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.

Helpful Hints

  • 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 or dots.
  • 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 to get‘”
  • 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).