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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At the moment, miraculously, I feel the least anxious that I have felt in months! We sent our son back to daycare for about a month, and then a few days before Thanksgiving, I decided to pull him out again. We told him that he would stay home with me for at least two weeks after Thanksgiving and for two weeks after Christmas, but in reality, I am prepared to keep him home all through December and mid-January if the local COVID numbers don't look good. I was really hoping that his daycare families would be cautious for Thanksgiving, but he came home the week of Thanksgiving to let me know that most of his friends were planning to go over to someone's house for Thanksgiving dinner, and that one of his daycare families kept one sick and coughing twin at home while sending the other one to school. The combination of those two pieces of news was just a wee bit too stressful for me, so I was honest with my son and asked him if he would feel alright if we kept him home even for the few days before Thanksgiving. He responded brightly, "Sure," much to my relief and surprise. So, back to being holed up with just our sweet and screamy little family, for a little while. Even though my kids are loud and needy and they suck up all of my energy, I really enjoy having both of my kids home. We have had a rare stretch of sunny, dry weather this week, and my son was able to get back on his pedal bike for the first time in about two months. This week, he has been riding his bike, while I push his little sister in a trike stroller, to go to a park a mile away from our house. It's a decent ride because it's uphill to the park and downhill back, and because he was out of practice, the first day I had to push his bike uphill for the last few blocks leading up to the park. After the first day though, he has been able to make it there and back, and is quickly re-gaining his confidence on the bike. (We don't have a fancy bike for him. Actually, the bike he rides is heavy, rusted, and very basic. It has back-pedal brakes and no gear-shifting, the handlebar looks quite worn, and I got it for free. So, I empathize when he finds the hills challenging and thinks hopping on and off the bike is cumbersome, but I also think it builds... stamina?!) We usually spend most of a dry morning getting to the park, playing, and getting back. I do squeeze in a short math lesson every few days, mostly to keep him thinking mathematically. Speaking of math, L is doing very well with visualizing quantities under 10, which makes this math mama very proud! For example, if I show him a picture of 7 dots, he can quickly tell me that he sees 7 dots, because he sees 3 and 3 and 1 more. I am starting to work with him on making subtractive statements like, "I have 7 dots on my card, and you have 2. I win this round (of War) because I have FIVE extras!" With only a little bit of help from me, he also has learned to skip-count by 2's, up to 10. He says, "2, 4, 6, 8, 10!" and actually understands what it means to count by 2's, so I am now trying to add on a bit more, to encourage him to skip-count by 2's up to 20. Recently, he looked at our scrambled Advent calendar and re-arranged the drawers to be in the correct order. He also told me that he counted there to be 12 Advent drawers on each side of the train, which made a total of (he counted) 24 drawers, "because 2 and 2 make 4!" It is so fun to hear him making his own mathematical observations, even though he would probably not peg himself as being particularly mathematical. We have also been continuing with our Chinese lessons, which happily only last about 5-10 minutes per (week)day. I alternate daily between doing 1 or 2 new characters out of the Sagebooks, and just doing review. When we review, L either fishes out the characters to form a sentence that I dictate, or he reads sentences that I create. I think we are up to about 35 characters now that he recognizes, and the best part is that he is still enjoying it! We are moving at the right pace for both him and me, and 5-10 minutes is just the amount of focus I can get from him at the end of a day, with his rambunctious sister running around. (See below - picture from about a month ago!) Lastly, I am a proud mama today of my son, because he learned to zip up TWO of his jackets by himself. He did those two zippers each once yesterday and twice today! He also recently learned to put on his socks without stretching them out. He's just emerging to be a big kid all around. So proud of this kid! Now, if he could just be consistently nice to his little sister...
