third, fourth and fifth grades to be learning high-level math when they haven’t mastered addition, subtraction, multiplication, division, and fractions. It’s just too confusing and frustrating. But it seems that politicians are far too interested in competing with Asian countries’ test scores (which aren’t accurately reported) than in how our kids actually learn.

My daughter’s high school math teacher told me that she was frustrated by the way the lower grades were being taught in our district. She told me that she had to reteach all the incoming freshman from scratch. My daughter had the hardest time with math and math now causes her severe anxiety. But I knew she was grasping math when she took Chemistry and did well. Because it was a class she enjoyed (she is a science wiz) and it WASN’T a math class. she performed well with Stoichiometry. She does well in ALL her science classes. She now attends community college and did well in her remedial pre-algebra and algebra classes but she still suffers from anxiety.

“But most people won’t have to work with advanced math all their lives. ”

Well flowers are useless for most of us, as are Michelangelo’s paintings; most people won’t work with elephants, won’t go to Italy, and certainly won’t have to deal with pharaohs.

Should we then skip all this stuff in school?

I don’t think we should skip it totally. But if every single student including those who aren’t really going into a field where higher math is used is expected to know trig and calculus in and out, I think that’s a little too much.

I was a terrible math student, and cannot weigh in how it should be taught, but it seems to me that, within reason, whether classroom math is “used” later in life almost irrelevant: learning math develops pattern recognition and thinking skills that are useful.

Likewise, I have little specific recollection of anything I learned at CCNY many years ago, but attending that school (when it was tuition-free, btw) helped teach me how to think, and for which I’m grateful.

“I wish the majority of people felt that it was important that everyone spoke French.” go to Canada and look for a federal gov. job…. At one time they required this in British Columbia and Alberta where hardly anyone spoke French. …. You will have it made…. except for housing prices in Vancouver.

My own son,who is not a scholar by any definition other than the ability to retain enough information to pass tests and therefore earn “A’s,” was a star pupil in a math class at Bronx Community College. Students asked him how he was able to do so. He had no answer other than “I studied.”

Having taught in primarily low SES schools and classes, I often found that interest and effort were the real drivers of success. At my best, I taught from my passion for the topic, motivating the students. In addition, providing immediate feedback and reward (points, grades) kept students on a push to develop inner control of the topic. However, what students needed at base was strategies and techniques for studying. One student could not understand what his difficulty was in passing a test since he had reread the material multiple times.

I feel that how to study is often overlooked. Parents may not have advice to give and teachers might overlook this step as studying seems intuitive to people for whom it has been second nature.

“I feel that how to study is often overlooked.”

Exactamundo!

I was in a college prep program a zillion years ago. Algebra II, trigonometry, and pre calculus were courses taken only if you intended to be a math major in college or enter a science/engineering field with a high demand for math. The whiz kids of the era carried around slide rulers.

And those slide rules put humans on the moon, so maybe the kids don’t need to be in front of electronic devices in school all the time; they already spend the rest of their lives on them.

Good thing Bill Gates wasn’t involved in puting men on the moon.

I picture Neil Armstrong confronted with the blue screen of death (figuratively and literally) frantically communicating with Bill Gates at Mission Control, who is telling Neil not to worry, but simply to reboot the landing computer with “ctrl-alt-delete” .

I think people are trying to come up with answers when we should be asking questions. For instance, do all college freshmen need to take math? Why? To what level? I took math all the way up through calculus in high school and college. The day I took the GRE was the last day I ever used it.

And to whatever extent the problem is student motivation/effort (or lack thereof), again, why? What is it about the way we teach math or about the way kids are connecting with math that turns them off?

A good number of students graduate from Harvard, Yale and Princeton without ever having to be burdened by any advanced math. They can even graduate phi beta kappa with their English or History degrees.

I’d like to see EVERY student – regardless of what college they matriculate – be forced to take those exams the first day of college.

I took as much math as you have, but I’ve only retained it up through algebra. Almost every day, I encounter some situation where my mathematics limitations force me to stop dead in some line of inquiry, rather than go on to the next stage.

That is surprising that your algebra doesn’t get you through your daily needs. And you have to stop dead instead of being able to use the knowledge you gained to figure out how you can refresh what you know to go on to the next stage. It sounds as if your college may be to blame.

In terms of my job, I do a lot of work that involves arguments about damages calculations, statistical sampling, extrapolation, etc. I’m not as bad as many attorneys, but there is no doubt that I would be better at my job if I were fluent in these areas.

In terms of my life, I am curious about the world and the universe. My curiosity often leads me to questions that cannot be answered, or even understood, without a better foundation in mathematics.

As an adult, I’ve spent a lot of time trying to learn things that I never learned well when I was younger, such as hockey, electronics, music theory, and, in fits and starts, physics. All of these things are a lot easier to learn when you’re young.

But you just said you DID take that math when you were young! You took it up to calculus. You just said taking it when you were young did not help you retain anything beyond algebra. That’s why I am confused.

FYI – if you help your high school kid with math homework you may find that you will re-learn everything you learned already and then forgot. or perhaps you will be like me and be shocked at how much more advanced even basic Algebra is from what was taught decades ago.

Yes, I forgot most of it. And probably never learned it that well in the first place.

Reblogged this on David R. Taylor-Thoughts on Education and commented:

Texas went through this phase of “every student is going to college”. It turned out to be a failure. It did not increase student achievement but only increased the school’s ability to make the numbers look good.

I looked back at something I wrote 4 1/2 years ago and the same applies, not all students are going to college and if they do go, their chances of completing it with a degree are low.

https://davidrtayloreducation.wordpress.com/2012/10/12/what-about-the-other-80/

Interesting, David!

Living in a rural area the importance of technical and skilled trades stands stands out. I’ve known students who have gone the technical and skilled trades routes who are now doing quite well for themselves. I worry though that down the road when the next bubble bursts and we enter a serious downturn in the economy those students will be devastated by a lack of jobs as happened during the Great Recession when some of my skilled trade worker neighbors lost their homes due to no work.

Imagine what that did to their children. As much as they tried to hide their home or should I say lack of home conditions I could see it in their eyes in the classroom. It’s part of the rural poverty problem that never seems to get any attention.

The main problem being that the US has chosen to allow corporations to ravage the manufacturing sector through the various international trade agreements. Those jobs aren’t coming back. Isn’t it amazing that your fellow Texan R. Perot was so correct stating that “the giant sucking sound that you hear is all the jobs being sucked out of the country” (rough paraphrase) in regards to NAFTA.

The monetary supply is limited and when so few control so much wealth, far more than can be imagined as “fair or equitable” those peeons at the bottom have nothing leftover for them to acquire and that goes for the job situation also.

What part of Missouri are from? I grew up in Kansas and my grandmother was a dairy farmer for the first 15 years of my life.

I may live in the city now but I have country roots.

I grew up in “white county” oops, I mean Southern Saint Louis County back when it was farms, fields and woods. Had a nice little creek running through the back yard. It’s all built up now, although the creek is still there and some of the woods behind the house (my sister lives in the house we grew up in) are still there due to the quite steep terrain.

Now I’m about 60 miles west of St. Louis in southern Warren County. I call it the “Beautiful Missouri River Hill Country of Southern Warren County”. I live about 4 miles north as the crow flies of the Missouri River. Nothing fancy but I own it, the it being twelve acres with a barn and my 30 year old mobile home. Ain’t much but it’s home. I never have needed much in the way of a fancy house.

How about yourself? What part of Kansas?

All over. Dad was teacher & coach and we moved a lot. I claim Hays KS as home where I went to college. I lived there more than any other place. Fort Hays State University. My younger brother has been in Lee’s Summit schools for over 20 years.

And thanks for sharing!

“It did not increase student achievement but only increased the school’s ability to make the numbers look good.”….

Yes this has become a specialty at most schools and districts these days,

Any student who passes the NYS Regents (algebra, geometry and Trig scores of 90+ will not have any problem doing college level math. They lowered the scores because teachers are asking students to figure out problems on their own and many don’t have the skills to even know where to begin. The problem is our current education training. I’m in graduate school getting a master’s in education. Have students figure things out on their own is the current mantra. In essence we are told, have the students come up with Pythagoras theory on their own. If they can’t, well they don’t really need it.

It’s not the teachers, it’s the education system that dictates and perpetuates ignorance.

Just saying.

it’s just as bad in language instruction (I teach high school ESL), where teachers are compelled to overuse group work, under the mistaken assumption that the students will teach each other a language they don’t yet know.

Ah, yes! “Discovery learning” at its worst.

“Bad Language Instruction”

The language that they use

Will certain words abuse

When students teach their peers

The effing word appears

My sentiments exactly!

Dear Usually, You have that right about teaching practices and perpetuating ignorance with “figure things out on your own” or using inquiry to arrive at a solution.

Meanwhile the nation of Singapore consistently gets vastly superior results to the USA in math and uses more traditional methods of instruction rather than wasting students’ time. … but never fear Ed-U-Jargon tells us that USA teachers are using “Best Practices” so everything is just fine.

2015 TIMSS Math 8th grade

Singapore 621

USA 518 …………………….. Gap = 103 pts.

Was a chemistry teacher but taught some math and I think the professor is spot on. We haven’t stopped to evaluate the negative impacts of technology.Calculators in the fourth grade … why? Some argue that the earlier we can get these tools in their hands the better. This is not good thinking. Should we be letting fourth graders drive cars? How about semi-truck trailers? Jet fighters?

I read a wonderful SF short story about a little girl in school. Her math teachers were grading their students math skills by how many processing seconds their desk computers did to make the calculation assigned. This prodigy kept solving math problems in zero seconds. First she was accused of cheating. Then she explained to her incredulous teachers that her Grampa had taught her how to do the calculations in her head! They were gob smacked! I think it ended were her being required to do the problems the “right way” and with her hoodwinking her teachers into thinking she was.

As the professor comments, I have had students working through a problem input “times 1″ into their calculator. Nobody who knew what they were doing would have wasted their time doing that. Calculators become both a distraction and a barrier to learning. We really need to take a step back and evaluate the role of technology in our classrooms. Currently politicians provide funds to stuff some tech wizardry into classrooms so they can say they have done something for education. Compare this with the Finnish system–very little ‘ed tech.”

Calculators were the first of technologies placed into the hands of every student. Math books were rewritten in order to support/sell calculators. An another long time chemistry teacher, I agree with your comments. When students lack number sense and when their temporal lobe is not exercised, they have problems doing math. Technology is not substitute for the computer that resides between our ears. Sadly, we are not going to see this conversation in the mainstream media because it doesn’t sell stuff. Instead someone will propose yet another round of “$ecret $auce” to help those kids.

Ah yes…. No Vendor Left Behind and Race to the Bank.. the guiding principles of school reform. … gotta buy that $ecret Sauce .. to eliminate the opportunity gap.

Incidentally, off topic, but according to Jennifer Berkshire, Randi Weingartner is traveling to rural Ohio today with Betsy Devos to visit a school together. Am I the only one nauseated?

I saw the same thing in the Washington Post, I believe. ~scary organ music~

“Weingarten, president of the nation’s second largest teachers union, cited the visit as evidence of DeVos’ willingness to “walk the walk.”

WTFsquared!!

From huffpo article on the joint “visit”. https://www.yahoo.com/news/betsy-devos-visits-public-school-211531330.html

Great link Duane! The headline should read Weingarten Panders to DeVos.

Current math curriculums value breadth over depth and students don’t ever seem to have an opportunity to just play around with numbers to figure out how they work. My child is in third grade and his homework makes my head spin. He seems to ‘get’ math pretty well, but I can see how a mathematically illiterate student begins the struggle early and ends up in a remedial class later on. I think the youngest kids are taught too much, too fast and without any context.

