Addition Division Multiplication Numbers & Operations in Base 10 Subtraction

Some Numbers and Operations in Base 10



Explanations? What lessons are there about the way kids think in this work?

10 replies on “Some Numbers and Operations in Base 10”

Here’s something that I’d add, as a bit of a hypothesis: many (most?) students read (and register) numbers before they register the operations.

If this is true, then there is a whole moment when the mind can jump to conclusions between when the numbers are read and the operations are read. This could help support the idea that many math mistakes involve students having an association with certain numbers, e.g. 100^1/2 = 50.

Adding is a relatively easy concept. The affect of [other] operations on quantities is underemphasized as a component of number sense in the majority-implemented pedagogical approach of implementing procedures over conceptual understanding. Or so I’ve come to hold as a personal belief.

I think I see this happening with some of my kids with learning disabilities (officially identified or not). What you describe sounds similar to the way we read (mostly); not letter by letter, but in chunks. Our mind fills in the blanks based on our experience of associations. I think that is why highlighting helps; essentially it forces the student to read symbol by symbol instead of in chunks.

Wonder if we would see different responses if you used words rather than symbols: i.e. “What’s 39 divided by 3?”. The student may see the symbols as all equivalent, or may be just ignoring them after the first problem. But can we differentitate the symbolic issue from a mechanics issue?

I think they see the first addition problem and then think “this is a bunch of addition problems” and don’t read the subsequent ones carefully enough. Or maybe adding is what they know how to do, so they do it!

It seems like this goes hand in hand with reading directions. Many students don’t read the directions, they look at the first problem and think, “I know what to do”, and do all the rest of the problems the same way. I need them to READ THE DIRECTIONS!

Asian kid? His answers all look right, but he just cruised through doing addition for all of them. 99 + 5 is 104. 13 + 7 is 20. 33 + 17 is 50. 39 + 3 is 42, but he accidentally wrote 二, which is 2 in Japanese or Chinese.

I’d say just tell him to slow down a bit, he’s making mistakes because he’s bored and trying to set a land speed record.

No wait, scratch that. Part of the ‘2’ just didn’t show up on my screen until I changed the zoom a bit. Still agree with the others… check them on the other operations specifically to verify he knows how to do them, then chalk it up to inattentiveness if they do.

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