Jonathan Bartlett on ending the war on math

_{Denyse O'Leary

November 23, 2020

Education, Intelligent Design, Mathematics}

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First, he says, we must understand why we teach math in the first place

Math teaches students how to think more clearly in all areas of life but it mostly performs this function silently, invisibly…
Mathematics gives students practice in core reasoning skills with concrete problems that have definite answers in order to help them achieve mastery of the reasoning process. That will allow the skill to be applied later to fuzzier problems where answers are not as certain.
Jonathan Bartlett, “How can we really fix the way math is taught?” at Mind Matters News

See also: The progressive war on science takes dead aim at math

and

Which side will atheists choose in the war on science? They need to re-evaluate their alliance with progressivism, which is doing science no favours.

Also: Jonathan Bartlett’s calculus paper reviewed in mathematics magazine. The paper offers fixes for long-standing flaws in the teaching of elementary calculus.

Comments

I think good teachers (I teach with a good group) in all the core academic subjects have thinking well, and expressing those thoughts well verbally and in writing, as a priority. For instance, my English teaching friend has a discussion technique where students are taught and evaluated on backing up their ideas with evidence (usually from a reading source that everyone has read beforehand), listening to others and staying focused on relevant replies, summarizing their understandings of other's positions before they critique them, etc. I think this type of thing is better than debate because it's not so polarizing, and leaves room for students to learn from others and help their own perspective grow. Also, in writing, she always emphasizes "back up your assertions", and she works hard on well-structured writing, in everything from major research papers to in-class impromptu short writing responses. She is very good. Similarly, the social studies teacher uses similar, but less structured, techniques. And of course social studies is non-fiction, but there is still and also evaluation, analysis, synthesis, etc. - all those components of good thinking. And science is non-fiction, but requires clear thinking, especially in physics problem solving. And there are always current events to pull all these things together. I know there are dull teachers. I think there are more good ones than the general stereotypes give credit to.Viola Lee_{November 25, 2020
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Well, you both must have had better teachers than I did then. We read the classics, and wrote reports on them to prove we read them. But there was never any deep discussions of what they meant, or what applications they had to real life as far as I can remember. Practical reasoning is far more important in my opinion, and it is far easier to get useful meaning from non-fiction (where the meaning is overt) than fiction (where it is often covert, hidden in a dense thicket of irrelevant details). Now as an adult, I would be able to see the deeper lessons in the classics, but that's because I have more capacity for understanding those things than I did in high school or college. High school is just too early to expect kids to get the deep meaning out, even if the teacher does teach it. There has to be something in the curriculum that could be cut to make room for getting kids to think more clearly. If not fictional literature study, then what? There is only a limited amount of time to get the most important things packed into their heads...EDTA_{November 25, 2020
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Good response to EDTA, johnny, about the value of literature. However I would disagree with your statement "but nobody explains why we are reading them. Nobody says, “here is something that you will get from reading these things,” or even, “here is the connection to our cultural history.” I am good friends with some high school English teachers, and they focus on connecting the lessons and perspectives in literature to important issues in the students' lives, from understanding themselves and relationships with othesr to understanding broad historical conceptions. Sure, some teachers are better than others, but I think most teach literature to bring alive perennial human issues that will help the students grow as people.Viola Lee_{November 25, 2020
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By the way, the second installment of the math series is out. Check it out here: https://mindmatters.ai/2020/11/straight-talk-about-fitting-the-math-curriculum-to-the-student/johnnyb_{November 25, 2020
