New York policy makers saw a problem: too many students were failing the Algebra exam required for graduation. Result: more kids failed. What happens next? The tests will be made harder. What do you think will happen now? Will the policymakers blame teachers? Will the public figure out that making tests harder increases the failure rate? Why do legislators and policy makers think that kids work harder and learn more if the tests are more rigorous? Tests are not instruction. They are measures.
Some students take the Algebra exam four, five, six times. At one school that raised its passing rate on the Algebra test, the school dropped art, music, and health.
I have been reading Andrew Hacker’s “The Math Myth.” He does a good job of demolishing the claims that everyone needs Algebra.
Common sense, anyone?
Diane Ravitch's blog 
The isolation of math into its various silos, all more or less hierarchically arranged from arithmetic for the elementary grades through geometry, algebra, trig, calculus, and so on, takes all the meaning and fun out of math. Math is about manipulation, measurement, and then the re-imagining of the world. It’s no more about mere numbers than communication is about mere words.
Your comment is poetic.
In arts, students build upon their skills. If a child loves to play saxophone, he is taught saxophone. Nobody says that you got to excel with piano too because that’s what the curriculum says.
After reading this article, I did my own google, and came across this file – http://alpha.math.uga.edu/~davide/THE_MATH_MYTH.pdf. It says, most of the work-force, including scientists and engineers, seldom use more than eighth grade level mathematics.
It’s a conjecture. However, it got me thinking – If it’s true, we are wasting a lot of creativity. Probably, a lot more than student lives.
Can someone explain how the 9th grade (Class of 2018) cohort had a 63% pass rate on the CC regents Algebra I test in June 2015, yet this same group only managed a 33% pass rate on their Pearson CC pre-algebra test in June 2014? A whopping 30% increase in math scores should be celebrated! Who knew that NY had so many highly effective math teachers capable of showing a nearly impossible jump in outcomes.
Or maybe just maybe, the tests are so unreliable as to yield useless data?
Or maybe the passing score is set AFTER the tests so they can prove more public schools are failing. That way, their cronies can create more charter schools.
Yes. High school EOCs determine whether or not students graduate. 8th grade scores do not. So the cut scores are lowered significantly for the Algebra 1 test — it would be politically untenable otherwise.
There weren’t so many standardized tests when I was a kid, and somehow the powers-that-be managed to figure out which kids were (and weren’t) learning algebra.
As a science teacher, I loved math as the language that described natural phenomena. As a kid, I enjoyed math as a puzzle. As an administrator, I hate math because it is subverted to achieve an end. It’s almost killed the natural love I have for data. Almost.
Kids need the arts, it’s true, for complicated reasons related to thinking and connections. And kids need algebra also for myriad reasons related to the development of logical thinking and connections.
Let’s not risk dumping algebra as recklessly as the arts were dumped.
“And kids need algebra also for myriad reasons related to the development of logical thinking and connections”
As a fellow scientist I say “where is the evidence?”
In the UK we can give up maths altogether at 16, I can’t actually remember any algebra from school, although I’m sure we must have studied it. Is the average US college graduate superior at logical thinking and connections to the average UK university graduate? Certainly if measure by ability at algebra they would be. But at general logical thinking and connections – I’m not so sure.
Kids can learn logical thinking, sequencing, and problem-solving, and stimulate creative and imaginative thinking by learning string games….They can even learn algebra that way! (see the work of James Murphy, http://www.torusflex.com/ )
Reblogged this on David R. Taylor-Thoughts on Education.
I would contend that these new tests are not academically harder. I am certain, however, that they are put together stupidly. I sat with my 9th grader who took 1of 25 practice tests they are forced to complete through the year, in order to be prepared for the end of the year Language Arts assessment. I was shocked as I read one inane question after another. The questions were sloppily worded and muddled, and I was forced multiple times to rephrase the question so that my student could answer a simple question. I was left disgusted that some “genius” got some of my tax dollars to create such drivel. When I addressed my concerns with the teacher, she agreed, and said that most of her gifted students score a C – not because they lack the skill or intelligence, but because the tests are so flawed, that they cannot possibly measure the truth. These tests are appalling and an insult to our kids. The tests are nothing more that a grand sociological and corporate experiment – and our kids and teachers are the guinea pigs who will pay the price.