I now teach Kindergarteners but taught First for many years – your last sentence – too much, too fast, and I will add too soon is the problem. The students need to sit with it for a bit before rushing to the next concept. Also drill and kill does not kill if given in small consistent and progressive doses.But most important is ‘ in context’ – thank you for bringing that up…it is of utmost importance.

…huge amount of comments because this topic hits a nerve…

also am worn down as many teachers are about failing schools and failing teachers but not about failing students…as if we don’t care…

“also am worn down as many teachers are about failing schools and failing teachers but not about failing students”

What we have is failing, corrupt politicians who don’t take care of the country so that it won’t produce disillusioned kids; politicians who prevent teachers from taking care of business.

Caligirl, Yup drill and kill…. when learning to play an instrument or become proficient at a sport … it is called “Practice” … and you won’t go far without it. Making good habits “rote” at one time was considered a strength… Rick Barry 90+% free throw average.

But USA Education Profs are into publish or perish and have lots of ideas which are often funded by NSF-EHR …. we need the innovative today…. apparently OK when unproven innovation replaces what works.

I don’t questions his observations, but a little historical information is useful so we don’t rush to judgement about the state of our k-12 system. As you well know math teachers in colleges have been saying the same thing for at least 117 years!

Best

David

David C. Berliner

Home: 120 E. Rio Salado Pkwy., #205

Tempe, AZ 85281

☎︎ 480-861-0484

Office: Regents’ Professor Emeritus,

Mary Lou Fulton Teachers College,

Arizona State University,

Tempe, AZ 85287

I now teach one math course and 5 world history courses. I see 155 children a day. Before is year I have been teaching math, mostly geometry and precalculus.

My advice would be to continue to place students in remedial classes if they need it and quit wringing hands over it. Make sure that the ones who cannot do the coursework do not pass. Word will filter back to their high school friends, and we will see an uptick in effort.

All of what you say is true. I have seen students score a 25 on the math ACT and still quake at the sign of any manipulation of fractions. On a high school level, we are faced with telling a kid who is a senior he cannot graduate if he does not pass our class, despite the fact that he has impressed the ACT. He knows he is going to graduate, so he skates and loses instead of working. By the time he gets to your college, he has developed bad habits. He does not study. He relies on the calculator instead of learning.

Meanwhile, the academic fight over whether the children should be learning how to manipulate algebraic expressions or solve problems produces testing that is focused nowhere. I see the value of being able to solve a physics problem with a graphing calculator. I see the value of using computers and calculators to find instant answers. But I also see the value of being able to understand the fundamentals of why theoretical math works. Why is 0!=1? Why is rot -1 imaginary? These are important too. Each teacher has to decide, in consultation with the students who return and report on their college experiences.

What we all need is more dialogue between high school teachers and the professors where some of their kids are heading. That would be a good start.

“My advice would be to continue to place students in remedial classes if they need it and quit wringing hands over it. ”

Profs don’t have problems with these courses, since it’s more business for the university. It’s the students who are screwed because they need to pay for these extra courses.

So we are wringing our hands for the students.

As a special ed teacher who teaches third, fourth, and fifth grade kiddos Common Core Math,the shear number and volume of standards we are expected to cover in a single school year is ridiculous, along with some pretty developmentally inappropriate expectations for younger learners. In fourth grade, kids are expected to both do mental computation AND use calculators. The PARCC test give third/fourth grades FOUR separate sections of math tests, some allow calculators and some do not. But they are all convoluted and confusing.

In the old Illinois standards, pre-Common Core, we had grade ranges (ie early elementary, middle elementary, etc) and students were not expected to cover every topic every year. There was less to cover so you could spend more time on certain units. Now, we are just flying through concepts (especially harmful for my kids with special needs) and kids are not retaining things. Common Core makes scaffolding very difficult because most of the curriculum seems to be in the form of multi-step word problems instead giving kids a chance to build up to those complicated ideas.

I wrote more about the problems we’ve had with Common Core math here: http://mskatiesramblings.blogspot.com/2016/04/the-problem-with-common-core-math.html

I am an art teacher in Central Falls RI. Not so long ago only 7% of our high school students qualified as “proficient” on math assessments. I believe the poor scores were a direct result of our former math program “Investigations” which did not emphasize the importance of learning the times tables.

A few years ago I learned from a colleague, a music teacher, that our fourth graders did not know how to multiply. I then asked each class to answer a few simple calculations and it was true they had no answers even for the easy ones. I was flabbergasted. Math is not my strength but It seems to me that in memorizing the times tables one becomes aware of the relationships and patterns in math.

Of course some of the teachers knew this was a problem. They tried to assign homework to fill this need. I saw the memos from the administration saying that any teacher who sent work home that was not specifically prescribed by Investigations would be written up. Another time I saw one of our most effective teachers come into the teacher’s room, slam down her paperwork, face beet red with frustration saying “I just did something I wasn’t supposed to do – I taught them fractions”. Still another time I was corralled into a classroom teachers’ meeting during which they were brainstorming ways to get around the math program. I asked “if it isn’t a good program why don’t you get rid of it?” We’ve tried, they don’t listen to us”.

Our principal called learning the tables “drill and kill”.

So many teachers do this – make their own material to get around nonsensical curriculum.

I taught physics at the college level. I was tutoring a student who was failing all of her tests. I couldn’t figure out why. After multiple times of her showing me her work on paper and then doing the calculations with the calculator, I finally realized the problem. The calculator was in radains, She had no number sense to know that it was wrong….I remember that because it was sin 30 times gravitational acceleration. I was like sin 30 is 1/2 and g is like 10…so you should get 5…she was not…and had no idea… Her grades remarkably improved after that.

I also tutored students in math. You’d be surprised how hard it is to do factoring in algebra 2 if you don’t know your times tables….

I teach high school trigonometry. When students are getting crazy answers the first place to look is the mode setting on the calculator. Radians or degrees? I have corrected that same error hundreds of times.

At least that is an easy mistake to fix. Then the student starts getting the problems correct. It shows the importance of getting a calculator and sticking with it, not changing to a different calculator. They function differently , and a student needs to get used to their own machine.

I am from the far left coast near The Evergreen State College where rather than teach students how to use proven effective and efficient strategies for math instruction, teachers are taught to be activists against societal oppression and racism. There the progressive mathematics instruction of the Netherlands is held in high esteem. {Netherlands is one of the few countries in the world to have declining math scores on TIMSS 2015. dropped 1995-2015 ; dropped 2011-2015}

The East Asian countries are the world’s highest performers on TIMSS math and especially so in grade 8. Singapore 621 , USA 518 = gap 103 points. These East Asian countries believe in:

(1) good textbooks (unlike no books EngageNY or Connected Math Project in middle school)

(2) that prior learning and knowledge is the greatest determinant of what children can learn, regardless of their physical age.

(3) Curricula should be both mathematically coherent and logically sequenced for learning from novice to expert. (unlike the jumble produced by unguided inquiry)

(4) memorization and practice: two elements in the development of both procedural and problem solving skills. (these reduce cognitive load)

(5) Student effort, which can positively influence achievement.

(6) Time spent learning outside the school day is beneficial.

But the Ed Gurus with Math Education degrees (not math degrees) have other plans and those folks are the decision-makers today. NAEP fact in WA State the NAEP scores for Black students in grade 8 plummeted by 10 points from 2013-2015. It is really hard to learn math in many schools without tutoring and parental help outside of school because materials and practices are now of such low quality. DO NOT blame teachers – as they are forced to follow orders.

Math teacher shortage? You bet. Hard to believe in Ed Guru fairy-tales and stay sane.

Danaher M. Dempsey, Jr

http://mathunderground.blogspot.com/

Like!

“(4) memorization and practice: two elements in the development of both procedural and problem solving skills.”

Guys, what’s there to memorize in math besides the multiplication table?

Let me see if I can remember: Perhaps basic geometric concepts such as “the total degrees of the angles of a triangle equal 180”. Now it helps to know the reason why and both should be emphasized. Or the volume or area formulas and calculations along with knowing (memorizing) that pi = 3.14 for all practical purposes. I’m sure there are plenty more but it’s been over 45 years since I was in high school so I can’t be relied on to come up with more. (cheesy excuse, eh!!)

Definition of sine, cosine, and tangent. Sine 30 degrees = 1/2

sine 90 = 1 etc. Circumference of unit circle = 2pi

pi radians = 180 degrees etc.

=============================

But memorized basic math facts including through 12 x 12 by end of grade 4 would be nice. [[or if in India through 16 x 16 , if you were in one of the good schools]]

How are these facts useful for the general population? How are these facts part of general culture that enriches people’s lives?

I guess one of those questions that needs to be decided before we can talk about how good freshman are at math is “what is math?” Is it basic operations/algorithms/formulas as many seem to be arguing here? Or is it a way of looking at/understanding the world?

I think math is different for every person and for what they choose to pursue in life. You’re correct that someone needs to define what this man is talking about. I think everyone should be proficient in the elementary basics (multiplication, fractions, decimals etc.) so that they can get along in life everyday. Why does an art major need to take calculus (unless they want to)?….but I certainly want the architect building my house to know higher math and the laws of physics.

I know of no college where art majors have to take calculus. Do you?

NYU for a BFA requires 3 math or science courses for graduation. You could take three one semester science courses. “Introduction to Bird Watching” and two more.

Should students who can’t multiply 2×3 be enrolled in any college? I think not.

As long as they can multiply 3×2, I would admit them.

Perhaps more important than his calculator observations is his observation about word problems and supposed “real world examples” – and how they have taken over math class to replace the discipline and repetition of learning how numbers work.

With an MS in Applied Math and a career around numbers (and many other things), I watched my boys from K through high school I agree that this is a very serious problem.

Word problems turn “math homework” into reading homework. They often had to struggle more with words than math while doing “math”. Why? Those writing the textbooks have to perform outrageous mental gymnastics to create word problems that are at all useful. And very often they fail.

Real world examples are a big bust. Students need to be fairly well advanced in math before real world problems are useful. But also, they are arbitrary. And students struggle with the huge load of “answer this arbitrary thing” that is asked of them in school. My youngest is on the Autism spectrum and one of the most fascinating things is to watch his brain reflect what mine wants to do – reject silly questions that are meaningless. He simply can’t do them. I can do them – but it’s a real struggle.

In my older son’s primary grades work, an approach was adopted where they solved problems as a group. That’s horrific for a strong math brain (which his is) because it means words are more important than the math. And very often the powerful math brain is not closely connected to the verbal cortex (at least in my experience – don’t know what the research would say).

In saying all this, I’m also trying to keep in mind Thomas Hacker’s admonition that we need “adult arithmetic” to be more important than algebra. I concur with Hacker. The question is, when does that happen? How do we work it in? How would it change these remediation numbers?

As a businessman and mathematician, I am fascinated at how students today lack an inherent sense of numbers. We need kids who have a powerful enough number instinct to look at a set of adult arithmetic numbers and instinctively say “something feels wrong”. Then the discipline to sort out whether their instinct was right or wrong. Because the most powerful truth emerges in that pursuit of the numbers.

There’s a lot of pieces of good truth here. (Not living in NY I have no comment on the NY state tests.)

” We need kids who have a powerful enough number instinct to look at a set of adult arithmetic numbers and instinctively say “something feels wrong”. ”

I am so glad you said that. I spent an entire year emphasizing knowing whether an answer made sense or not. I was teaching remedial math in middle school. These were kids that had struggled through trying to memorize algorithms and never really knowing why. Other than the one student who was behind because of chronic health problems, the students were functionally illiterate in math. Teachers had tried to compensate for their struggles by handing them calculators. The problem was they had no idea whether their answers made any sense no matter whether they used a calculator or not. Since it was not unusual for them to mis-key in a problem, their calculator answers were frequently wrong, and they did not know it! We spent class after class on estimating as we reexamined all the basic math concepts they had never fully understood or mastered. Knowing that an answer was in the ball park became a real mark of understanding and pride for them.

