What strikes me about this piece of student work is how clean and predictable their mistake is.
Is this sort of mistake the rule or the exception? Does a mistake like this reflect the fact that many/most student errors are due to coherent mental models, or is it the rarer exception in a world dominated by stormy minds that fling ideas at math less predictably?
Thanks again to Dionn!
5 replies on “Money and Decimals”
I think this kind of pattern is pretty common. There are mistakes, more along the line of typos or momentary lapses of mind, that are mostly random though there are certainly places where they are more probable, and then there’s the big errors that come from, as you suggest, a different conceptual model.
I love the way the quarters and dimes live each in their own place value! The $1.40 is especially interesting.
I also just realized that this student’s work is perfectly correct, if only we meant addition when we wrote two numbers next to each other like that. So maybe it’s a small distance away from the correct answer, depending on what the kid thought it would mean to write .50.20 and the like. Could be a big misunderstanding of place value, or maybe subtotals on the way to a final answer.
I agree with you Joshua, that it seems to be a misunderstanding with the idea of place values. It seems that the decimals are a way for the student to be able to keep different values (quarters, dimes) separate. That due to misunderstanding of place values, the students also doesn’t exactly know how to add quarters and dimes together, unless they have four quarters to equal a whole (Ex: 1.40).
It would be interesting to see what the student would do with two “whole” sets of dimes and quarters (10 dimes = 1, and 4 quarters = 1). If the student would understand to add these two holes together to = 2, or if the student would follow their same patter and write 1.1 (which would from their previous work, indicate that the student sees four quarters equaling 1 whole, using the decimal point to separate quarters and dimes, and then seeing that 10 dimes equals another whole.).
If Joshua is right, and I think he probably is, then the $1.40 is even more interesting. Why wouldn’t it look like $1.00.40? This is where I would start the conversation with the student. Ask him/her what $1.40 means. Ask the student to SAY how much money is in your hand if you have two quarters AND two dimes. Tie the AND to an addition process.
$1.40 says to me they know what to do when there is a whole dollar, but are unsure how to combine cents.
What’s with 8) and 9) being identical?