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-skillsI’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?**

February 2, 2018 at 7:01 am

Your posts recently all seem directly related to what I’ve been thinking about! I have a kindergartener who loves math too. He taught himself multiple digit addition and subtraction. Oddly, he doesn’t carry numbers but has this system he taught himself that rounds numbers, and then he uses either subtraction or addition to calculate the smaller numbers. It doesn’t make intuitive sense to me but he does it quickly. Right now he has a blank notebook, and I just write random equations, which he then figures out. He can also do basic multiplication because he’s good at counting by multiples. And he wants to talk about numbers ALL the time. I’m thinking that maybe I should get him one of the books you’ve mentioned. It sounds like he’s at the same level as your DC2. Would you recommend the Singapore 1b book for him?

February 2, 2018 at 7:09 am

That’s very Singapore. :)

He might be able to start on Singapore 2a. There are placement tests on their website that he can take. http://www.singaporemath.com/Placement_Test_s/86.htm

Also: I cannot recommend DragonBox apps enough (if you have the hardware for it). They are brilliant! He might also enjoy the Algebra and Geometry apps too. (Geometry is especially fun– basically guides people through proof-based geometry without using words.)

February 2, 2018 at 7:32 am

Thank you for these suggestions! I’ll have him take the placement test when he gets home from school. He’ll be excited! And I’ll look into the DragonBox apps too. We haven’t done too many digital games like that because my 2.5 year old gets too interested once any electronic device gets turned on, and it tends to causes too many distractions.

February 2, 2018 at 10:00 am

I think I looked at Dragon Box before and thought my gal was too young for it. Looking deeper, she is definitely ready (and has been for awhile), so I’ll buy some of those tonight. Thank you!

We love this app for younger kids for building shape awareness (and, honestly, I think early math awareness with sizing). It’s called Shape Gurus: https://itunes.apple.com/us/app/shape-gurus-teach-shapes-for-my-preschooler/id1015403712?mt=8

Fun and not annoying! I actually enjoying doing this too and seeing the shapes they have available.

February 2, 2018 at 10:04 am

Dragon Box hasn’t had Numbers and Big Numbers for very long, so it is entirely possible that you thought algebra and whatever they call the geometry app were too old.

Yay learning apps!

February 2, 2018 at 12:55 pm

yes, I’m stoked for numbers and big numbers! She will definitely be able to do numbers. We are driving an hour tomorrow to go to a hockey game, so she’ll get some app time in the car.

February 2, 2018 at 4:41 pm

Big numbers is more fun than numbers, but numbers is fun too. Yay!

February 2, 2018 at 10:19 am

I’ve got nothing on the math question, although this is a nice reminder that I need to get off my butt and figure out what math enrichment we’re going to do with my 5th grader since her school math isn’t really challenging her.

Mainly I’m commenting to roll my eyes at the people who give you dirty looks for doing math in public with your kids! We sometimes play a spelling game to keep our 2nd grader happy while we wait places (I name a word, she spells it, she wins if she gets 5 right before she gets 5 wrong) and no one has ever given us a dirty look for that! We get approving smiles and compliments for not just pulling out a screen (which… uh, we do a lot, too. Sometimes the screen’s not handy is all…) People are so weird about math.

February 2, 2018 at 10:39 am

I haven’t tried spelling games, but DC1 has had better spelling than I do since zie was 6! (I’m still beating out DC2 on spelling, and my pronunciation is much better than DC1’s mainly because I’m not as wed to phonics. Sadly, DC2 seems to have inherited my mild undiagnosed dyslexia.)

February 2, 2018 at 12:45 pm

Do you think it’s just a matter of making the games (apps/workbooks) available and seeing what they do? Or do you encourage a steady effort at them on a regular basis? Or engage in active teaching? My approach to literacy has been to 1) read outloud a lot and 2) put apps (with approaches I know to be valid) on my kids ipads and then when they are having screen time to just let them have at it. This seems to be working in reading because my pre-k kid is “getting it quickly” according to her teacher. Math… hmm… I am not convinced I know how to evaluate math apps or my child’s math aptitude. And she has discovered that the ipad can hold tv apps and not just school apps so it requires actual attention to keep her on things that are challenging and at the edge of her abilities. Thoughts? Did I mention that persistence isn’t her strong suit? So should I focus on like 10-30 min per weekend day of educational apps before moving on to other ipad time (note that weekday ipad time is close to 0 just because of our schedules and weekend ipad time is usually 30-90 min). I guess my question is — how much of what you are describing is making interesting toys/tools available and checking out and how much is deliberate cultivation of something you observe as a strength?

February 2, 2018 at 4:43 pm

I don’t know—it probably depends on the kid and the parents.