In my work in aerospace earlier in my career I learned a “discipline” of guessing. It was critical to the work because it let us proceed without wasting time perfecting answers – and made sure we acknowledged when we were guessing.

Schools (and businesses, too) get so obsessed with minute perfection we forget how it’s probably more important to “feel” the numbers. There’s always time to perfect the calculation.

Feel for you in that challenge. love what you have to say on it.

Exactly with Doug’s quote. It is amazing how many people will repeat (or share on fb) something that is so obviously outrageous you have to wonder if they have any “feel” for numbers at all. I see this sort of thing all the time.

Ah yes… Real Word problems … likely required by Ed Gurus who have rarely if ever encountered a real word math problem that required more than addition. … Yet far too many hours are wasted going nowhere … instead of presenting material in a way that it can be efficiently learned. ……. WOW those Math education majors need to take more math as apparently they have very little idea on how math is learned in an efficient way.

As one who was a practicing industrial mathematician for a while and uses math all the time in my job…couldn’t agree more. I’ve never really

encountered a real world situation that sounded anything like a word problem.

I was never a very good math student. I could get to an answer, but I never really “understood” Algebra – pre-calc. I’m just not a math person….but I am glad that I was forced to learn multiplication, division, fractions, decimals and percents WITHOUT a calculator. Learning the basics made it easier for me to take the higher maths and it helped with the sciences and physics. We use basic math everyday and that is important. I don’t know why there isn’t more emphasis placed on learning the basics in elementary school. I have 1 in MS and 1 in HS and when they were in ES, I made sure that they knew the basics because the math curriculum was downright awful. My kids hated “mommy math”, but they are now glad we had those lessons.

“Word Problems”

The problems of the word

Are often for the bird

If plane went north

But headed south

Then where was engine heard?

Not that it’s all that relevant but I did surprisingly well on the SAT back in the day, despite being numero-phobic and a math class charity case (though I did learn my multiplication tables in elementary school), precisely because there were so many word problems. I could reason them out, while the mathematical formulas/procedures might as well have been hieroglyphics, and made me freeze up.

Yet more proof of how invalid the test was/is, since those problems in numerical form would have resulted in my guessing or skipping them.

That you succeeded by reasoning was evidence for the success of the test. I think a student who can reason a math problem is exactly the kind of person who should be attending college.

3 variations to the same question: why do colleges admit kids who cannot add or divide? How do these kids pass ACT? Why does ACT let them pass?

Also: Why do colleges require gened courses? Shouldn’t K-12 schools take care of basic knowledge?

K-12 schools are undertaking something far loftier than teaching basic knowledge (how 19th Century!). They are creating 21st Century learners with 21st Century skills. All knowledge, including math facts, can be looked up on Google. Stocking the memory with knowledge is obsolete, don’t you know? Paolo Freire and Sujata Mitra and many other education authorities have declared it so.

Sure, the kids can look it all up on Breitbart News.

“How do these kids pass ACT? Why does ACT let them pass?”

Didn’t realize that the ACT was a pass/fail test. Not that it makes any difference as the results and any interpretations of the test are COMPLETELY INVALID.

The current consensus of scientists who study how the brain works is that the math professor is entirely correct. Current US students are not able to solve calculations because of state K-12 standards in most states that (as one of many problems) have required teachers to require student to become dependent on calculators.

Cognitive science has found and verified that in the “working memory” where our brain solves problems, at any one time we can store 3-5 small elements of knowledge that we have not memorized “to automaticity,” plus everything we can recall quickly from our long-term memory. As a result, “memorization to the point of quick, accurate recall” is essential when solving problems.

The current generation cannot solve math problems in part because with memorization of arithmetic facts discouraged, explanations of math since first grade have rarely made mental sense.

In 2012 OECD PIAAC testing in numeracy, US 16-24 year olds finished 22nd among 22 nations. But teachers did not cause the problem. Teachers did not decide the standards. In most states since 1990, standards written and adopted far above the school level have forced teachers to teach students to solve math (and other) problems in ways that 2017 cognitive science say the brains of non-experts (students) measurably cannot do.

In most US states in math, K-12 standards and the curricula to implement them at crucial points are the opposite of what cognitive science recommends. Until this denial of science changes, many students will enter college with problems that remediation cannot repair.

The need for thorough memorization as a foundation for higher-level thought may be discouraging, but how the brain works is how the brain works.

For detail on the many reasons that science says state math standards have not worked, see “Automaticity in Computation and Student Success in Science Courses” at

http://arxiv.org/abs/1608.05006

For why the Common Core math standards do NOT fix these problems, see

http://www.ChemReview.Net/CCMS.pdf

— Eric (rick) Nelson

“Cognitive science has found and verified that in the “working memory” where our brain solves problems, at any one time we can store 3-5 small elements of knowledge that we have not memorized “to automaticity,” plus everything we can recall quickly from our long-term memory. As a result, “memorization to the point of quick, accurate recall” is essential when solving problems.”

Why is there a need for quick recall? Is there a need to solve math problems quickly?

It’s one less piece of information that has to be held in working memory if information from long term memory can be quickly integrated into working memory. I don’t have to stop and think about what 2×3 is when I am doing a long division problem. I can access more fundamental info on which I no longer have to devote mental energy and integrate it into more complex problems without effort.

Try to read a book in a language that requires you to look up every third word in a dictionary, and you will understand the need for fluency. It’s not to win a competition–it’s CTO allow you to focus on the important things rather than spend time on mechanical trivia.

Yes. Speed in solving is essential. When dealing with not-well-memorized information, working memory is limited not just in capacity, but in duration: the data you need to hold and process in WM to solve the problem (the goal, steps, data) starts to drop out after 3-30 seconds. That’s “how the brain works 101.” It’s the science of how the brain solves problems that in 2017 educators use to design effective instruction — if standards give them the authority to do so.

Students must solve quickly and using “shortcuts” such as “cross multiplication” because of the working memory bottleneck on duration.

Do – your – homework. Read on how the brain solves math problems at http://arxiv.org/abs/1608.05006 and the references therein.

“Do – your – homework.”

What homework? Why should I limit a kid’s time to solve a math problem to 1 minute (as ACT and most tests do) when I know that they can do it in 5 minutes? What’s the rush? Why not let them think instead of whipping out answers? Are you testing whether they can think or whether they remember an appropriate amount formulas?

“Read on how the brain solves math problems at http://arxiv.org/abs/1608.05006 and the references therein.”

That paper is complaining about the lack of computational skills for the physical sciences. Most people are not going to do physical sciences. So why torture the 99% for the needs of the remaining 1%? If the (applied) physical sciences need quick computational skills, develop them for majors in college.

The same applies to the tests in any other subject. Just because lawyers, emergency room physicians, pilots may need quick thinking, it doesn’t mean, the rest of the remaining 95ish % should be tested on this particular skill.

When my daughter asked her English teacher why she needs to read a long paragraph and answer 5 questions in under 2 minutes, the teacher said “well, in an emergency room, if the doctor doesn’t think quickly, you may die.”

Now how ridiculous is that?

With that painful non sequitur, your daughter’s English teacher demonstrates that she/he needs a class in reasoning and identifying logical fallacies.

The solving math problems quickly protocol arose out of choosing speed as a surrogate marker for automaticity. We can’t really measure (Duane) automaticity, so we measure the time it takes to solve a problem. There is more than one argument against rigidly adhering to this protocol, but depending on the task and the student, it can give you a rough idea of where a student is in their grasp of a concept. It’s a mark of how effortlessly you can manipulate information. In Spanish, it’s kind of like the day you realize you are thinking in Spanish and not translating everything into English, or vice versa, first. It’s a real kick to know what a word means in Spanish but to have forgotten the word in English!

Mate Wierdl, Look up John Sweller’s Cognitive Load Theory and you can get the scoop on “working memory” etc.

You guys keep giving me the same advice which is about how memory works. How does this explain why kids are tested in math by through speedy calculations, and hence they are prevented from thinking?

How does a theory that is described as

Cognitive load theory provides a general framework and has broad implications for instructional design, by allowing instructional designers to control the conditions of learning within an environment or, more generally, within most instructional materials.help kids understand math better?

” As a result, “memorization to the point of quick, accurate recall” is essential when solving problems.”

Not only when solving problems but in learning a second language memorization is especially needed to build the vocabulary base “to the point of quick, accurate recall.”

Solving math problems in a way that is worthwhile to all kids is not similar to learning a language and speaking it. For the general population, there is no value in being able to solve 60 math problems in 60 minutes, while your Mexican audience gets bored to death if you are slow recalling every single word.

For the general population what is useful is the following scenario: give a problem to a class, and the kids communicate and argue with their neighbors how to solve the problem. If they have a chance of doing this, the few math concepts needed automatically walk into their memory. The importance of the concepts is completely negligible.

It’s another matter that even learning a language, rote memorization of words and grammatical rules don’t develop feeling for the language.

“. . . the few math concepts needed automatically walk into their memory.”

Máté, I am not sure that one can verify that which you propose to be true. It may or may not but certainly there is no verification of that occurring across all, or even most of, the children in a class. For me, that is one of those education pronouncements without any basis in valid research and defies common sense.

And, while memorization of words may or may not help the student develop a feel for the language, I’ve found that vocabulary repetition along with self quizzing from the native tongue word to producing the desired second language word does indeed increase that vocabulary that the students need. Oh, and the research? Over twenty years of having students tell me it works.

Now I never had the students “memorize the grammar rules.” I always used grammar as a bridge for understanding sentence structure. In doing so, I had many students tell me that learning the simple grammar terms and the function of words in a sentence helped them with learning English as they hadn’t been much exposed to that very “dirty and denigrated” in modern language instruction, part of learning one’s own language, much less a second one. Again, the “research” being the students’ comments.

The developing a feel for the second language comes with learning words and how those words are put together in each language to form meaning. And that almost always requires living somewhere where one cannot escape using the second language (I hesitate to use the word “immersion” due to the pedagogical concerns).

“Máté, I am not sure that one can verify that which you propose to be true. It may or may not but certainly there is no verification of that occurring across all, or even most of, the children in a class. For me, that is one of those education pronouncements without any basis in valid research and defies common sense.”

Which common sense? The statement is that there are very few math concepts (addition, equation…) which are needed to be known to students, and a teacher uses them so often that there is no need to memorize them.

It’s another matter that nowadays an enormous number of useless math terminologies is taught to kids—exactly because the recollection of these definitions can be tested while real math can’t be tested.

Because of this and the forced pace of teaching, kids need to memorize concepts, formulas.

The problem of forced pace arises is many other subjects. One way of learning a language is to memorize, say 3K words in a semester. Another way is to teach only 300 words, but instead of memorizing the words, the teacher and kids have lots of conversations using the 300 words, and kids will automatically remember them. This is how toddlers learn a language, and it seems to be remarkably effective. Of course, toddlers are given many years to accomplish the task.

Personal experiences don’t matter, but I was taught Russian for 12 years and English for 7 years with the memorization technique. My Russian is nonexistent and coming to the US, I understood nothing people were saying, and I spoke with ridicuously slow speed, constantly searching my memory for words. Then I started following two soap operas, and within a month, I understood people, and after 3 months, I was ready to teach.

So what I am “claiming” is that the immersion technique works very well in math, too, while the memorization technique is useful only to prepare kids to take CC and ACT tests.

