It's interesting to hear you both talk about teaching math. I work on math with my three year old, not intensively but I try to make it creative and fun. She counts into the twenties well but she losses focus beyond that and I'm not being a drill sargent. I do things like put out a pile of M&M's and we count them. Then she has to make two piles with the same number of M&M's in them and count them. I did even numbered piles the first few times we played this game and then I started introducing piles with odd numbers. "There is one left over! What is going on here!" Talk a bit about even and odd number piles, hope to move to piles of three with the same number of objects soon. No idea if this is a very good game for teaching but we have a good time. Puzzles seem great for young kids and spacial relations. We have some picture puzzles with boarders some that are in the shape of the object being puzzled (stuff like fruits) and another free form geometric shape puzzle where you can try and copy form or just do what you want. We talk about how triangles can look different and still be triangles but also that it's strange that rectangles, rhombuses and squares are called different thing but are so much alike. Reading what you guys wrote I'm realizing that it's time to go three dimensional, I see a construction project in our future this week. Cones, cylinders and spheres will be interesting.
That sounds great cgod! Those are all really good things to do! After your daughter has counted like, 8, things, try adding one more and asking "how many now?" and see if she can answer without counting again. Try taking them away one at a time to practice one-fewer relationships as well. Only 20% of 1st graders can count backwards from 25. Counting by 2s and 3s and 5s and other multiples are really fun too. By the time my daughter was in 1st grade she could add and subtract 3 digit numbers mentally, including numbers that crossed over hundreds, and she could manage things like 135 minus 200. Her amazing number sense continued until she learned the standard algorithm -- and then she could no longer add mentally. She eventually came back to mental math, but it really made me mad that they started teaching the algorithm in her class when most of the kids had very little number sense. Algorithms are the beginning of the end for kids and math, they literally stop thinking at that point. I see lots of complaints from parents in the US about the "new" methods of teaching -- many schools are starting to focus on a variety of mental math methods which I think is absolutely brilliant. Parents are dead set against it because they don't understand that this is really really important. Parents see kids doing strange ways of subtracting 17 from 45 for example by thinking "17 + 3 is twenty, plus 20 more is 23, and 5 more makes 28" or thinking 45 - 17 is the same as 48 - 20 (add 3 to both parts) and so its 28. Parents insist that this is a waste of time when they learned to just write out the algorithm and manipulate digits and get the answer. But that is a rant for another day. Keep up the good work!
Teaching that way blows my mind. When I help someone with math I guess I've always used the standard algorithm as a shared language but I know that when I've asked people how they resolve a problem in their head almost everyone does it differently. I've learned better ways of doing problems in my head by hearing how other people go about solving problems differently from me. Feels like there is something useful in having a standardized way of expressing basic problems even if I know that most people will have a bunch of "tricks" they use to actually do math. It's kind of a strange paradigm shift for me to think about not teaching the way I was I was taught. Even with that I already planed on teaching my kid easier ways to get to their final answer. Even in college mathematics I remember being penalized on tests and if I didn't work backwards to express things I had already calculated another way in standard notation. I don't think I even had a way to express how I calculated some things in notation, just little rule of thumb stuff.Parents see kids doing strange ways of subtracting 17 from 45 for example by thinking "17 + 3 is twenty, plus 20 more is 23, and 5 more makes 28" or thinking 45 - 17 is the same as 48 - 20 (add 3 to both parts) and so its 28.