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“Is my child learning enough math?”

It’s a question that bothers many parents, especially homeschooling parents. After all, being responsible for a child’s math education is a heavy load to carry.

There are two major things that can go wrong in math education:

  1. Students can be pressured, over-drilled, and forced to do a lot of symbol manipulation that doesn’t have much meaning to them. They grow to dislike math, and all the practice doesn’t seem to help them actually understand anything anyway. They become bitter towards math as adults, and describe at length the sadistic teachers and parents who ruined the field for them with their insistence on repetitive, empty exercises.
  2. Student get away with avoiding math and never really learn anything at all. (This is a particular risk in unschooling!) Having no real skills, they continue to avoid it as they get older, since, having no experience with the basics, they’re unable even to get started on thinking about more complicated problems. They end up being terrible at it, and describe at length the well-meaning but deluded teachers and parents who ruined the field for them by never insisting that they learn anything.

We have our Scylla and Charybdis in math education, and we run real risks if we over-pressure or under-insist. What to do?

To this question, there is an elegant solution: do math with your child every day, but don’t worry too much about exactly what kind of math you’re doing. Follow your child’s lead, and don’t sweat it if your child isn’t “where they’re supposed to be”; in fact, your main job is to find the kind of math that will be most stimulating and engaging for your child, and do that. If you do math every day and make it fun, you’re ahead of the game. Way ahead.

To do this successfully, we need to expand our notion of what mathematics is to include more than arithmetic. (This is a fringe benefit, and needs doing anyway.) Games, cooking, puzzles, measurement, patterns in art and nature; all these things touch on mathematics, sometimes quite deeply. Moreover, children tend to love mathematics naturally. It’s their nature, and ours, to make order out of our world, to seek patterns, to determine structure. It’s common for children to count for fun, to compare and classify different objects as a kind of game, and to seek mastery in mathematical thought from a very young age.

Think how wonderful this is! We’ve got young children already interested in math! Our primary goal is just to avoid ruining it for them! And how can we do math without destroying the joy of it? Play games, do crafts, cook, garden, role-play as salespeople, build with blocks, take stuff apart, ask big questions and let them ask big questions. And feel free to do arithmetic too–just don’t stress it. Let the child lead the way, and while you can gently nudge them in the direction you want them to go, be aware if they tell you it isn’t the right thing for them.

But Doesn’t My Child Need to Know X by the time they’re age Y?

An excellent question, and here’s the answer: if your child is doing math regularly and enjoying it, you almost certainly don’t need to worry. Now, if your child isn’t really doing anything mathematical at all, and watches TV all day, then you may have a problem. But if they’re engaged, you don’t have to sweat it if they don’t have all the formalities in place.

I’d like to quote from a summary of some studies on this topic.

In these studies formal arithmetic instruction was withheld in one group and administered as usual in another group. At the end of the experimental period, the comparative achievements of the two groups were measured. In each case the experimenter recommended the postponement of “formal” arithmetic…

On the basis of these and other studies the plan of eliminating formal arithmetic instruction from grades one and two, sometimes also grade three, has been adopted by a considerable number of school systems. In some systems there is not even an approved plan of informal or incidental arithmetic. Such a procedure fails to recognize certain very important facts about the studies referred to above. A careful reading of the reports of these four experiments shows that while formal practice on computational processes was postponed in the experimental groups, there was a great deal of use made in these classes of various kinds of activities, games, projects, and social situations through which the child was brought into contact with numbers and given the opportunity to use them informally in meaningful ways.

We have here, of course, the classic way that schools take a good idea and mess it up in the implementation. If you remove mathematics altogether, you end up with kids who can’t do mathematics. But if you postpone formal arithmetic until kids are ready for it (and hungry for it!), you can focus on the more foundational mathematics that they’re ready for and that lays the groundwork for real success in math.

So don’t worry about technicalities, but make sure they’re working with numbers, shapes, games, etc. “informally in meaningful ways.”

Should I use a curriculum if I’m homeschooling?

Sure, as long as it passes the acid test that the child is excited to work from it. If you hear them saying that they hate math, then you need to change things up.

What do we really want here?

That’s a question for you. What do you really want your child’s relationship with math to be? And what it is now?

Comments 11

    1. Post
      Author
      Dan

      I have, Sue, and I wish I hadn’t. For a while, I was having some serious doubts about homeschooling because I was seeing students with virtually zero exposure to, ability, and confidence in math. Then my sample size increased: I’m much more positive on homeschooling now. But category 2 is a real thing.

