Using Problem Solving for Instruction and
Understanding Student Thinking
Problem solving as an instructional strategy can also be applied to teaching and learning
of fraction, decimal, and percent equivalency. Principles and Standards for School
Mathematics (NCTM, 2000) suggests instructional programs for mathematics teaching
and learning should enable students to:
1. Build new mathematical knowledge through problem solving.
2. Solve problems that arise in mathematics and in other contexts.
3. Apply and adapt a variety of appropriate strategies to solve problems.
4. Monitor and reflect on the process of mathematical problem solving.
The Qatar Mathematics Curriculum Standards also states the importance of problem
solving used as an instructional strategy in the elementary classroom. Most, if not all,
important mathematics concepts and procedures can be taught through problem solving.
To begin, let’s consider the engaging task below.
Engaging Task: What percent profit will be made?
At the Home Center Furniture Store, the owner has priced all of the furniture at 20
percent over wholesale. In preparation for a sale, she tells her staff to cut all prices by 10
percent. Will the owner be making 10 percent profit, less than 10 percent profit, or more
than 10 percent profit? Explain your answer.
1. What strategies did you use to solve the Percent Profit problem?
2. What math concepts and skills are important for the understanding of this
3. If you were teaching a class and a student in class had difficulty beginning this
problem, what would you suggest?
Activities in this lesson will provide opportunities to solve problems using various
strategies and select appropriate problem solving tasks for elementary math instruction.
1. Solve fraction, decimal, percent equivalence problems using problem solving as an
instructional approach to elicit student understanding.
2. Learn how to design and select appropriate problem solving tasks.
Activity 1: Problem Solving as an Instructional Strategy
A best practice instructional approach to teaching mathematics is for a teacher to create
an environment in which students can grow as problem solvers. Creating a classroom
environment that supports risk taking, reflecting thinking, and cooperative work allows
students to engage in mathematics through the use of problem solving. Students’
metacognitive skills play a critical role in helping students become problem solvers.
Metacognitive skills make students aware of their own thinking and the thought processes
of others as they explore problems in both whole-group and small-group settings. Good
problem solvers regularly monitor their thinking and are aware when they should rethink
the problem or switch to a new strategy. Metacognitive practices can be learned, and
often students who learn to monitor and regulate their problem-solving behaviors, show
improvement in their mathematics abilities.
As a beginning teacher, it is important to give adequate time to the planning of lessons—
especially if using a problem solving instructional approach. Choices of problem-solving
tasks and how they are presented to students must be made daily to best fit the needs of
students and the objectives you are hired to teach. The powerpoint slides posted below
provide important guidelines to consider in learning to teach through problem solving and
planning problem-based lessons for the mathematics classroom.
Click here to view powerpoint slides. Teaching Through Problem Solving
1. Problem solving as a principal instructional strategy.
2. Examples of problem-based tasks
3. Three-part lesson format
4. Teaching about problem solving
5. Developing problem solving-strategies
Based on the slides you viewed, respond to the following questions. Use information you
learned from the notes to support your responses.
1. If you were to begin teaching a class of 4th grade students who had never
experienced learning mathematics in a problem-solving environment, they are
likely not to know how to work at solving problems. Describe what you would do
so that students would develop an understanding of their role in the classroom.
2. During the engaging task of this lesson, you were asked to solve the Percent
Profit problem. Consider this problem again. Describe how you would develop a
problem-based lesson using this problem. Select the grade level that would be
appropriate based on the TEKS and design the lesson using the three-part lesson
format as discussed in the Teaching Through Problem Solving slides.
Activity 2: So Many Out There: Designing and Selecting Appropriate Tasks
In Activity 1 of this lesson, you viewed slides that discussed items to consider when
planning for problem-based instruction in the mathematics classroom. One of those
items included identifying sources of problems and being able to select tasks appropriate
for the intended mathematics curriculum. Curriculum books, articles you read or in-
service workshops you attend as a teacher, will suggest activities, problems, tasks, or
explorations that someone believes effective in helping students learn key concepts in
mathematics. Selecting appropriate tasks that address important mathematics knowledge
and skills is one of the most significant decisions teachers make in affecting students’
learning. There are a variety of sources to consider in selecting effective tasks. These
sources include textbooks, Standards-based curricula, professional journals, curriculum
guides, and internet websites.
For this activity, there are two parts.
Select three problems from the various sources described above. Solve each of these
problems and respond to the questions provided.
Evaluate the three problems based on the four-step guide that was outlined in the notes
included in Activity 1.
Templates for each part of activity provided below.
Part 1 Template:
Problem 1 Problem 2 Problem 3
Source of Problem
Why was this
Part 2 Template:
Problem 1 Problem 2 Problem 3
What makes this a
How is this
What is the
purpose of this
Will the problem
What must be done
by the teacher for
this problem to be
used in a lesson?