Educating Risa

Over the last while I’ve been feeling like something isn’t quite working in our math curriculum. While we do lots of fun activities in math, we’ve been using Math-U-See as a spine in this area, along with a few other workbooks from the Critical Thinking company. While Daegan LOVED Math-U-See Primer last year, and booted through the material at quite a clip, Math-U-See Alpha has been a bit of a slog. Don’t get me wrong: Steve Demme does a great job teaching the material on the DVDs, his explanations are clear and he uses lots of mental math and teaches for understanding—but the whole Alpha workbook learning nothing but basic addition and subtraction facts is quite a shock after the way Primer skipped around from one subject to the next (counting, addition, subtraction, place value, baby algebra, geometry, time…just to name a few). I realize now I should have pressed on after Daegan understood a concept, even if he didn’t have all the addition/subtraction facts memorized. I really don’t know why I let us get so bogged down in “drill and kill”. I never taught that way in school, and I personally found doing puzzles like kakuro, or playing math games like “make ten go fish” much more effective in the long run in solidifying the facts. I’m pretty sure my own strong math skills are directly related to the number of card games I played regularly with my family growing up: cribbage and canasta my two faves, among countless others, along with board games. Oh well—sorry Daegs. Raising eldest children is a bit of an experiment. Live and learn.

I also recently read a book about teaching math, and one part really resonated with me: in Asian countries, a class—even in elementary school—will spend an entire lesson discussing, puzzling over, and working cooperatively on ONE problem. Not countless worksheets and timed drill of “mad math minutes.” So I started thinking about how to build more of that into our day, and somehow stumbled across this site for DynaMath magazine. The “problem of the day” pages caught my eye. I dipped a toe in by writing a problem on a whiteboard to start us off one morning, a question easy enough that Gareth was able to join in. (Day 20 here). And the next day, with a question Daegan found harder. (Day 6 here). Things got even better a few days later, when I put up a problem I knew would be a stretch: baby algebra. I adapted it from Day 17 here).

3 shamrocks = 1 leprechaun

4 leprechauns = 2 pots of gold

How many shamrocks equal 1 pot of gold?

Daegan and I solved this two ways: using manipulatives, and then again by drawing on the board. He chose his dark green cuisinaire rods to represent shamrocks, light green for leprechauns, and yellow for pots of gold. His first step was to use the rods to show the problem using these physical objects:

Our next step was to figure out what 1 pot of gold was equal to. (Recall, we need to know how many shamrocks equals 1 pot of gold.) Daegan was able to see intuitively, and with no help from me, that if 4 leprechauns (light green) = 2 pots of gold (yellow), then 2 leprechauns = 1 pot of gold. Which told me he has grasped ideas about division, ratios and multiplication…well beyond addition/subtraction facts!

So how do we relate this fact (2 leprechauns = 1 pot of gold), to the info we have about shamrocks (3 shamrocks = 1 leprechaun)? Daegan went to work changing the shamrock equation into one involving 2 leprechauns, by doubling. If 3 shamrocks = 1 leprechaun, then 6 shamrocks = 2 leprechauns.

Now, by transitivity—and Daegan could see this intuitively, he doesn’t know this term!—since 6 shamrocks = 2 leprechauns, and 2 leprechauns = 1 pot of gold, then 6 shamrocks = 1 pot of gold.

And then I added the final step to our Problem of the Day focus: I asked Daegan if he would like to construct a similar problem. He jumped at the chance! And having him create problems, and not just solve them, will allow me another way to see any gaps or errors in his reasoning. Daegan created the following—dictating to me—and then solved it intuitively and created a drawing to show his reasoning:

 

Note the period (.) between the three small pea pods, as they help make sense of his drawing.

We will keep doing these Problems of the Day (though not every day) and have Daegan (and eventually Gareth) create their own problems of a similar sort. The challenge of creating something to try to stump Mom is quite appealing for my two!