Gary Rubinstein teaches at Stuyvesant High School in New York City. In this post, he questions whether the math taught in school is “useful” and concludes that it is not. This is the beginning of a series of posts in which he explains why he is disappointed in the usual school math and what he thinks should take its place.
Gary writes:
I’ve dedicated my life to teaching a subject I love and have loved since I was a small child.
This country, and throughout the world really, a lot of resources are dedicated to teaching students math. From Kindergarten to 12th grade almost every student takes math and in many elementary schools math is taught for ninety minutes a day. And then in college students often have to take some math, sometimes a Calculus class, as part of their degree, even when the degree is in something like business. And for all the time and money that are put into math in this country, when it is all done very few adults remember anything about math. Maybe they know a little about percentages and vaguely something about how the angles of a triangle add up to 180 degrees.
Yes, the same could be said about some of the other subjects, like how much Chemistry or Physics do most adults remember from high school, but the difference is that math is done for 13 years so you would think that more of it would be retained. Fo all that we invest into math in this country, we are not getting the ‘bang for our buck.’ I think I know why this is. I think about this on a daily basis since it is my life’s work and I’m so bothered by it. I’ve written about this before but I want to go deeper into this and explain what the issues are, what it would take to fix the problem, what the obstacles would be in improving math instruction, and whether or not it might be better to diminish the obsession that we have in this country with math instruction.
Part of my evolution in thinking about these ideas comes from watching my own kids who are now 15 and 12 go through the standard math curriculum. They have had decent teachers throughout the years and have always gotten 4s on the New York State tests so you would think that I’m thrilled but when I look at the things that they learned (because they were part of the curriculum) and the things that they have not learned (because they were not part of the curriculum) it frustrates me. Many parents who are not math teachers might feel the same way when they look at what their children are learning in math but they don’t dare question it. It reminds me of The Emperor’s New Clothes, nobody wants to seem like they aren’t smart enough to know why we have to learn how to multiply mixed numbers with different denominators. But as a math teacher who thinks about things like ‘what is the goal in learning this concept?’, ‘Is this concept needed to learn a more difficult concept?’, ‘Does this topic provide opportunity for the students to have ‘aha’ insights for themselves?’, I am constantly critiquing what I see my children learning about. And within my own teaching I am always trying to teach whatever topics are in the curriculum in a way that gives my own students an experience where they get to use their reasoning skills and not just blindly follow an algorithm.
The title of this series is: Is most school math useless? Depending on what you think ‘useless’ means, you will have different answers to this question. There are different ways to define ‘useless’ but the most straight forward way is to say that something is ‘useful’ if you will one day have an opportunity to ‘use’ it for something in your life or your job. We hear all the time that if you don’t know math you won’t be able to compare two competing cell phone plans or you won’t know how big of a ladder to buy so that when you put it at an angle it still reaches the height you need it to. We are told that math is ‘useful’ in this way and while it is true that some math is useful in this way (like knowing the difference between a loan that has a 2% interest rate vs a 20% interest rate, for example), the vast majority of the math that is taught in school is absolutely not useful.
To follow Gary’s thoughtful reasoning, open the link and read the rest of his post.

I think about this on a daily basis since it is my life’s work and I’m so bothered by it.
Mr. Rubinstein is a reflective fellow. A lot more people (e.g., all involved in education or in education policy) should be thinking about this on a daily basis. It’s a national scandal, and it’s truly astonishing how unreflective most people are.