I’m with you Duane. My students never had concepts automatically walk into their memories. As a matter of fact, I don’t remember much of anything “walking” into my memory although some things were easier to learn than others. Understanding what I was doing was pretty important although the sophistication of my understanding most certainly changed with age. One mistake I think people do make is assuming that one must be able to verbalize his/her understanding to show that s/he really does understand. Shouldn’t being able to consistently use a concept be a marker of understanding on some level?

speductr “Shouldn’t being able to consistently use a concept be a marker of understanding on some level?”

It depends. One thing is for sure: consistently recalling a concept from memory doesn’t mean understanding is attached to it. For example, just because kids have memorized the multiplication table, doesn’t mean, they understand what 7 times 8 really mean. They can tell you “7 times 8 is 56” 100 times, and their understanding won’t improve.

The same can be said about most of the “math facts”: kids can recall the rule that “in case of multiplying two powers of the same number, we have to add the exponents”, they can even use the rule thousands of times on various tests during their life time, they can get admitted to college, and still do not understand what the rule means.

Practically no student know why long division works, and almost none understand why the multiplication algorithm works. In developing number sense, knowing these procedures is as useful as calculators.

Math education seems to be geared toward more and more to recall concepts and procedures. CC seemingly tried to address the problem, but has made the problem worse with all the testing requirements.

I reemphasize that I make no general statement about the uslessness of memorization in general. For example, poems, songs need to be memorized. But I think the role of memorization needs to be thought over, since rote memorization often gives questionable educational advice. For example, when kids are told to memorize words in Spanish (I picked Spanish since that’s what my bilingual daughter has been struggling with for years), it’s mostly done by asking the kids to translate the words from Spanish to English or the other way around. But this is not how a language is used in everyday life: we don’t translate.

“almost none understand why the multiplication algorithm works.”

Hell, Máté, I have no clue what the “multiplication algorithm” even is, much less knowing why. What is the multiplication algorithm?

As far as translation, it makes a big difference as into which language one translates. From second to first one is practicing recognition, which is fine to a degree but only about 1/4 of what needs to be done in learning a second language. The harder and more important is to go from first language to second which results in production which is what the vast majority of second language learners struggle with (without getting into the “fear” or “strangeness” that is felt when working in the second language.)

I have no problem with repetition, memorization and translation as tools to begin to learn a second language. But to have those three things come together so that one is more fluent in the second language it takes a fair amount of time in a situation where one HAS to work in the second language. Again I hesitate to use immersion for all the pedagogical baggage that term carries. While your experiences with learning a second language appear to obviate the need for that memorization, the fact is those words were more likely than not “in there”, laying dormant, waiting for the proper conditions, i.e., when you had to really begin using them.

Can I “prove” that? No, but the reason I say so is that many, if not the majority of older immigrants to this country hardly ever learn English; even with living in this country for years, as most had not had any prior instruction. They can survive through family and friends helping with communication.

Learning a second language is a fascinating area of human cognition and there is no one silver bullet to doing so. But I say, “Hey, use all the techniques available and let the chips fall where they may.”

“What is the multiplication algorithm?”

You just pointed out an example of a useless terminology: kids should never have to learn that the method they use to use to multiply two 3 digit numbers is called the “multiplication algorithm”. They should be just told “multiply 123 by 345”.

I’m still confused. What exactly is it? Can you define “THE (you didn’t use “a”) multiplication algorithm”? I’m assuming there is one multiplication algorithm by what you have written.

Well, enter your favorite two numbers here and see how it’s done by 3rd or 4th graders. http://www.webmath.com/k8ipmult.html

You mean the old fashioned long hand multiplication that is an efficient way to multiply (as long as one has paper and pencil, eh). Is the method considered an algorithm?

Of course. You can call it procedure, if you want, but in math anything you do according to a recipe is called an algorithm. My point is, kids don’t have to know any of these names, while nowadays a good deal of time is spent on memorizing these names for algorithms, concepts, theorems, formulas, or even just notations. Bizarre, since mathematicians themselves try to minimize the names they are using in their work exactly because it gets in the way of communicating and thinking.

Thanks, your comments are making a lot more sense now with your and speduktr’s explanations!

What is also interesting is the concept that learning is more quantum than linear. What do I mean by that? I noticed for years that in sports a person will stay on a certain level for a long time no matter how much extra work and effort is put in. And then poof, the person jumps up to the next level of proficiency (god I hate that the edudeformers have bastardized that term), stay at that next level for a given period, then poof up to the next level. Many times each “higher” level requires a bit more work than the prior, but at others it just seems that “things come together” just right and that leap may be sooner than expected.

The learning isn’t linear in the sense of amount of and quality of effort result in an ever increasing capability. And I believe that learning any subject matter follows the same quantum pattern and not a linear x amount of effort = x amount of gain. That quantum aspect is often shown by the student’s “ah ha!”, light bulb turning on, moment which so many teachers so cherish.

“What is also interesting is the concept that learning is more quantum than linear.”

Yes! That’s exactly it! And it’s different for every person! Thank you, Duane. I think I had a kind of light bulb moment.

Your welcome. And yes, it certainly is “different for every person”. But hey, lets’s standardize the teaching and learning process, eh!?!

Perhaps sometimes we don’t express our thoughts because, in a world of supposed “experts” we probably don’t consider ourselves expert enough. My guess is that there are a lot of pedagogical “gems” out there in the minds of teachers, it’s just that we (especially the edudeformers and adminimals) don’t give enough credit for the brilliant ideas concerning the teaching and learning process that many teachers have. It’s all top down, do this do that without input from those who know the most, the classroom teacher (and auxiliary folks)..

“You mean the old fashioned long hand multiplication that is an efficient way to multiply (as long as one has paper and pencil, eh). Is the method considered an algorithm?”

Yes. An algorithm is basically a process and/or the rules guiding a process. Basically, it’s a fancy word for rules. Not a terribly useful term for this non-mathematician but one that seemed to get thrown around in my teaching world. I remember needing to look the word up to know what the heck they were talking about. As a special education teacher, I needed to be familiar with everyone’s buzz words.

“As a special education teacher, I needed to be familiar with everyone’s buzz words.”

And all those glorious acronyms!

My first full time teaching job when I reentered teaching, I quickly learned to ask what those ubiquitous acronyms meant. (One good thing about being older is there is more of a chance that you have outgrown that fear of looking stupid.) The district was so acronym happy they had invented their own unique list in addition to the ones associated with the profession as well as those from government agencies/programs. The district even included a list of meanings for those acronyms they had invented in our new teacher packet.

Hah! Are you in NYC? We had a Bloomberg Quality Review coming up. There was a LOT riding on those QRs (there’s an acronym right there!), so our principal handed all of the teachers a binder filled with about 30 pages made up exclusively of acronyms, about a week before the review. We were told to get to know what they meant, ASAP, because there was a good chance we’d be asked!

They did ask us a few. But not the whole shebang.

No, while my roots are in New England, I am in suburbs of Chicago. It was years after I was married that I finally called it home. My husband, who was born and bred in Illinois, took years to finally see the charms of New England after many summer vacations there.

I do not think, calculators are the basic problem. The basic problem is the expectation of correct answers to problems instead of expecting the student to understand mathematics.

We know very well that students can get correct answers to, say, algebra problems just by memorizing formulas and some basic formal manipulations.

There is absolutely no reason to understand math to arrive to the correct answers on any of the ACT math problems.

In my experience, many (most) of the kids who can solve an endless collection of algebra problems are simply obedient and are willing to learn useless stuff, but certainly not math whizzes , while those who claim they are bad at math are often the kind of people who simply refuse to learn something they do not understand.

So the appearance of calculators in K-12 is just an expression of this deemphasis of understanding in math—and in many other subjects.

I agree it’s not the calculators.

And, sadly, it’s not just college freshmen.

It’s the “plug and chug” approach, prevalent even in many “disciplines” that claim to be mathematical.

Econometrics is the prime example.

With the widespread availability of software packages for economic modeling, lots of economists just plug in data and take whatever result pops out.

They did this during the housing bubble with catastrophic results.

Most of the models did not take into account the role played by the banks — especially not the fraudulent behavior of many of the biggest banks with regard to liars loans.

Most economists also never asked themselves whether the housing price increases they were seeing were consistent with historical trends (which they weren’t).

All the numbers that came out of their models were essentially garbage but the vast majority of economists did not recognize them as such because they were in plug and chug mode, I’mquestioningly trusting the answer.

IMHO, the most important thing a person can get from math education is the ability to do a “reality check” to judge whether a result seems reasonable.

It’s hard to do such a check if one can not do fairly simple addition, subtraction and multiplication without a calculator.

Just to underlie what you are saying: not understanding what math maybe behind some formulas could explain the following contradictory results.

Here’s a study from 2010 showing that teachers’ merit pay doesn’t increase test scores

https://news.vanderbilt.edu/2010/09/21/teacher-performance-pay/

and here is a study from some of the same people this year, concluding the opposite

https://news.vanderbilt.edu/2017/04/11/teacher-merit-pay-has-merit-new-report/

It seems to me your comment does point out the problem with an over–reliance on calculators. There is no necessity to understand the underlying concepts–just plug in a formula and spit out an answer whether it makes sense or not.

The calculator is a problem. The calculator’s use has contributed to if not caused a huge decline in number sense.

On a tangent but something that I think is quite important for all involved in the teaching and learning process.

And that is: The human mind/brain is an amazing forgetting machine. It’s just a hunch of mine but I’d say that we easily do not “remember” 99.9%, in other words, almost all) of what we take in with our senses in a given day. Think about that and the implications for learning.

So the question becomes: How can we assist students in learning how to overcome that “forgetfulness”? (Which relates to West Coast Teacher’s comment above about how to study.)

I have few answers but rote memorization should be a part of any number of subject areas, not the exclusive/only method of learning but rote memorization has long been a no no for many educators (as noted by Karen langlais’ last comment about the principal and “drill and kill”.) And there are techniques for making memorization work efficiently if the student puts in the effort (as many have noted above).

” have few answers but rote memorization should be a part of any number of subject areas, ”

Apart from the multiplication table, rote memorization has no place in math.

But of course, memorizing poems is a different dish.

Not being a math teacher (although I did take calculus in high school and come from a “math family”) I do not have any solid knowledge of math pedagogy and only am relying on my personal experiences in learning not only math but especially a second language where building a vocabulary base is the most important aspect of the very many aspects involved in learning a second language. And the best way to do so fairly quickly and efficiently is rote learning. I say that from the comments of former students who actually followed my technique of repetition to learn the vocab and who confirmed it worked better than anything they’d come across. But I left it up to each student to determine how they wanted to learn the vocab.

Addition and Subtraction facts need to be memorized in the primary grades. The concepts surrounding add and sub computation need to be fully understood but the add and sub facts should be practiced to fluency. I think what happens is those of us from a prior generation did not think about memorizing add and sub facts because we just knew them in primary because we were not burdened as students are now with all these concepts and word problems. Simplify primary math – really learn the basics….

I prefer to multiply poems.

That’s why I keep writing them.

love you – some dam poet !

There are a few other basics that should be memorized in high school math, such as the special right triangles and the 6 basic trig derivatives. One needs a base of fundamentals to build other, deeper ideas from.

But, I generally agree, it is wise to “minimize what’s memorized” and teach students how to think.

I agree with much of the author says, and I want to share two-three observations.

First, the foolishness of pretending that all kids must become college ready, and effectively labeling those who are not as failures. Many kids are not college-ready because they didn’t study, but even more are simply uninterested in college and would rather study arts of trades, yet we have decimated vocational education across the country. In other words, the foolish Common Core promise of “every kid will be career- and college-ready” was translated into “college-ready,” turning our high schools into college prep factories rather than preparing students for life with all its varied interests.