A few posts back, I briefly mentioned that I had just started teaching my son to read in Chinese. After some back and forth and asking my son for his opinions on Sage 500, I bit the bullet and ordered the Sage 500 system today! I am not sure how it will go, but at $420 (which includes the international shipping, 5 sets of books that teach the most commonly used 500 characters over the course of 500 lessons, plus some leveled picture books to go with the lessons), I felt like it would be worth the investment -- particularly because it is a fraction of the daycare costs we are still paying for every month, without actually sending him to daycare. I have been using just Set 1, Book 1 with my son to try it out before purchasing, and it has been surprisingly both fun for him and easy for me. Realistically, I don't know if he will ever become fluent in reading Chinese while growing up in America, and that's okay. To me, short Chinese lessons at home are an easy way to offer him both cultural appreciation and extracurricular enrichment, so, why not? His speaking has come a long way since the start of COVID (even when I was in the bathroom the other day, I heard him explaining something to his toddler sister in Chinese, and on a separate day I heard him reading to himself in Chinese while looking at an English book during quiet time), but he isn't a fluent speaker yet; even though he sounds pretty clear to me, the speech-to-text feature on my phone often cannot transcribe what he is saying to the correct characters, and it does not have the same issue when I am speaking. I am hoping that reading will help with L's Chinese-speaking to improve its clarity/enunciation, the way reading in English has helped him to better enunciate certain words like "immediately" and "crayon." I also hope that having some basic Chinese reading skills will affirm his ethnic identity and build his confidence as a Mandarin-speaker. I thought I would share what has worked well with us thus far in our beginning home lessons. Right from the start, I decided to incorporate matching cards to help L with reviewing the learned characters everyday, both because long-term memory is not my own strong suit in learning and because I think it is a good opportunity to normalize a good study habit/strategy. Before we go into a new lesson, we always warm up by going through the deck of cards we have so far, for him to match each picture to a learned character (see below). Whenever possible, I try to make the definition cards pictorial only, because I think linguistically it's more beneficial for our brains to match a concept directly to Chinese, rather than from a concept to English, then to Chinese. As my son matches the cards, he also sounds out the character (since L already knows the language natively, this part is easy for him. I am trying not to introduce pingyin because I have read from other parents online that it can become a crutch to always be looking for the pingyin, when we want the kids to build direct visual recognition of the characters; I also don't want to confuse L when he is reading in English, because there are some differences between pingyin and actual English phonetics). After the matching warm-up, I usually collect the cards and put together a short sentence comprised of some of the characters that we have seen, then ask him to sound out the sentence from sight based on his visual knowledge of the characters. Today, I tried to orally dictate a sentence and have my son fish out all the characters from the pile to create that sentence visually. (I do this because he is too young for me to ask him to write the characters. We run his fingers along the printed characters in the book lessons to reinforce stroke recognition/memory, but I don't actually expect him to write out a character or a sentence independently.) I dictated two short sentences, and both times he did very well in choosing the right characters to formulate the sentence! I did not give him a new lesson today, since he was excited about reading our library books from yesterday. I feel like the consistency of practice, rather than quantity of characters, is what I would like to shoot for as we slowly build L's reading vocabulary. We are going about this casually, so every week we cover only maybe 3 or 4 new characters. At this rate, it could easily be 3 or 4 years before we finish the 500 characters, and I am mentally prepared for it to be a years-long undertaking, while determined to keep it fun.
I am excited to have made this decision to embark on this -- frankly, unexpected and -- ambitious journey with my son! Let's see where it will take us. PS. I decided to go with the Simplified Chinese curriculum, because as a Traditional Chinese reader, I am always frustrated by how prevalent the Simplified characters are, and it is not always easy for me to read them. I feel like L would have a better chance of encountering Simplified Chinese (which is used in Mainland China) in his life. Plus, teaching him would give me an opportunity of getting up to speed with recognizing the most common Simplified characters myself. In my previous post, I talked about how I noticed that my son had stagnated or maybe regressed in his math development at school for about 6 months, by the time he turned 3.5. I began taking an interest in working with him on math at home. I started with counting practice, and since he loved being read to, I wanted to look for some books to encourage and elevate his interest in math. Here are some books that have emerged as my favorites and a little bit about why I liked them. The first is One is a Snail, Ten is a Crab. Here is a kid reading it out loud, so you can see what it's all about. My son loved how silly it is, and he began to pick up on the pattern that if you are looking at 60, you can peek at the first digit to know that 60 is 6 crabs! He was able to look at 100 and say, after a couple of times through the book, that it would be ten crabs, because if we cover the last zero, what remains is 10. The book was an excellent bridge to us doing some practice on the western abacus. After we had read the book consistently for a few weeks, I got a free hand-me-down abacus from my neighbor, and we started playing with each row of ten on the abacus being a "crab." My son was able to say, "28 has twenty, and that is two crabs, or two tens!" and we would move two rows of the abacus over to get 20, and then count up single beads 21, 22, 23, 24, ... until we get to 28 (see picture of abacus below for 28). A lot of repetition later, he now understands both how