My Answer is Five!
Several times a week I offer study sessions to my
pre-service teachers for Praxis Multiple Subject Mathematics, one of five tests
elementary teacher candidates have to pass to teach. My preservice teacher came across the
following practice problem from Math Made Easy:
Jan ran 30 blocks in
6 minutes. Assuming that she ran at a constant speed, how long did it take Jan
to run one block?
My student commenced to solving the problem. She said so I
divide 30 by 6 to find out how much time it will take to run 1 block and the
answer is 5. After reading the problem again. I ask her to notice the problem. Remember
if the speed is constant, should it take her 5 minutes to run 1 block? She thought about and decided it did not make
sense.
I am
writing this in support of one of the Standards for Mathematical Practices from
the Common Core State Standards. Reason abstractly and quantitatively. Students proficient in mathematics make sense
of the relationship of quantities in problem situations. They carefully examine
problems and determine if the quantities make sense before and after the problem
is solved. Mathematical proficient students can decontextualize, contextualize,
and pause as needed to during the manipulation process. Decontextualize refers
to abstracting a problem to represent the problem with symbolic notations(www.corestandards.org).
Here, my student really didn’t pause to
determine if her manipulation and answer made sense quantitatively. She attempted
to decontextualize the problem by noticing she needed a number smaller than 6
so she said 5. She did not noticed that other parts of the problem that refer
to “the speed being constant”. After
talking through and making sense of problem, she determined she need to set up
a proportion to solve it.
I believe service teachers are like any other
type of student dealing with high stakes timed assessments. They look for numbers
to compute without really thinking about the problem. Time constraint do not allow
for deep understanding of the problem especially when not given previous
instruction on how to really think about problem to deconceptualize it.
Therefore, the relationships of the quantities are not discovered.
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Yes! So often we are "trained" in elementary school to look foe those numbers to compute, or find those "key words". It is more important to allow students more opportunities to think.
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ReplyDeleteWow!! Such an amazing read!!
ReplyDeleteOften times our students focus on the part which are the numbers, instead of focusing on the whole! This is why I believe it is extremely important to teach and explain the importance each mathematical practice. This way students understand just what the problem is asking of them.
The last paragraph spoke volume to me because students see number and see the “GREEN” light and does not thoroughly read and comprehend what the problem is truly asking them to do.
Exactly. Students focus on the numbers and not the context wrapped around the number.
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