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.
Don Steward’s Blog and Mr. Barton
Another big collection of which we know nothing.
The Catholic Schools’ teaching materials for the Australian Curriculum (added 29/07/24).
A free online resource, suggested by commenter M Ware (added 29/07/24).
A free online resource, suggested by commenter Sentinel (added 29/07/24).
An amazing collection of exams, competition papers, problems and so forth (added 05/10/24).
Bernhard Krötz’s German Textbook Collection
A collection of beautiful textbooks from twenty-ish years. One doesn’t need to read German to see how good they are or to be able to use them. (added 27/05/25).
A large collection of little maths books put out by Mir Publishers. Most beyond the (non-Soviet) school level, but plenty of school material as well. (added 12/06/25).
JJ found him, and I have no idea who he is, but he’s written a lot (and pirated a lot) (added 16/09/25).
A lovely book by Bowers and Bowers, a really good fleshing out of arithmetic. Suggested by Ed Barbeau (added 02/10/25).
Treeby and Ainsworth’s Enrichment Mathematics for Secondary Students
David and Gareth’s excellent two-volume “extension mathematics” text, discussed here (added 30/11/25).
Hammack, a mathematics professor at Virginia Commonwealth University, has a calculus text (lecture notes) and Book of Proof, both freely available online. (added 31/01/26).
A very well organised online version of Euclid’s Elements, including links to the propositions used in the proofs, and so forth. (added 02/02/26).
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. 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.
I’ve often used problems from Don Steward’s website https://donsteward.blogspot.com/, often accessing them via the organisation provided by Craig Barton’s website https://www.mrbartonmaths.com/teachers/ (resources arranged by topic, and then the Steward problems located under the ‘Rich Tasks’ section for each topic).
Thanks very much, Mark. I’ve added both links to the list.
In response to comments on this post, I’ve updated the post above with links to a few more resources.
Dear Marty,
As discussed, here is the link to get old days MIR publications of Little Math Library. Possibly these were written by eminent mathematicians for school children who were prepared for international Olympiad Level.
With Regards and thanking you and team for creating such a platform.
Best Regards,
Supratim Chanda.
“Team”?
Thanks very much, Supratim. Added.
It’s great to see my recommendation being appreciated. Kind regards.
Hi everyone,
With programs like InitiaLit showing great results for reading, I’m wondering if there are any similar, well-designed programs for teaching primary Mathematics. I’m talking about full units with lessons and resources that are actually good quality. Apart from saving teachers from spending weekends planning and recreating the wheel, something like this would also help reduce the variation in how maths is taught from class to class.
Since it’s now 2025 and this thread started back in 2023, I thought I’d check if any strong contenders have emerged. Paid programs are fine, as long as they’re genuinely good. Any recommendations?
Hi Jeremy, and welcome to the blog.
I’m not really your guy for this and the post is old, but hopefully the following is some help and maybe someone more knowledgable will chime in.
I am not quite sure what you mean by “programs” and I’m not sure how they may be preferable to traditional resources (and mostly doubt that they are), but here are my thoughts.
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There are series of primary textbooks, the best of which I know are:
*) Maths no Problem (link above)
MNP is (I think genuinely) based upon Singapore Maths, and they seem to me good. Colourful and friendly, but not fluffy.
*) Jump Math (link above)
This is a Canadian Series of texts, which also seem very good from the little I have looked.
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There are also “programs”, which amount to fuller suites, with (essentially) online texts and lesson plans and whatnot. The two (and a half) good ones I know are:
*) Ochre (link above)
This is free stuff, based in Australia. It seems good, but I think the suite aspect tends to detract from the quality (although of course it makes life easier).
*) White Rose (See here)
This is an English product, with an Australian version. I think *maybe* WR is better than Ochre, but that is on very little evidence, and it is not free.
*) Explicit Maths Program (See here)
This is a new, smaller player, and I think they may only have materials for around K-3 so far. They are very strongly skills based, heavy on worksheets and the like, which I like.
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In general the properly online stuff, such as Mathletics and Edrolo seems to me utter garbage. I’m not convinced kids learn anything with these programs. However, one worth mentioning is:
*) Numerical Acumen (See here)
NA is focussed solely on the practising of mental arithmetic: the basic integer operations, and fractions. It is clunky but it is excellent for what it seek to do. NA is not free but it is hilariously cheap.
I really appreciate this, Marty. Thank you!
The link for Treeby and Ainsworth’s Enrichment Mathematics for Secondary Students leads to the page for Arithmetical Excursions
Whoops. Thanks very much, FYI. Fixed now.