to quickly represent any two-digit quantity on the (western) abacus, and how to look at the abacus and identify the quantity numerically. This practice has helped him to understand the magnitude of two-digit numbers, not just how to sound them out (which, if you recall, he mostly learned from being interested in riding busses). As the child grows, I can also see One is a Snail, Ten is a Crab growing with them, because the book actually also includes principles like counting-on from a known quantity and the commutative property of multiplication. The child in the video I linked to above does a stellar job explaining those mathematical connections. I would say this book is worth buying, even though I checked it out from our local library (and coincidentally got to keep it for several months, during their COVID hiatus). Another really great book that I have enjoyed is Press Here, which we also picked up for free, I think from a Little Free Reading Library. It is such a wonderful book that even my one-year-old daughter loves to flip through it and to read it with us. The book is highly interactive, and takes you through almost a video game-like series of interactions. It has some basic event counting, like, "Press the yellow dot 5 times," or "Clap 3 times!" and some qualitative math, like when you clap, the child can see that the dots grow bigger. It also has some pattern recognition, because on one page, it briefly mentions that two elements in a pattern got mixed up in the dark. It was a really great discussion with my son about how we can figure out which two elements are mixed up. Overall, we love this book and I would recommend buying it. My son learned to count collections of objects up to ten in school, mostly, but in terms of reinforcing counting at home, the books that I like are the following: Tumble Bumble, The Very Hungry Caterpillar, and Spot a Lot Vehicle Adventure. I love Tumble Bumble because it does counting-on, which is basically the idea that if we already know how many items we have (say, six), and we add one more, the child should be able to increment the existing count instead of counting all over again starting at 1. When I first started working with my son at home on counting, I noticed that no matter how many fingers I put up on my hands (say, I put up 5 fingers on one hand and 2 more on the other), he would always count starting from 1, even though he could already tell me that one full hand is 5 fingers. It took us a lot of consistent practice to count-on from known quantity, instead of starting over from 1 every time. Tumble Bumble counts the total number of animals without starting back at 1, so it makes a good math discussion, once your child is developmentally ready for it. I love The Very Hungry Caterpillar because it is a beautiful story that even very young kids can enjoy (we love many Eric Carle books here, mostly or all gifted by the grandparents, and even my one-year-old loves this particular book), but I also appreciate how the book is so cleanly laid out, so that on each page, we can count the objects in a different order (left to right, or right to left), in order to emphasize that the count remains the same no matter the order of objects. It is also very clever that the fruits being eaten in subsequent days physically overlap in this book, because you can visually see that 4 strawberries is just one more fruit than 3 plums, and that 5 oranges is just one more fruit than 4 strawberries. Developmentally, that understanding definitely comes later than simply counting the number of objects in a collection. Spot a Lot Vehicle Adventure is a good resource for daily practice of counting. The pictures are vivid, and there is a lot of stuff to count on every page, actually too much to get through in one sitting for a young child. My son loves vehicles, and for a while he wanted to read this book and count the objects in it every night before bed, and he would actually always count until he was exhausted and expired. There is not much of a story line in this book, and on some pages the objects are a bit tough to keep track of (because the instances don't all look the same), but it was still really good practice for him to try to stay organized by counting from left to right or from top to bottom in a page. Overall, I would recommend it if your child likes transportation and needs a little encouragement to count regularly and carefully. When my son learned to read, I bought him some beginning reader books to celebrate his accomplishment, and one of the books that I saw on a beginning readers' list is a math story called The Cookie Fiasco. I remember once gifting this book to a friend's child, so when I saw it on the list, I immediately ordered it, excited to have an excuse to add it to our collection. It has been fabulous for us! My son loves reading this book with me, and he now reads it to himself or to his dad. Because we have been regularly using the terms half and quarter with him while eating bagels at home, he is able to follow the math in the story and can tell me at the end of the book that each friend eats 3 quarter pieces of the cookie (even though the book never mentions the word quarter). Amazing! As a middle- and high-school math teacher who has seen so many kids intimidated by the idea of fractions, I love how this book contextualizes fractional division in a really fun way. Other math books that we enjoy include: Pete the Cat and His Four Groovy Buttons, which talks about zero and the idea of subtraction; Five Little Monkeys Make a Birthday Cake (there's not a lot of math in it, but my son enjoys observing that they definitely used too many eggs); and Round is a Mooncake, which is about shapes and has references to Chinese culture, which I appreciate, of course. We don't have this book, but obviously Five Little Monkeys Jumping on the Bed is also about counting down, contextualized in a story so the child can see that counting down corresponds to having one fewer. I think a lot of times young kids get exposed to counting up, but not as much to counting down in their preschool life, so anything we can do to encourage their facility with counting down is going to be great for their mathematical development. (For example, when we are lifting our two-year-olds out of the bath or out of the high chair, we can always count down, "10, 9, 8, ...., 5, 4, 3, 2, 1.... blast off!" We can make it fun, but this helps them to internalize the sequence backwards, which will make subtraction operations easier down the road.) Honestly, books and math -- what's there not to love?
