I wanted to give a little update on how I talk to my son about math at home, since I realized that the last time I had a post about math was before Christmas. This post is mostly for me, to remember what I did with L when my daughter becomes a similar age, but maybe this would help someone else as well. 1. For many weeks, we did division math using snacks. After Chinese lesson everyday, I would hold out a handful of yogurt puffs to my son, and ask him, "If you split this evenly with your sister, then how many can you get?" I would throw him any number even or odd, up to about 8. Let's say I hold out 7 yogurt puffs, then he would look at it and say, "3." To see if he's just guessing, I would ask, "If you take 3, then how many would remain?" Sometimes he would answer incorrectly at first, and correct himself when I posed the follow-up question. (If there is a remainder, that extra puff always goes to me.) Recently, I also occasionally would throw in a division by 3 problem, but only with 3, 4, or 6 puffs. ("If you, your sister, and I were to split this evenly, then how many can you each take?") What I like is that these problems are real, they are quick, they give us daily practice, and my son is practicing visual division, which helps him to decompose small, single-digit numbers into parts visually. 2. On Thursdays, we keep our son home because he has feeding therapy and OT. On those days when he is home with me, my son often says that he wants to stay up a little extra after I put his sister down for a nap. (He does not nap anymore, but he does quiet time still. He tries to get out of it if he can, so I've leveraged this to my advantage to get him to do some math.) If he wants to delay/shorten quiet time by an hour on those days, then I ask that he uses part of that time to do math with me. He enjoys this! I rotate through what we do -- we've done subitizing review with 10 frames (like I put down a small quantity of colored magnets, then uncover it quickly for him to see, then cover it back up and ask him how many he sees and why). We also use the cards Tiny Polka Dots quite a lot. We use them to play "War", and I ask him questions like, "Who has more?" "How many more do you have than me?" "If I want to have as many as you, how many more do I need?" I like the cards because they are a mixture of different representations -- some cards have numbers on them, some have colored dots arranged in different forms, some have dots filled into ten frames. I also like varying up what I ask him during each hand, so that he is constantly practicing hearing language that signals either addition or subtraction, without explicitly saying "plus" or "minus". 3. Recently, his class in pre-K started doing some addition and subtraction. I decided to reinforce this at home, but to really focus on the process instead of the answer, because I worry that at school he may receive a different message. Instead of doing division problems like we used to do with the post-Chinese lesson snacks, I have been giving him small numbers at a time (any number between 1 and 4), and asking him to give me the running total of how many yogurt puffs he has eaten. We just started this exercise this week, and I can see that he understands counting-on, but needs some more practice for fluency. (No problem, I love that it's something we can practice together.) I always ask L to justify each answer to me, even when his answer is correct. I try to suspend feedback about whether he is correct or not, until he has justified his answer with a verbalized process. Yesterday, when we were doing this, at one point he had already received 13 yogurt puffs, and I was going to give him another 3. I asked him how many that would make, and he said 17. Instead of saying that he was wrong, I asked, "Okay, how did you get that answer?" When he started to explain, I pointed out that he had skipped 14 in his counting sequence, so he re-counted and changed his answer to 13+3 = 16 without me telling him that 17 was originally incorrect. Subsequently, I asked, "Okay, so now that you have had 16 puffs, how many more will I need to give you so that you can have 20?" He initially said 5, but again, in the process of explaining himself, he changed it to 4 without me pointing out any error. This is the power of asking kids to articulate their process! They can and should do it as soon as they start to learn early math (and they should do it throughout the rest of their math career). Accuracy does not matter as much as the practice in articulating their thought process. 4. I also want to encourage my son to see math as an open-ended endeavor, while still practicing decomposing numbers into smaller numbers. (I just feel like decomposing numbers is a really good number sense practice at this age.) So, today I asked him, "If I want to give you 5 yogurt puffs, then I can give you first how many, then how many?" He was happy to say, "Oh, I have an idea. You can give me 2 and then 3 puffs." I obliged. Then, I asked him, "Now, if I want to give you 7 yogurt puffs, then I can give you first how many, then how many?" He thought for a bit longer, then said, "5 and 2!" I liked that, but I wondered if he could see that 7 could also decompose into 3 and 4? So I asked him, "Okay, and I also want to give your sister 7 puffs, but I just gave her 3. How many more should I give her?" He thought about it for a little bit, and then told me 3. I said, "Okay, so if I give her 3 and 3, that makes 7?" He said, "Oh, no, 4! 