There’s no been shortage of Bad Stuff posts lately, even by the wallowing standards of this blog. So, today, let’s have an uplifting chat:* what are the *good* mathematics teaching resources?

This is the third and final post inspired by mysterious commenter texas. First, for who people should read on maths ed, see the discussion here. Then, for the discussion about good (and bad) mathematics curricula, go here. Now it’s on to mathematics teaching resources, by which we mean anything that can contribute to the content of teaching: notably good textbooks, problem sets and so forth.

Of course in an ideal world a teacher would already have their well-chosen, well-written textbook set for the class, and other resources would be the cherries on top. We are obviously far from an ideal world, however. So, solid banks of sense may be very helpful to teacher folk out there. Feel free to list any books that come to mind, even if specialised or expensive or difficult to obtain. Websites are also relevant for this discussion, but techno games are not and videos of smiling clowns are not.** The emphasis should be on quality *content* and the presentation of that content, preferably with a clear indication of the content’s purpose or uses.

(*) Readers should enjoy it while they can. Tomorrow it’s back to the swamp, with Eddie Woo.

(**) See (*).

## UPDATE (09/08/23)

We’ll add appropriate suggestions and links here, as they appear in the comments. (We thought it was clear enough, but this is a post for written mathematics, resources for teachers, so they can teach. Not cute videos, and not general “what is maths about” stuff). Her are the first couple, together with a couple suggestions of our own.

The famous, hard series by the famous AoPS guys, including the primary Beast Academy series.

A series of more enrichy books from the Canadian Mathematical Society.

The UK series of “Asian mastery” style primary level texts, discussed a bit here, and in the comments. Cheap “homeschool” (but very similar) versions here.

The excellent topic by topic problems books by Tony Gardiner, tied to the MNP series. Not expensive, but hard to find with low shipping. Occasionally they appear reasonably priced at abe.com or ebay.

A series of online modules, with accompanying PDF versions, going through the Australian Curriculum topic/concept by topic/concept.

A UK website, with connected modules on A-level (advanced senior) mathematics.

American Maths Competition Problems

An excellent archive of AMC and other competition problems, courtesy of the AoPS guys.

A guide to and resources for the Victorian curriculum, by commenter Alex.

A Canadian series of primary and junior secondary textbooks

Books, and a program, presumably for Californians who want to escape the clutches of Jo Boaler.

Catriona Agg’s Geometry Puzzles

No idea who Catriona Agg is, but it’s a nice collection.

I have something to share.

Here are YouTube Channels which are interesting:

3Blue1Brown – https://www.youtube.com/c/3blue1brown

Matt Parker StandUp Math – https://www.youtube.com/user/standupmaths

A single video by Quanta Magazine on the Riemann Hypothesis (very good and accessible for a younger audience) – https://youtu.be/zlm1aajH6gY

Some amazing books:

I can’t over-recommend Art Of Problem-Solving Resource; we are using their books

https://artofproblemsolving.com/store

I believe every school worldwide, especially every Math teacher, would benefit from Art Of Problem-Solving books. Also, they all come with Solution Manuals.

There are also many very good books, mainly on the IMO level.

https://www.bookdepository.com/publishers/Xyz-Press

The book I would strongly recommend for any math educator is

It discusses the right level of abstraction and methodology for teaching math.

Some seriously amazing video courses:

Prealgebra. This strongly correlates with Y7 and Y8 curriculum

https://artofproblemsolving.com/videos/prealgebra

Algebra for Y9 – Y11

https://artofproblemsolving.com/videos/algebra1

Counting & Probability. I think Y10-Y11, but you would know better

https://artofproblemsolving.com/videos/counting

Ugh. No damn videos. Why is this hard?

I can sorry, but you said resources. These are resources. You never specified that those mustn’t be videos.

Also, I strongly believe that some might find resources useful.

Also sorry for typing mistake. I am on mobile without glasses

Maybe read the post again when you have your glasses on.

Totally agree – it’s not a panacea but short videos certainly help with engagement. Here’s a video, the key line of which one of my Year 9 Remedial class voluntarily repeated back to me: https://www.youtube.com/watch?v=uvLi3C_5rWg&list=PLK7VaCOgLhaZx3-u0AQ6jI4TbK17RX1xB&index=2. This guy is excellent! And a science educator.

“Engagement”.

If rap makes somebody engaged with math so be it. However, video courses by Art Of Problem Solving with Richard delivering them aren’t some ‘light video’. These videos are high quality explanations supported by bunch of books with numerous exercises. Dismissing them is myopic to say the least.

Whatever their merit, it has nothing to do with this post.

“Now it’s on to mathematics teaching resources, by which we mean anything that can contribute to the content of teaching: notably good textbooks, problem sets and so forth.”