Second, we know that only around 1/3 of the cohort is actually college-ready (about 2/3 continue to college, and only about half of them ever get a 2- or 4-year degree). Consequently, Common Core tests cannot set their bar at true college readiness as it would fail 60%-70% of the cohort. So they set it at a fake low level of “college-readiness” and then — by laws and regulations! – forced state colleges to accept this ersatz readiness and prohibit them from placing unprepared students in remedial courses. It seems the author is not in a state college, so it can still administer placement test and use remediation. Sandra Stotsky and I wrote about this danger very long ago, when Common Core was just a glimmer in few people’s eye.

http://www.mindingthecampus.org/2009/12/by_sandra_stotsky_and_zeev/

Finally, I appreciated the author writing “Questions [of the placement test] are asked in a straightforward manner (unlike the current NYS common core based regents exams).”

This is very important. Most (all?) Common Core tests these days ask question in a convoluted manner appropriate for brain teasers rather than for curriculum-based test. Curriculum-based tests ought to be straightforward so anyone who studied the material can — and should — get close to 100%. For years (2000-2013) had such a test, with no heavy language load, no long and wordy prompts, and no IQ-test-style problems. It worked very well, even though the Solons in Education Week sometimes called it “shallow”; in their ignorance they paid attention to the complexity of the prompts rather than to the depth and breadth of the required underlying mathematics. Unfortunately, it was replaced by the Smarter Balanced Common Core idiocy in 2014. Common Core tests are largely meaningless.

the foolishness….agree x 100

brain teasers…agree x 100

More confirmations in the Nonpartisan Education Review…

Garelick:

http://nonpartisaneducation.org/Review/Reviews/v11n2.htm

http://nonpartisaneducation.org/Review/Essays/v5n2.htm

http://nonpartisaneducation.org/Review/Essays/v2n6.htm

Bishop:

http://nonpartisaneducation.org/Review/Reviews/v10n1.htm

Quirk:

http://nonpartisaneducation.org/Review/Reviews/v9n2.html

http://nonpartisaneducation.org/Review/Reviews/v9n1.html

Dancis:

http://nonpartisaneducation.org/Review/Essays/v8n1.htm

http://nonpartisaneducation.org/Review/Resources/Pretend_Math.htm

http://nonpartisaneducation.org/Review/Resources/TeachersNeed2KnowMath.htm

http://nonpartisaneducation.org/Review/Essays/v7n8.htm

Stamm:

http://nonpartisaneducation.org/Review/Essays/v7n6.htm

Klein:

http://nonpartisaneducation.org/Review/Resources/NAEPMath.htm

http://nonpartisaneducation.org/Review/Reviews/v3n4.htm

http://nonpartisaneducation.org/Review/Reviews/v3n3.htm

From the Stamm paper

The data on topics per grade show emphasis on quantity carried to an extreme degree. In first and second grades the number of topics covered in the U.S. is almost five times that of the A+ countries. This is at a stage in a child’s development when the greatest care should be taken to foster understanding and mastery of the basic ideas that form the foundation of all later learning in mathematics. This excess in U.S. curricula precludes anything but the most superficial treatment of the topics studied.US (math) education is not patient: it pushes kids at an early age. This results a tremendous slowdown later.

Education, thanks to top-down pressure, is a shotgun approach and the shells are all filled with rock salt.

yup… “This results a tremendous slowdown later.”

For verification note the drop in every cohort of USA 4th graders on TIMSS math in grade 8 – four years later. Exposure to a range of topics produces scores in grade 4 than cannot be sustained in grade 8 as the underlying skills and knowledge are perhaps superficial.

Yet a contributing factor may be extremely poor instructional materials and defective pedagogy in use in grades 5, 6, 7, and 8.

agree…agree…agree – from a primary teacher

We must drill the skill. Practice is what the kids need. Most curriculums give one day max on each concept. Students need more than one day to ‘get it’. I have been looked down upon because I am so far behind in teaching the units. But I make sure my students know their times tables, fractions, decimals, etc. So I never get to the intro to the next grade because I am just barely finishing the fourth grade stuff.

Oh…My students want to know how I knew they used a calculator to do their long division with remainders homework.

But there is no time to practice if the material to be covered is huge.

NYS (SUNY) community colleges and 4 yr colleges and universities still use placement testing.

The prior NYS Regent exams were not any better than the CC Regent exams.

They were not raw scored grades and they also built in an ~ 20 point curve.

Hence to get a 65% you really only had to reach a raw score of 45%.

And since SpecEd students had a “safety net” they only had to get a 45 or 55%, and therefore only had to get about a 25 or 35% raw score to pass.

None of this equates to mastery of the material.

True mastery would mean a student needed to get an Honors Regent diploma to ensure college readiness.

Just go back and search on the Regent exams and the scoring keys and you will see how they are giving the facade that students are scoring better than they really are on the Regent exams. The scores do not equate to proficiency and mastery of the material they are tested on. And they usually spend the last few weeks if not more, teaching to the tests. (And the majority of students still cannot excel on them. So what does that tell ya about how useless teaching to the test is, yet they keep doing it.)

I have been a mathematics professor CSULA for 45 years and the problem has grown from minimal to modest to very bad to untenable. Solution? Mandate that all math courses Asreceive university credit; some extra time to focus on the basics, maybe, but no non-credit university courses. Voilá! Problem solved! Students no longer held up or turned away because of remedial math and/or English! Combined with California’s dropping (retroactively!) it’s CHSEE, High School Exit Exam with the huge jump in “successful” high school graduations and those cynics who say, “At least it can’t get any worse,” are not cynical enough. It can get worse and it will get worse. Oh yes – Don’t forget prestigious schools dropping their SAT/ACT requirement to make it easier to tilt in favor of a few students with strong moments but weak demographics. All the easier for the rest of us to follow suit thereby weakening the overall genuinely successful prognosis for hundreds of thousands is not millions of students campuses such as mine serve.

Wayne, not blaming you but it doesn’t help when college professors complain to K-12 teachers about freshmen lacking “thinking skills, problem-solving skills, reading skills and writing skills”. K-12 educators hear this and say, “You see? We need to teach more thinking skills, reading skills and writing skills!” It is precisely the misguided effort to teach these things directly that leads to such feeble minds. K-12 schools CAN teach math facts, geography facts, grammar facts, history facts, science facts, etc. very well and solidly. All these facts ENABLE strong thinking, reading and writing. Yet we scorn to teach these facts in the vain faith that we can teach the skills themselves directly. We can’t! But we glom on to failed curricula that PURPORT to teach these things. If only we could! But no one has ever taught these things and no one ever will because it’s impossible. What is possible, transmitting knowledge, has been mostly abandoned as outmoded and “discredited”.

“college professors complain to K-12 teachers about freshmen lacking “thinking skills, problem-solving skills, reading skills and writing skills”.”

Unless you mean the ability to read straightforward, “cookbook” if you will, word problems with clear intent and straightforward, calculator-free solution intended, I think you’re talking math ed professors (and similarly science ed professors) not math (and hard science) professors. One group has no reason to exist.

Ponderosa … Amen!!! Consider the term “Conceptual Understanding” in math. Too many folks have decided that following their perception of the “Standards for Mathematical Practice” means teaching of conceptual understanding directly…..

Wow.. just WOW … would not Conceptual Understanding arise from a familiarity with numbers and procedural fluency? We are walking on the bleeding edge of crazy these days.

” would not Conceptual Understanding arise from a familiarity with numbers and procedural fluency? ”

Nope. You can perform hundreds of additions or multiplications (without a calculator) and you still have no idea what you are doing, what addition or multiplication mean.

Yeah it doesn’t help when elementary schools in Delaware bring in Art, and PE teachers to help teach math…. and it’s Math I have never seen before in my life. Who says, one thousandths, two hundredths, and fifty tens as a number?

You got me baffled with that terminology, maryjane!

Yeah, 4th graders were learning about place value. I think I have the spelling a little off since I experienced this 3 years ago at a school I “used” to teach at… Check it out yourself, Engageny.org. Engage New York Math, fourth grade, module 1, copied from their website, “(4.NBT.1). They recognize that each sequence of three digits is read as hundreds, tens, and ones followed by the naming of the corresponding base thousand unit (thousand, million, billion).” So students would read numbers out loud, together, one hundreds, two tens, and five ones (1,205) in hopes of learning place value. They wrote the words out that way too. I argued that we do not read numbers that way and that students are going to get this wrong later in life. I kept hearing, but we are teaching place value. So as an art teacher, I teach how to mix colors, but I am not going to teach how to care for a paintbrush because I am only teaching color mixing. It makes no sense in the real world because everything is linked. One major reason I left that school.

A little off topic, but I think the place value unit in 4th grade was a prep for understanding decimals (percents, and fractions) later on. I had to go back and teach place value at a basic level to my struggling 7-8th graders before they could use decimals for computation and understand the relationship with fractions and percents. If place value is taught as just a rote memorization task, there are going to be a significant number of children who have trouble with its application later on. I literally had students who had no idea of the relative difference in size of 10 an 1,000. It’s kind of like seeing no difference in big and bigger or less and a lot less. Numbers give us a vocabulary for describing the world in all its wonderful patterns just as adjectives enrich description in language. I never went beyond algebra 2 in high school, and I don’t really remember much of what was included in that last class. I do know that I missed a lot of stuff that left me totally unprepared for a calculus class in college (my advisor should have known to nix that!) that I took of my own free will, not even realizing that that 4th year of high school math was a necessary precursor. It was in figuring out how to teach struggling middle school students that I first really understood the beauty of math for itself. I had never had trouble with applying it in the sciences, but I was not a math class aficionado. I am a person who needs to understand what I am doing. That being said what understanding looks like for a 4th grader and what it looks like even to a 6th grader are much different. What that looks like for 6th graders individually can be quite different; math instruction is maybe less forgiving when it comes to recognizing those differences.

“what understanding looks like for a 4th grader and what it looks like even to a 6th grader are much different. ”

And of course the teacher is also at a different level of understanding. Perhaps, it’s best to use the word “makes sense” than understanding. At any level, we need to make sure, math makes sense to the kids—and that they learn to demand from the teacher that whatever they learn, makes sense.

“Perhaps, it’s best to use the word “makes sense” than understanding.”

Okay. “Make sense” implies being able to use the information. Saying, “Do you understand?” is likely to get a nod that may or may not just be expedient. In either case, the teacher has to make sure the student can demonstrate that it makes sense. The younger ones are less likely to demand that a teacher make sense.

I teach Algebra I in the Buffalo Public Schools district and I COMPLETELY agree with everything this teacher has said! I feel that the lack of number sense is a major concern for and major reason why many students (and adults for that matter) do not grasp mathematical concepts. We as a country decided that building those operational foundation skills early on was apparently not working so we do less on those skills and overly complicate math early on with lengthy word problems. I love the technology that is available to my students but definitely see many students heavily relying on the graphing calculator for simple computations. The lack of basic skills such as taking 20% of a number or doing 7•6 cannot be quickly computated without major thinking.

Although I teach remedial reading at an upstate NY community college, I also regularly teach basic-level arithmetic skills–combined with reading–to students who are failing the developmental pre-algebra course.

As the poster, says, combining remedial and college-level courses works for a very few students in any field, mostly those who once mastered the basic skills and have been out of college for long enough to forget them. Certain they do not work for students who never learned to form a correct sentence, let alone a paragraph, and will not work for a student who literally (I teach English, and I am using that word correctly) cannot add 5 and 3 while using her fingers. But speed-up courses are the latest silver bullet and are sold wholesale to panting colleges who need to beef up their “graduation” rates, even if they graduate functionally illiterate students (which my college has).