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And here’s what I know…I first starting teaching third grade. My own personal math (how I used it) was for building things and budgeting things. I had a paper route from 9-15 and was my own business owner meaning I had to purchase my papers, buy my rubber bands, and go collect my payments and pay my bills on time (now that I think of it, I was a pretty rich little kid with wads of cash on collecting nights). My dad said, “If you want things, you are going to learn to pay for them.” Fast forward to my third grade class: I would teach a concept and then tell them, “You know why this is useful? Here’s why. I know your parents work hard for their money. I know they take care of your little brothers and sisters and send you to the corner market for supplies now and then. If they give you five dollars and you buy two things for $2 and $1.50, how much change should you get back? You need to be smarter than the person behind the counter; your parents work hard for that money. You don’t want to get cheated.” And, it took longer, but I taught my kids about recycling aluminum cans. I decided to show them if they could recycle “x” amount of cans, they could save for whatever they wanted. Lupe decided she wanted a computer. As a class, we collected cans and weighed them. We determined there were 22 cans per pound (we learned to use a scale as well). I found out the going rate per pound and we used that in our calculations. The kids had a plan, a goal, and a way to get what they wanted and especially when my kids (97% on free/reduced lunch) I no extra money. In the end, we had photos and a class presentation. There was always a reason behind what I did. Throughout the years, I would say, “You know, math is in everything. You need to get the right ratios when you mix paint; you need it when you are trying to figure out just about anything and boy if you ever bounce a check, you just want to ALWAYS be on the right side of your checkbook, get it? I believe I told them about “try to save a penny for 30 days, but double the penny each day, i.e, day 1 = 1; day 2 =2; day three = 4; day five = 8. Try that and tell me what happens. This along with “A thousand Grains of Sand” explained the concept of compound interest. Be smart with your money and your life will be easier. Be a person who “learns by doing” I always saw kids struggle with math. My wife and I had watched a PBS special and a friend of hers from high school was a math teacher, well, and also a skateboarder. When he taught geometry, once the kids learned the key concepts, he then had them APPLY that math to making their own skateboards. Once again, “Check it out. Isn’t that cool? See how those geometric concepts came into play?” As Gary stated, there is so much more to math than “getting ready for a test.” To me it was alway static. I always tried to have projects that needed math (and I would try to pass them along) but didn’t “hit them over the head with it”. But, hey, what do I know? I was just the art teacher.
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The most of the mathematical topics taught in elementary school are important in every day life in order to budget, understand discounts and percentages and calculate square footage. I can see value in algebra 1 and even geometry, but the usefulness of algebra 2 and calculus escape me.
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AGREE! But I also think that MOST 6/7/8th graders aren’t mentally ready for the abstract concepts of ALG I. It boggles my mind when I see kids failing Algebra I and II because they don’t have basic math knowledge imbedded into their brains, yet……fractions, law of exponents, order of operation, properties etc are very lacking in the K-8 curriculum. The BS math that they learn in school is only to prepare them to take a test…..and usually WITH a calculator!
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I address this very issue, Lisa, in a note that is in moderation, below.
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Lisa: I read of a British study several years ago when they started being able to measure electrical activity in the brain. Seems the places that light up when a person does Algebra are, on average, underdeveloped until a person reaches the mid twenties. I do not know if more study has been done, but this parallels my own experience as a math teacher of all students for 29 years. It also makes sense in my own experience as a person who studied math. It begs also the question of whether our society selects the best people to do math by choosing to teach these skills at a young age or not at all.
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As a geography teacher, I see this lack of basic math knowledge firsthand. We do scale maps, and many of the 9th graders cannot read a ruler or know the basic decimal to fraction conversions. I have to teach those. Many students also cannot do basic skip-counting, which means they cannot tell time. We are so into having 1st and 2nd grade littles doing algebra that they don’t learn basic practical math
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yup
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I don’t know if it is true or not in middle and high school math, but one criticism I read about in our math instruction is that we try to introduce too many topics in a given year instead of fewer topics in greater depth that most European countries apparently follow in their math curriculum.
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“we try to introduce too many topics in a given year instead of fewer topics in greater depth”
This was my major complaint during my teaching career and I didn’t teach math. I taught English in middle school for most of 14 years and 16 at the high school (1975 – 2005): reading, literature, what all the terms meant (how to identify them and use them in writing), grammar, mechanics, et al.
When California came out with the state standards (I don’t remember the year), we were required to teach at each grade level, my first complaint was there’s too many topics to cover properly so our students would remember them.
