Intermediate mechanics students start the semester more familiar with the integration constants (+C) method than with the limits method, and the +C method remains preferred by at least one student even after instruction modeling the limits method¶

Claim · All claims
Evidence · 1 study · qualitative r2 · q2
Currency · newest study 2009 · not yet checked against its sources · not reviewed by a person

Subclaims¶

q2 i? Students at the start of instruction on air resistance are more familiar with the +C method than the limits method, and preference for +C persists after instruction for at least one student. → Black 2009

Evidence¶

Black 2009¶

Black, K.E. and Wittmann, M.C. (2009). Understanding the use of two integration methods on separable first order differential equations. https://perlnet.umaine.edu/imt/

q2 · i? · the article prints no effect size for this finding · qualitative · r2

Qualitative analysis of videotaped miniviews and a group quiz in intermediate mechanics at UMaine. The authors' summary states the integration constants method "is preferentially employed by two groups at the beginning of instruction" and remained preferred by one student on a post-instruction group quiz. No effect sizes are reported.

"The integration constants method is preferentially employed by two groups at the beginning of instruction on solving air resistance problems, and is still the preferred method for at least one student during a group quiz following instruction in which the limits method was modeled."

Discussion¶

Related Claims¶

• Students initially leave variables out of their integration limits, using only numerical values, suggesting that variable ('running') limits of integration are unfamiliar — related
• Students using the limits method initially choose unphysical integration limits, failing to consider the functional relationship between limits on either side of the equal sign — related
• Lower-order habits persist after being superseded and resist new ways of working, requiring constant effort to overcome — related