Bridge Project — Papers

• The Vector Calculus Gap (the paper which got us started)
• Electromagnetic Conic Sections (a new way to look at divergence and curl)   (HTML version; ©)
• Using Differentials to Bridge the Vector Calculus Gap (the core of our approach)   (corrected version)
• Bridging the Vector (Calculus) Gap (suggestions for teaching about vectors)
• The Murder Mystery Method (finding potential functions made easy)
• Spherical Coordinates (a proposal for bridging a language gap)
• Bridging the Gap between Mathematics and Physics (language differences between disciplines)
• Bridging the Gap between Mathematics and the Physical Sciences (more on language differences)
• The Geometry of the Dot and Cross Products (a geometric approach)   (MathML version; plugin)
• Why is Ampère's Law so Hard? (student difficulties mastering this material)   (HTML version; ©)
• Putting differentials back into calculus (differentials in first-year calculus)
• A Difficult Climb (a dialogue about paths on hills)   (©)
• Finding Geodesics (further comments on hills)   (Mathematica notebook; ©)
• Using differentials to differentiate trigonometric and exponential functions (further uses of differentials)
• From Fear to Fun in Thermodynamics (uses of partial derivatives in thermodynamics)
• Partial derivative games in thermodynamics: A cognitive task analysis (how some experts use partial derivatives)
• Experts' understanding of partial derivatives using the Partial Derivative Machine (more expert reasoning)
• An extended theoretical framework for the concept of derivative (new representations of derivatives)
• Thick Derivatives (blog post on partial derivatives)
• Interpreting Derivatives (more on representations of derivatives)
• Using Embedding Diagrams to Visualize Curvature (curvature via dr-vector)

(Full citation information is available on this website. A BiBTeX file is available here.)

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