|The original problem was 72 + 47.|
Some noticing and wondering:
- These students have underlying issues with place value.
- All these students have seen and used base-10 blocks. They've been taught to add, subtract, and multiply using partial sums, differences, and products. For some reason they default back to a traditional algorithm, even though many of them haven't even encountered the traditional algorithm yet. So they must be picking it up somewhere. Maybe on the bus?
- Are these examples of what I've heard called over-reliance on the traditional algorithm?
- All of the answers are wrong, but some egregiously so, like 1,000- 500 = 1,500. Or 37 x 35 = 245.
- Is there a difference in the way kids do these kinds of calculations when they are presented vertically vs. horizontally? Has anyone done any research on that?
- These are not necessarily representative; many kids can add, subtract, and multiply multi-digit numbers just fine. But do we confuse some kids by attempting to teach them multiple ways to do these multi-digit calculations? Are some kids better off just learning one way? Or at least one way at a time? This is something I hear quite often from teachers. Are they right?
- Graham Fletcher, in his addition and subtraction and multiplication progression videos, urges us not to rush students through conceptual stages of understanding. My guess is that what we're seeing here is the result of such rushing. It's also likely that there are students who are calculating correctly by following the traditional algorithm, but have little or no understanding of the underlying concept. Masked by correct answers, their misconceptions go undetected, and that is just as troubling as what we see above.
|And there's always this.|