I’m so tired of the fight. Even as I type these words, corporate lobbyists/congress (one and the same) are voting to reauthorize No Child Left Behind… the nail in the coffin for good public education.
Sorry to be a rain cloud today… I’ve worked alongside teachers and students for 20 years, and I’ve seen the decline and the damage inflicted. Sometimes it breaks my heart.
The tests are crappy, poorly written – but that’s why test questions are a secret because they are afraid of public scrutiny or being judged by teachers who actually know how to write decent questions.
I think John Allen Paulos had the right approach with his book Innumeracy (written over two decades ago)
He started by identifying precisely the things that he thought were important for people to know *** because they are directly relevant in a technological society like ours *** and then made suggestions as to how we might go about teaching those things.
I don’t recall any algebra in his book, at least not factoring polynomials and the other things normally found in a basic algebra course. primarily, he talked about basic probability and “risk’ and things of that nature.
Deciding what is important and specifying why it is important should be the very first step in any process to develop standards for our schools.
But the irony is that the people “making up” (quite literally) requirements (David Coleman, Jason Zimba and others) really don’t know how to approach problem solving. They establish the standard first and then go hunting for a rationale. No good engineer or scientist (or any rational person, for that matter) would ever approach anything this way. It’s completely bassackwards and illogical.
I agree with Paulos that the most important math skill to have — and to teach in schools — is knowing how to identify BS so one is not taken in by shysters and crackpots (you know, like the ones who are “reforming” our schools)
Poet writes “Deciding what is important and specifying why it is important should be the very first step in any process to develop standards for our schools.”
I think before we decide what’s important to teach we need to decide what we mean by important.
A common mistake is to decide what’s important to teach based on what the economy needs, and what people might need in their future job. This is the view of the reformers and this is the justification for much of CCSS.
Not sure if you have read Paulos’ book, but he was not talking about making the general populace “job ready” but about making them numerate enough to be able to understand things like relative risks (of car, airplane, smoking, etc) and to distinguish between bogus claims and real ones.
The reason I said ‘Deciding what is important and specifying why it is important” is that that forces the person making the requirement to justify it.
I have yet to see any reasonable justification for making algebra a high school requirement. The claims that “people will need it for their job” or that “our economy depends on it” are just laughable.
Even the claim that people need to take algebra to learn logic and other high level thinking is ridiculous because there are lots of ways of acquiring those skills that do not require learning how to factor polynomials and solve systems of equations. I’d argue that a Skakespeare course teaches high level thinking as well as (if not better than) a basic algebra course.
Some have implied (even on this very thread) that arguing that algebra should not be required for everyone is tantamount to arguing that “it is useless”.That’s just an illogical claim, of course. (How’s that for irony?)
It should be obvious to anyone with more than half a brain that algebra is needed by those wishing to pursue science and engineering in college, but that is a different matter entirely. No one is suggesting that we eliminate algebra (and higher math) from the high school curriculum.
Diane, I agree, not everyone needs math. The cavemen didn’t need math. Folks that live in rural, sub-Saharan Africa or the rice fields of Asia may not need math. Folks that don’t want to understand public policy debates such as marginal tax rate policy or incremental spending on public health initiatives don’t need to understand algebra or calculus. In general, anybody that wants a low-paying, manual job and is not inclined to be an informed citizen might not need algebra.
There, I said it.
Well, anecdote is not data but your comment Virginiasgp isn’t backed up by any references so here goes:
I didn’t take calculus and I only remember the most basic algebra but I managed to have a long professional career in non-profit management. I can think of lots of other “desk” careers that don’t require anything beyond elementary school arithmetic, such as calculating percentage and fractions, either.
I understand marginal tax rates and can give a very cogent explanation of why they are important and necessary. I admit I can’t explain anything to do with health insurance or policy (beyond the fact that our country is very behind every other developed nation in ensuring all our citizens can get the health care they need) but then again, my husband the math genius (perfect math ACT and current computer engineer) is never sure he is picking the right plan for us. There is too much that is unknowable to do so.
Your comment brings to mind the statistics course I took in graduate school. The teacher gave an example of a chart that showed that college-educated people made more money than those who weren’t, therefore the numbers showed that college = prosperity. One of my fellow-students, a librarian, objected. He pointed out that people from well-to-do backgrounds were more likely to go to college so perhaps the cause and effect went the other way. The teacher did not like that answer. Now who had the more comprehensive answer, the teacher who understood how to calculate statistics backwards and forwards or the librarian working on his MPA?