So, I ignored the standards and kept teaching the way I had been doing all alone — teaching fewer topics in greater depth.
Admin didn’t bother me because my students’ standardized average test scores were way higher than all the other students at the same grade level in the district where I taught.
Strange. I don’t know how that happened since I never taught to the tests once that crap started.
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Here’s my take: The capabilities of the human brain develop over time. We know, for example, from longitudinal fMRI studies that the prefrontal cortex develops (undergoes new growth and rewiring) throughout childhood but that its development is not complete until around age 25. Now, that part of the brain does a lot of things, including
Analytical thinking
Emotional control
Planning and acting according to a plan
Some short-term memory and attention activities
Reflexive behaviors
Abstract Reasoning and generalization
Problem-solving
What Mr. Rubinstein identifies is the almost universal FAILURE of our current system of teaching mathematics. Why such a harsh assessment? Well, people in the U.S. who complete high-school have ALL gone through 12 or 13 years of mathematics instruction, but if you interview them as adults, they are basically innumerate. Example: one study showed that 60 percent of American adults could not calculate 10 percent of something even though all that’s involved in doing that is moving the decimal place.
If the goal of our mathematics instruction is to produce adults who can do math through Algebra II and Geometry, clearly, we fail. The failure is so dramatic that one would think that only an idiot would say, hey, wow, we’re doing the right stuff.
So, why the failure? Well, note that the geniuses who gave us the Common [sic] Core [sic] decided that one thing they needed to do in mathematics is to introduce abstract reasoning a lot EARLER in the curriculum–so, for example, learning the CONCEPT of the variable in Grade 3.
But that’s all wrong developmentally, and so is our entire approach to K-12 mathematics.
Have you ever tried to turn a little Philips screw head with a butter knife? Not easy. It’s the wrong tool for the job.
Well, until the areas of the brain that do abstract reasoning and problem solving are well developed, we are asking kids to do tasks for which they don’t yet have the tools. They are not yet equipped with the cognitive functioning necessary for reasoning abstractly and solving mathematical problems based upon that abstract reasoning, and so they fall back on kludgy alternatives–mostly just following rote procedures, but under the new CCSS Math, they are forced to reason abstractly, and so they fail.
So, here’s what I think we should do: We should hold off doing any but the most basic instruction in addition, multiplication, subtraction, and division until late middle school–say Grade 8. Prior to that, we should have kids do, INSTEAD OF MATH, exercises on pattern recognition, which have been shown to grow neural networks for abstract reasoning.
I contend that if we waited until kids have the proper cognitive tools in placed, they would LEARN FAR MORE and RETAIN FAR MORE than they now do having math for 12 or 13 years.
I used to be married to a woman who was extremely math phobic. My son was in high school and struggling with some problems involving factoring of polynomials. I was up against an intense deadline, and a LOT of money was riding on this–a LOT of our family’s future. So, my wife grabbed his textbook, read the chapter, and then helped him. Afterward, she said, “I could no more have done that when I was 16 than I could have flapped my arms and flown.”
And I think that this is exactly the case.
Our mathematics instruction fails because we start it too early, when the minds of kids are not developmentally ready.
And we have exactly the opposite problem with regard to foreign languages.
I have an extremely low opinion of the ability of our education establishment to think clearly about what it is doing. The utter failure of our math instruction, and the failure to recognize its cause, is a case in point. People will keep doing what they have been doing even if it is, as Rubinstein says in this superb series, “useless.”
NB: There are children who, at very young ages, do have this abstract reasoning ability–the little Gauses among us. It’s important to identify those kids and pull them out into an entirely different instructional track than what I am suggesting, above, for most kids.
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A foolish consistency is the hobgoblin of little minds adored by little statesmen and philosophers and divines.
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Damned right!
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Bob, in 1965-66 I was in Algebra 1 class using SMSG Math (remember Yale Science & Math Study Group?) with guys who went on to Harvard, med school. They were ready for that; I was frustrated. I agree about identifying those kids.
