10 ◆ Real Stories, Deep Understanding
first laid out the process for us with his problem-solving questions involv-
ing the four phases (see Figure 1.2). These templates build on Pólya’s original
phases (see Figure 1.2). They help to scaffold the thinking and with use
over time the students begin to internalize the process. Eventually, the
templates are phased out. Have anchor charts set up that talk about the
process of problem solving. Also, have the students make their own mini
anchor charts. Once the template use is phased out, still have the students
sketch out the template into their problem-solving notebooks. When students
are organized, they are much more likely to succeed.
Problem Solving in Guided Math Groups
After the mini-lesson for the day, students settle into the student work
period. Students will go to workstations or teacher-led groups. Sometimes
in those teacher-led groups, students will do problem solving (see Fig-
ure 1.7). These lessons are much more focused and intense and differenti-
ated toward the needs of the students in the group. These lessons could
be concept lessons, procedural lessons, strategy lessons or reasoning
lessons.
Concept In this lesson, students are trying to understand what the
different types of problems are. Some students may be working
on change unknown problems and other students may be
working on part-part-whole problems. The teacher knows the
students and can shape the problem to fit the levels that students
are at. This is important because problems should be scaffolded.
You want students to be able to unpack the problem so that they
can reason about what they are looking for. They have a much
better chance of finding it if they know what they are looking for.
Procedural Procedural problems teach students how to do something. How
do we add fractions? What are the rules and procedures for
doing that? How do we multiply decimals by modeling it on the
number line? How can we model the subtraction of decimals
with decimal grids? How do we show it with numbers?
Strategic Strategic lessons are about students using different strategies to
solve problems. Students should be familiar with a variety of
strategies and know when and how to use them when problem
solving.
Reasoning Reasoning problems involve students thinking about, justifying,
explaining and challenging the thinking of others and defending
their own thinking,Figure 1.7 Guided Math Problem Solving Lessons