Abstract
Trigonometry is integral to mathematics education. The field of trigonometry plays a crucial role in the study of mathematics and its applications. Despite the importance of the subject, students struggle to understand trigonometric constructs such as angle measure. It has also been noted how students struggle to understand transformations of functions generally. Our review of the literature found few studies specifically on students’ understanding of transformations of trigonometric functions, but evidence exists showing students have difficulties with the concept. Here, a MATLAB program called TrigReps is discussed. TrigReps accepts four inputs for the algebraic representation (a)sin(bx + c) + d, and provides three additional representations as outputs. Students are presented with a graphical representation, an auditory representation, and a dynamic representation of a radius rotating around a unit circle. TrigReps has potential to be a useful tool for teaching transformations of trigonometric functions. In particular, it may be able to help students justify why combinations of horizontal transformations are counterintuitive. TrigReps is analytically sound in its design: it is interactive, dynamic, and displays Multiple External Representations (MERs) simultaneously. Initial data support its usefulness in a trigonometry classroom, but more research must be conducted to draw firm conclusions.
Highlights
Trigonometry is integral to both pure and applied mathematics education (NCTM 2000; NGA 2010)
Discussion amongst the group showed that the students made predictions regarding function transformations, used TrigReps to examine the transformations, and reflected on their predictions
This study demonstrated that TrigReps can be a useful tool to teach transformations of trigonometric functions when used in conjunction with classroom activities that promote inquiry and reflection
Summary
Trigonometry is integral to both pure and applied mathematics education (NCTM 2000; NGA 2010). Trigonometric functions are used frequently in the STEM fields They are present in engineering tasks such as digital image processing and finding orthogonal force vectors (Lay 2002; Rosen, Usselman, & Llewellyn 2005). TrigReps accepts inputs for a, b, c, and d in the function f(x) = (a) sin (bx + c) + d It simultaneously provides three additional representations: a static representation of the graph on the Cartesian plane; an auditory representation of the function as a pressure wave over time; and a dynamic representation of a radius rotating around a circle. This circle has radius a and is centered at (0, d). The radius has a starting position c radians from the positive horizontal axis, and it rotates counterclockwise from that position at b 2p revolutions per second
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