EDIT: typos
'Can I have 50% of this, half of that..., can you give me two sweets, how many do you have left' etc.
When they are a bit older introduce them to money and let them buy small items. Doing it this way is more subtle, if you push studying too much you might end up with the opposite, them hating maths etc.
I've found mathematical inspired art projects to be quite effective. For example we'll cut tangram shapes out of card, make tangram animals, stick them on the wall and draw eyes on them and so on. You'll find lots of ideas if you search for math art projects for kids.
[0] https://www.goodreads.com/book/show/12689040-math-from-three...
The books have lots of puzzles in which they put different shapes on scales and your goal is to identify how many on each side results in a balanced scale.
I remember doing these in middle school, but with guidance, I think 3 year olds could pickup on it as well. It definitely reinforces underlying principles of algebra.
I guess the math app is good (but I hadn't try it). https://play.google.com/store/apps/details?id=com.sinyee.bab...
If you search for "Math Academy" on Twitter, you'll find all sorts of great stories about it. The creators have studied the science of pedagogy pretty well to optimize the learning process at scale to every user. Justin Skycak in particular on Twitter discusses what goes into creating the content, the scaffolding, interleaving methods they use, buildup of automaticity through memory, and how working memory affects rates of learning. Justin has even shared a textbook on his Twitter page that details a high overview of the various teaching methods that go into the curriculum (although from what I understand it's still a work in progress).
You can even try it yourself. A few mathematicians use it to brush up on old concepts they haven't used in a while or to add a little that they didn't know previously.
They're also constantly expanding the courses.
There was a great Reddit thread where the creators answered some questions about the program and why they made certain decisions (posts from thread below).
Highly recommend since it'll answer a lot of doubts you may have about it. I really do believe it's probably the most effective way to learn math today.
" '[Question 2] It's hard to believe that 5 hours a week for a year starting from basic multiplication tables (found on your homepage) will have me completely prepared for higher-level university courses. I'd prefer an explanation for people who are not familiar with the XP system.'
Yeah, I realize that this can be a bit shocking!
I think the most convincing way I can answer this question is to start by telling you that in our original in-school program, 6th graders start at various places in Prealgebra, and then do about 40-50 minutes of fully-focused work per school day for the next 3 years. This takes them all the way through Algebra 1, Geometry, Algebra 2, Precalculus, and AP Calculus BC, passing the AP exam by the end of 8th grade.
Of course, I realize that also may seem kind of shocking, but we have the AP scores to prove it, and there's been plenty of news coverage over the past decade: https://www.mathacademy.us/press (Let me know if you'd like me to elaborate more on this.)
Now, look at the numbers: 40-50 fully focused minutes/schoolday x 180 schooldays/year x 3 years comes out to about 24000 minutes or 400 hours, and our Foundations series is about two-thirds the size of that (since roughly a third of topics are not actually prerequisites for university math), which comes out to about 267 hours, and then divide by 52 weeks in a year, and you're at about 5 hours per week.
Anyway, if there are parts of this argument you want more clarity on, or any parts you're finding unconvincing, let me know and I'm happy to elaborate."
Source: https://www.reddit.com/r/learnmath/comments/1edeuw8/comment/...
One of the other reasons why I recommend Math Academy over textbooks is because fundamentally the process can be so much more efficient than a textbook could ever provide. Justin himself notes the same:
"...Yeah, MIT OpenCourseWare (OCW) is what I used to self-study a bunch of advanced math while growing up. OCW is a good resource and I came a long way with it, but for the amount of effort that I put into learning on OCW, I could have gone a lot further if my time were used more efficiently. (These issues are not OCW-specific; they apply to textbooks in general, Khan Academy, etc.) That's one reason why I’ve been so motivated to help build Math Academy. We take away as much of this learning friction as possible and maximize your learning efficiency.
By the way, I wrote more about my experience here: https://www.justinmath.com/why-not-just-learn-from-a-textboo..."
Source: https://www.reddit.com/r/learnmath/comments/1edeuw8/comment/...