Abstract
An important aim in school mathematics is to help students experience algebra's power to express generality. Researchers have been investigating figural growing pattern generalization as an early route to developing students’ understanding of functional relationships. More recently studies have been considering ‘open’ or ‘free’ tasks involving figural growing pattern construction. This study explored twelve Years 7–12 Australian students’ intuitions and connection of meanings for quadratic functions through growing pattern generalization, graphing, and construction activities during individual task-based interviews. The students who evidenced complementary correspondence and covariation views when generalizing appeared to handle pattern construction activities in productive ways, regardless of their prior formal study of quadratic functions. Areas of difficulty with graphing growing patterns and potential benefits of pattern construction tasks for exploring quadratic equations and for formative assessment are discussed.
| Original language | English |
|---|---|
| Article number | 100689 |
| Number of pages | 17 |
| Journal | Journal of Mathematical Behavior |
| Volume | 54 |
| DOIs | |
| Publication status | Published - 1 Jun 2019 |
Keywords
- Figural growing pattern construction
- Figural growing pattern generalization
- Multiple-representational activities
- Quadratic functional relationships
- Secondary mathematics
Cite this
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Investigating secondary students’ generalization, graphing, and construction of figural patterns for making sense of quadratic functions. / Wilkie, Karina J.
In: Journal of Mathematical Behavior, Vol. 54, 100689, 01.06.2019.Research output: Contribution to journal › Article › Research › peer-review
TY - JOUR
T1 - Investigating secondary students’ generalization, graphing, and construction of figural patterns for making sense of quadratic functions
AU - Wilkie, Karina J.
PY - 2019/6/1
Y1 - 2019/6/1
N2 - An important aim in school mathematics is to help students experience algebra's power to express generality. Researchers have been investigating figural growing pattern generalization as an early route to developing students’ understanding of functional relationships. More recently studies have been considering ‘open’ or ‘free’ tasks involving figural growing pattern construction. This study explored twelve Years 7–12 Australian students’ intuitions and connection of meanings for quadratic functions through growing pattern generalization, graphing, and construction activities during individual task-based interviews. The students who evidenced complementary correspondence and covariation views when generalizing appeared to handle pattern construction activities in productive ways, regardless of their prior formal study of quadratic functions. Areas of difficulty with graphing growing patterns and potential benefits of pattern construction tasks for exploring quadratic equations and for formative assessment are discussed.
AB - An important aim in school mathematics is to help students experience algebra's power to express generality. Researchers have been investigating figural growing pattern generalization as an early route to developing students’ understanding of functional relationships. More recently studies have been considering ‘open’ or ‘free’ tasks involving figural growing pattern construction. This study explored twelve Years 7–12 Australian students’ intuitions and connection of meanings for quadratic functions through growing pattern generalization, graphing, and construction activities during individual task-based interviews. The students who evidenced complementary correspondence and covariation views when generalizing appeared to handle pattern construction activities in productive ways, regardless of their prior formal study of quadratic functions. Areas of difficulty with graphing growing patterns and potential benefits of pattern construction tasks for exploring quadratic equations and for formative assessment are discussed.
KW - Figural growing pattern construction
KW - Figural growing pattern generalization
KW - Multiple-representational activities
KW - Quadratic functional relationships
KW - Secondary mathematics
UR - http://www.scopus.com/inward/record.url?scp=85061553099&partnerID=8YFLogxK
U2 - 10.1016/j.jmathb.2019.01.005
DO - 10.1016/j.jmathb.2019.01.005
M3 - Article
VL - 54
JO - Journal of Mathematical Behavior
JF - Journal of Mathematical Behavior
SN - 0732-3123
M1 - 100689
ER -