In every field, if we could a) begin teaching specific skills at an appropriate age, instead of forcing children to do things for which they are not physiologically prepared, b) teach foundation skills first, thoroughly and correctly, maybe we wouldn’t have remediation in college.

I, too, have seen things get worse and worse. The latest wrinkle is “I can’t–or won’t–or don’t like–the work you have assigned so could you redesign the course–or my assignments–to satisfy what I like and what I can do?” Maybe this is why high tech companies prefer to hire competent foreign workers over products of the US school systems. And I, too, do not blame the K-12 teachers, many of whom are frantic trying to satisfy the insane demands of Corporate American while still trying to teach.

Good comment.

“Maybe this is why high tech companies prefer to hire competent foreign workers over products of the US school systems. ”

Horse manure. They hire foreign workers to pay them less than American workers and then hold that employment over their heads so the foreign workers have to acquiesce and comply with less than ideal working conditions, being overworked without proper compensation, etc. . . or otherwise risk being deported when they challenge their overseers who decide they can hire another more passive and acquiescent worker.

Bingo!

Jane, associated with this is the push for Algebra I in seventh or 8th grade… sometimes for all students. So what is the hurry? Are all these kids planning on taking Calculus I in the junior year of high school…. This speed push results in superficial knowledge for many…. so what is the point?

I can chime in pretty directly on this one:

I attended the initial presentation workshop of the “New Math” (process over product/deciphering word problems), here in NYC. It was the first presentation that included both special and general ed, up to that date.

During the question and answer period, I asked when I’d have a chance to teach basic arithmetic skills. They told me to “fit it in somewhere” if I thought it was necessary. My classes were made up of 5th grade kids with extremely violent tendencies, but they really enjoyed the no nonsense/write or wrong aspect of arithmetic.

I then asked why they were making this wholesale change, in the first place. The answer was enlightening. Though not a direct quote, this is what we were all told:

“We got together with some of the most influential CEOs of the top Fortune 500 companies and asked them what they wanted from our NYC graduates. They told us “We want problem solvers. We can put a calculator on every desk for next to nothing”.

What followed was a complete abandonment of basic arithmetic skills in favor of word problems at every school in NYC, both general and special education. All of our remedial math programs were literally thrown away. We were only allowed one grade level of books per class and were not allowed to split the kids up during common math periods. Very few of our kids were performing anywhere near to grade level in either math or reading. There was no time to “fit it in” during the regular school day.

My kids missed the old routine in a very, very, very big way. They couldn’t read and there was no longer a “right or wrong” that they could measure their progress with. Their violent tendencies began to take over. Very little of anything ended up being taught during those math periods, as a result.

Education asked big business what they wanted and big business took the reins from then on. It was, for me, the beginning of what we’re seeing, today. Education professionals have taken a back seat to amateurs with MBAs.

“What followed was a complete abandonment of basic arithmetic skills in favor of word problems at every school in NYC,”

Before you create poems in English, you need to speak the language, don’t you?

Yes

Oh, my, are you naive, my dear! Don’t you know that the latest in creative writing (actually, it’s a throw back to the ’60s) is that as long as you feel, sincerely, and emote on the page, that nothing else matters? Forget the language, don’t bother to learn anything about poetry or read any boring poetry that anyone else might have written, just paste a bunch of words together and be sincere!

Yes, I’m being sarcastic. My community college now offers a “creative writing” associate’s degree to anyone who wants to enroll in it. Students need to pass only one composition class with a C before they can frolic in “creative writing.”

Yes… teachers have become the servants of CEOs. Who wants to be in a “profession(?)” where the big decisions are made in the most inane way? Teacher shortage in Math. Now why would that be? … Perhaps because many leave because of the requirement to teach in an incredibly inefficient and ineffective way …

No time to read the comments above yet so forgive me of this has been said already:

As a physics teacher whose original degrees are in engineering, I am amazed at the number and caliber of students who are admitted into university, even in engineering. I have talked with my math teachers who agree. These students do not have stellar grades in high level courses or even in low level ones. We were all worried about getting into college and most students are not.

Penn State alone has a large number of branch campuses that take more marginal students, those that need remediation, those that drop out after a year of accruing debt. Perhaps those students should not be admitted to college and instead go to a community college. Perhaps we are admitting too many students to college directly after high school?

The combination of The New World Order (aka: outsourcing) and automation have dealt a pretty devastating one/two punch to the unskilled (and, in some cases, “skilled”) worker in the USA.

A college degree is often seen as the new “high school degree” in terms of being ready for the labor market.

So now we’ve raised the K-12 academic bar higher in hopes that the kids will jump higher so that we, as a nation, can remain “competitive” in this new world job market. Whether we believe in the legitimacy of the past 10-15 years of curriculum change here in the US, many students are NOT jumping higher or are simply giving up. Many CAN not jump higher. But they’re getting passing grades (which can sometimes provide them the minimum for getting into college) for more than a couple of reasons, one of which is that they’ll never pass unless they’re given a minimum passing grade.

My view is that you can’t fit the square peg into that round hole. Some people are just not academically inclined. But others who have much more clout than do I seem to think differently. Time will tell.

The math standards are good. The problem is with resources and student motivation. I do not acquiesce to the concept that teachers are absolved of responsibility regarding student motivation.

As a retired elementary teacher, I agree that the state’s approach is what’s causing much of the problem. Teachers are pressured to teach to the test, and must spend their time trying to get kids to understand the wacky wording of the problems,and how to verbally explain their answers (as my grandson gr 1 puts it- I did it in my head- it was easy to a 2 digit addition problem. Sadly, his is not an ok answer. It’s not ok to intuitively understand basic computation. One must use the proper jargon and the same convoluted wording of the problem. No time to develop understanding at a deeper conceptual level. No time to learn the “number facts”. Add in the kids with emotional, behavioral problems, don’t try, don’t study, just don’t care, and you’ve got the answer.

” It’s not ok to intuitively understand basic computation. One must use the proper jargon and the same convoluted wording of the problem. ”

Exactly. Insane.

Sue, teaching to the test would be fine …. if the test was not such a convoluted piece of insanity…. we use SBA in WA state and it is interesting looking at how results levels 1, 2, 3, 4 compare with NAEP results for 2015…

The SBA level 1 well below standard – percent of students at this level is about the same percent as on NAEP level 1 below basic…. But the Others …

look like fine examples of grade inflation.

There are way more at the top SBA level 4 than at Level 4 advanced NAEP. …. so no surprise .. the system making itself look good.

By trying to keep everybody happy.

“Words” (by the Bee Gees)

Math, a Common Corey math

A math that brings a smile to Gates

Let sum and multiply be gone

Cuz that would bring the bile to Gates

Old math has lost its glory

Let’s start a brand new story

Now, my friend, right now

There’ll be no other time

And Gates can show you how, my friend

Math in everlasting words

And dedicated all to Gates

And I will teach them all my days

I’m here to seal the student fates

You think, that I don’t even mean

A single word I say

It’s only words

And words are all I have

To take your math away

The tendency for understanding to take precedence over procedures pre-dates Common Core. Tom Loveless of Brookings Institution has quite accurately characterized Common Core math standards as containing the “dog whistles” of math reform–key words/phrases embedded in the CC standards like “students shall explain” and “students shall understand”. Reformers pick up on these code words and interpret and implement Common Core with the emphasis on understanding. Common Core has been gasoline on the fire of math reform that has been raging for decades.

Emphasizing “understanding” as opposed to what the reformers refer to as “just ‘doing’ math” has become the way to teach math. The movement gained steam with the NCTM’s publication of its math standards in 1989, and now has gained even more power with such ideas becoming synonymous with Common Core. Schools and administrators may resist an approach that does not require students to master a supplemental approach (using methods, pictures, techniques other than standard algorithms) to help add numbers. This is because standardized tests—the mechanism of accountability for many in education—may require reform math approaches to math problems.

The fear is that students will do poorly on such tests because they will not know how to write explanations that demonstrate the so-called understanding. But such thinking confuses cause and effect. Forcing students to think of multiple ways to solve a problem, or using “making tens” as a method to explain why, for example, 9 + 6 equals 15, does not in and of itself demonstrate understanding. Those who believe it does seem to be saying: “If we can just get them to do things that look like what we imagine a mathematician does, then they will be real mathematicians.” It is an investment in the wrong thing at the wrong time. The “explanations” most often will have little mathematical value and are on a naïve level since students don’t know the subject matter well enough. The result is at best a demonstration of “rote understanding.”

Interestingly, the nations that teach math in the traditional fashion seem to do quite well on tests like PISA, the international exam that is essentially constructed along reform math principles. Perhaps this is because basic foundational skills enable more thinking than a conglomeration of rote understandings.

I wish more teachers had the grasp of the Math Wars that you do. Most just accept “authority” and are unable to think critically about what they’re doing. I teach history, but when I have to cover a math teacher’s class, I see defeated looks on kids’ faces. Common Core math is not working. It is a giant fiasco.

Ponderosa – you being a history teacher, I would not teach the jfk assassination in a primary grade but I would in high school. Why would I teach prealgebra in primary ? …because that is what CC is asking me to do.

Ponderosa, I am never sure if it is the content standards or the nutty way that the progressives who dominate math decision-making care to interpret things.

Like I’ve mentioned instructional practices that are effective have been replaced with best practices.

Check out 15 minutes a day of Number Talk.

http://www.mec-math.org/number-talks/

“Forcing students to think of multiple ways to solve a problem, or using “making tens” as a method to explain why, for example, 9 + 6 equals 15, does not in and of itself demonstrate understanding. ”

This is completely correct, but instead of your apparent conclusion of abandoning a push for understanding, what we should conclude from what you are saying is that understanding and tests don’t fit together, and prescribing material to be covered in a given year don’t work well with understanding, either. CC commits both mistakes: it demands tests for understanding and a mandate for what material should be covered—hence the enormous problems with it.

Being able to

domath beyond the basics is just a skill, and not an important one for the vast majority of the people. But understanding math is (or should be) as much part of general culture as learning about Shakespeare or Ancient Egypt or Evolution or DNA or the Solar system.Sorry, too thoughtful, Maté. Come back when you’ve absorbed the full dose of “Ain’t It Awful?” required to weigh in with the invasive forces of educational nostalgia.

I don’t think I concluded implicitly or explicitly that we should abandon understandings. Certainly teach for understanding, but don’t fret if some kids just go for the procedures and don’t really get the underlying concepts. Some do, some will get it later, some never.

It is absolutely amazing that in grade 8 on TIMSS Math Singapore => 621 USA => 518 and yet the USA math gurus pay zero attention to the practices in use in Singapore to teach math. HOW ARROGANT!!!

http://mathunderground.blogspot.com/2017/04/8th-grade-math-singapore-crushes-usa.html

Many if not most of our chief policy makers here in the USA aren’t educators. They’re looking for quick fixes. So if something works in Singapore, they buy a lot of it and it’s “problem solved in a box”.

Seen that “singapore math” (as packaged here in the US.) Seemed to be a rather crazy way of going about math.

“the USA math gurus pay zero attention to the practices in use in Singapore to teach math. HOW ARROGANT!!!”

The arrogance is in making that absurd and unsupported pronouncement. However, if you actually paid attention to the politics informing parental views on math education across the country over the last half-dozen years, you’d find quite a few CONSERVATIVE parents who are under the impression that Singapore Math is a Common Core-mandated program in their state or district, and hence rail against it as the second coming of Soviet-style communism or worse. Get out of the ’90s, Danaher: it takes more than mere knee-jerk reactionary politics to sort out the Math Wars these days. Bummer, eh?

