Two facets of the 'Making Meaning of Mathematics' epistemic game: Finding a Family of Functions and Fitting the Physical Situation¶

Theory · All theories
Evidence · 3 claims (3 for) · 1 study (1 qualitative), q2 · 0 of 1 report an effect size · 3 claims rest on one study

Description¶

The authors describe two versions, or facets, of the large-scale epistemic game 'Mapping Meaning to Mathematics' in the context of solving separable first-order differential equations. They "call these versions 'Finding a Family of Functions' (the +C method without finding the value of the constant) and 'Fitting the Physical Situation' (the limits method)". The facets have similar moves but differ in finer-grain analysis: Phil requires an equation that can "cover everything", while Max seeks consistency between mathematics and physics. The two methods are procedurally different but lead to equivalent solutions.

Design Implications¶

Context¶

Requirements¶

• Epistemic games are personally and contextually dependent; the games available depend on the setting, the individual, and resources already activated.

Constraints¶

• The article notes the Fitting the Physical Situation game is not necessarily fully formed: Max did not insist on limits on the v-integral until Phil's use of Add Constant activated those resources. Plotting other students' methods on the resource graph would likely result in some re-ordering of arrows.

Target Learners¶

• intermediate mechanics undergraduates solving differential equations

Target Learning Objectives¶

• solving separable first-order differential equations with boundary conditions in physics

Claims¶

• Students Start Semester More Familiar With Integration Constants Method Than Limits Method [+M]
• 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 [+W]
• Students initially leave variables out of their integration limits, using only numerical values, suggesting that variable ('running') limits of integration are unfamiliar [+W]

Related Theories¶

• Procedural Resources Resource Graphs Integration

Examples¶

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Key Sources¶

• 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/