Reddit reviews Measurement

First, you might want to start with /r/matheducation. They’re actually experts in this subject.

You can read work by hundreds of experts in child psychology/development, pedagogy, the philosophy of mathematics, the intuitive/psychological foundations of mathematics, etc. Personally I’m a fan of Piaget, Bruner, Papert, and like-minded thinkers, who advocate a child-centered “constructivist” approach to education. But there are certainly respectable educators and researchers who favor a more structured and top-down approach.

If you want to read concretely about the differences between typical US instruction and Chinese instruction in the 1990s, read Liping Ma’s book Knowing and Teaching Elementary Mathematics

Or watch this video from a few years ago discussing the TIMSS study and criticizing Khan Academy.

Or to see what a particular group of young children could learn with some expert guidance, check out Zvonkin’s book.

You might have read Lockhart’s Lament. He provides an alternative way of teaching high school mathematics in his book Measurement.

I like this concise theory of mathematical learning. YMMV. Here’s a short essay by Minksy about why mathematics is hard to learn.

If you want lesson plans and curriculum guidance, look to the American NCTM, who have been making detailed materials available for decades. Also look up math circles (both online materials and physical groups meeting in your area).

You might like this book by Van de Walle about general elementary teaching, or this book by Lenchner about problem solving.

Many people seem to like the Singapore math books. Read about Singapore’s curriculum.

If you ask homeschooling parents in your area, you can probably find strong opinions about curricula. Just searching around the web, many keywords about elementary math books etc. seem to lead to homeschooling sites. (This makes some sense: they have some free time, like to write about their experiences and form online communities, and do more personal evaluation of curricula than schoolteachers can necessarily have time/political power to do.)

There are hundreds of available books of mathematical puzzles and games, dozens of different types of physical manipulatives, and thousands of books, papers, essays, etc. about how to organize, order, and teach students of every imaginable age and background

If you have a particular age group / level of prior preparation / desired set of topics in mind, there might be some more specific materials people can point to. Are we talking about 4-year-olds? 10-year-olds? High school olympiad preparation? Are you interested in basic arithmetic? Geometry? Algebra? Do you have 1 advanced student to teach? 50 students of varying skill levels?

No, you really shouldn't.

Open textbooks are a better route to go than paying hundreds of dollars (especially for high school/early college material). The Stitz-Zeager College Algebra text is a good book.

Also, Paul Lockhart's Measurement is also a good place to start.

Last time I ordered something that came in below the 35$ limit, I preordered a math textbook!

It should show up on my last day of classes! I can't wait!

Hell yeah!

Like, my brain and special interests all lean towards the Liberal Arts and Humanities.

But math, logic, and programming calm me the hell down.

Do you have any idea how stressful it is that people can't agree on historical interpretations? Or how to best lead a group of people?

Math has answers and makes sense. I'm with Plato. It is this pure and glorious thing. It's why I love Jesus being described as "ὁ λόγος" (which relates to logic and all the rest). To be clear, you don't need to believe Jesus is the logos to appreciate how kickass math is. Plato sure didn't :P

Also, OP! This book by a Mathematician has a really cool take on teaching and learning and understanding math. Since you do it for fun, definitely would be worth checking out.

If you can't afford it, PM me and I'll send you my copy when my wife is done reading it :)

I honestly thought I was in /r/Showerthoughts for a moment.

> Geometry class is pointless

On topic. I really think you should read Measurement by Paul Lockhart Maybe it will reframe what a proof is and why this is valuable.

Try to find entry points that interest you personally, and from there the next steps will be natural. Most books that get into the nitty-gritty assume you're in school for it and not directly motivated, at least up to early university level, so this is harder than it should be. But a few suggestions aimed at the self-motivated: Lockhart Measurement, Gelfand Algebra, 3blue1brown's videos, Calculus Made Easy, Courant & Robbins What Is Mathematics?. (I guess the last one's a bit tougher to get into.)

For physics, Thinking Physics seems great, based on the first quarter or so (as far as I've read).

Measurement