I will credit SMSG grades 7-9 for developing reasoning, problem solving.
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The fate of new math was sad indeed. I was fortunate to have an Algebra teacher in Grade 8, I think it was, or perhaps 9, who was fully conversant in it and extremely interested in the foundations of math in logic and set theory. Her introductions to those topics were the first time that I started awake in math class. OMG. Here’s is something that is actually interesting!
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By starting formal mathematics instruction too early, we ensure that kids learn the following in mathematics class:
I am no good at math.
Math is really boring.
Math is really hard.
Math is useless.
All of which adds up to
I HATE MATH.
Most adults graduate from their 12 or 13 years of math instruction hating math. Every publisher knows that including ANY equations in a book will vastly decrease its market? Why? Because school has taught people, primarily, this in math: that they hate it.
I have a dream that we change this, that we start doing abstract mathematics later, when kids are actually beginning to be developmentally ready to deal in abstractions and that, as a result, there would be a LOT MORE adults who figure out that there’s a lot there that is really, really freaking interesting and there would be a lot more adults who understand that, for example, there is a reason why, in the area of healthcare, Americans have poorer health outcomes but TWICE the average cost of other 38 nations in the OECD.
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I pay $30/mo in Hungary (which includes free dental and eye care as well) while the monthly cost of my health insurance in the US is $900 (I pay $200 and $700 is paid by the state of TN), and it covers only 80% of my care plus copayments. Then I pay separate for dental care…
I think we should start using the word disaster more often in this country: health care disaster, climate disaster, retirement system disaster, math education disaster. This is how we can grab people’s attention (as we can learn from the experts on the right), and in fact we get a much more accurate description of the true state of affairs than the maddeningly polite conversations we conduct nowadays on these topics achieve.
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Extraordinarily well said, Mate!
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Máté,
Is Viktor Orban the fascist he seems to be? Why does he hate LGBT people? I’m going to Europe in a few weeks, and I arranged the trip to avoid Hungary.
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I cannot speak for Orbán, but the views on LGBTQ are similar to those in the us: cities are supportive, countryside not so much.
I wouldn’t judge a nation by their leaders, even if they are elected. For example, I’m puzzled by banning athletes based on the politics of their country.
Similarly, just because Orbán is an ahole doesn’t mean teachers in Hungary need to be left alone in their struggles that are similar to the struggles of us public school teachers.
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For example, the latest move by the us administration to restrict travel by Hungarians to the US is difficult to explain to me.
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I [suck] at math.
Math is really boring.
Math is really hard.
Math is [pointless].
Bob
Pardon my tweaking; loved your list just my slightly altered take.
Imagine taking one of the most important forms of language ever developed and leaving countless millions of Americans with the big take away that it is “pointless”.
This post also puts a spotlight on the sham known as STEM education.
M is viewed as pointless and rarely is incorporated into STEM challenges in the classroom
T and E are subject areas hidden in the enormous null curricula, thanks to our collective ignorance and negligence. Absence of teacher training is just one of the missing puzzle pieces.
If I could wave my magic wand, I would require the teaching of MEASUREMENT. It is our best chance of making math and the long list of unit labels that go with those pointless numbers meaningful to your average student.
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Máté Wierdl
Whether sanctions work as intended or not is up for debate. In fact the record is pretty dismal as 60 years of Cuban sanctions prove. On the other hand business as usual certainly does little to dissuade autocrats.
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I suspect that we would have been far more successful in Cuba with a policy of active engagement rather than with one of withdrawal and sanctions.
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I agree about Cuba. We should have engaged. Sanctions impoverished the people but not the leaders. Sixty years of failure is enough. I visited Cuba in 2013 and it had many tourists from Latin America and Europe. The people are very friendly. The island is beautiful.
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Bob Shepherd
Certainly what is / was lacking was the carrot after the stick.
Certainly long before the time Obama finally lifted some restrictions, it was time to offer the carrots.
