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Math education: It’s not about numbers, it’s about learning how to think

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Re: Math education: It’s not about numbers, it’s about learning how to think

#191

Post by kaitai »

gnaritas wrote: post #179
ghettoCoder wrote: post #131

Earlier quoted context omitted.

I disagree. I am not uncomfortable with math in general or the "new math". What I am uncomfortable with is the fact that my kids, and everyone else's kids, are essentially lab rats in a massive experiment. The result of which is 1+ generation of kids who can't calculate tax in their head or split a restaurant bill . They can't manage more than a few number without a calculator and are missing many of the basic blocks…

You're confusing "New Math" with common core.

Disagree. If you read the common core standards, they are very sensible and make no curricular or pedagogical recommendations. "Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph." CCSS.MATH.CONTENT.HSF.IF.B.6.

The way people are teaching math in the US is baffling and weird, but Pearson's textbook design has little to do with the common core per se. Most common core-labelled material is from something else with a new shiny CC cover slapped on.

Re: Math education: It’s not about numbers, it’s about learning how to think

#192

Post by acjohnson55 »

kaitai wrote: post #146
acjohnson55 wrote: post #110

Earlier quoted context omitted.

Nailed it. I remember "hitting the wall" in Honors Algebra II, when I just couldn't keep up with all the new things I was expected to compute: radicals, synthetic division, logarithms, etc. It was a major dent in my math confidence, which up until that point had be reinforced by being told I was "good at math". I didn't start regaining that confidence until Chemistry, when I learned what pH actually meant. That spark…

This is compounded in the weird American class called "precalculus," which is just a random grab bag of math crap that might maybe needed before calculus but might not. In most precalc classes I've encountered, not only is there no explanation of why the concepts will be used in calculus, but there is little attempt to relate the concepts covered in the class. Let's go from linear equations to complex numbers to pola…

> In theory, I strongly support "math for liberal arts"-type classes instead in college.

I love it. They could call it "math"! ;)

Seriously, I think that captures an important concept: for the most part, math was developed to serve the needs of humanity.

I used to wonder, how do we know our numbers are the "true" numbers? Did we just happen upon one way of computing, and there are countless alternatives that could have been explored?

Of course, the answer to that is actually "kinda, yeah". Abstract algebra leads to all sorts of systems that behave more or less like our familiar numbers and operations. And besides the whole numbers, which represent physical quantities, every extension to things like integers, reals and complex numbers are used not because of their tangible reality, but because they do a good job of modeling human concerns. Because my brain has a limited ability to pursue abstraction for its own sake, its this aspect of math that really captivates me. I think that's true for most people.

Re: Math education: It’s not about numbers, it’s about learning how to think

#193

Post by kaitai »

dsfyu404ed wrote: post #180
kaitai wrote: post #146

Earlier quoted context omitted.

This is compounded in the weird American class called "precalculus," which is just a random grab bag of math crap that might maybe needed before calculus but might not. In most precalc classes I've encountered, not only is there no explanation of why the concepts will be used in calculus, but there is little attempt to relate the concepts covered in the class. Let's go from linear equations to complex numbers to pola…

>"math for liberal arts"-type classes I took a class that met in a room used by a class like that the period prior and got to listen to the better part of it. In the one lecture the prof coaxed them into creating an algorithm for the number of moves to solve a rubix cube based on the number of cells who's configuration is known and where those cells are located on the cube. In a different lecture they were doing the…

> The quality of those courses depends on the prof.

Entirely. In theory they are great :)

The one you listened in on sounds interesting!

Re: Math education: It’s not about numbers, it’s about learning how to think

#194

Post by ng12 »

Merovius wrote: post #159
d3ckard wrote: post #19

Maybe I'm wrong, but I have always believed that if you want people to be good at math, it's their first years of education which are important, not the last ones. In other worlds, push for STEM should be present in kindergartens and elementary schools. By the time people go to high school it is to late. I never had any problems with math until I went to university, so I was merely a passive observer of everyday stru…

> Maybe I'm wrong, but I have always believed that if you want people to be good at math, it's their first years of education which are important, not the last ones. In other worlds, push for STEM should be present in kindergartens and elementary schools. By the time people go to high school it is to late. I indeed believe you are wrong. I started getting interested in STEM when I was 16 and now have a masters in mat…

First, 16 is still pretty young. Second, just because you didn't have STEM hobbies when you were young doesn't mean you weren't given the framework to excel at STEM. It's not "you learn math or you don't", rather the argument is "you develop the framework for mathematical thinking or you don't".

For what it's worth I also did better with literature and history than math when I was young. Also, I struggled to pass Calculus 2 but breezed through upper level CS courses. It's a very fuzzy thing.

Re: Math education: It’s not about numbers, it’s about learning how to think

#195

Post by gnaritas »

kaitai wrote: post #191
gnaritas wrote: post #179

Earlier quoted context omitted.

You're confusing "New Math" with common core.