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! It's fall, and I love fall. I love when the leaves change color; I love the breezy, dry fall days; and I love Halloween. This year, I wanted to make the fall season feel special for my children, even though they are not going to school. I decided to pull together Halloween costumes for the kids, even though trick-or-treating may not happen this year. I offered my son a few options: Elephant & Piggie; a train; something generic like a tiger; or a train signal. He was exuberant about the prospect of being a train signal, so we have been working on this costume together the last few days. He helped me cut, paste, paint, and color in parts of his costume with a marker. I had to let go of my perfectionist tendencies, but I am really quite happy about the joint effort thus far. (PS. My son proudly told my husband, "Dada, I colored this in. You see that C, I, and N? That's me. I did that." It's funny that he thinks it needs to be clarified. I also decided that we would make a series of Halloween crafts throughout the month, and use them to decorate our living room. (We have a little bit of reusable Halloween decorations that I can dig up, but I feel like it would be fun for him to make the bulk of our decorations this year, since he normally would do the same at school.) I found a site with lots of easy ideas here, and made a run down to Joann's Fabric to get supplies during my kids' naps this week. I helped my son make a spider with googly eyes earlier this week, and tonight we did a family crafts night after dinner, and made three different skeletons to hang up. Can you guess which one is my son's? We have also begun learning to read Chinese characters! I bought a single book from Sagebooks 500, which is like the Bob Books of Chinese, designed for native speakers who wish to learn the written language. I bought one booklet (Set 1, Book 1), used, from a local parent, for like $5 or $10. I wanted to just try it and see whether my son would be interested at all, because he has shown a lot of interest in speaking and practicing Chinese lately. We are only three days in, but thus far he has been really excited to do the lessons everyday! The system seems like it will work well for him, so much so that my husband who is really budget-minded has supported the idea of buying the entire system to be shipped to us internationally. (The entire system costs about $550, and teaches 500 of the most common Chinese characters. Similar to Bob Books, the kids are empowered to read illustrated short sentences and leveled books independently, after learning a new character in each lesson. It receives raving reviews from parents, but I still have not yet decided if I would order the whole system new or if I should hold out to buy it used.) I decided that I would start to make and use matching cards with L to help him reinforce his visual memory of the characters, and today was the first day that we used the matching cards I made, and he was totally into it! I would show him a picture, ask him what it shows, and he would say it to me first in English then in Chinese, and then go find the character that represents that object. Overall, I still really enjoy spending time with the kids at home everyday, and cherish this once-in-a-lifetime chance I have to be my kids' teacher. I have also signed up for a free online class on teaching early childhood math, that I think is going to be really helpful for me in terms of working on math at home with my kids and bridging the gaps between my identity as a mom and a high-school math teacher. I have just started the course, but I am encouraged to see that the early concepts in the course map almost exactly to what I have seen from my son, and what I have done with him at home based on my math-teacher instincts and research. More on early-childhood math later, but the premise of that online class is that most kids are ready to explore mathematics starting at age 2. That is absolutely what I believe already!
Besides the state of our country and the world, I have also been thinking a lot about home-schooling my preschooler. I began the home-schooling journey back in March, when we first decided to keep him at home. We are still paying for his daycare now, so it was always intended to be a temporary home-schooling setup, but this fall we decided to continue home-schooling, as I will not be returning to teaching in a classroom this year. (I am still doing some virtual/no-cost tutoring just to help out with families that have greater learning or financial needs than us, but it only happens a couple of times each week, while my two kids are napping.) We are still paying for his daycare for now, but emotionally I am prepared for the possibility that my son would be at home with me at least through January, and possibly through the end of the school year, which would land him straight in Kindergarten next year.