Ok, Barbara, I’ll take you up on that. You claim you understand algebra with relation to marginal tax rates. When does the AMT kick in? How should you manage your deductions to avoid getting stuck with AMT taxes despite thinking you were “saving” money on that home mortgage deduction? I’ll give you a hint: it’s pure linear algebra. I have the xls sheets to show you if you show me yours first?
While many folks “think” they don’t need algebra or calculus in their jobs, they are often mistaken. You ran a non-profit. Did you advertise? Did you allocate resources (personnel, money, etc.)? How do you know if you were generating positive marginal returns from those resources (not average productivity or average advertising eyeballs but marginal ones). You see, that is the basis of calculus. And prior to Google, Facebook, etc. there were few resources to do it well and few STEM-educated managers who had a clue. That’s no longer true.
You are correct that college != prosperity. The problem with that myth about college degrees automatically inferring additional income is that they are measuring average income of college educated individual and not the incremental ones who can just barely get accepted. There are a number of reasons that a typical college graduate (parental income but more importantly pure intelligence) earns more than a typical non-college graduate. The fact that your instructor was poorly educated does not prove your point. It does show that the librarian had a natural understanding of logic and Bayesian statistics and maybe should have considered a STEM field.
Virginia,
I hire an accountant to prepare my tax returns. Algebra wouldn’t help me even if I did them myself. What he knows is the tax law, and he didn’t need algebra to keep up with constant changes in tax law.
Diane, accountants/attorneys/marketing execs all need algebra. You would be amazed at how many family attorneys don’t understand the simple algebraic formulas used to calculate spousal and child support. They purchase some xls tool and then can’t figure out what’s going on when a slight deviation needs to occur.
Accountants often get confused about the benefits of different investments (Roth IRAs and regular IRAs generate the same returns except for the final tax rate – many accountants swear there are other factors when the formula is pretty simple).
And marketing execs must understand how to best deploy their limited resources. That’s a marginal return problem (similar to VAMs actually). They often use average returns which can be very misleading.
The problem is that so many folks don’t understand that they need math to perform their jobs well. How did Rumsfeld put it: unknown unknowns!
Virginia, all those guys with algebra, calculus, trigonometry,etc. got us into Vietnam and Iraq, because they lacked a moral center. Which is more important?
Diane, didn’t you say right here on this blog that we shouldn’t look the other way while innocent civilians (and priceless relics) are being slaughtered in Syria? Many folks with a “moral center” (including one with a Nobel Peace Prize) just seem to look the other way and write them off. I for one think we should destroy that scourge that is ISIS even if it means we risk some lives.
And yes, my children will be eligible for the military in a few years. It is not a risk-less goal, but I think our indifference in 1939 was pretty inexcusable as well.
Virginia,
There are times when it is necessary to go to war: against Hitler, for sure. Historians now generally agree that WWI was a mistake. Many think that Vietnam was a mistake. Many think that invading Iraq created chaos and ISIS.
It requires wisdom to know when it is right to fight, and when it is right not to fight.
Anyone who wants to argue that algebra is not needed for certain professions may want to review the math requirements for undergraduate majors. Those for UW-Madison are at the link.
http://testing.wisc.edu/centerpages/madmathreq.html
These requirements are periodically reviewed by the faculty in these departments. Presumably the faculty bring expertise and experience in the field when deciding on these requirements. I’m interested in the debate, but would start by giving some respect to the judgment of the higher education faculty in these fields.
With respect to Hacker, I think he makes some good points regarding what math pathways students should take during high school. I do not feel he makes much of a case for omitting algebra, but makes a good case that some students are taking calculus when other math might be a better match for their interests and future aspirations.
I think the story about the librarian and the statistics professor shows the librarian was a sociologist at heart. I don’t think any numbers were part of his (pun intended) calculations.
I don’t think we want to teach stuff in K-8 based on what people might need in their jobs. Do people need to read Dante, Shakespeare (or the Bible, for that matter) to do their job well? Do they need to know who Michelangelo was in order to be great doctors, attorneys, or most else?
Some math knowledge is part of education—any education, and for the same reason as Hamlet or Ancient Egypt is part of any curriculum.
We can argue about what part of math should be part of education, and probably there is no single best offer here.
