Several friends have written to ask me about the Common Core check story as well as the follow up post by Hemant Mehta:
The short answer is this – math education debates exhaust me . . . .
Here’s a longer answer.
We taught the kids at home until this year, and now they are attending the local public schools in 4th and 6th grade. Other than making sure that they’ve completed their homework, I don’t pay that much attention to the math the kids are doing in school. Instead I try to find fun supplemental activities to do with them such as our “Family Math” projects on this blog.
I’m sure, though, that there will be some point where they ask me about their math homework and I will be in the position of not really understanding what they are being asked to do. At that point I’ll put Tom Lehrer’s “New Math” on the playlist and they hopefully take the approach that Mehta did by spending a few minutes on Google trying to see what’s going on.
For the specific example that caused all of the fuss here – “ten frame” cards – I’ve never heard of them before reading Mehta’s piece. Thanks to Mehta I get the general idea and understand why someone might want to spend a little time talking about numbers with kids using the idea. The general idea isn’t something that I think is new at all, btw.
My Montessori pre-school in Omaha (so, 1975 ish) had a big collection of red and blue rods that were used to represent numbers. Maybe they were unique to my school, or maybe lots of schools had them – I honestly have no idea – but I loved playing with them. Sister Lorraine used them to teach me math all the way up to division. Maybe my parents were so frustrated by this approach to learning about arithmetic that sent checks to the school using blue and red rods, I’m not sure, but for me they were a fun way to think about numbers. Also, those rods from 40 years ago don’t really seem that different at all from the “ten frame” cards being discussed this week.
While teaching the kids at home I used several different geometric ideas to help the boys think about and learn about numbers. Three examples come to mind as I’m writing:
(1) For learning place value, we spent a lot of time talking about numbers in different bases and made a “binary adding machine” out of duplo blocks. This was a really fun activity that I probably spent two weeks on with both kids:
(2) When we learning about dividing fractions, we also turned to numbers represented by blocks to see what was going on:
(3) Lastly, I used a representation of numbers in rectangles to show why a negative number times a negative number is a positive number:
So, representing numbers is ways that don’t seem like numbers doesn’t bother me that much. You never know what is going to grab a kid’s attention – those red and blue rods from pre-school sure grabbed my attention. 40 years later I’m still happy to use non-number representations of numbers if it helps kids learn math.