How We Do Maths: Daily

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After having read What’s Math Got to Do With It? by Jo Boaler, I posted previously some notes and excerpts from her book about the state of math education in the United States and her recommendations on what parents could do to promote math literacy at home.

I ended that last post with a promise to describe what I personally am doing as part of homeschooling my seven-year-old son (my two-year-old daughter mostly just tags along and picks up things by osmosis). It’s certainly a work in progress and not a generalizable program that I’d recommend anyone else simply plug into, but I’m going to list a lot of resources I came across that hopefully might be of interest. To make it manageable for myself, I’ll do it in chunks. Today: what I do daily.

Overall Objectives

It’s important to know what your objectives are, first. Biggie is mostly ahead of the curve already in math, at least by Common Core standards,, so the pressure is off in terms of establishing familiarity and mastery of some foundational skills. I also have the advantage that Biggie is not math-averse and likes puzzling out computations and problems, for the most part. So my goal is to keep up that enthusiasm, stoke his curiosity and interest, and reinforce some key grade-level concepts — especially, place-value in base-ten notation, measurement, shapes, and arithmetic computation (addition and subtraction mostly).

I currently have a plan to do a daily math exercise, a weekly math project, and occasional forays into math-enrichment events as the opportunities present themselves. I’m also keeping my eye out for most intense, perhaps more structured, programs for the future.

Daily Problems

In absolute honesty, we actually don’t do this absolutely every day. Things are not that nailed down yet, but this is what we’re working towards.

So (most) days, we tackle a problem from Bedtime Math. Every day a short article about something interesting or topical is posted, accompanied by suggested math activities for “Wee Ones” to “Big Kids.” You can also get these posts in a daily email, a tweet, or on their mobile app. We usually go straight for the “Big Kid” problem, which is just about the right challenge-level for Biggie. Most of the problems are not brain busters but fairly straightforward computational problems—but ideal for number talks.

Here’s a sample problem we worked through:

If a family pays \$24 total to bring their 6 dogs into the pool, and each dog costs \$3, how much extra did the people pay to swim themselves?
from Pooches in the Pool

You can see from Biggie’s original scratches–and my notes from our subsequent conversation–that he first computed how much it cost for 2 dogs to be in the pool, then 4, then 6. Once he figured out all the dogs cost \$18, he confidently announced that the people had to pay \$6. I had to then talk him through how he got that answer, and I took notes in mathematical notation so that he could see how his process got visualized. We then talked about how he could have grouped the dogs in different ways, by 3s instead of pairs, or 4+2.

Here’s another one:

If every 3 regular crayons can be melted to make 2 fat triangle ones, how many new crayons can he make from a dozen regular ones?
from Giving Crayons a Second Chance

Biggie first noted that 3 crayons yield 2 triangle crayons. He then worked in additional increments of 3: 6 crayons yield 4 triangle crayons, 9 crayons yield 6 triangle crayons, 12 crayons yield 8 triangle crayons. I then showed him this is essentially doing the process four times, that is, multiplying the equation throughout by four.

You may be wondering why I don’t do more, like, say, assign a worksheet of problems. Flippantly, I might refer you to the previous two posts in this series on teaching math. In short, though, building up algorithmic fluency in solving certain kinds of math problems is not really a priority of mine. I don’t really care that Biggie becomes really good at adding up two-digit numbers automatically, without any help or discussion. And building up that capacity risks making math tedious and hateful to him.

What’s more important to me is that he understands how he can use and manipulate quantities and relationships to solve problems. Maths. That’s why our daily exercise focuses on having a brief but involved discussion around solving a single problem. And guess what? More problems naturally and inevitably arise throughout the day (calculating tips, estimating distances, etc.) Our Bedtime Math problem is simply the routinized formality.

For example, we were reading this Wonderopolis article on how chocolate is bad for dogs, which mentions that dark chocolate has three times more theobromine than milk chocolate, baker’s chocolate has three times more than dark chocolate, and cocoa powder has twice as much as baker’s chocolate. Naturally, I want him then to suss out how much more theobromine is in cocoa powder than milk chocolate:

I do understand the benefits of developing computational mastery and speed, however. To stave off some of the negative side-effects of drill-and-kill practices, though, it makes sense to me to gamify the process. I’m currently having Biggie go through and systematically vet iPad math games and apps during the time he has to himself while his two-year-old sister naps. I’ll report my recommendations in the future.

I expect that by next year or so, Biggie will have outgrown these Bedtime Math problems. A more sophisticated alternative might be to do Estimation 180, a series of ongoing estimation challenges developed by a middle school math teacher, or Visual Patterns, a gallery of pattern recognition and prediction problems. Both of those web sites include copies of handouts that you can use or use as a template to guide your mathematical discussion.