Unfortunately (not really :)), algebra is needed to learn any reasonable math. The good news is that only a fraction what is currently taught in algebra is necessary. The necessary part of algebra is simple, and everybody can learn it.
The real problem is that what they normally teach under algebra appears tricky and overly technical. Why? Because, if they only taught the basic, essential stuff, all the kids might end up getting an A on tests.
For some reason, we don’t like all A’s. We want to distinguish, rank kids. We don’t know exactly why, do we?
Part of the answer is that we have been under the influence of text book publishers for too long who prefer thick, heavy books they sell for $1-2-3 hundred. These ever increasing books need to be filled with something, and just the essential stuff won’t do that.
Now, many kids don’t know even basic algebra. Why? Because teachers rush through the basics to get to the tricky parts since the text book is filled with those and so are state mandated tests.
I spent this evening with helping my 10th grader daughter with her Algebra 2 homework. The whole thing made me mad. Less than 10% of what she had to do is necessary. I am a mathematician and I never ever use the formulas, tricks she needed to deal with: boring, technical stuff, only needed to screw kids on tests and fill text books. Really.
I can say the same things about most of low level college math as well, btw: Calculus, College Algebra are packed with completely superficial stuff needed only by textbook authors and publishers to make an enormous amount of $.
How much can they make? Here’s an article about an author
http://www.theglobeandmail.com/news/toronto/james-stewart-devoted-his-life-to-math-and-music/article22168574/
Mate Wierdl, I think we are in agreement. Teachers get so deep in the formulas without keeping students’ perspective at the 10,000 ft level that the students can recall the big picture at the end of the semester/year. The concepts should drive everything. And maybe there should be different variations on the class.
I understand colleges often have similar approaches. My dad is always telling me how every student at Georgia Tech takes calculus even the athletes. But I think there are different versions with some glossing over the more technical algorithms to solve the equations and focus on the concepts.
But we must all work to end this notion that algebra is a waste of time. The proponents of this notion (including many teachers) are often folks who did not perform well or enjoy math as a student. And most of them likely just had poor math teachers who couldn’t convey the concepts. Rather than end math, we should work to hire/recruit excellent math teachers (STEM majors) who understand what math is all about and can actually communicate it in an intuitive manner. Otherwise, we will be left to hold such public policy debates without any true comprehension of the basic (statistical) facts involved. That is the reason why so many teachers disparage VAMs – they simply don’t understand the science.
virginiasgp,
I don’t think the purpose of Diane’s post was to propose to end algebra in schools. It was more about criticizing the latest heavy emphasis on STEM subjects at the expense of other subjects, especially the arts.
The usual justification of STEM subjects is “they are needed for the economy”, and the cited literature indicates, what many of us always knew, that the vast majority of people use very little of the math they learn in school in their jobs.
As for VAM: the unindorsement of the American Statistical Association is enough for us to doubt the scientific value of VAM.
But for any teacher, it’s clear that tests shouldn’t be tied to teacher performance evaluations. One: teachers do not perform, they teach. Two: the same test given by the same teacher to two different classes, even on the same day, could easily show dramatic differences. Three: teaching is not a science, so using a scientific method to evaluate it is inappropriate. Four: learning is not a science, hence not measurable, hence trying to use (quantitative) tests to evaluate it is inappropriate.
VAM can’t even be used to deal with math: Yes, you could measure how accurately kids can calculate. But the purpose of teaching math is not to enable kids to do quick, accurate calculations. More generally, the purpose of education is not to produce accurate individuals. The educational value of tests, especially those of speed tests that are used almost everywhere, is little.
You know Virginia (if you are still here), nobody here disagrees with you that teaching math, all kinds of math, is an important undertaking and that high schools should offer high-level math courses. I’m talking here about subjects like calculus and advanced algebra, not the basics of elementary school arithmetic such as time, money, fractions, area, percentages and the like, which are as necessary as knowing how to read and write fifth or sixth grade-level English.
We just disagree whether or not learning math, especially advanced math, is appropriate or desirable for all students. There are lots of things that can be understood only with math, and lots of things that can be understood without any math at all.
You seem to think whatever success I had in the non-profit world surely rested on math, but I will tell you it had much more to do with charming donors (individuals, foundations, government agencies) and separating them from their money. Lots of skill involved but of the interpersonal kind.
