Mathlessness, vol. 2
Our math AUSSIE came to sit in on my math tutoring session after school today. Only four of my six students were present, and they were as pissy as I've seen them recently, trading insults, kicking each other under the table, and even snapping at each other (literally, with their teeth!). After a certain amount of this, I read them the riot act, which caused three to settle down while the fourth sulked.
Anyway, my AUSSIE brought some worksheets to assess the students' understanding of decimal place value. They'd had it drilled into their heads in sixth grade, but could they use their supposed knowledge to help them solve problems?
One of the problems looked like this:
Angela purchased 4 bracelets. She worked out the price for one bracelet on the calculator. The result was 6.125. How much is that in dollars and cents?
Most of us easily see that it's $6.13. I figured the kids would have trouble figuring out how to deal with the three digits after the decimal point. While they were working, my AUSSIE leaned over and whispered that kids always write $7.25 because they think the 125 is 1.25 and should be added to six. No way, I said.
One by one, the kids handed in their papers. $7.25. $7.25. $7.25. $7.25.
Another question looked like this:
Lily said, "When we put books on the library shelf, we put 74.8 before 74.125 because 8 is less than 125," but Dan didn't agree. Who is right? Why do you think that?
All the children thought Lily was right.
Other problems asked them to sequence decimal numbers, like this:
0.3, 0.6, 0.9, _____, ______ (add on 0.3 each time)
Nearly all the children answered something along the lines of
0.3, 0.6, 0.9, 0.12, 0.15
Paperclips come in boxes of 1000. Jenny counted the loose paperclips in a tray and said there were 1480. Jose said that's 1.48 boxes of paperclips. Could they both be right?
Not one child saw that 1480 paper clips and 1.48 boxes of 1000 paperclips were equivalent. Not one child.
The practice we've been doing in workbooks is just extra repetition of algorithms. Their fundamental understanding of numbers and what we can do with them is so flawed and flimsy, it's terrifying.