(Part 2) Top products from r/matheducation

The Grapes of Math and the other books in that series are pretty good. Kind of a mix of numeracy and recreational math, but for kids.

There's a good book called Innumeracy, but that may be over the head of a child that young.

Once he's had a bit of algebra, A Long Way From Euclid is an excellent book. Even without the algebra, he might benefit by reading it together with someone.

You may also want to look at the library for introductory material on Euclidean geometric constructions, orgami, tessellations, fractals, topology (Flatland?), stereograms, Logo ("turtle graphics"), combinatorics, celestial mechanics.

Or for more hand-on stuff: play with Newtonian physics - build stuff with catapults, marbles, etc. The Art of the Catapult is a good book with plans for various machines.

Also, building kites, or paper airplanes:

The Paper Airplane Book

Paper Airplanes and Other Super Flyers

The Great Kite Book

25 Kites That Fly

Kites For Everyone

When you say everyday calculations I'm assuming you're talking about arithmetic, and if that's the case you're probably just better off using you're phone if it's too complex to do in you're head, though you may be interested in this book by Arthur Benjamin.

I'm majoring in math and electrical engineering so the math classes I take do help with my "everyday" calculations, but have never really helped me with anything non-technical. That said, the more math you know the more you can find it just about everywhere. I mean, you don't have to work at NASA to see the technical results of math, speech recognition applications like Siri or Ok Google on you're phone are insanely complex and far from a "solved" problem.

Definitely a ton of math in the medical field. MRIs and CT scanners use a lot of physics in combination with computational algorithms to create images, both of which require some pretty high level math. There's actually an example in one of my probability books that shows how important statistics can be in testing patients. It turns out that even if a test has a really high accuracy, if the condition is extremely rare there is a very high probability that a positive result for the test is a false positive. The book states that ~80% of doctors who were presented this question answered incorrectly.

Honestly, if you're wanting an understanding of statistics, I'd recommend Statistics for Dummies. Don't be deceived by the title, you'll still have to do some real thinking on your own to grasp the ideas discussed. You might consider using textbooks or other online resources as secondary supports to your study.

I can also give you a basic breakdown of the topics you'd want to develop an understanding of in beginning to study statistics.

Descriptive Statistics

Descriptive statistics is all about just describing your sample. Major ideas in being able to describe the sample are measures of center (e.g., mean, median, mode), measures of variation (e.g., standard deviation, variance, range, interquartile range), and distributions (e.g., uniform, bell-curve/normally distributed, skewed left/right).

Inferential Statistics

There is a TON of stuff related to this. However, I would first recommend beginning with making sure you have some basic understanding of probability (e.g., events, independence, mutual exclusivity) and then study sampling distributions. Because anything you make an inference about will depending upon the measures in your sample, you need to have a sense of what kinds of samples are possible (and most likely) when you gather data to form one. One of the most fundamental ideas of inferential statistics is based upon these ideas, The Central Limit Theorem. You'll want to make sure you understand what it means before progressing to making inferences.

With that background, you'll be ready to start studying different inferences (e.g., independent/dependent sample t-tests). Again, there are a lot of different kinds of inference tests out there, but I think the most important thing to emphasize with them is the importance of their assumptions. Various technologies will do all of the number crunching for you, but you have to be the one to determine if you're violating any assumptions of the test, as well as interpret what the results mean.

As a whole, I would encourage you to focus on understanding the big ideas. There is a lot of computation involved with statistics, but thanks to modern technology, you don't have to get bogged down in it. As a whole, keep pushing towards understanding the ideas and not getting bogged down in the fine-grained details and processes first, and it will help you develop a firm grasp of much of the statistics out there.

The first place I'd look would probably be a physical book - something like this. Encyclopedia-style books with one concept per two-page spread would also be among my go-tos, but those might not be long enough for your purposes. Additionally, do you know anyone who did a history of mathematics class in university? Some of those classes are open to history majors as well as math majors, so they could potentially have more history than math.


Oh, and just for fun: here's a Christmas-themed piece about Pascal's Triangle.


I wish I had something more concrete to offer you. Best of luck!

> popular if controversial amongst math educators

I see some great suggestions being put forward on this thread. I am partial to CGI, which has a very strong research base, but this is technically a program for teachers learning to teach elementary math, not a curriculum for children. However, it is an easy read and gives great insights into how children learn arithmetic and how teachers can guide such learning.