There is a reason that IQ tests have separate sections and scores for math-related areas. We have evolved as a species to include all kinds of minds and intelligences. The story I told about my old statistics teacher and the librarian is a story about two people with very different intelligence sets.
But something tells me that no matter what arguments the commentators here make will make a difference to you.
Barbara, quite the opposite. I am fully aware that in many jobs, including some that should have math skills like financial advisers, numeracy skills have little to do with one’s ultimate success. When it comes to sales jobs (that’s essentially what a financial adviser or a non-profit director or even a partner at a law/consulting/financial firm are), the ability to lie trumps all. I’ll give you that. I’m being a little snarky but not much.
Yes, interpersonal skills matter and I advocate teaching them in high school including sales. I’m glad you used the phrase “separate them from their money” because that’s exactly what it is. We could have a long discussion on the merits of “sales” (I think it can have very productive purposes such as informing consumers about great new drugs in addition to less useful purposes such as providing huge commissions when clients were going to purchase a product/service regardless) but that’s not the point.
As others have stated, it’s the concepts behind the math that are important. Effective teachers teach both concepts and techniques. In fact, effective teachers allow kids to understand and retain the technique because they teach them via concepts. But even if you never learn how to solve a differential equation, you should understand the concept of “marginal X”. Without that understanding, you can’t understand marginal tax rates, or marginal profit, or marginal advertising returns, or even the dreaded marginal teacher effectiveness (otherwise known as VAMs). Please explain to me how we can have a discussion on evaluating teachers and policies when you have no clue what a partial derivative is? Forget calculating one, I’m just talking about the concept. If we don’t have a common language to discuss VAMs, you can easily see why the conversations on this board go awry so quickly.
I did not grow up in NY, but I am raising my kids here. I have mixed feelings about the Regents exams. On the one hand, the fact that our students have to pass a number of these means that a diploma from a NYS public high school is well-regarded. I have heard employers in several states (mostly Southern) say that they look at resumes for people who went to high school in NYS because they know those people will be well-educated.
However, requiring these Regents tests for graduation also means that we have a low graduation rate. The current passing grade is 65, and SED is moving to change that passing rate to 75. My child, who has been accepted at selective colleges (ca. 25% acceptance rates) failed one of her Regents at the current pass rate and would fail a couple more if the rate is moved to 75. In fact, I know some students who are thriving at Ivy League schools who did not score that high on all Regents. What does all this mean for kids who may never go on to college? That they shouldn’t even receive a high school diploma because they can’t pass these tests? That is ridiculous and is setting these kids up for failure already at age 18.
Why should a cognitively disabled child with an IQ of 60 have to pass this Common Core Regents test in order to graduate HS?
Why should a cognitively disabled child with an IQ of 60 be given a HS diploma? Doesn’t that pretty much undermine any value that a HS diploma has? I wish the child is able to lead a productive life but for goodness sakes, there has to be some standards. Or maybe you agree with Duane that life just comes down to different perspectives. A simple child’s sketch is just as good as the masterpieces of the all-time greats.
virginia, we may need to have gradations of high school diplomas. Some with distinction, some regular, some local diplomas.
In my adopted state, Ohio, everyone who completes high school gets a diploma, including those with ID (Intellectual Disability). Students who are high-achieving graduate with honors.
I’ve never seen any evidence that Ohio high school diplomas are taken less seriously than those of other states, including my native New York. Kids around here are accepted into all sorts of colleges despite having gone to school in the Buckeye state. So you don’t have to worry about the value of our diplomas being undermined, Virginia.
Wow! I am so tired of arguing about math.
I began my teaching career in the mid-90s, at the height of the Math Wars that were created by the NCTM’s insistence that discovery learning practiced in a small group setting was the ONLY way to teach mathematics. A review of actual research demonstrates that this is not true.
Now the canard is that Algebra is pointless and useless. Algebra has existed as a mathematical discipline for thousands of years and word problems of the type encountered in many Algebra textbooks are just as old. I would suggest that a discipline and educational approach that is so deeply rooted in human civilization is important and deserving of attention. Algebra is a powerful form of reasoning that allows us to see things we would not otherwise see and know things we could not otherwise know.
As to the issue that few people use the concepts of Algebra in their work life, how often are people required to quote Shakespeare in their workaday lives? and why is this the sole determinant of whether an academic discipline is useful? I specialize in mathematics, but I have many other interests both civic and personal. The broad liberal arts education I received has helped me over the years to think independently about these many diverse issues.