It has been said that the Beatles brought down the Soviet Union. The exposure to Western Culture (“consumerism”)created unrest in the Soviet Union. The exposure to Western Capitalism rapidly brought Authoritarianism back.
But we are drifting.
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Gary and Mate both rightly point out that a pared-down mathematics curriculum should be heavy on probability (and statistics). I just have this to add: heavy on Pascal’s Triangle for the sheer freaking fascination and joy of it.
And on exponential functions:
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Good old Obama Common Core to dumb down America.
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Hey, Big Mike, why did the Saudis pay Jared Kushner $2 Billion?
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To get to the other side.
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Left or right side?
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Why did the chicken cross the road? To get to the other side. Why did the Saudis pay off Kushner? To get to the other side, the United States. To get to the classified boxes at Mar a Lago? Maybe to get to the PGA. Who knows? It wasn’t because they liked him.
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LOL how does that have anything to do with obamas common core debacle? That was 6 months after office and looked at by ethics and has no bearing. You seem fine with 10 billion in equipment left for the taliban to literally kill the world and the 100 billion tax funded money to Ukraine which is used for money laundering and much worse.
https://www.reuters.com/world/us/us-house-panel-probing-saudi-arabias-investment-kushners-firm-2022-06-02/
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I’m fine with supporting Ukraine against Russian aggression.
Don’t forget it was Trump who made the deal with the Taliban to pull out of Afghanistan completely, not Biden. Biden kept Trump’s promise.
I am not a military person but I thought at the time that we should have left a garrison of some 3,000 soldiers behind to guarantee a safe exit for our troops and our friends.
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As for Common Core, I was against it from the start.
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Common Core was and is a debacle.
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So, Big Mike, what did Republians do about Common [sic] Core [sic].
Well, the oh-so-reverend Mike Huckabee (that’s a portmanteau of Huckster and bee) went to the annual ghoul’s convention known as CPAC and told the assembled ghouls that Common Core was universally hated. Then, he gave them advice: Go back to your home state and do not do away with Common Core. Instead, change its name to something state specific like The Ohio Straight-Shootin’ Buckeye Standards or The Florida Skyway Standards so that it LOOKS AS THOUGH THE STANDARDS HAVE BEEN CHANGED TO SOMETHING STATE SPECIFIC. In other words, go back home and LIE TO YOUR CONSTITUENTS. PRETEND YOU’VE CHANGED THEM.
And that’s just what the Republican governors all did.
And that’s how Republicans work. Forget about reality. Figure out what propaganda you can feed the average ‘murikan.
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Yes Bob the liberals own and work in 95% all colleges and education and the education sucks so lets blame republicans lol. NYC kids cant read or write, lebron james school not one kids can pass state tests. Forget about gender and all other garbage and go back to the basics
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Big Mike,
Our public schools educated 90% of all Americans. Those are the people who built America. Do you think America sucks?
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I have friends who imagine that Barack Obama was some sort of liberal or progressive. He absolutely was not. He got completely behind the top-down, oligarch-driven Common Coring of America, he continued Bush Jr’s insane antiterrorism and military policies utterly unchanged, and he bailed out the big banks instead of ordinary homeowners–a fact that continues to have enormous repercussions for our economy. Sickening. It’s difficult to say that the was a Democrat in name only because so many Democrats in recent years have been these sorts of Neocons. All this is so sickening that I would have abandoned the party if the Repugnicans were not EVEN WORSE, had not gone right over the deep end into outright Fascism.
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The veritable worship of Barack and Michelle Obama by most Democrats tells you that they think business as usual in America is just fine.
Look, we had an African American president. Things are working!
Quit rocking the boat!
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It’s sickening. Seriously. The Republicans would never win another election IF the Democrats would stop acting like Republicans.
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Democrats: party of business as usual
Republicans: party of business as delusional
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That’s perfectly put, SomeDAM!
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Of course, criticism of a Democrat is the cue for someone to jump in and chastise you for aiding and abetting Republicans.
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Personally, I don’t see any way out of the current quandary.
