Articles Related to Geometric Functions
The articles and papers listed here are related to geometric functions, by which we mean the use of geometric transformations to provide students with sensorimotor experiences that develop their understanding of function concepts by creating and manipulating the variables and the function rules while attending to relative rate of change and other important function-related concepts.
- A Geometric Path to the Concept of Function.This article from Mathematics Teaching in the Middle School describes how transformations using dynamic software can provide a unique perspective on a common topic.
- Why Students Should Begin the Study of Function Using Geometric Points, Not Numbers
Abstract: By beginning the formal study of functions through geometric transformations that take a point as input and produce a point as output, students can form stronger and clearer concepts of independent and dependent variables, domain and range, relative rate of change, function notation, composition of functions, and inverse functions. This paper describes cognitive, kinesthetic, visual, and structural advantages of a geometric pathway to function concepts, and concludes by describing connections between geometric (ℝ2 → ℝ2) functions and numeric (ℝ → ℝ) functions that can facilitate students’ ability to transfer these function concepts between the two realms.
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Using Multiple Representations to Teach
Composition of Functions. This article from the November 2012 Mathematics Teacher describes how "Experience with multiple representations fosters students’ robust understanding of what functions are, how they behave, and how they can be composed.
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- Connecting Functions in Geometry and Algebra. This article, the cover story of the February 2016 issue of Mathematics Teacher, was selected as the Editorial Panel's favorite article of the 2015-2016 year.
Abstract: Students use geometric transformations to create a generalized linear function and construct its Cartesian graph. They dilate and then translate a point, restrict these points to number lines, and ultimately observe that in the algebraic equation y = mx + b, multiplying x by m corresponds to dilating x, and adding b corresponds to translating the result.
Support: The article is supported by two units of activities based on Web Sketchpad. The activities are freely available through a Creative Commons license, and are available here:
Activities for Introducing Functions Activities
Activities for Connecting Geometry and Algebra Through Functions
05 November 2015: Created this page.