Mathlessness, vol. 2
(See the original post).
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
Finally,
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.
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
Finally,
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.
posted by ms. v. at 6:30 PM
11 Comments:
And how do we fix this? I'm tutoring 6th graders in math and we're working on percents right now. They loved doing discounts and they loved figuring out sales tax -- although they were really thrown by the idea that they had to ADD the sales tax instead of subtracting it. And, then when I tried to show them how you can do both -- discount something and then add sales tax -- they completely shut down. They were all but putting their fingers in their ears shouting lalalalalalalala.
Frustrating.
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
It took me a while to see why this wasn't right.
I did get all the others though. Phew...
It’s frightening how confused students are by real world applications of math. I’m tutoring a 5th grader who looks at me like I’m nuts when I ask her what 20% off of t-shirt means. “I have to add…multiply…subtract…” All the while watching my expression for a hint. Later in the hour I told her I liked her new shoes. She told me they were on sale. Real world/school, real world/school, how can we make them see??
You may think students need to know basic facts, but Klein does not. God Bless Every Day Math and the defunct TrailBlazers.
The adding .3 is something I thought, before, when I was an inexperienced and idealistic teacher, was no problem.After I entered the real world and tried that type of activities, I knew better...
On type of activity that does seem to work to get them to have a better understanding of the sequence in decimal numbers is using a number line and hab=ving them place the numbers on it. Eventually, they'll see that the number 3 increments after 0.9 is 1.2 and not .12.
Oh yeah, and I see the same problems in our 7th grade students, and here we start studying decimal number in 4th grade...
Many are not better in college. I have 20-year-old students who would make the same mistakes and not be able to understand an explanation of why they are wrong.
In the literate (hah) world, kids learn grammar and can analyze some fairly complicated sentences, but cannot write simple ones of their own.
Why can't they apply what they know? Because they spend so much time as spectators instead of getting out and doing stuff?
I first teach decimals using $ and cents. Then I go into putting decimals in order from least to greatest and greatest to least.
A majority to the students seem to make the connection. When they take the test, the read the decimal as money. Some still have a hard time with .081 and .1 so we go over the place value as dimes and pennies instead of tenths and hundredths. Every time they read a decimal to me: 7 tenths or 7 hundredths they also tell me if it's worth 70 cents or 7 cents.
My daughter is in 7th grade and when I gave her the problem verbally was able to convert 6.125 to dollars and cents. Whew.
I remember elementary school in the 1960's. They had us drawing abacuses, endlessly, endlessly. I realize that they were drilling the base 10 number system into our heads. You get so used to counting 9, 10, 11 and learn to do it very young so it's really not intuitive. They don't do that kind of thing anymore, do they? I don't remember my daughter doing that for school, although I think it was in some of the math workbooks I picked up for her at the drugstore.
希望大家都會非常非常幸福~
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