My son's earliest numerical understanding was that the answer to "How many do you want?" was either 1 or 2 (which simply meant plural to him -- anything over 1 was considered 2 by him). We took a long road trip of about 3000 miles shortly after he turned 2, and during the many hours in the car, I started playing a number game when offering him snacks in the car. I would ask him if he wanted 1 or 2 (or sometimes 3) puff snacks, and then BOOM! pop open my palm and give him that many at a time. At the time, I don't think he understood what 1, 2, or 3 meant, but I remember that he giggled a ton at the exchange. Later that year, maybe when he was 2.5, I was amazed to find that L had internalized counting 1 and 2 objects. He could look at 1 or 2 objects and immediately tell me how many there were, without counting, and he could do so while the car was quickly driving past 2 objects. This ability to internalize small numbers, I only very recently learned, is called subitizing. I remember thinking that L must be working on subitizing at daycare, because certainly at home we did not ever talk about math at that time.
That same year, in the 2-year-olds class, L learned to recite numbers to 10 and learned to read single-digit numbers, 1 through 9. Although it seemed early at the time, it also seemed developmentally appropriate, because at the time, he also learned to identify some letters of the alphabet and began paying attention to written symbols in the world around us. I am not sure if he knew what the numbers meant or how to count with them, but when we would read stories at home that had numbers in them, I would often count the objects on the page out loud, and try to do so in various order (left to right, or right to left, or...) to show that the number means that's how many objects are on the page, and to imply that quantity remains the same no matter the order of counting. When my son was 2 and 3 (pre-COVID pandemic era), he loved getting on busses with just me. Before his little sister was born, he and I used to go for an entire morning just riding on public transit through the city. When he turned 3, he started learning the landmarks of our city and would narrate to me, "We are heading downtown. This is the ____ Bridge. We are now in [insert part of town]. Oh, look! We passed the [very famous landmark]. We are now in [insert another part of town]. We have to get off the bus soon, to transfer to [another mode of transport]." I had read somewhere that busses and stop signs are a good way to teach kids the power of written symbols. Long before we formally taught him any math or reading at home, he was already learning the names of all of the bus lines and learning to read their numbers and letters by sight, just out of sheer interest, and even liked looking at the bus maps while waiting for the bus with me. Many of the bus lines near us have two-digit numbers, and so by the time my son was 3.5, he could habitually sound out many two-digit numbers, even though he had no idea what "28" actually meant in magnitude. In September 2019, L moved up to the 3-year-olds room. Right before we stopped sending my son to daycare due to COVID, I learned through our annual parent-teacher conference that his daycare teacher in the 3-year-olds preschool room does not do much math during the day. (The teacher is an excellent pre-literacy and arts teacher, so I am not writing this to disparage her at all, but it is true that she seemed taken aback when I casually asked what math activities they work on in her preschool class.) The extent of the math that they do is to teach days of the week via a calendar, and they sometimes count the snacks they get. After the conference, I made a mental note to start to pay more attention to my son's mathematical development. Soon after, I found myself in the situation of home-schooling him due to COVID precautions. I actually really struggled with whether I should teach my son any math. On one hand, I think that in America (or perhaps just in certain daycare settings), there is such an imbalance between early exposure to language/reading and almost zero early exposure to mathematical reasoning. On the other hand, I have heard from many math teachers that you can really turn your own kid off from math by giving them too much pressure as a math-teacher parent. I started home-schooling by teaching my son reading and some science and deliberately stayed away from math, but eventually, I thought, "Okay, I am a math teacher. I can't be afraid of doing math with my kid. Even if it is just 5 minutes, a few times a week, I should make sure he is seeing enough math at home that he won't be scared when he sees it in school." Flash forward a few months, I have so many feelings and tips about doing math with kids at home! First of all, I have learned that even a tiny bit of math everyday can go a long way in developing both interest and confidence in a preschooler. When I decided that my son needed to see more math at home, the first thing I did was to incorporate counting into his daily routine. I started offering him a snack food everyday that he could count out. At this point, his little sister was about 6 months old, so she was eating baby puff snacks everyday, and I would offer him a bunch of her baby puff snacks if he could correctly count out how many there were. At first, we just did single-digit counts, because I noticed he needed a lot of practice counting accurately and moving the snacks from one pile (the yet uncounted) to another pile (the already counted) while incrementing the count. Then, I started teaching him more numbers past 10, so that he could count up to 11, then 12, then 13... Since the memorization of the "teen" numbers is rote, it was very important to only teach him one new number at a time, and to really practice it multiple days, before teaching him the next number. It took a long time for him to be able to count to 20, but I would encourage him to say numbers in games, like if he was about to chase me in the park, I would first have him count up to _____ before he could start chasing me, and use that to gauge his comfort in reciting the numbers. I also remember joking one day while walking home: Me: "12 is the biggest number! After 12, there is no more. That's it." Son: "No, there's more! There's... 13!" Husband: "Ohhh, right, 13. But, actually, that's it. 13 is the biggest number. There are no more numbers after 13." Son: "No, after 13 is...14!" We kept joking like this until he got to 18 or 19, and I remember thinking to myself, "Whew, it took so many weeks to get him to learn these teen numbers, but look at how far along he has come!" What I noticed, after doing the daily practice for a little while, was that my son became interested in counting everything! He suddenly was not afraid of using numbers anymore, which was an amazing and tangible transformation. Currently, I am taking an online class on how best to teach math to young kids. The premise of the class is that kids ages 2 and older are capable of reasoning mathematically, and must be exposed to concepts in a developmentally appropriate sequence. When I looked at the document that outlined their numerical development based on research, the progression was spot-on for my son. Subitizing (the ability to recognize small quantities without counting) is the first skill in the developmental sequence, and it is extremely important. Young kids before Kindergarten need to learn to subitize up to 3, to be able to successfully access the Kindergarten curriculum. Once they can subitize up to 4, research suggests that they can often figure out how to count larger collections of objects, but if they cannot subitize, they would start to develop math gaps in Kindergarten. We can think of subitizing as the initial foundation for number sense, and every parent can help our kids build the ability to subitize by using the language, "Do you want 1 or 2 chicken nuggets?" and then offering that many. Once the kid has internalized 1 and 2, then ask, "Do you want 1, 2, or 3 slices of apple?" and then handing them that many. Keep giving our kids ages 2 and older the opportunity to hear those small numbers and to see the corresponding physical objects. This post is getting long, so I will keep writing in future posts about what I have done with my son to build up his math skills at home. Stay tuned, because I have many thoughts about this!
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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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