It wasn’t bad enough when this erstwhile education blog turned into Hillary Clinton campaign headquarters. Now it’s become the new host site for Mathematically Correct, NYC-HOLD, and some NW haters of anything and everything that isn’t just like they imagine things once were for everyone (no matter how narrow their experience of what actually happened for a lot of people who didn’t grow up in their shoes, schools, or communities).

Careful what bedfellows you make: not a lot Hillary Clinton fans weighing in here from the Math Wars.

MPG,

As you no doubt remember, I said during the primaries that I would support the Democratic candidate, whoever it was. When the race was over, I endorsed Hillary. I can’t imagine supporting Trump or Stein.

So now we have Trump. His Supreme Court choice just cast the deciding vote to put a man to death in Arkansas. He will cast the deciding vote on abortion, vouchers for religious schools, gay rights, individuals vs. corporations, etc. we know how he will vote.

Do I regret supporting Hillary Clinton over Trump? No. Not at all. I would do it again. Consider the consequences. I know you can’t see any difference between the two. But I do.

I recall that the standard response to this is “When did I ever say there’s no difference between Hillary and Trump? Stop putting words in my mouth!” And then more words, often including “Hillary was on the board of Wal-Mart from 1986 to 1992!” and “Hillary showed no regard for Colonel Gaddafi’s life!”

MPG .. suggest you look at presentation by Berinderjeet Kaur, PhD of Singapore on July 29, 2016 at the 13th International Conference of Mathematical Education in Hamburg, Germany.

icme13.org

She presented the in depth pertinent information about teaching practices in Singapore. I’ve watched Dr. Kaur’s presentation online and downloaded her slides.

Unfortunately USA persons of authority in math leadership positions take at best a passing interest in Singapore’s consistently outstanding performance. (Reminds me of Lilly Tomlin’s We don’t care, we don’t have to. We’re the phone company.)

============================

What do you think of Dr. Kaur’s presentation?

Video of presentation

https://lecture2go.uni-hamburg.de/l2go/-/get/v/19771

Michael:

I remember our last math war, here. I respect knowledge and ideas on the subject.

Now I’ll ask you not to so quickly dismiss or diminish the comments of myself and others, here.

My experiences had nothing to do with a fictional “good ol’ days” and, although the kids I taught had special needs (aka: remedial study in both math and reading), they did and still do represent a significant percentage of our student population, here in NYC.

The blatant fact is that I was forcefully stripped of an effective method of teaching remedial math (and, later; reading) instruction, made up of multi- grade level textbooks, workbooks, and teacher (me) made materials. What was given me (and all teachers) in replacement was a single grade level system per class called “Everyday Math”. A program that was being used in the most advanced schools in NYC.

It did not work because it was inappropriate for the development level of the kids I was teaching.

It was completely in

Wish we had an edit function.

Anyway: I meant “developmentAL” level and I know what worked and didn’t work for the children we were teaching at the time.

And I know why.

I’m pretty sure my comments were addressed to a few recent arrivals here, gitapik: people who are still fighting the Math Wars as if it’s 1995 and everything boils down to using Saxon Math or something developed out of the NSF initiatives in the late 1980s/early 1990s. Didn’t realize that included you, but if so, the issue isn’t textbooks and never will be for any competent mathematics teacher in any grade with any population. A good math teacher can take just about anything and work around it, at least given reasonable autonomy.

What’s changed from the mid-’90s is that politically-motivated initiatives from both Republicans and Democrats – particularly No Child Left Behind and Race to the Top – coupled with an insane obsession with high-stakes testing and phony accountability, have destroyed any semblance of autonomy for states, districts, schools, administrators, and teachers. National standards – e.g., the Common Core – have added an even greater push for lock-step student and educator performance, though many states, etc., were already looking for a one-size-fits-all approach before the Bush and Obama administrations made it increasingly difficult for independent educational judgment.

Reading the comments of many people here is like stepping into a time-warp, however: nothing has changed for many people in their understanding of just how cramped and restricting school mathematics has been for millions of Americans over the past 125 years or so, how irrelevant, how intimidating, how painful, how frustrating, and ultimately how loathsome. People here are certainly free to harken back to an imaginary Golden Age before the Common Core, before the NCTM-inspired reforms of the 1990s, before the New Math projects of the 1960s – and there is no dearth of such people here and in our schools, despite the narrow perspective offered here that would have one believe that most teachers have been successfully convinced to go to what the self-appointed Math Warriors would no doubt characterize as “the Dark Side” if they were a little more creative than they tend to be in their nostalgic diatribes; as someone who has spent the last 25 years in a variety of roles in high-needs, mostly inner city public and charter schools in Michigan and New York City, it simply “ain’t so.”

That said, I’ve been battling to help teachers improve the quality of their mathematics instruction and their students’ learning of that subject for too long to quietly let the usual suspects have a field day moaning about the falling sky due to alleged progressive mathematics educators who know no mathematics and couldn’t care less about real continent. No need to summarize the polemics above: they speak for themselves and clearly have found many supporters here among already-disgruntled nostalgia buffs. And sorry to say, it would be impossible for me to respond to them without apparently seeming to be rejecting your viewpoint, even though I wasn’t. I’ve worked with many special education teachers in Detroit and similar places and am well aware of the challenges they face. The developmental inappropriateness of significant parts of the Common Core Math CONTENT Standards for early elementary students is only one of the issues I wrote about extensively before conservatives and reactionaries decided that they had something in the Common Core “State Standards,” with which to attack Obama, regardless of the previously enthusiastic promotion of that same initiative by a majority of conservative and Republican governors in the early days of its release and implementation. Some of us haven’t forgotten how people like Jeb Bush and Bobby Jindal LOVED the Common Core until it suddenly became a political liability to do so. Jindal completely did a 180; Bush didn’t and that likely hurt his run for the GOP nomination last year.

Not being a governor of any state, I didn’t have to change my stance from the early announcement of CCSS: I opposed it then and still oppose it, though I also recognize and decry the attack on the Standards for Mathematical Practice – the one reasonable part of the Math Standards that the “Math Warriors” here and elsewhere have always found unacceptable (and always will).

The ridiculous distortions of the old Math Wars crowd who’ve shown up here to re-fight the battles of 20 years ago make clear just how little has changed for them. They remain the same humorless bunch (see Danaher Dempsey’s response to my glaringly sarcastic comment about Singapore taking over the US and Canada as a textbook example), still relying on a scorched earth, by any means necessary approach to, ahem, honest, open, logical debate (have four simple English words ever been more abused by a small group?) in the service of opposing anything that doesn’t fit their narrow and rigid views of education that they were when they started surfacing online c.1995. I’m not expecting to move a single one of them an angstrom from their entrenched viewpoints or get them to be any more fair-minded or reasonable. Sadly, growth in those areas of thinking and discourse appear to be impossible for them. And for those here who embrace those attitudes, practices, and beliefs, I hold out no more hope than for the “old guard” Warriors. I’m sure that these people have found fertile ground on what was at one time a relatively progressive forum for discussing the education deform movement and how to combat it. Those days appear to be effectively over for reasons I prefer not to rehash.

So enjoy, by all means, the incursion of the forces of Mathematically Correct and NYC-HOLD (along with Mr. Dempsey). I wish I could say that they’re going to lower the level of analysis, but it seems they’re just putting more fuel on the bonfire and providing welcome pitchforks for storming (mostly) the wrong castles. Have fun burning the witches of progressive math education. Never mind that there is a significant core of gifted and inquisitive mathematics teachers out there who don’t take their marching orders from NCTM or any other organization, who have found their own voices independently, and are connected with one another through a wide range of on-line and face-to-face resources and meetings throughout the country and much of the rest of the world. The Math Warriors here aren’t going to undermine the efforts of smart, insightful, and reflective people out there who not only aren’t hamstrung by the Common Core, but also aren’t going to quake in fear if what they’re doing is attacked by 1990s Math Warriors who think that “the answer” lies in banning calculators or forcing Saxon Math or Singapore Math or some other nostalgic panacea down everyone’s throat. Now, if we can survive Betsy Devos’ plans to make all American schools into fundamentalist Christian indoctrination institutions, as we survived Obama’s attempts to sell public education to Wall Street, there’s likely still hope for at least some high-quality mathematics education.

“… A good math teacher can take just about anything and work around it, at least given reasonable autonomy.”

A piece of paper, folded and torn/cut into 4 equal pieces will go a long way towards introducing the concept and application of fractions.

But I did like that remedial program of text and workbooks. It was well thought out and paced well for my kids.

I found Jeff’s post, not far below this one, about the problem not being in the calculator, itself, so much as the way in which it’s utilized by the teachers and students, to be very interesting.

I was one of the original techs whose responsibility it was to usher the use of technology into the classroom. Despite all my PDs and newsletters, many teachers at first (less as time went on) would still use the Smartboards and computers as movie screens and rewards for work done as opposed to incorporating the tech into the lessons. What was (and still is) a tremendous tool to be included in the classroom routine is now evolving into the teacher as tool of the technology (turn it on and monitor of student attention).

I’m wondering if there’s a parallel with the calculator. Great tool at your disposal unless you take the easy route and just let the kids mindlessly push a few buttons and move on with the “take for granted it’s correct” answer.

“… A good math teacher can take just about anything and work around it, at least given reasonable autonomy.”

A piece of paper, folded and torn/cut into 4 equal pieces will go a long way towards introducing the concept and application of fractions.

But I did like that remedial program of text and workbooks. It was well thought out and paced well for my kids.

I found Jeff’s post, not far below this one, about the problem not being in the calculator, itself, so much as the way in which it’s utilized by the teachers and students, to be very interesting.

I was one of the original techs whose responsibility it was to usher the use of technology into the classroom. Despite all my PDs and newsletters, many teachers at first (less as time went on) would still use the Smartboards and computers as movie screens and rewards for work done as opposed to incorporating the tech into the lessons. What was (and still is) a tremendous tool to be included in the classroom routine is now evolving into the teacher as tool of the technology (turn it on and monitor of student attention).

I’m wondering if there’s a parallel with the calculator. Great tool at your disposal unless you take the easy route and just let the kids mindlessly push a few buttons and move on with the “take for granted it’s correct” answer.

I’ve been a teacher for the past 10 years in an urban district, where I’ve taught everything from remedial algebra to AP Statistics.

I agree that our current math curriculum leaves a lot to be desired, but I wouldn’t be so fast to blame calculators as the cause. I see over reliance on calculators as a symptom of a larger problem: most curriculum isn’t designed to utilize technology to aid understanding, and teachers don’t always use technology to help students develop understanding. To clarify, when calculators are used strictly as “answer getting” machines, students miss out on learning a lot of number sense. However, when a lesson is designed and implemented effectively, technology can aid in developing a deeper understanding of the content.

For example, an elementary teacher introducing division and remainders can show their class how to type in “4+4” to get 8, then “+4” again to get 12, then press enter repeatedly to keep on adding 4. The class can count how many times it takes to get to 100. The class can repeat the process with 3, and stage a “race” to see who gets there first, but the kids will realize that they don’t get to exactly 100.

This is just an example, but I’ve noticed that teachers who complain about overuse of calculators usually don’t know how to use calculators very well and haven’t received much training on how to effectively teach with them. The teacher usually just sees them as a crutch to get answers.

Nice point.

I was one of the original techs at our school. A central responsibility was to usher the use of technology into the classroom. Despite all my PDs and newsletters, many teachers at first (less as time went on) would still use the Smartboards and computers as movie screens and rewards for work done as opposed to incorporating the tech into the lessons. What was (and still is) a tremendous tool to be included in the classroom routine is now evolving into the teacher as tool of the technology (turn it on and monitor student attention).

