Abstract
In this paper we present a laboratory experiment in which 157 secondary-school students learned the concept of function with either static representations or dynamic visualizations. We used two different versions of dynamic visualization in order to evaluate whether interactivity had an impact on learning outcome. In the group learning with a linear dynamic visualization, the students could only start an animation and run it from the beginning to the end. In the group using an interactive dynamic visualization, the students controlled the flow of the dynamic visualization with their mouse. This resulted in students learning significantly better with dynamic visualizations than with static representations. However, there was no significant difference in learning with linear or interactive dynamic visualizations. Nor did we observe an aptitude–treatment interaction between visual-spatial ability and learning with either dynamic visualizations or static representations.
Highlights
Students in the fields of science, technology, engineering, and mathematics (STEM) often have to acquire knowledge about a process, i.e., a situation that changes over time
This kind of dynamic thinking is subsumed in mathematics education under thinking of function as covariation in contrast to thinking of function as correspondence (Vollrath, 1989; Confrey and Smith, 1994; Thompson, 1994)
The present study investigated the following three hypotheses: Hypothesis 1 (H1): Dynamic visualizations of geometrical situations dyna-linked with the corresponding graph are more beneficial than only providing static representations of a geometrical situation and the corresponding graph for learning about the aspect of covariation of a function
Summary
Students in the fields of science, technology, engineering, and mathematics (STEM) often have to acquire knowledge about a process, i.e., a situation that changes over time. Calculating the function value of a given function (e.g., f (x) = 2x2 + 3x + 1) for a particular value (e.g., x = 5) or finding the zeros of the function f are typically function tasks that address the correspondence conception of function. This static view of a function as pointwise relations plays an important role in teaching the concept of function in school (Hoffkamp, 2011; Thompson and Carlson, 2017). The covariation conception, focuses on the interdependent covariation of two quantities, that is, the effect of a change
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