Chapter 7, page 144
- Word problem. Kramer swims 1 mile along the East River in 30 minutes.
How fast is he swimming?
Student 3: Do you know how to do this?
Student 4: Not really. But I remember that I should start with the meaning
of rate. Rate is defined as how far you go divided by how long it takes.
Student 3: That makes sense because if you go 40 miles per hour, you’re
going 40 miles divided by 1 hour.
Student 4: Right, so in this case, rate is just equal to how far over how long,
which is 1 divided by 30. So that’s 1/30 miles per hour. Oh – wait a
minute, that can’t be right, because 30 is minutes, not hours. It
doesn’t make sense because that would mean that in 1 hour, he would
only go 2/30 miles, and it said that Kramer goes 1 mile in just half an
hour, which is more. So it must 1/30 miles per minute, and in 60
minutes, that would be 2 miles, so 2 miles in an hour.
Response:- The students don’t use self-explanation. Student 1 is just describing the
algorithm used to answer the question. There is no attempt to explain why
any of the steps are taken. - This example shows effective self-explanation by the two
students. What we see is that the students don’t really understand
very well, but by trying to explain each step, they get better as they
goes along. They don’t just repeat the formula; student 3 tries to
explain why it makes sense: “That makes sense because... .” Student
4 checks to see whether her results make sense when she realizes that
their initial answer is inconsistent with the information given in the
problem. Even though the students have imperfect understanding, the
explanations are good because in the process of explaining, they are
improving their understanding.
Formulating problems. The Reflection at the beginning of this chapter comes from a study of
elementary school students by educational psychologist Carol Chan and her colleagues (1992). Chan and
her colleagues found that the students who understood and remembered the passages the best were those
who formulated problems based on what they read in the text. Examples include these two students’ think
alouds in response to this text:
TEXT: Harmful germs can get into your body in three ways, through your nose, your mouth, and by
cuts and scratches in your skin.
Student 1: They get in through your mouth and nose, and um... cut... what I am thinking is, how can they
get in because the cut is so little... but maybe it really got in through your skin... so it might not
be getting exactly right in.
Student 2: Why do they get in only through your nose and your moth and scratches? Can they get in through
your ears or something... because your ears sort of have holds... maybe the eardrums block it or
something.