That was a quote and my point is that these videos hugely contribute to the content of teaching.

“Websites are also relevant for this discussion, but techno games are not and videos of smiling clowns are not.”

Videos of smiling clowns belong to circus, no doubt. However, yet again videos of Art Of Problem Solving are well made material delivered by one of the most notable math educators in the world.

Jesus. That’s not the fucking point.

The purpose of this post is to list resources so that teachers can teach. Textbooks, problem lists and the like. Videos have no place here, whether by smiling clowns or by God.

The Canadians have a little series of books called “A taste of mathematics” (https://cms.math.ca/publications/atom-booklets/). But this is enrichment stuff.

Thanks, Franz. There’s They seem a little enrichy for what I was suggesting, but still in the ballpark. I’ll include when I update the post.

I’ve found the AMSI Times modules to be pretty good: http://schools.amsi.org.au/times-modules/

Unlike other resources they lay out and explain each topic in a sensible way, which I found is useful even if you already know the stuff.

Thanks, Anita. I don’t believe you, but I’ve added it.

I’ve used the UK Underground Mathematics resources a few times for inspiration:

https://undergroundmathematics.org/

As with everything, some good, some less good, use it for ideas rather than ready-to-use resources, but I guess it all helps.

Thanks, RF. I’ve never heard of that one. Added.

I put all my resources and others I collate here

VIC Maths Notes

I try to make them as high quality as possible and constantly go back to improve and expand upon them. There’s also the Teacher’s Corner page that has more links to other websites.

The complete archive of historical AMCs (8/10/12) and AIMEs and higher level exams (and solutions) are freely available here:

https://artofproblemsolving.com/wiki/index.php/AMC_Problems_and_Solutions

I was assigned these problems routinely when I was in high school, and I use them with my own students.

Excellent. Thanks, VJ. Added.

Can never seem to get a link to work in the comments, but I put all my resources and others I collate here https:// vicmathsnotes .weebly .com

I try to make them as high quality as possible and constantly go back to improve and expand upon them. There’s also the Teacher’s Corner page that has more links to other websites.

OK, I found this comment and others by you in the spam folder. It may your commenting name plus links that triggers the filter.

Can never seem to get a link to work in the comments, but I put all my resources and others I collate on VIC Maths Notes

I try to make them as high quality as possible and constantly go back to improve and expand upon them. There’s also the Teacher’s Corner page that has more links to other websites.

Hi Alex. Not sure why you can’t just include the link as text. Or you can use html code. Or, just email me and I’ll look.

I’ve tried pasting text, using html, working around any filters spelling out the dots, but the comment never sends. I’ll email it.

Huh. If the comment contains too many links then the comment is held for moderation until approved. But I should get an email that the comment is in limbo.

Literally one link so I’m not sure. If the comments ended up in moderation approval limbo there may be several attempts. Have emailed the link .

I know video is not your thing, but I have shown this one to my year 8 and 9 classes with good effect: https://youtu.be/kkDfT8ixwzY (I don’t believe subtraction exists by James Tanton).

I am also wondering what your opinions are on Maths Pathways. Our school uses it rather than streaming in the lower high school years. We start streaming in year 10.

In my year 8 class I have some students working at year 4 level and actually learning.

What was the good effect? As for Maths Pathways, it is a crime against humanity.

Maths Pathways. Why? It meets the students where they are at. Allows the brighter students to move ahead at their own pace and not be restricted by where the rest of the class is. The ‘textbook’ contains much direct instruction and the teacher also teaches small groups with whatever method he or she wants.

As with anything it can be used badly. To teach it the teacher really needs to be able to teach from counting through to the end of year 10 extension, but it tends to be used in lower secondary where out of area teaching of maths is way too common.

Nonsense. The students are learning nothing.

I really like the JUMP Math textbooks and materials (all from Canada). I’ve used the “JUMP at Home” series with my daughters at various times when their math education in school was really terrible.

https://jumpmath.org/

Thanks, Sanjoy, and for your other suggestions in your other comments. I’ve heard about JUMP somewhere, but I can’t remember where. Anyway, I’ll look later and add your suggestions.

For sure. I am glad that you are making these compilations.

p.s. JUMP are mostly paper based, which I like. But there are lots of sample materials as PDF, on their website and on websites all over.

Added.

Here is another resource ‘The Berkeley Math Circle’ with some interesting books

https://mathcircle.berkeley.edu/books

Thanks, Mike. I’ll look soon.

Added.

Here is the website with a good number of geometry problems – Catriona Agg’s Puzzles.

https://notes.mathforge.org/notes/published/HomePage

Every problem has a bunch of suggested solutions, all tracked through GitHub. Everyone can participate.

Thanks, Dr. M. It looks very nice. I’ve added it to the list.