Mathematics taught badly is a demoralizing experience, as is any sub-par educational environment. I have had students in my classes who told me that their previous math teachers told them NOT TO ASK QUESTIONS. This is one of the saddest things I can imagine (educationally speaking). Without being allowed the freedom to explore and question, education turns into indoctrination. In fact, indoctrination is a method of instruction without an appeal to reason.
A procedural approach to teaching and learning mathematics can be deadly dull. Lessons are focused on procedures without justification. A conceptual approach justifies the reasons that a procedure might be valid and what alternative procedures might also work. However, explaining a procedure does not mean the students must develop an understanding of the concepts behind the procedure or reproduce the procedure themselves, though this should be the goal. A discussion of the reasons behind things like fraction division (“invert and multiply”) or why multiplying two negatives make a positive, or why multiplying by a negative flips the inequality sign can be fun, motivational and enlightening. The concepts of place value inform an understanding of the standard algorithms for computation, but there are other algorithms besides these and if someone has a preference for a non-standard algorithm and can consistently and efficiently produce correct answers using – great! That’s part of the beauty of mathematics.
Mathematics should be presented at a level that is comprehensible to the student population. A mathematics program that fails half of its students is itself a failure. All mathematics is built on a foundation of arithmetic, what the Greeks called arithmos. What is important in arithmetic, as in algebra, is not to beat students over the head with problems that are too difficult for them, but to find a level of difficulty that allows them to understand the concepts and to think independently about the subject. It is not coincidence that receiving a doctoral degree indicates (or should indicate) a high level of independent scholarship.
The same is true in algebra. Unless the goal is to “weed out” a high percentage of students, then the material must be understandable and presented in a coherent way. Classes with more able students will be able to probe more deeply into the material; those with fewer able students will achieve a certain level of mastery and call it good. It has never been my experience in 20 years of teaching mathematics that a significant portion of people “can’t” learn arithmetic or algebra. Discalculia is real, but I’ve seen it in no more than a handful of the several thousand students I’ve taught over that last 20 years.
I find it sad that there is so much misdirection and bad faith in mathematics education today, but the importance of the foundational subjects of arithmetic and algebra won’t dissipate or disappear just because we have machines to do these things for us.
Eddie Sacrobosco, I just see that your reply agrees with much of what I just finished writing.
It may be worth emphasizing that math is not about calculations, algorithms that need to practiced over and over. It just appears that way for most people because that’s how they were taught and that’s what they were taught: algebra, arithmetic, calculus, much of which are justified because of their use in statistics.
For general education purposes, I think the heavy and pretty selfserving emphasis should be taken away from these calculations.
Let’s not forget that the powers that be know this! It wasn’t that long ago that NYC was caught up in an inverse adage… “When tests are easier, students do better”… Suddenly, NYC students were making notable gains on high stakes tests for consecutive years (a few years back). And then… the truth revealed itself… adding a few easy questions enabled this result! Gaming the system enabled Bloomberg to make snake oil claims that under his lead, NYC public education improved.
I hope that the book of Hacker is better argued than his original article
http://www.nytimes.com/2012/07/29/opinion/sunday/is-algebra-necessary.html.
An important argument in the article is based on what people and the economy *need*. Well, those pragmatic arguments have been used to cut back on the arts, and to promote reading a lot of nonfiction in English classes.
I’m assuming nobody is arguing for eliminating math from K-12 curriculum. So the good question is what kind of math should be taught. The argument in the article is strikingly similar to what the rationale behind CCSS math is—not exactly a widely accepted one.
How about analyzing a math program that proved to be successful from an educational standpoint? What do the Finns do?
Using math exams as a way to get rid off a large number of applicants to medical and business schools is an outrage, but widely practiced at every college I know of.
In a series of reports from 2000 to 2004, economists Anthony P. Carnevale and Donna M. Desrochers (then working for Educational Testing Company) made the case for a high school curriculum that included Algebra 1 and 2. Their work provided much of the rationale for the American Diploma Project and Common Core State Standards.
These economists made use of data circa 2000 about job markets, growth, income potential related to education and so on. Their analyses also made use of a long term record of course taking in high schools with follow-on economic information from and about those students (The National Educational Longitudinal Study, NELS:88). The economists put together some charts and graphs to suggest that high school courses taken by students who went on to get high-income jobs should be taken as exemplary for students in middle and high school being prepared to enter the labor pipeline.