It’s an inevitable downward spiral.
We’re screwed.
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But pretty soon the Supreme AI will take over, and IT won’t give a damn about Republicans or Democrats, the president, Congress, Supreme Court or any of the rest of our silly human traditions.
So none of it will matter anyway.
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A few remaining humans, watched over by machines of loving grace. LOL. Hmmmm. I feel a short story coming on.
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Say what???
for all the time and money
that are put into math,
very few adults remember
anything about math.
the vast majority of the math
that is taught in school is
absolutely not useful…
The proof of a strategy
is revealed in the results.
See the more than
1.8 trillion in outstanding
student loan debt…
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NoBrick
“1.8 trillion in outstanding student loan debt… ” Has nothing to do with math education and everything to do with Political Science.
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It’s all moot at any rate, since AI is going to soon replace everyone (except plumbers, carpenters and electricians, who do stuff that robots now have and will continue to have difficulty doing)
The vast majority of people won’t need to know math or anything else. Just how to sit on the couch and press the TV clicker
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Do they even teach the latter in schools?
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I was never taught to press the TV clicker. . .
. . . but then again back then there weren’t any TV clickers.
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Technology both tools and materials has de -skilled many of the construction trades as well. It takes far fewer skilled Journeyman to do an instillation than even 30 years ago.
The problem is not the increase in productivity but how those increases are shared. In earlier periods as productivity went up hours worked went down and wages went up.
https://economics.stackexchange.com/questions/15558/productivity-vs-real-earnings-in-the-us-what-happened-ca-1974
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Wrong link I only wanted the Graph of Productivity vs Wages .
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I always go back to a simple question when we think about what is good for all of us. What do we find in mathematics that will be good for all of us. Note that this is a different question than the one Rubenstein poses: “what will be used?”
Society has specific needs. For technology to exist, we need people who are skilled in using mathematics make the next battery or design plumbing that really works (a rare item). This will not require a huge percentage of the population. But all of us need the best people to be the ones who design things, take care of the booster club treasury, and put a man on the moon.
What we need with our educational system is to build a fertile intellectual soil from which children who have a particular talent are awakened to the possibilities of their talent, and appropriately taught so that they get to do something they enjoy and that helps us all.
We should not lose sight of the fact that most
Members of society will take a part in: parenting. Most people will raise a family. So every student needs to be introduced to some portion of general knowledge that will help along in the process. That is true for math, humanities, or other fields.
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Your 3rd paragraph is a powerful statement
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Amen. Agreed
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We need to show ‘possibilities’ to young people. Sometimes, when they see it, they can dream it. Some of them will achieve it.
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When… your mind is moving low, go ask Alice. I think she’ll know. When logic and proportion have fallen sloppy dead, and the White Knight is talking backwards, and the Red Queen’s off with her head, remember what the Dormouse said: “Feed your head. Feed your head.”
Let’s face it, the world has gone topsy turvy. A lot of people everywhere are following the White Rabbit down his rabbit hole, dug by thieves and aspiring despots. Tea Parties led by Mad Hatters. We need enlightened citizens. We need logic and proportion. Rising voters need to practice thinking in the abstract while following rules of syllogism. People need some kind of calculus of life, as many people as we can reach.
Eat your math. Make an irrational number and strawberry smoothie and drink your math. It’s part of a balanced, nutritious breakfast. Feed your head.
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You know who really needs to learn math? The people at CREDO who turn tiny standard deviations into “days of learning” when looking at NAEP math scores do. We might need math, but we sure don’t need math standardized testing, constant CBE math data collecting, or using math score misinterpretation to kick and scream about public education. Maybe keep the math and throw out the junk math.
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I have concluded that most of these people do this for two reason: 1) They disliked or couldn’t succeed in the classroom, or 2) They realized they could make a lot more money concocting “instruments” and other grand busy-work, and selling them to our politicians by fearmongering about the incompetent teachers who aren’t earning their pay and the impending collapse of civilization.
