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.