To begin with, I was a reluctant home-schooler. I feel confident about my ability to teach my child anything that I know, but I think 1. he needs the socialization that comes with being in a formal school setting, and 2. it is not necessarily good for him to advance too quickly in any academic area, because it could result in boredom with school down the road, or a fixed mindset about learning. But, given that my son was already home with me for months on end, I decided that we needed a little bit of structure to our days, in order for him to not start jumping off the walls. I followed his school's general structure of going outside twice a day to play, and designating regular lunch and nap times, and reading lots of picture books throughout the day, but I wanted the days to have a little bit of academic focus to tie the days together with meaning and purpose. I already had a book from my neighbors, called Teach Your Child to Read in 100 Easy Lessons, which I had kept because other teacher friends of mine had raved about it in teaching their own preschoolers to read. I am all for trying to do what I can, with what resources I have, so I started to slowly make our way through that book of reading lessons. Flash forward, my 4-year-old did finish it, but it was a bit of a painful process. It was a combination of his stubbornness and mine; on the days when he struggled with the mechanics, he would push himself to read two lessons instead of one, because he did not want me to tell him it was time to stop; and on the days when he was just clearly defiant, I would power through half a lesson just to stick to the daily routine. In hindsight, I should have obviously mixed up the extremely boring book lessons with hands-on activities and Bob books -- which I did incorporate subsequently, and I saw my son's engagement go way up, as did his reading fluency. Hindsight is always 20-20, but it is a little embarrassing to say this as an experienced teacher, that it took me so long to realize the format was not really working for my son and that there were better alternatives. In the beginning of March, I was just trying to survive each day. I came up with a daily schedule that was incremental by 45-minute blocs of time. I knew at all times of the day what we were supposed to be doing, and having a detailed schedule quickly brought routine and comfort to both me and the kids. (My baby was still home with me, but it was a big adjustment for her to have her big brother around all day, everyday. It was also a big adjustment for me, because my daughter had to receive help with completing PT exercises multiple times each day, because of her gross-motor delays.) I also decided quickly that we should do a variety of activities. Besides being outdoors regularly and reading lots of books, I also incorporated hands-on science activities and bought a book on how to use scissors for daily preschool cutting practice. Those first days flew by quickly, until the scissors lessons ran out and I was exhausted from trying to do super innovative science lessons everyday. So, we entered Phase 2 of homeschooling. I dropped science, and started working in more extensive actual play activities. My son was starting to enjoy jigsaw puzzles, so we spent a couple of months really working on his skills of thinking strategically to assemble new jigsaw puzzles. He was able to independently play for longer and longer, and we also worked actively on learning to ride a bike when we were outside everyday (with some bribes on my part, since my preschooler really is physically risk-averse). During this second phase was when we introduced a lot of dancing and singing, at first everyday, and then it tapered to when my son was feeling really in the mood for it. As my daughter grew older and more mobile (a little after her first birthday), I began to remove the play pen for a period of time everyday, to ease both kids into sharing toys together. Eventually, she dropped a nap and they got on the same nap schedule, and the play pen was stored away. I would say that, right now, we are in Phase 3 of home-schooling. The kids do a pretty good job of alternating between individual play (in the same space) and communal play. In the mornings, I still do an academic lesson with my son -- we alternate between practicing reading and doing some math each day, but the lessons only last about 15 or 20 minutes. (I will write about the math that we do on another day.) I am trying to incorporate more creativity into our days, because I don't want my son to grow up to be too rigid. A few weeks ago, we painted rocks and shells, and I was thinking up mime scenarios to act out with the kids everyday, to encourage my toddler's artistic risk-taking. Last week, we had a group chalk session, where I asked my son to contribute ideas to my drawings, and he in turn took some pieces of chalk and added on his own abstract contribution. (The baby also scribbled on the side, which is good for her fine-motor development. A few weeks ago she was not able to hold the chalk to make any mark, but I could see that she is getting stronger recently after a lot of fine-motor practice / OT.) In another post, I will talk more about the math that we do, because as a math teacher, I feel so passionate about exposing our young kids to math (either informally or formally, whatever you feel comfortable with), the same way you would expose them to early reading experiences! But I am also curious what has worked for you, if you have tried to "homeschool" your young kids? |
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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