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Credo isn’t interested in math or accuracy. They are more interested in spin doctors and propaganda.
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A lot of basic math is better learned by doing, than taught in isolation. Consider the advantages of having wood shop (with hand tools) as a “special” every school year, like music and art. See Richard Starr’s book “Woodworking with Your Kids” for an account of his many years teaching boys and girls in grades 1-8 at a New England school.
See the Wikipedia article on “Sloyd” for a corresponding Scandinavian program required in most schools.
In real life, a lot of our use of math involves estimating and mental “ballpark” calculations, yet these are often overlooked in math class in favor of exact answers. There are accessible books explaining mental math shortcuts, estimating the height of trees with your thumb, etc; some children find this to be fascinating, like magic tricks.
Which reminds me of all the great math books out there, most of which have a chapter on magic with numbers. No doubt all of this is also on Youtube.
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Bob: “Prior to that, we should have kids do, INSTEAD OF MATH, exercises on pattern recognition, which have been shown to grow neural networks for abstract reasoning.”
I made my more detailed comments on Gary’s blog. In abstract mathematical terms the goal of math ed should be for high school kids to understand the basics of probability, geometry and the exponential function. It’s not because these three will be useful for them in their profession (likely, they won’t be), but because these are the main concepts which are needed to understand the world around them: investments, computers, economy, weather, engines, electricity, stars, rivers, radio activity, bar codes, board games.
They then will laugh at a politician who would try to counter a claim about the developing climate disaster by bringing in a snowball from the outside while asking theatrically “How can be global warming if it has just snowed today?”.
To reach these three goals in math by their high school years, as Bob said above, in earlier years they can do stuff like coin flipping, dice throwing, balance geometric objects cut out of paper, use ruler and compass, cut cakes, etc., that is, they can do activities which would give the concrete foundation for the abstract notions. These activities can be tailored to correspond to their brain development.
Math is “simply” a language to describe common patterns concisely, such as 3 is common to “apple apple apple” and “doll doll doll”. For kids to understand this abstract language, they need to first encounter the concrete objects or events abundantly which are then described by the common language of math.
It’s hard for me to imagine a situation where it’s useful to start with the abstract descriptions like “length, fraction, area, probability, variable, function, equation, straight line, circle”. It would be similar to making toddlers say “dog” before them seeing an actual tail wagging dog, or making them read before they saw a book and somebody read them fairy tales or poems.
Yes, current math education is too abstract too early and useless concepts, formulas, manipulations, derivations flood the text books. The curriculum is designed according to the suggestions and needs of employers, profs and politicians instead of the actual interests of kids. The situation really is a disaster and I have no proper understanding why it has been tolerated for so long.
I add that much of math taught in colleges is similarly overstuffed for no apparent reason that would benefit the students.
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Beautifully said, Professor Wierdl!
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I hope, as one who was not a good math student, to explain this properly.
Before internet, I remember reading of an exchange of Chinese and US math instructors, I think in the late ‘80s. Each group spent time in the other country’s math classrooms, and commented on the other’s way of teaching math. I only remember the critique by the Chinese teachers. Americans, they said, have children memorize formulas, and spend class & hw time applying them to different sets of data until the process is learned/ automatic. In China, children work with manipulables and are encouraged to develop different ways to solve problems– essentially, to derive formulas and try them out. A typical class would be divided into several teams, each collaborating to find a method for solving a problem that teacher puts on the board. Each has a rep explain their method; under teacher guidance they compare results. Is the solution correct, why or why not; which is most user-friendly/ efficient; how would we notate it, etc. The Chinese math teachers felt most US kids, using our methods, would not grasp the logic behind a formula, nor would they understand there are different approaches to problem-solving.
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I would not single out the us when it comes to reducing the math curriculum. I suspect, every country has the same problem in this: bloated material, too formal or too technical presentation.
Does anybody have an example that could be followed?
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Bob, Pascal’s triangle is part of the tools needed to understand probability, so your craving for beauty and the needs of kids meet.
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