On doing and undoing in general and applied precalculus-calculus tracks
Haile Gilroy^ & Isabel Harris*
^McNeese State University, Lake Charles, Louisiana, USA
*Rice University, Houston, Texas, USA
Note: This page is under construction. Work in progress!
Link to full paper: Coming Soon!
Sections Analyzed
Applied Precalculus
Dennette & Kaskosz (2020)
Ch 1, Sec 1-5
Ch 2, Sec 1-3
Ch 3, Sec 1-4
Ch 4, Sec 1-4
Ch 5, Sec 1-5
Ch 6, Sec 1-3
Ch 7, Sec 1-4
Ch 8, Sec 1-5
Total # of Examples: 329
This textbook is open-source, and can be found here.
General Precalculus
Sullivan (2018)
Ch 1, Sec 1-4
Ch 2, Sec 1-6
Ch 3, Sec 1-5
Ch 4, Sec 1-6
Ch 5, Sec 1-9
Ch 6, Sec 1-6
Ch 7, Sec 1-7
Ch 8, Sec 1-5
Ch 9, Sec 1-7
Ch 10, Sec 2-7
Ch 11, Sec 1-8
Ch 12, Sec 1-4
Ch 13, Sec 1-3
Total # of Examples: 953
Applied Calculus
Hughes-Hallett (2014)
Ch 1, Sec 1-10
Ch 2, Sec 1-5
Ch 3, Sec 1-5
Ch 4, Sec 1-8
Ch 5, Sec 1-6
Ch 6, Sec 1-7
Ch 7, Sec 1-3
Ch 8, Sec 1-6
Ch 9, Sec 1-7
Ch 10, Sec 1-3
Total # of Examples: 467
General Calculus
Stewart (2016)
Ch 1, Sec 1-5
Ch 2, Sec 1, 7, 8
Ch 3, Sec 1-4, 6-8
Ch 4, Sec 1, 3, 7, 9
Ch 5, Sec 1-5
Ch 6, Sec 5
Ch 7, Sec 1
Ch 8, Sec 4, 5
Ch 9, Sec 1, 2, 4-6
Ch 11, Sec 2
Ch 14, Sec 1, 3, 7
Total # of Examples: 326
Examples of Doing and Undoing Processes
Evaluating <=> Solving
Evaluating (Doing)
Solving (Undoing)
Simplifying <=> Expanding
Simplifying (Doing)
Expanding (Undoing)
Composition <=> Decomposition
Composition (Doing)
Decomposition (Undoing)
Forward Conversion <=> Backward Conversion
Forward Conversion (Doing)
Backward Conversion (Undoing)
Strategize and Execute (Doing & Undoing)
Precalculus Example. Notice that the doing and undoing processes are structured as different prompts within the task.
Calculus Example. Notice that here, the undoing process is implied in the first statement of the solution. Unlike the precalculus example, students must grapple with "undoing" before "doing", but only "doing" is explicitly prompted.