|Model problems for the class and explain each
step when teaching students how to be active problem solvers.
Think out loud for students as you reason through a problem,
choose a strategy to use, decide if the strategy is working,
etc. Have students talk through problems with each other as
||To promote strategy use and adjustment, ask
students guiding questions as they solve problems, e.g., "Is
there an easier way to do that‘", "Will that strategy
always work‘", etc.
||Have students communicate their understanding
of a problem through both oral discussion and written explanation.
||Have a brainstorming session with students
to discuss the types of behavior or steps are involved in problem
solving, characteristics of ‘good problem solvers’,
etc. Some ideas may include reasoning, looking for patterns,
patience, persistence, hypothesizing, stating the obvious, creativity,
||Encourage students to explore multiple strategies
that could be used for solving a math problem. For example,
ask students to find the length of the diagonal of a 12"
x 16" rectangle. Students will likely recognize that the
rectangle is made up of two right triangles, and apply the Pythagorean
theorem. One approach might be to calculate by hand or to use
a calculator for the computation (12² + 16² = ‘) to
eventually come up with the answer of 20 inches.
||However, an alternate view of the problem
makes it even easier to solve. A student might notice that the
12" and 16" sides are both divided evenly by 4, resulting
in a triangle with sides of 3" x 4", respectively.
The student will likely recognize the missing diagonal length
to be 5", making the standard 3" x 4" x 5"
triangle. Then, simply multiplying the 5" back by 4 would
give the answer to the diagonal: 20 inches. No lengthy computations
would be needed. (Adapted from Brumbaugh, Ashe, Ashe & Rock,
||Have students practice selecting what strategies
might be appropriate for solving a given problem. For example,
in each case, would it be helpful to act out the problem, make
a model, draw a picture, make a chart or graph, use logic, guess
and check, break it into parts, etc.’
||Promote students’ flexible thinking
by presenting situations in which there is more than just one
right answer. For example, have students take out a piece of
paper, fold the paper in half, then fold the paper in half again.
Ask students to count how many rectangles have been formed.
Answers will vary depending upon how the second fold was made
in the paper, if students count the whole piece of paper as
one of the rectangles, etc. Have students discuss how different
folding approaches resulted in different ‘answers’.
(Adapted from Brumbaugh, Ashe, Ashe & Rock, 1997).
||Give students practice estimating the
answers to problems. Have them move from estimation to calculation,
then back again to estimation. Help students develop their sense,
before starting calculations, of what a general solution to
the problem might be, and also to take time to examine their
answers, after calculation, to see if they seem credible. Students
may require guidance in useful strategies for estimation, e.g.,
rounding numbers, creating a visual image, etc.