The economists did not anticipate the financial disaster of 2008 or other developments bearing on labor markets. These two economists provided the data and the rationale for Achieve’s American Diploma Project, the forerunner of the Common Core.
But, there is a little publicized factoid buried in two of their reports:
Less than 5% of high paying jobs require mathematical prowess beyond arithmetic.
Look at Table 20 (p.55) in the linked report below, and the surrounding discussion, you will see claims about the virtues of studying algebra that are not at all new.
Here is what the economists say: “Does the fact that only 5 percent of workers use mathematics beyond arithmetic on the job mean that teachers should stop teaching algebra, geometry, trigonometry, and calculus in high schools? Does the fact that even fewer people use Shakespeare, world history, or French at work mean these studies are a waste of time? Not necessarily, …. these higher-level courses are the means by which people learn higher-level reasoning skills. Throwing out the current curriculum without a superior alternative in place would be like throwing out the baby with the bath water.
Click to access Standards-for-What.pdf
If you want to learn more about the algebra wars, read Diane Ravitch, Left Back: A Century of Failed School Reforms, Simon and Schuster, 2000
or this brief history http://www.csun.edu/~vcmth00m/AHistory.html
There in paragraph 2 should be their.
Attached is a list of the top twenty best paying jobs. I know that some might consider such a motive uncouth, but in this day and age just having a job that allows you to live a middle class life is getting more and more out of reach. Most of these jobs require a minimum of calculus at the college level (not sure about Art Director) or the ability to work fluently with linear or exponential functions. These are the times we live in.
http://money.usnews.com/careers/best-jobs/rankings/best-paying-jobs?page=2
Abby, most of these jobs don’t use any calculus whatsoever.
Tons of jobs use calculus, certainly calculus concepts, even if folks don’t realize it. The concept of “marginal” anything is, by definition, calculus. Whether that is marginal profit/marginal cost (construction/lawyer/finance), marginal eyeballs (advertising), marginal lives saved/marginal benefit of a given treatment (health care), marginal execution speed (computer code), or weight/forces (engineer) all of these jobs use the concepts of calculus.
If their practitioners were more familiar with calculus concepts, then maybe they might be more successful. I have an attorney friend whose firm accepts all types of cases: bankruptcy, contract law, family, etc. Some cases are more profitable than others but they simply don’t track that information. They are leaving money on the table and not deploying their resources effectively by ignoring that information. And it’s actually a disservice to the client to not be able to determine how much a given case will cost based on the factors involved at the very beginning. If you asked an attorney if they used calculus, most would say no. I would suggest they need to understand calculus concepts to perform their jobs well.
I understand, virginiasp, but I don’t think this is a strong argument for going through the whole pain of calculus as it is taught in high schools and colleges: in the same way *everybody* needs to learn calculus, since everybody needs to understand the concept of a speed limit—which does require the understanding of instantaneous speed, ie derivative.
So should police academies require their students take calculus?
The whole argument is about what to teach and what not to teach in math in K-12. Presently, way too much unnecessary technicalities are taught. We certainly don’t want to go back to the entirely pragmatic and concepts-only math education, but the crazy emphasis on algebra and calculus drills need to change.
It’s entirely possible to teach the concept of derivative in high school, but I don’t see why torture kids with calculating derivatives of crazy functions.
Similarly, a Gened Math course in college could include a couple of weeks of understanding the derivative and integral.
The main sin of Common Core math is that while it’s talking about better “conceptual understanding”, adopters end up teaching new and crazy technicalities since the CC tests require it.
So the CC math creators preach water but teachers and students end up with whiskey.
Let’s face it, conceptual understanding of math (or anything) cannot be tested, and the teacher personally needs to probe a student’s mind for it.
I’m not suggesting that we teach the current calculus curriculum to the majority of kids. I even think that algebra can be scaled down for the “average” or less student. But I think to suggest that algebra is not needed or even “Algebra II” (Virginia’s standards are much worse)only deals with esoteric skills is short sighted. Why don’t you point to the standards that are useless (outside of the polynomial factoring) and I’ll demonstrate how it’s used in real lives of ordinary folks.
