Toddler introductions to higher mathematics

I bought my youngest (now 10 months old) "Introductory Calculus For Infants" by Omi Inouye a while back. It's actually an ABC book about the letter x and how no one ever plays with him until he meets the letter f and finds that together, they can be anything. In the process, the book visits each letter of the alphabet and gives a brief picture of some concept in high school analysis (what is usually trigonometry, precalculus, and calculus) that starts with that letter (e.g. "You can be Absolute!" with a picture of the absolute value graph). My oldest (6 years) also likes the book because he is starting to understand graphing and likes to try to figure out what they are talking about, but also just likes the story which is really cute. I like the book for it's hidden geek value, but also because it gets my kids comfortable with the language. I think having a picture of the landscape of mathematics and being comfortable with the major landmarks gives one the ability to pick which areas one wants to visit and learn more about. It keeps their interest about mathematics up as they realize it's breadth and scope and just how deep it goes, and it gives them a feeling of control choosing the direction.

I try to give similar views to my kids with other resources. There are books like "Non-Euclidean Geometry for Babies" by Fred Carlson and another on the Pythagorean theorem by him that I know of. I also have found some video resources online that kind of stretch the idea a bit. MyWhyU on youtube, for instance, has some nice cartoons on Topology and Number Systems, but it's clear when they get to Algebra and other topics that it is aimed at an older audience. My youngest also loves to watch the videos by TyingItAllTogether (Fusion Knots), but that is not really conceptual knot theory, it's application set to some nice post rock or IDM.

I'd really like to find some good resources for my youngest that he can grow into over the next few years that follow the same idea as the Inouye piece. Book, video, interactive applications, anything that:

1. Introduces some undergraduate field of mathematics - bonus if it is graduate material.
2. Does not try to hide advanced terminology from young toddlers. I am looking at age 1 to 4ish.
3. But doesn't look to be a textbook either and instead just shows the wonderful ideas of the field in a playful toddler-friendly story.
4. Is very visual, to keep my preverbal kid drawn in.
5. But is also very readable, and continues to be fun and interesting as they learn what is going on in the story (outside the math).

I am not looking for resources geared towards my oldest (6 year old). He can read independently now, and there are tons of books aimed at him (the Sir Cumference series, Penrose the Cat, Tetrascroll, etc.), along with plenty of online interactive stuff. I specifically want resources that are actually aimed at prereaders where the point is not to teach the math, simply to provide an entertaining story that gives comfort with the ontology of a given math field and some basic visual cues as to what might possibly be meant. My older one loves the younger-oriented material as well and will likely devour anything that responses might offer, but he has other materials specifically targeting him.

I understand if no one has yet written a "Neron models for toddlers smooth at heart", but I think the fields of combinatorics, knot theory, graph theory, and even group theory have atomic visual elements that should be great fields for such an approach.

I hope this is a clear enough ask. I understand if it seems vague, but I think there is a clear genre here with a well-defined pedagogical goal. It's about expanding the vocabulary when it is easiest and providing a foundation for future growth and exploration. I think this is a field that may have lots of material I have yet to find and was really hoping the curious people here might have some good pointers.

[This should be a community wiki, I believe.]

• Possibly related (Asaf Karagila's #2). Commented Jul 18, 2013 at 20:56
• @DaveL.Renfro: Haha! I do want to make this a community wiki, though, and don't want any points if I can figure out how to get a moderator to do that. I checked meta and it seems I can't do it myself? Also, I can assure you my kids don't understand calculus or group theory, but I want them to be comfortable to explore it when they feel ready. The resources I listed are real, and they are very enjoyable for their age. It's not an attempt at drilling flash cards into them. Commented Jul 18, 2013 at 21:01
• I just flagged it for you, so the mods know you want it moved. Commented Jul 18, 2013 at 21:13
• 10 months old? Hm...
– Pedro
Commented Mar 12, 2014 at 18:42
• @PedroTamaroff: Well, he's 18 months now. But he's loved ABC's since before he was 10 mos. That's the point with this. To the toddler, these are just more colorful books with cute, simple stories. It just so happens that some of the words used are advanced mathematical concepts, but they obviously don't get that. They do become familiar with the words, though, and form rudimentary ideas from the pictures on their meanings. Doing this throughout childhood means they are not frightened off at a much later age when the words are used. The books exist. It's a real pedagogical position. Commented Mar 12, 2014 at 20:07