Just a side note: teaching for conceptual understanding (which you seem to understand the importance of) is well accepted and not controversial at all among math educators, only among the general public and a few mathematicians, who sometimes do not understand the importance of a conceptual base in elementary education.

Hmmm. There is an entire academic field dedicated to this question, and most serious stuff will be found in journal articles rather than books. The Singapore Math curriculum is essentially designed for homeschoolers, and they offer some good guides on how to best use their particular product. If you're interested in a more inquiry-based approach, you might check out

http://www.theatlantic.com/education/archive/2014/03/5-year-olds-can-learn-calculus/284124/

And

http://www.amazon.com/Out-Labyrinth-Setting-Mathematics-Free/dp/0195147448/sr=8-1/qid=1167859040/ref=sr_1_1/002-8958891-7740062?ie=UTF8&s=books

As for the journal, the biggest one is the Journal for Research in Mathematics Education, but there are a ton of them. I don't know prices, but it might be worth looking into a membership to the National Council of Teachers of Mathematics or the Mathematical Association of America.

Good luck, it's a rabbit hole!

One of the best books I've read that places mathematical discoveries in their historical contexts: Journey Through Genius. Dunham tells the story of math through different great theorems - why they were historically important, why they are important today - and then walks you through the proof. My copy is at school, so I can't say anything more tonight, but give it a shot.

Good luck!

I also recommend using math folk tales like Stories to Solve to make the problems more interesting. I have four books with these stories from other cultures and times and the kids love them.

Jo Boaler has also done some interesting (contemporary) work on math education. I find her books (like What's Math Got to Do With It?) really reader friendly, but they also give a good overview of some of the issues prevalent in the field and her take on them based on her research.

This was my textbook for an undergrad class I took in math history. I believe it covers everything in your list, and it's all super interesting!

https://www.amazon.com/gp/product/0030295580/ref=oh_aui_search_detailpage?ie=UTF8&psc=1

I'm a big fan of Willingham. His book Why don't students like school is a good read for an intro to the cog psych of education (but not specifically maths)

The I Hate Mathematics by Marilyn Burns is a classic and fantastic for extending mathematical thinking. She has a whole line of fun books.

I like the Safe-T compass

https://www.amazon.com/Learning-Resources-Safe-T-Compass-Pack/dp/B07NC7RBDQ/ref=sr_1_2?crid=32L0V4XMMQUO6&keywords=safe-t+compass&qid=1558482307&s=industrial&sprefix=safe-t+com%2Cindustrial%2C127&sr=1-2

So I might actually suggest a 'math for elementary teachers' book for yourself (alternate here), so that you can get an idea of how to approach these kinds of problems with visual aids, such as what kinds of ways you can draw pictures of long division, etc. In other words, most people don't use textbooks with 4th/5th graders, but a lot of worksheets and packets, with activities and explorations drawn from curricula like this.

Have you read Edward MacNeal's book "Mathsemantics?" You might find some inspiration there. MacNeal's thesis is that the difficulties some people have with word problems are actually semantic issues, not mathematical issues. Essentially, they need to learn to establish the logical relationships between things as they read the question, and then the math part comes relatively easily.

Check out Thinking Mathematically
and Betterexplained.

Khan academy sucks for this reason. I strongly recommend this book if you are spending a lot of time piecing things together https://www.amazon.com/College-Algebra-7th-Robert-Blitzer/dp/013446916X/ref=zg_bs_13887_88?_encoding=UTF8&psc=1&refRID=P6E5V44ND250Y76AW1S0

It walks you through everything with plenty of practice. There are other books in the series

From another discussion (http://www.reddit.com/r/statistics/comments/2mqyn5/where_to_learn_statistics/):

http://www.amazon.com/Cartoon-Guide-Statistics-Larry-Gonick/dp/0062731025/ref=sr_1_1?s=books&ie=UTF8&qid=1416393382&sr=1-1&keywords=cartoon+guide+to+statistics

I agree that Khan Academy is a good resource--another one I always recommend to my students who struggle with math basics is this book. A lot of people are embarrassed by their poor math skills. Unfortunately, there are plenty of bad math teachers and since it builds on itself, you can miss one concept and have trouble with so many other things further down the line. Don't get too down on yourself about it! It's not who you are, it's just one aspect of what you know, and with the right teacher/book/explanation, you can understand it.