And I disagree that conceptual understanding cannot be tested. You can provide multiple choice questions that ask whether the information provided is “sufficient” to solve the question asked. That often tells you if the student knows how to apply the information. Or you can give several example situations and ask which concept could be used to “solve” the issue.
But I agree that in these courses it often gets too technical for most students. These courses are sometimes used as quasi-IQ tests to determine which students can “hack it”. I would prefer we keep the SAT as the quasi-IQ test and only teach the useful skills. We should emulate colleges who teach “business math” type courses.
Virginiasp writes ” That often tells you if the student knows how to apply the information.”
Imo, this is where the problems begin: you propose to test student understanding from a pragmatic viewpoint. This is why CC (and ACT) math tests are full of word problems too.
Do you want to test and score the situations where the student applies what she learnt from Shakespeare, Beethoven, Leonardo, Plato?
Worse still: why the speed tests? Why don’t they give kids time to think instead of whipping out answers asap? Are a CC test or ACT to see how well kids would do in the emergency room?
I am not exactly against tests—but I certainly am against scoring because it implies ranking something which normally is not rankable.
An experienced teacher looks at the students work, talks to the student, and gets a good impression of the student’s understanding. Trying to attach scores to this is an afterthought by those who want to rank.
Why rank? So that later we can attach another number to a person: her salary as a quantitative measure of merit.
Mate Wierdl, in college I took an acoustics class from Professor Bose (of the speakers variety). He would provide us un-timed exams. He even provided ice cream to keep folks interested. Notionally these were 2-hour exams and often included about 3-4 total problems.
I saw very few students remain after two hours and none of them ever indicated they provided valuable information on their answer sheet after about 1.5 hours.
For the most part, the same applies to these timed tests. Yes, some tests may be time constrained but if you ask most students, when time is up, most students have no more to add. You could double the time on those tests and the scores would not appreciably change. But then folks would use the extra time limit as “proof” that we were persecuting these kids via 5 hour tests.
We understand why teachers want to pretend all teachers are effective and no teachers are ineffective. That is just simply not the case. I’m not suggesting most teachers are bad. But to claim that there are no differences in effectiveness and these very real differences are not important to the success of students is … well simply not credible.
Virginia, of course teachers differ in their effectiveness but test scores are not an effective way of differentiating which teachers are best. Some teachers are better with some students than others.
Diane, slightly different topic but as you recall I was trying to hold a charter school advocate (and right-hand man of Imagine Schools billionaire owner Dennis Bakke) accountable for failing to disclose his conflict of interest when voting on charter schools as Chairman of the local school board.
Yesterday, the judge issued sanctions against me for merely bringing the case. I have already appealed her dismissal (will post the transcript here in a few days but very confident on appeal. I have a hearing at Virginia’s Supreme Court on Tuesday, Dec 8 to argue her first ruling on FOIA).
She claimed that even though Bakke owns/controls both his own foundation and Imagine and that Bakke also serves/paid as high level employees of both ($195K as Chancellor of Imagine and Chrm of Bd/Treasurer of his foundation), they were not “affiliated” business relationships. In Virginia’s Conflict of Interest Act law, that is the very definition of an affiliated business/orgs.
She ordered me to pay ~$6500 in legal costs. But fortunately, besides being reversible on the basis for awarding sanctions, this judge is not very good with math (well, maybe she just can’t read the Virginia Supreme Court rules). Rule 1:1 (yes, the very first rule in the book) disallows a judgment of sanctions when the final order was issued over 21 days ago. This has already been decided by the Virginia Supreme Court (Roberts v Clarke – 1994) but apparently my “personal judge” doesn’t know Virginia law.. The judge issued the sanctions award 28 days later. Not really surprising since she graduated from what some rate the 7th worst law school in the country. You see, I told you math was useful in ALL fields! Yep, she’s a judge in my county and gets all my cases.
Needless to say, this was an attempt to scare me from filing more cases to expose corruption. I don’t scare easily. I think this judge is trying to set a record for the most overturned decision in a single year in Virginia. Maybe even most overturned relative to a single party.
I did not say they USE calculus. I said they REQUIRE calculus. Try getting into dental or med or engineering school without it. Any MBA will have to have taken Business Calculus. I am not disagreeing with you, only stating the realities.
I see what you are saying. Even those majors which require calculus, usually don’t need it at such a technical level as it’s taught.