2 ◆ Real Stories, Deep Understanding
knitting on the board. He then looked at me like “Help.” I smiled and
said, “Okay, I’m going to start with a different problem.”
I sat in the wooden chair, faced the students and asked them how many
stopped at the corner bodega that morning (which is a common routine
among the schoolchildren). I asked if they had $3.00, how many egg sand-
wiches could they buy. Everybody began calculating and they figured it
out. Then I posed a different problem. I asked what if I had 75 cents, how
many mini bags of potato chips could I buy? The children knew instantly
how many bags of chips I could get, because they do that every day.
These are real-life problems, problems that the students live in their
daily lives. That’s what students need—real-life problems. I gave them
several problems about the bodega where they had to divide decimals, but
I didn’t tell them what they were doing specifically, until we were deep
into it. Then I said, “Hey, what we are doing is dividing decimals. There is
a way to do this with numbers. Mr. Amancio^1 is going to show you.”
We ended the period with an exit slip that asked the students how
they felt about dividing decimals. Most everybody said it was easy. You
know why. Because it was connected to their everyday lives. Mr. Amancio
eventually got to that text-book problem, but only after the students actu-
ally understood the math.
This experience resonates with the National Research Council’s (NRC,
2001, p. 130) research that shows students can engage successfully in
reasoning about problems when three conditions are met:
- Students have a knowledge base.
- Students understand the problem and are motivated by the
content. - The context is familiar and comfortable.
Problem Solving Throughout the Math Class
Problem solving should be done every day as a whole class routine (see
Figure 1.1). It should also be done in small guided math groups and math
workstations. When done in whole groups, the emphasis is on developing
the habits of mind and ways of doing that good problem solvers need. The
focus here is not on quickly solving a problem but on going through the
process of problem solving. It is a practice that is developed over time. Great
problem solving is interwoven throughout the math block (see Figure 1.1).
Perseverance
One of the most important things that students need to know about problem
solving is that they have to persevere with the problems. They need to get the