Every time a student has access to symbolic representation of a problem, his brain is being conditioned to look for all possibilities. After he has examined alternatives and verified that his answer makes sense, he can better articulate reasons for those answers. 

Mental Agility

Mental agility is demonstrated when a student can switch between concepts to determine the most appropriate fit for a problem. Tangible math is a great tool for training the brain to wrap itself around the situation presented and apply the optimal concepts. Students begin by identifying known and unknowns using concrete tools. Then, they can take inventory of which concepts may apply, assess the information they have, and analyze what information they may need to look up. When new scenarios are presented, tangibles allow students to think of concepts as flexible and apply them appropriately. Flexibility in application demonstrates depth of comprehension. 

Bring Back the Beans?

Maintaining the use of tangibles throughout the transition from elementary math gives you an opportunity to reframe upper-level math. If your teen understands that math is pictures, and that those pictures evidence concepts, then he has a basis on which to tackle more complicated math material with confidence. Turning complex problems into pictures in the mind by using manipulatives, games, and riddles makes the study of mathematics more personal, dynamic, and creative. 

Leave the beans in the pantry, though, because you are no longer limited to elementary tools. A wide variety of creative and age-appropriate techniques is available to solidify complex mathematical concepts in the minds of your teenage students. Tangible tools for higher math have come a long way in recent years. Programs such as Mathematica are designed to create animations that help students play with and visualize concepts such as tessellations and spirographs. Prestigious universities utilize open source software to make portions of their coursework available online. Riddles, games, and illustrations are bound together in subject-specific volumes and are terrific resources for extra practice when necessary.

Put It Into Practice

If all of this seems a little too theoretical for comfort, check out some of the resources listed in the sidebar for more in-depth ideas on how to make math come to life for your high school student. In the meantime, here are a few examples to illustrate how you can implement tangible math in your current coursework:

  • Use a Frisbee to determine different variables, such as wind speed.
  • Pump up the water rockets and use triangulation to calculate height or speed.
  • For the student whose mind is on driving, let him calculate the financing for that all-important first car.
  • Take helium balloons (tied to strings) outdoors, and release them in order to study differing rates of climb.
  • Let your more artistic student create a work of art using trigonometric functions.
  • Use Riemann sums to estimate the area under the curve of an arch in your student’s favorite piece of architecture, or determine the volume of a cone using huge waffle cones (and calculus).

The Internet is a terrific resource for activities to integrate with whatever mathematical concept your student is currently studying. Simply type in a math term, for example, implicit differentiation, with the word activity or illustration, and you will be directed to many hands-on or electronic idea sources, including many that have been contributed by major universities. Better yet, have your student do this research to design her own practical work.  By taking this initiative, your student will become more familiar and comfortable when the time comes for the more self-directed nature of study he or she will encounter in college.