| Autor: |
Zekiye Özgür, Amy B. Ellis, Torrey Kulow, Caroline C. Williams, Joel Amidon |
| Jazyk: |
angličtina |
| Rok vydání: |
2015 |
| Předmět: |
|
| Popis: |
This article presents the results of a teaching experiment with middle school students who explored exponential growth by reasoning with the quantities height (y) and time (x) as they explored the growth of a plant. Three major conceptual shifts occurred during the course of the teaching experiment: (1) from repeated multiplication to initial coordination of multiplicative growth in y with additive growth in x; (2) from coordinating growth in y with growth in x to coordinated constant ratios (determining the ratio of f(x(2)) to f(x(1)) for corresponding intervals of time for (x(2)) > 1), and (3) from coordinated constant ratios to within-units coordination for corresponding intervals of time for (x(2)) < 1. Each of the three shifts is explored along with a discussion of the ways in which students' mathematical activity supported movement from one stage of understanding to the next. These findings suggest that emphasizing a coordination of multiplicative and additive growth for exponentiation may support students' abilities to flexibly move between the covariation and correspondence views of function. (C) 2015 Elsevier Inc. All rights reserved. |
| Databáze: |
OpenAIRE |
| Externí odkaz: |
|
