Leah asks:

How did DC2 learn so much math? And when did you start? We’ve started discussing addition using finger counting or counting treats, but I’m not sure my little gal is picking it up yet. I sometimes wonder if I should be doing something more formal (or trying more) or if it’s fine to just chill. I do fractions and percentages when we cut nails (1 nail done, that’s one out of ten, or 1/10th, or 10%, etc).

So, this is based on a comment from a post about how my DC2 is age 5 in kindergarten and is doing multiple digit addition and subtraction with carrying and borrowing as well as some simple multiplication (no times tables memorization yet).

First off– I can’t take much credit for the multiplication. DC2’s Montessori taught all the “big” kids multiplication. This is pretty standard in a lot of Montessoris and I think it is part of the curriculum, though I do not actually know how it is taught.

Here’s some suggestions from people in the comments:

Becca says:

If you don’t know about Bedtime Math yet, get the app or the books :-)

A big part of very early math is pattern recognition. Grouping items according to different criteria, making designs with blocks or beads are good things to do.

The vocabulary of positions (over/under) and sizes (bigger/littler) and so on can also be good to get down early.

Other stuff, from a pretty evidenced-based group: https://www.zerotothree.org/resources/299-help-your-child-develop-early-math-skills

I’m also a firm believer in counting during swing pushing at the park. It gave me something to do, and gave Roo exposure to numbers bigger than 100 (ok, so we may have both had an inordinate patience for swinging).

I have to admit that we own the first Bedtime Math book (on Laura Vanderkam’s recommendation, along with Family Math, if I recall correctly), but we haven’t really used it. DC1 already owned Aha! and Gotcha! (and had kind of outgrown Math for Smarty Pants), so we briefly looked through it but really had outgrown it. I haven’t dug it out of DC1’s bookcase to try with DC2. Maybe I should.

We have two different sets of brightly colored manipulables that I will dig out to play math with the kids with. One set is a set of pixel-blocks that DC1 loved to play with. Zie has always been into small things (and not into putting things into hir mouth), so pixel blocks work well for that (not safe for many small children!). DC2 prefers a set of bigger circular pieces that DH initially bought to use as game pieces for game design (I can’t easily find them on amazon, but there are a lot of reasonably priced options if you search for manipulatives). We also have lots of fun toddler sorting games because apparently I never grew out of them. (I may be messy and disorganized in most of my life, but I find sorting to be extremely soothing. This is part of why my bookcases and spice cabinet are beautifully alphabetized.) Back when we had access to swing sets (our town has removed them all for “safety”/lawsuit reasons), we definitely counted pushes. Once my kids were able to talk, I would ask, “How many pushes do you want this time?” and then I’d count out that many pushes and ask again.

omgd says:

I started trying to introduce fractions by talking about sharing. As in, “There are 6 apples and your friend takes half. How many do you have left?” She doesn’t really get thirds or quarters yet, but I think it’s because of the vocabulary.

I have to admit, I haven’t really thought about teaching fractions other than what DC2 is getting in hir brainquest book. They will become more prevalent in the Singapore book a book or three from where DC1 is right now [Update: the day after I typed this, DC2 had to color in halves and quarters in hir Singapore Math 1b book, but only for a couple of pages].

Ok, now back to me:

When my kids are bouncing off the walls someplace that they shouldn’t be bouncing off the walls, we practice counting. When counting is too easy, we practice skip counting. When skip counting becomes too easy, we will practice multiplication. Then division. I use this technique with my brilliant but overly energetic nieces and nephews who are too excited at being with extended family to be controlled by their parents. (Back when I flew Southwest, I would keep the small children I invariably ended up sitting next to given my need for a window seat occupied by figuring out what their math level was and teaching them the next thing. There are kids who learned long division from me because I wanted them to stay still!)

I LOVE Singapore math SO much. It’s really great because it sneakily builds up to future concepts. Examples are chosen specifically to help the subconscious pattern-match to figure out new things that won’t be introduced for chapters. It is lovely. Plus they teach a lot of really great mental math techniques that those of us who are really comfortable with use automatically (things like realizing that 10-1 = 9, so sometimes it’s easier to mentally add 10 and subtract 1 than it is to add 9 directly). I am extremely impressed at how much facility DC2 has with numbers right now. Here’s me talking more about the workbooks the kids do.

DC2 had learned the borrowing and carrying from Brainquest (and me)– we spent about a month slowly cranking through double and triple digit addition and subtraction. There are a lot of problems on a page and I would have hir just do 3 a day once we got to carrying and borrowing. But zie wasn’t really facile with it until we got Dragonbox Big Numbers which is an enormously fun and addicting game (I finished it, but I still sort of wish I could be picking apples now. It is a really great game.) DC2 sped through it (as did DC1 and I– I finished first, then DC2, then finally DC1 sometime after that English project finished [for those who are curious, it wasn’t interpretive dance next… they’re doing another powerpoint (or, she suggests, PREZI UGH) use MOTION!… and a bunch of other suggestions that are super bad powerpoint etiquette].) By the end of Big Numbers, DC2 was a multiple digit addition and subtraction wizard.

DC2 is mostly through DragonBox Numbers right now and is really good at it, but it’s not really as much fun as Big Numbers was, and it’s got some bugs which are irritating.

And, as I said earlier, I do break out the manipulables a lot. Sometimes we use them to illustrate a particularly tricky workbook problem, but sometimes we just have fun doing number patterns. We’ll also do patterns with fingers. I really like playing games with these and making 10s. So you start associating 3 and 7, 4 and 6, and so on. We can also do grids of squares and rectangles with the manipulables to get used to multiplication (which I did more with DC1 than with DC2 because DC2 came home from preschool one day completely understanding multiplication). There are a lot of fun ways to mix and match numbers and different colors to get an understanding of the patterns (and the beauty) of mathematics.

We also give the kids an allowance at a pretty early age, at first so they can get familiar with money and learn the denominations of coins and dollars. (After the sticking random things in mouths stage though!)

Later on, I will introduce Hard Math for Elementary Students, but DC2 isn’t ready for that yet. DC1 is really enjoying Hard Math for Middle School right now, as well as Saturday Math Circle, and zie just started doing every other week competition-based Math Club once a week after school, though zie is skipping the competitions this year/semester. (Mainly because the first qualifying one is at the same time as a birthday party! But also partly because zie does math for fun, not to compete.)

Later on, DC2 will also get introduced to Martin Gardner and Aha! and Gotcha! But not yet.

Should you be doing more or is it fine to chill? I’m sure it is fine to chill. But I can’t not teach math anymore than I can not drink water or keep from breathing. It’s my nature. It’s what I do. And I gotta say that counting/practicing tables is the best for getting kids to behave while waiting for food at a restaurant, though occasionally it does get you dirty looks from other people who think you’re somehow harming your precious child or doing this to show off and don’t realize how much the alternative would interfere with their dining experience. (Pro-tip: It is often more fun when you trade off saying the next number, especially when sometimes you get it right away and sometimes you pause dramatically to think for a bit. This also helps them to notice that skip counting by 2 is literally skipping every other one, and that skip counting by 10 is the same as every other 5. It’s pretty amazing when they make that Aha! on their own.)

Oh man, I love math so much.

**Grumpy Nation: What are your math teaching tips?**