  1. Stephanie O

    Thanks for this info and support! I’m homeschooling my 7 year old son (he’s never been to school), and this is how we’ve been approaching math. Once in a while I wonder if I should really teach him the standard algorithms for addition and subtraction, but I want him to see why we need them before we learn them. For now, we’re using a “living math” approach, talking about math, and doing mental math (see livingmath.net for lots of amazing resources in categories by age and math topic). With Ed Zaccaro’s “Primary Grade Challenge Math” and “Math Without Words” (http://www.lulu.com/browse/search.php?fListingClass=0&fSearch=math+without+words) as our current primary sources, we’re just playing with math. I do the writing when we need it, but I’m using “you’ll be able to do better math problems” as a hook to keep him practicing handwriting. Who knew math could motivate handwriting? It’s fun to see him wanting to learn the multiplication tables so he can solve problems faster without doing so much addition in his head, and it’s cool watching him figure out problems with simple fractions (only dealing with 1/2 and 1/4 for example) in his head. I can see it working…

    1. Post
      Author
    2. Chenebe

      Hey Stephanie,
      Our approach to math is so similar to yours, what you wrote could be a description of what we do. I also use math to get my son to do writing, too! (actually we started “talking math” from very young because I didn’t want to not start math just because he couldn’t hold a pencil properly to fill a worksheet – and we haven’t looked back since). Another interesting off-shoot was that we recently picked up a foreign language and he immediately dived into counting numbers, figuring out the quirks of the Chinese number system, and he’s started calculating in Chinese too. Again, who would have thought math could be used to help learn a language!

  2. Stephanie O

    About “category 2″ – I’m an adult who falls into category 2 with respect to history, actually (and I went to public school and graduated from Caltech). I was a math and science nerd in school and in college I took things like “history of cancer and cancer research” instead of learning any complete story of how our civilizations came to be. I’m very comfortable with a relaxed and interest driven approach to math, because I can see math all the time in our everyday activities. I can’t do the same for history because I don’t know any, so I found a good, age appropriate, complete curriculum to do with my son. Since I’m learning along side him, I *can* start to see hooks in everyday life to history. If I knew that material already, I might be willing to go with a more interest-driven approach in that subject.

    I’m not sure how exactly to relate this to math-phobic parents. If they’re willing to learn along with their kids, they can probably use a primarily-interest-driven approach, but I understand how they would be worried about finding enough math in the world when they can’t see it themselves. I also understand if math phobic parents don’t *want* to jump into learning math. I’m only learning the history because I have to listen to audio lectures with my so to keep him on task listening. If he were more independent, I may not be learning along side him…

    1. Post
      Author
      Dan

      Thanks for the comment, Stephanie. I think that a good curriculum can be invaluable, and the best test is whether you (as the parent/teacher) enjoy working on it too. It’s great that you’re able to encourage your child in history even though it isn’t a passion for you. I think parents can do similarly in math.

      Honestly, when a parent is deeply math-phobic, it can be challenging. The best way to get your child interested in something is to be able to have fun doing it with them.

      However, even if math (or history) isn’t your subject, and whether or not you’re using a curriculum, I think that there’s a way to cultivate the right habits of mind in your child. Mainly, the person who never found anything they liked in a subject needs to remember that it doesn’t have to hurt to be good for you.

  3. Sue VanHattum

    Hmm, I’d love to talk about details with you. I have some great chapters in my (soon to be published) book by unschoolers, who suggest letting kids follow their interests. I am curious whether the kids you met were behind on other areas too, whether they had experiences that made them uncomfortable with math, how old they are (sometimes kids are just on a different timetable than the school timetable we know best).

    Interested in chatting on the phone?

  4. Katrina

    #2 has been a concern of mine ever since I set aside the Saxon math for my then 6-yr-old because he was becoming #1. Even though I substituted games for most of the drill I found it more rigid than I wished, and since, according to Saxon placement tests he was doing “1st grade” as opposed to “kindergarten” math, I felt I had time to try a different approach. My desire is for my son to feel very comfortable around numbers, comfortable in manipulating them, and constructing and desconstructing them in MANY ways. Gregory Tang’s books were eye-openers for me because I had never looked at numbers in this way–I still find that sad. (And although my son is familiar with the symbolic forms, I rarely write anything down at this point, it’s primarily mental math.) However, because math doesn’t come naturally to me, I lack confidence, especially since there is more to math than numbers; I use blogs such as this one and others to help me identify our strengths and weaknesses. I find it takes considerably more work than using a packaged curriculum but provides, in the case of my son, better results. Recently, using only index cards, I combined Peggy Kaye’s Grasshopper Math (from Games for Math) with Cranium Hullabaloo to come up with what I call MOVE! Math. I became sick of it he wanted to play it so much (we take turns), and I can make the index card directions anything I want; he even writes some of them. I still sometimes miss the “reassurance,” false though it may be, of a linear curriculum, though.

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