Mental imagery refers to the process of picturing
an event, concept, or procedure in your mind.
In math, one way students use mental images is
to reinforce their understanding of new concepts. By translating
a verbal description of a new concept into a visual picture, a
student can better "see" the mathematical relationships,
and create an association that improves comprehension. A student’s
ability to effectively move between verbal instruction and visual
representations in math depends upon skills in attention and spatial
abilities. Students must be able to sustain focus on details,
shift between words and pictures, and interpret and organize spatial
relationships by linking new instruction to existing knowledge.
Students also use mental images when solving
mathematical problems. During problem solving, students must actively
create visual images in their minds to represent the components
of the problem. This process of visualization involves the ability
to preview; that is, to form an image of an event or outcome before
it occurs, e.g., to imagine what will happen when two cups of
water are combined into a larger cup, etc.
Here are some strategies to help students develop
their use of mental imagery in problem solving.
|Have students draw pictures to represent what
is going on in a word problem. Students may draw actual objects
from the problem (e.g., 3 shirts, a 6’ by 12’ garden
plot, etc.), or they may represent objects with check marks
||Engage students’ imaginations by proposing
a number sentence, e.g., 6 +4 or 5(12 X 5), and having them
come up with a story problem for that number sentence.
||Incorporate problem solving activities using
maps, diagrams, graphs, and tables to strengthen students’
use of visual/spatial materials. For example, have students
calculate the distances of trips taken by students in the class,
then display this information in a graph or table format.
||Involve students in making predictions in
situations where visualization can aid problem solving. For
example, ‘If I place three green marbles and one red marble
in a bag then pull one out, what color marble am I most likely
||Help students practice manipulating
images in their minds in order to solve a problem. For example,
provide students with a variety of shapes made from connected
squares, some of which can be folded to form an open box. Ask
students to find the shapes which will make an open box. Students
will need to visualize the anticipated results in order to solve
the problem. Many may need to develop their ability to visualize
by making cut-out models and actually doing the folding. (Adapted
from Brumbaugh, Ashe, Ashe & Rock, 1997).