3 and 3 make 6, so 3 and 4 make 7!" I love this dialogue, because I can see that he is thinking about number relations flexibly and creatively. 5. My son and I just started looking at the (Western) abacus again. A little while ago, we practiced putting two-digit numbers on the abacus. Like if we had the number 32, he learned that it means 3 tens and 2 ones, so he would move 3 rows of 10 beads over on the abacus, and then on the fourth row count out two more beads. Yesterday and today, we brought that notion back in talking about percentages. We have an Amazon Echo at home, and it always reports the likelihood of rain showers via percentages. My son, who has not yet turned 5, cannot understand what that means. I realized though, that I could just show him visually on our abacus. First, I move all the beads to the left, and tell him that is 100%, which means that it will definitely rain. Then, I move all the beads to the right, and tell him that is 0%, which means that it will definitely NOT rain. Then we count out 88 beads to represent 88%, and I ask him if that looks like it's more likely to rain or not? He is able to visually see that more beads are on the "rain" side than on the "dry" side, which means that on Sunday it will very likely rain. Not bad for a percent visualization that is friendly to a pre-schooler?? 6. There have also been the one-off talks about fractions at our house. We try to normalize using the terms "half" and "quarter" when talking about food. Our son knows what a half is (from talking about bagels and pizzas and such), and he also knows that "a half of a half" is a quarter. So the other day, while eating leftover sausages, I first gave him half of a sausage. Then, he asked for more, and I asked, "Do you want another half sausage or just a quarter sausage this time?" He said, "A quarter." I took out the full sausage and asked him where he thought I should cut it, in order to make a quarter sausage. He was pretty spot on! After that quarter though, he wanted another quarter. And then afterwards, he wondered who had more sausage -- he or I? I talked to him about how 1/4 + 1/4 + 1/2 make a whole sausage, which was also how much I had eaten. So we had eaten an equal amount! That was just a passing discussion, but I do try to go with the occasion and bring up math wherever possible.
7. A while ago, my son's school was doing a farm learning unit... I don't really know exactly what they learned about farms, but it inspired me to ask L if there were two cows and a chicken on a farm, then how many feet would there be? My son enjoyed thinking about it and explaining to me how he knew that it was 10 feet. Or, another time when he asked me if I am old enough to die soon. I said, "Well, I hope not! Actually, my grandparents lived until their 80s, and I am almost 40. So, that means I might have another 40 years to live! 40 plus 40 equals 80, because 4 tens plus 4 tens is 8 tens." My son was so tickled by the fact that 4 tens and 4 tens would make 8 tens. (It makes even more sense in Chinese, because "4 tens" is literally how you say "40" and "8 tens" is literally how you say "80." It helps to be bilingual sometimes.) Or, when my son, my husband, and I split two pieces of Twizzlers on our road trip, I talked to my son about how we first split the first Twizzler into thirds, and we each had one "third piece." Then we did the same with the second Twizzler, so in the end, we each had two "third pieces" (or 2/3 of a Twizzler). Conceptual math can be everywhere and it can all be so relevant to young kids! We just have to look for those opportunities. 8. We have not done any numeric writing practice for a long time, and only ever did a little bit, because I feel like writing is one of those things that is easier to learn once your hand/fine motor develops a bit more, but a couple of weeks ago, my son was so keen on writing and drawing various things, and one of the things he produced was a hopscotch that had numbers from 0 up to about 21. It was so cool to see him producing digits after not having worked on them for so long! (Even though he mixed up the order, like he would write "fifteen" as "51". I mentioned it casually at some point, but didn't stop him from writing whatever he wanted, because the point was more that he was taking ownership of this learning-oriented work during play time and produced it with so much pride and joy, which was so cool to observe.) Even though we have done mostly a mishmash of math stuff since L returned to pre-K, I feel pretty good about my son's math readiness for Kindergarten. I head back to work this fall to teach high-school kiddos, but I know that I will still keep a close eye on his math development. I am excited for him to have daily math time next year, and for math learning to be more social for him!!!
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About MeBorn in Asia, I have spent more than a third of my life living outside of the U.S. thus far. I currently reside in the Pacific Northwest with my techie husband and two biracial children. Categories
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