March 17, 2017 Filed in: Articles

While teaching uniform circular motion in high school, I struggled with developing the

If we approach it from the perspective of contextual learning

Begin with a pictorial sketch of the circular path of an object traveling at constant speed. Place a velocity vector, V

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Acceleration is the change in velocity/change in time, or ΔV/Δt. Have the students translate the

Finally, have the students divide Δ

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A doubling of the velocities produces a doubling of Δ

Soon after, a group will notice that the time to travel from position 1 to position 2 must have changed.

“What will this do to the acceleration?” I ask.

“So if the change in velocity is doubled AND the change in time is reduced to one-half, what is the effect on acceleration?” They quickly recognize the acceleration must have increased four times.

I then assign various groups to change the velocity by 3, 4, 1/3, etc. until all groups are assigned a unique value for the initial velocity. They repeat the process to determine the effect on acceleration. They record their results and we examine the class pattern. Tripling the velocity results in 9 ×

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Dividing Δ

The intellectual effort and the essential student discourse provides time and opportunity for the brain to properly integrate this deceptively challenging act of analytical reasoning.

The last important concept is how the direction of the acceleration is related to the velocity. In the specific example shown, the acceleration was at 45o to each of the velocities. Ask the students, what the angle would be if the velocities were apart by 30°, 10° or 1°. Finally, what would it be for 0°? Rather than a detailed treatment of limits at this stage, simply advise them that calculus will explore and expand the concept of limits. Tread softly to avoid muddying the understanding achieved by the

No doubt this method has been applied by teachers before but was a new discovery for me and may be helpful to others.

- Johnson, E;
*Contextual Teaching and Learning*; Corwin Press, 2002. - Johnson, J; Carlson, S; Kastl, J; Kastl, R; “Developing Conceptual Thinking: The Concept Attainment Model”;
*The Clearing House: A Journal of Educational Strategies, Issues and Ideas*, Vol 66, Issue 2, 1992. - McDermott, M; Hand, B; “The Impact of Embedding Multiple Modes of Representation Within Writing Tasks on High School Student’s Chemistry Understanding”,
*Instructional Science*, Vol 41, Issue 1, p 217-246, 2013. - Larkin, J; McDermott, J; Simon, D; Simon, H; “Expert and Novice Performance in Solving Physics Problems”,
*Science*, Vol 208, p 1335-1342, 1980.