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## Mathematical vs. Conceptual Understanding: Where Do We Draw The Line? Documents

#### Main Document

##### Mathematical vs. Conceptual Understanding: Where Do We Draw The Line?

written by Homeyra R. Sadaghiani and Nicholas Aguilera

This research involved high school physics students and how they learn to understand Newton's laws as they relate to falling bodies and projectile motion. Students in introductory, algebra-based, high school physics classes were evaluated based on their prior knowledge through a pretest, designed to assess their initial comprehension of the motion of falling bodies and projectiles. Groups were divided and taught separately with an emphasis on either mathematical derivation of equations, followed by brief conceptual discussions, or on thorough conceptual analysis, followed by a brief mathematical verification. After a post-test was given, an evaluation of the responses and explanations of each group of students was used to determine which method of instruction was more effective. Results indicate that after the conceptual group and math groups achieved similar scores on the pretest, the conceptual group obtained a slightly higher normalized gain of 25% on the post-test, compared to the mathematical group's normalized gain of 16% (unpaired two-tailed t-test P value for post-test results was 0.1037) and, while within standard deviations, also achieved higher overall scores on all post-test questions and higher normalized gains on all but one post-test question. Further, most students, even those in the mathematically-instructed group, were more inclined to give conceptually-based responses on post-test questions than mathematically-based ones. In the context of this topic, the dominating difficulty for both groups was in analyzing two-dimensional projectile motion and, more specifically, the behavior of each one-dimensional component of such motion.

Published January 24, 2013