Disagree. If you read the common core standards, they are very sensible and make no curricular or pedagogical recommendations. "Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph." CCSS.MATH.CONTENT.HSF.IF.B.6. The way people are teaching math in the US is baffling and weird, but Pearson's textbook…

I think you misunderstand, "New Math"[1] was a thing from the 60's, he clearly took it as an adjective talking about common core, the current "new math", but not the same as the "New Math" bitwize was saying had been tried and was a failure.

[1] https://en.wikipedia.org/wiki/New_Math

Re: Math education: It’s not about numbers, it’s about learning how to think

#196

Post by tpeo »

lordnacho wrote: post #4

I think a major issue with math problems in school is that they're obvious. By that I don't mean it's easy. But when you're grappling with some problem, whatever it is, eg find some angle or integrate some function, if you don't find the answer, someone will show you, and you'll think "OMG why didn't I think of that?" And you won't have any excuses for why you didn't think of it. Because math is a bunch of little log…

The issue is that being able to see that little path of logical steps is a skill on it's own, and most students don't know even how to begin approaching a new mathematical problem.

Re: Math education: It’s not about numbers, it’s about learning how to think

#197

Post by rb808 »

Merovius wrote: post #159
d3ckard wrote: post #19

Maybe I'm wrong, but I have always believed that if you want people to be good at math, it's their first years of education which are important, not the last ones. In other worlds, push for STEM should be present in kindergartens and elementary schools. By the time people go to high school it is to late. I never had any problems with math until I went to university, so I was merely a passive observer of everyday stru…

> Maybe I'm wrong, but I have always believed that if you want people to be good at math, it's their first years of education which are important, not the last ones. In other worlds, push for STEM should be present in kindergartens and elementary schools. By the time people go to high school it is to late. I indeed believe you are wrong. I started getting interested in STEM when I was 16 and now have a masters in mat…

Nice to hear some sense, I'm surrounded by tiger parents sending their kids to STEM summer camps & after school classes because it'll help them get into MIT or whatever. Its pretty sad as most of them would be much better off if they had some fun and had some friends.

Re: Math education: It’s not about numbers, it’s about learning how to think

#198

Post by Jtsummers »

sanderjd wrote: post #42
crb002 wrote: post #30

Programming needs to be taught alongside Algebra I. Especially in a language like Haskell or Scheme where algebraic refactoring of type signatures looks like normal algebra notation.

Learning multiple different highly abstract concepts at the same time does not seem like a solution to the difficulty of learning a single highly abstract concept.

My experience with this comes from college, but I disagree. I added a math major late into my education (I was one course from a minor, then 4 more from a major so why not?). I ended up in several math courses at once that were often taken separately, but specifically abstract algebra and a higher level (4xxx) linear algebra course.

I pretty much aced both, though I probably would have gotten an A in them taken separately. The reason I did better, though, was that they were both algebra. They were both expressing the same concepts, but on different types of objects. The moment that that clicked in my head, my Monday lesson in linear became the clarified by my Tuesday lesson in abstract, which was further clarified by my Wednesday linear.

If you structure it correctly (particularly, with programming, by selecting appropriate problem domains for programming exercises), I'm quite confident you could create a better math and programming education experience by properly pairing the two.

Re: Math education: It’s not about numbers, it’s about learning how to think

#199

Post by jtreagan »

You say "it's not about numbers, it's about learning how to think," but the truth is it's about both. Without the number skills and the memorization of all those number facts and formulas, a person is handicapped both in learning other subjects and skills and in succeeding and progressing in their work and daily life. The two concepts -- number skills and thinking skills -- go hand in hand. Thinking skills can't grow if the number skills aren't there as a foundation. That's what's wrong with the Common Core and all the other fads that are driving math education these days. They push thinking skills and shove a calculator at you for the number skills -- and you stall, crash and burn.

The article brings out a good point about math anxiety. I have had to deal with it a lot in my years of teaching math. Sometimes my classroom has seemed so full of math anxiety that you could cut it with a butter knife. I read one comment that advocated starting our children out even earlier on learning these skills, but the truth is the root of math anxiety in most people lies in being forced to try to learn it at too early an age. Most children's brains are not cognitively developed enough in the early grades to learn the concepts we are pushing at them, so when a child finds failure at being asked to do something he/she is not capable of doing, anxiety results and eventually becomes habit, a part of their basic self-concept and personality. What we should instead do is delay starting school until age 8 or even 9. Some people don't develop cognitively until 12. Sweden recently raised their mandatory school age to 7 because of what the research has been telling us about this.

Re: Math education: It’s not about numbers, it’s about learning how to think

#200

Post by brendan_a_b »

My mind was blown when I came across this Github repo that demonstrates mathematical notation by showing comparisons with JavaScript code https://github.com/Jam3/math-as-code

I think I often struggled or was intimidated by the syntax of math. I started web development after years of thinking I just wasn't a math person. When looking at this repo, I was surprised at how much more easily and naturally I was able to grasp concepts in code compared to being introduced to them in math classes.

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