I’m wondering if there’s a parallel with the calculator. Great tool at your disposal unless you take the easy route and just let the kids mindlessly push a few buttons and move on with the “take for granted it’s correct” answer.

Were you there before the slide rule? Ball point pen? Clay tablet and stylus? Pretty sure those (and paper, pencils, abacuses, knotted counting strings) are tech. I bet the sky fell when those came into classrooms, too. It always does for some sorts of people. I bet you can imagine the wringing of hands when pebbles in the sand and marks on sticks were made obsolete.

It’s possible to use any tool well or badly. Even books, worksheets, etc.

Piece of paper, folded and cut into 4 separate and equal areas, does the trick for introduction to fractions.

I’m saying that the calculator, with the teacher paying attention to the developmental level of the user and gradually teaching the concepts that it’s calculating can be an effective tool as well. As opposed to just teaching the kids how to push the correct button, assuming the answer to be correct. Add in the concept of estimation to keep it honest.

Some people on this thread think differently.

I’m a Math professor of 27 years at a large Canadian university. This fellow’s story is replicated in math departments at postsecondary institutions across the continent (and elsewhere that these pernicious ideas have taken hold in education schools). Other math professors and I have formed an initiative, WISE Math ( wisemath.org ; stands for Western Initiative for Strenthening Education in Math) to address these issues in Canada, particularly in the West where our own “common core” was called WNCP and, wherever WNCP was implemented (in a total of 8 provinces, eventually) test scores plummeted. WNCP is considerably worse than Common core; it rails against paper and pencil skills in the forematter and does not mention (in fact deliberately omits) the standard algorithms for addition, subtraction, multiplication and addition, foregoes the memorization of math facts, and does not introduce arithmetic with fractions until Grade 7.

It’s amazing that neither the US nor Canada has been taken over by Singapore.

MPG.. “taken over” or “overtaken”? Bizarre comment.

Singapore is a nation of 5.6 million people with a land area of less than 300 sq. miles. Are you looking for Japanese style expansionism like WWII? Given that Singapore became self-governing in 1959 less than 60 years ago, it seems its economic progress has been spectacular. Per Capita GDP $53,000 (7th in world)… USA per capita GDP $57,000 (6th in world)

Canada per capita GDP $40,500 (15th in World)

Look Canada has been overtaken by Singapore …. but not taken over. The Singaporean’s would have difficulty occupying 3,500,000 sq. mi.

Predictions are that at some point in the not to distant future Singapore’s per capita GDP will exceed USA’s.

I taught 10th grade world history, 11th grade U.S. & AP U.S. Hist for many years. The failure to require students to have fluent mastery of basic math – as well as other – facts was very apparent, esp. when I gave some simple math problems or questions, such as the following two. In both cases, I had to review the procedures.

1) When covering the U.S. Const’s 3/5th Compromise, I would give students the following hypothetical problem: A hypothetical slave state has a population consisting of 300,000 free people and 250,000 people held in slavery. For every 50,000 people the state gets one representative in the U.S. House of Reps. How many reps would this state have, if:

a) each free and each enslaved person was counted as one person?

b) only free people were counted, i.e. enslaved persons were not counted?

c) the state’s population was counted according to the 3/5ths Comp?

Some students would ask how to multiply 3/5ths. A typical question was, “what goes on top?” I would have to review the terms “numerator” and “denominator” and how to multiply a fraction times a whole number (note that the example doesn’t create a remainder).

2) Prior to a unit on slavery, I gave students a survey to see what they knew about the subject from earlier classes. One of the questions was:

“Of all the people transported as slaves from Africa to the Americas during the period of the Atlantic Slave Trade, approximately what percentage (%) of the total ended up in the United States or the previous Thirteen Colonies? _______ %

I found that I had to explain what percentage means.

I wonder what %-age of two-year college students were in remedial math courses when started teaching math at BMCC in NYC c. 1990, when calculators were hardly in general use in K-6 and all those NCTM/NSF textbooks were still being written. I don’t recall there being a dearth of non-credit math classes or students to fill them. But maybe that was only in Manhattan. I have no doubt things were vastly different in the rest of the country, and certainly before the New Math projects, every American could do trigonometry while milking the chickens at 5 AM.

Not 1990. Move that timeline back 15 to 20 years earlier.

“Calculators had already become important business tools, well before the handheld calculator. And in the 1970s, with a fair amount of debate about their effect on learning, calculators slowly began to enter the classroom.

Indeed, once students had access to calculators at home, it was pretty clear that they would be used for homework no matter what policies schools had in place for classroom usage. (A 1975 Science News article, “Calculators in the Classroom,” claimed that there was already one calculator for every 9 Americans.)” …

” In 1986, Connecticut became the first state to require the calculator on a state-mandated test, as the Connecticut School Board argued that calculators would allow students to solve more complex problems.”

from: A Brief History of Calculators in the Classroom

http://hackeducation.com/2015/03/12/calculators

Gee, Lloyd, I could have sworn that I knew what year I started teaching mathematics at Borough of Manhattan Community College, and it was Sept. 1990. So my timeline and the question I posed were based on facts you are in no position to dispute (not that that would stop you). Furthermore, if Connecticut (which, last I checked, is quite different from NYC and doesn’t send a lot of students to community colleges therein, particularly not back in 1990) started allowing or requiring (I’m not sure that latter word meant quite what you would like us to infer it to mean in that context) calculators on “a state-mandated test” (which one, exactly? I don’t think you know, and it matters) in 1986, a mere four years before I began teaching in lower Manhattan at a two-year college, could you explain what that has to do with the question I asked about why there were so many remedial students in that particular community college at that particular point when, as I suggested, elementary students were not yet getting access to those little electronic tools of Satan on a widespread basis in New York City, particularly not kids in poverty who tend to dominate the students at two-years schools there? Or, for that matter, how those calculators impacted the K-12 education of the then-40-something Haitian nursing students I had in significant numbers in my Algebra I classes?

The claim by SCIENCE NEWS that there was 1 calculator for every 9 Americans might be informative if we knew which Americans and where they had use of those calculators. After all, my boss had one of those large desk-top calculators with the paper tape on his desk in the mid-1980s when I worked in the food-importing business. He never used it. He was a whiz at mental math and inspired me to develop further my own abilities in that arena. But it wasn’t because he had such a fabulous mathematics education during the “Golden Age” before calculators. He dropped out of school at 6 to work and was able to pay for his younger brother’s education at NYU. Here is the obituary of that younger brother, whose closest friend was Isaac Asimov: http://nyti.ms/2pV796X I’m pretty sure that Izzy Adler didn’t go to BMCC. We didn’t get a lot of future PhDs there, particularly not in remedial mathematics classes.

I’m really not interested in arguing with you about calculators (or anything else, to be honest), but my point wasn’t that they’re good, bad, or indifferent, but simply that putting the blame on them for remedial mathematics students is an ignorant claim, likely willfully so in the case of the professor in the article, but perhaps simply a classic case of “common sense” that doesn’t really bother to check for facts when the person who is using it is so entirely sure of what the facts must be, even if they aren’t quite so. I have little doubt that you could provide your own evidence, rather than cite another article by someone who is part of that independent group of mathematics teachers who I mentioned in an earlier comment and who as is evident if you read the ENTIRE article, isn’t looking to make a case against educational technology (having followed her blog for about four years now, I’m confident that she’s far from being a Luddite).

So to be clear: I know what I was doing in 1990 as a mathematics teacher and my questions about how there came to be a host of remedial mathematics students in my classroom stands. But if you really want to plumb the depths of US educational history, let me pose another question for you: where did all the remedial mathematics students come from in my highly-regarded school district in north Jersey from 1955-1968 when NO ONE had a calculator at school? You can’t even blame “the” New Math for students in my graduating class who struggled mightily with arithmetic and/or algebra, etc. since the Dolciani series didn’t arrive in that district until we were already finished with K-8 math. Maybe they were importing water from Flint, MI via a time machine.

Bla, bla, bla, as usual.

MPG, your perception is limited to how far you can see and what you hear in your immediate surroundings. The calculator phenomenon had its start in the 1970s and by the 1990s it was full blown.

I provided a link to the history of calculator use in the schools. All you have is your own limited personal experience.

You said, “I started teaching mathematics at Borough of Manhattan Community College, and it was Sept. 1990.”

Sept. 1990 was when your perception of calculators in the classroom started. I started teaching in K-12 schools in California in 1975 and hand held calculators were in use then.

Yes, only a few students had them in 1975, but as the years slipped by on the way to when you were old enough to start teaching math, more and more children were getting calculators and/or schools were buying class sets just like schools started buying class sets of computers. In the beginning, a school might have one computer lab and classes cycle in and out of it. That’s why the district I taught in did. Eventually, there was a class set on carts and teachers could check them out and roll them to their classrooms.

The calculator phenomenon did not start with you in September of 1990. The world is a lot larger than what you can experience with your own senses.

Thank you for your cogent, respectful, and objective reply, Lloyd. I expect nothing less from you.

Many of the issues that have been discussed in these comments have been studied by scientists who study how the brain solve math problems. Some of these questions are settled (but non-intuitive) consensus science. I believe math educators would find the following to be very useful in designing teaching.

Written by UVa cognitive scientist Dan Willingham, “Is It True That Some People Just Can’t Do Math?” at

is a jargon-free discussion of how instructors can help students learn factual, procedural, and conceptual mathematical knowledge.

In more detail (but fascinating), written by 5 of the nation’s leading cognitive experts, Chapter 4 of the Report of the National Mathematics Advisory Panel is at

(Start with pages 4-1 to 4-10)

For a readable description of what the brain can and cannot do when solving math problems, see Clark, Sweller, and Kirschner’s “Putting Students on the Path to Learning” at

Science improves life — and can help with teaching.

— rick nelson

Willingham’s paper is a great read, there is nothing to argue there . In the last paper by Clark etal, the first questionable sentence is this

Research has provided overwhelmingevidence that, for everyone but

experts, partial guidance during

instruction is significantly less

effective than full guidance.

What does effective mean?

The main issue with the paper is that because of the apparent lack of success of minimally guided learning, the paper advises fully guided learning. Why make such a big jum from fully unguided to fully guided? In particular, the paper seems to advocate for recipe based learning in math—that is, it recommends total boredom in a math class. The paper doesn’t address the effectiveness of allowing kids to make small discoveries, hence to learn the joy of thinking and to trust their own ideas. The paper seems to recommend that an authoritative figure tells the kids how things are.

Imo, a good teacher knows excatly what kids know, what she can rely on, and asks questions from them which they can answer after some contemplation, but without getting frustrated.

Why take out the mystery out of learning for the sake of quicker answers to test questions?

What scientific studies have found and verified is that discovery must be VERY carefully managed by instructors, because students tend to discover misconceptions, and misconceptions can be exceedingly difficult to un-learn.

For one of the most informative and instructor-friendly short articles on how to structure instruction to avoid boredom AND misconceptions, see Barack Rosenshine’s paper at https://eric.ed.gov/?id=EJ971753

Unfortunately, the advice in the paper cannot be followed in today’s classrooms. Teachers are preoccupied with covering the large body of material that is mandated and prepare students for tests.

I wonder if it takes more time to learn more advanced math? In my school district the middle school kids do well on standardized tests. They have math class for 60 minutes every day (300 minutes per week). High school kids don’t do so well. They are on the Block Schedule. They have math for 214 minutes per week (almost 1.5 hours less). They also do not get daily reinforcement. Over the entire school year high schoolers have almost a month less of math instruction. I wonder if the block schedule and reduced time for instruction/comprehension/practice contributes to math difficulties for high school students.