Re: tv apps— we had to delete them off the iPad.

February 2, 2018 at 5:05 pm

I think it really comes down to how much your kid will drive this, and if that’s enough to hit the skill levels you’dlike to see.

Our older daughter essentially taught herself to read by watching some Leapfrog DVDs she loved. We would do word games with her using the foam letters in the bathtub, but that was really driven by her.

Our younger daughter was less self-motivated on the reading front, hence the spelling game. Her classroom instruction is all in Spanish, and we were getting impatient for her to read more fluently in English, so we started pushing a bit more.

On math, we haven’t really pushed yet, but we’re pretty happy with our school math curriculum, so we haven’t felt the need, until now (with the older one about to go to middle school). My main motivation for enriching math now is that I know that high school is a time when a lot of girls lose math confidence for all the crappy cultural reasons and I want to boost her up before that hits.

February 2, 2018 at 5:08 pm

Those leapfrog dvds are the BEST. The a says ah, the a says ah….

Does one of the local unis run a math circle? The one DC1 goes to is 100% fun math. Zie came home with a Klein bottle last week.

February 2, 2018 at 3:30 pm

Mom taught me math at home as a bit of punishment for being a smartmouth. It worked mostly as a distraction and I wish she had time to teach me the rest of the math that I had to learn at school, unsuccessfully. The way they taught made no sense to me and we’d like to avoid that happening with JB.

I’m now using counting as a fun way to distract JB when I need zir to stand still for a minute, and we can work up to using zir magnetiles to show fractions. Please keep sharing what you’re doing to teach math everyday, I avoided it so long that it’s not easy for me to incorporate it naturally.

February 2, 2018 at 4:38 pm

Math is a reward! CA’s current math curriculum is pretty good, so hopefully it will work out! :)

February 2, 2018 at 5:00 pm

A big part of ALL math is pattern recognition. It’s just that when you get into more advanced stuff the patterns are more abstract. Learning to generalize is probably more important than is any specific set of techniques for carrying out basic operations.

February 3, 2018 at 12:43 am

I was teaching my children from the time they were born, using their fingers first and saying numbers. My son had cars and blocks and they were the manipulatives we used. I named everything and used colors to describe–two red cars, etc. He demanded I tell him about “half.” I tried cutting a paper plate in half, but he really got the concept when I was giving him half a Hershey bar and the other half to his sister. They were both very bright children so teaching them was easy.

March 9, 2018 at 8:13 pm

Hi – I was trying to figure out how to submit the “ask the grumpies question” – hope it’s OK if I just post it here. Sorry!

Math questions here – need recommendations about extra math practice.

I have a kid who is not gifted, but in the normal-bright range. He is having a tough time with math (3rd/4th grade): he grasps new concepts just fine, does well on tests… and then 2 weeks later he can’t remember any of it! His school math program seems to fly from topic to topic, and even though his teacher assures me that even if he missed something this year, all the same or similar topics will be revisited next year, I worry that he hasn’t had the chance to master the basic concepts. It’s more of an issue with retention of the material than understanding the concepts. I know you love math – do you have any suggestions as to what books or methods may be helpful to practice 3rd-4th grade math? I believe it is so important for kids to get solid foundation at the elementary-school stage.Teachers simply shrug and say it’s the student’s responsibility to practice old material (well, I do agree with that) and point to Khan academy. The school is using the Envision Math program. I am terrible at explaining but love doing math puzzles and fun problems together with kids – and that doesn’t seem to be enough.

On the flip side of the coin – I have a second grader who is doing really well in math and needs more challenge. The teacher gives her additional (optional) higher-level worksheets, but my daughter doesn’t seem to be thrilled about those and prefers to read or draw. We are doing some fun logic and puzzle games at home, but maybe you have additional advice on fun math activities (books, games, workbooks) that provide additional challenge without being too much like homework?

March 9, 2018 at 9:13 pm

I can answer this quickly now and in more detail later—you want Saxon math for the older kid. If you click the math tag you should be able to find posts more applicable to your younger.

March 9, 2018 at 9:44 pm

Thanks so much! Will look into Saxon math and will check out your other math posts.

March 10, 2018 at 7:08 am

Reading up on enVision– you might instead benefit from going exactly the opposite direction and doing Singapore instead. The question is whether the enVision is too shallow (in which case Singapore would be the solution) or if there’s not enough repetition in the same year (in which case that’s what Saxon math developed made for). There are a lot of people online arguing that kids don’t retain enVision because it’s too shallow, and the annual repetition doesn’t go much deeper.

I will say that Singapore is a ton more fun than Saxon. But Saxon is really good for not letting kids forget concepts after each exam.