This past week new research came out of Stanford University that suggests that using visual tools is an important part of math achievement over the long-term.  The research focuses on how people naturally visualize problems when working on math problems, and the classroom should encourage and support opportunities.  The research suggests that memorization which has become part of many math curriculums is not a valuable part of math achievement.

Taking the research and bringing it into the classroom is the goal of many teachers.  While several news stories around this new study cite having students count on their fingers as part of visualization, more advanced classes need to be more creative to provide visualization opportunities.

Some topics are easier than others.  In geometry it's easy to work on symmetry or angles or even volume.  Students can draw the concepts.  Kinesthetic learners can fold or build structures.  Visualizing surface area?  Wrap a present!

Other concepts require a little more creativity.  When we start linear equations, my students "build" linear equations from legos, blocks, pennies, or other manipulatives.  Anything will work.   We drew "squares" for examining squares and square roots.  For compound interest as part of exponential growth, we use monopoly money.  For functions, we create a function machine.

Of course, one key strategy for problem solving is sketching the problem.  What is the question asking?  What does the question look like?  What would the answer look like?  How do we get there?  In the problem to the right, students can draw out the animals and count to problem solve before they can create the algebraic model for the problem.

The research supports what many of us already have found in our own classrooms.  I struggle with some topics to figure out how to visualize problems, but I hope that additional research supporting visualization in math will continue the discussion among teachers and provide additional strategies, particularly for advanced mathematics classes.

Math Mondays is a bi-weekly blog post (2nd and 4th Monday of each month) sharing tips, ideas, resources, and products for teaching math.  If you have questions or think there is something I should include, you can leave me a message in the comments section below or at the store in the question and answer section.