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Disagree heartily, EDTA. Literature is an absolute necessity. Now, I do think it needs realignment, simply because we don't tell kids what they should be getting out of literature. Namely, the ability to see things from a different perspective. To see the world through an entirely different set of ideas, assumptions, and feelings than our own. Done well, literature teaches empathy as well as an understanding of society. It helps people think of situations they may be in, and ask how they would respond, which is excellent in case they themselves ever get in that situation. It helps them reason morally ahead-of-time. The lack of self-understanding for why we read literature is what has been its main problem. We have an excellent set of things to read, but nobody explains why we are reading them. Nobody says, "here is something that you will get from reading these things," or even, "here is the connection to our cultural history." I teach a class where we read Oedipus Rex. The students are like "why!?!?" However, I think that Oedipus is one of the most underrated stories. It is a detective story. But, in the end, the detective uncovers the fact that *he* is the problem! This ability to investigate problems and discover yourself at the center is one of the keys to adult thinking. It is human nature to want to blame someone else, and to stop looking when it looks like the truth is that *you* are the problem. Oedipus is a hero because he *wants* the truth, even if it is costly, and even if it means that he was the one in the wrong. Many times in life we try to investigate what is wrong with our situations. Oedipus teaches us that sometimes, the common denominator of all these problems is ourselves.johnnyb_{November 25, 2020
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Well, not a war on art, but a refocusing of educational emphasis on practical reasoning over fiction. As long as kids can study fiction as an elective, we should be fine. We need a war on ignorance and foolishness. If we fail to properly educate kids so they can regain some control over our nutty world, art won't matter.EDTA_{November 24, 2020
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Ah, the war on art!Viola Lee_{November 24, 2020
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What we need is a war on other stupid subjects that do us little to no good at all. I'm thinking of those parts of English class that deal in fiction: poetry, literature, plays, and so on. Way too much time is wasted on those fictional things and too little time is spent teaching kids how to reason properly, and avoid demagoguery/rhetorical arguments, and all the other fallacious ways people in the media manipulate people. Let the study of fiction in all its forms be an elective. Use English class to teach reading and writing using non-fiction exclusively, and throw in practical reasoning topics to round it out. This won't fly of course, because English teachers love their classics and couldn't bear to give those up. They get a high trying to inculculcate a love for the classics into each new batch of students. And most of the English teachers I've had in school (all levels) wouldn't have been able to teach a practical reasoning class if their careers depended on it. (I went to college with a bunch of teachers; I know.)EDTA_{November 24, 2020
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Not doing the math tables has hurt the students in the local area schools. They need to rely on calculators to do basic mathematics. It's sad, really.ET_{November 24, 2020
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Thanks, Johnny, I really appreciate your post (and Polistra's also). I like how you described some things without any extreme rhetoric, which I have seen in other places on this topic: News is fond of the "war on math" phrase. Anyway, here are some comments. I disagree with the idea of not memorizing the times tables, but I think it could they could be taught in a more integrated fashion in elementary school. Then as time passes, students can learn to turn to a calculator when appropriate and yet use their understanding of their multiplication facts in mental math, or factoring, or other uses. Same thing with using computers. For instance, student should know how to use the quadratic formula, and its role in theory, and then learn to use a computer or graphing calculator in applications (such as in calculus). Much of this is just a matter of balance and moderation. Knowing the basics at a paper-and-pencil level builds fundamental understanding and good mental math, but as they move on to upper level math it's nice to let technology help when it can so the student can concentrate on the problem solving. I have no idea how this Hacker person thinks we shouldn't teach exponents. (I will say that many of the problems in the text books are too gimmicky though, on many subjects.) I think what you wrote here is excellent:
“Mathematics gives students practice in core reasoning skills with concrete problems that have definite answers in order to help them achieve mastery of the reasoning process. That will allow the skill to be applied later to fuzzier problems where answers are not as certain.” The problem with debates and mock trials is that it is often hard to differentiate between logic and rhetoric – you need to *already* have good logic skills to do this. Math is needed because we know that if we win in math, we did it through logic, while if we won in debate, we might have done it through rhetoric.
Here are two problems I have with debates. First, they are polarizing: they divide people into two groups whose goal is to win, not to come to some common understandings. Second, rhetoric always includes differing assumptions that are not necessarily part of the logical structure. In math, everyone starts with the same "givens". I also like Polistra's comment about the social aspect of teaching math.
Some of the ‘warriors’ are trivial, but many of them are seriously trying to bring math to students inside a framework of real-life and real-job experiences. Their framework is heavily flavored by Social Justice, which will make it more tasty and pleasant to the students who need it most.
We need to bring it alive to students, and differing cultural settings require some different techniques. My nephew was the gifted teacher on a Navaho reservation for a while, and he used the patterns in the traditional Navaho blankets to teach geometry, but someone in downtown Detroit would have to try something different. This is minor example, but it's important to think about the students, and not just the math separated from the students that we want to learn it. Thanks to you both.Viola Lee_{November 24, 2020
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Viola - first of all, the terminology of "war on math" is not part of the article itself, but I kind of agree with it. There are many who are currently aiming at "fixing" math in a way that I think is actually breaking it. For instance, in a recent Wall Street journal article, one of the math reformers, Jo Boaler, suggested that we stop making kids memorize the times tables. Conrad Wolfram is suggesting we not teach kids any manipulation that can be done automatically with computers. Some are indeed claiming that requiring math is racist (I kid you not). Andrew Hacker has suggested that we stop teaching kids exponents and exponent rules. Hacker thinks that we can teach logical thinking skills another way, such as through debates and mock trials, and that math is not needed for this. My take-home phrase to combat this, which I put in the article and a number of other places (pretty much any time I talk about math) is this: "Mathematics gives students practice in core reasoning skills with concrete problems that have definite answers in order to help them achieve mastery of the reasoning process. That will allow the skill to be applied later to fuzzier problems where answers are not as certain." The problem with debates and mock trials is that it is often hard to differentiate between logic and rhetoric - you need to *already* have good logic skills to do this. Math is needed because we know that if we win in math, we did it through logic, while if we won in debate, we might have done it through rhetoric. If you're interested, I did a two-part article on Andrew Hacker's book "The Math Myth", which presages several of the things I'm going to put in this four-part series. Part 1. Part 2.johnnyb_{November 24, 2020
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Viola, the 'war' is overhyped by conservatives who think math should be nothing but times tables and Euclidean proofs. Some of the 'warriors' are trivial, but many of them are seriously trying to bring math to students inside a framework of real-life and real-job experiences. Their framework is heavily flavored by Social Justice, which will make it more tasty and pleasant to the students who need it most. I wouldn't be attracted to that particular flavor, but I'm not the students who need to master math right now.polistra_{November 24, 2020
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That's a good article, Jonathan. I agree with it, and I think most math teachers would also agree. Math can teach logical thinking skills, clarity of thought, the importance and power of clear, step-by-step description of an argument, etc. It was geometry proofs that first taught me the power of structured logical argument, and hooked me on math as an intellectual pleasure. What I don't understand, and have questions about before, is what exactly is this "war on math" people talk about? I am certainly not for teaching less math. I agree that we need to emphasize data more, and quit teaching some outdated techniques that should, I think, be replaced by technology. (Example: teaching synthetic long division to find the roots of polynomials.) We need students to have some skill in the full range of math tools, including well-written work, appropriate use of calculators (I would not want to go back to students looking up trig functions in a table), spreadsheets (an essential tool for data analysis), online tools (when I want to know 56!/43! I turn to Google) and computer programs. We also need to teach a balance of theoretical math, competence in important techniques, and practical applications. I've been working on incorporated all of this into my math classes for years, starting with the NCTM standards that were introduced in the late 1980's, I believe. I agree that there is, however, a great deal of inertia in the math curriculum, and educational structure in general, that slows down progress. In my experience it has often been parents who are resistant to their children learning differently than they did. So I look forward to what else you have to say. But I'd also like to hear more about the "war on math". Is that just a phrase that applies to people that want to improve math along the lines of which you speak, or does it apply to those that resist such change, or what? I've been seeing that phrase but have yet to learn much about what it means and what ideas it is applying to. Thanks.Viola Lee_{November 23, 2020
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