The Use of Applets For Developing Understanding In Mathematics: A Case Study Using Maplets For Calculus With Continuity Concepts.

The Common Core State Standards for Mathematics (CCSSM) are founded on a long history of mathematics education research emphasizing the importance of teaching mathematics for understanding. The CCSSM along with the National Council of Teachers of Mathematics (NCTM) recommend the use of technology in the teaching of mathematics. New mobile technologies in society facilitate use in mathematics classrooms, and these technologies rely on software applications called applets. Certain applets have been developed for use in teaching mathematics. This study investigated the questions: Is it possible to determine the characteristics of applets that lead students toward greater understanding of mathematical concepts? And, can we determine specific actions and strategies learners develop while using applets that increase their understanding? Using a case study methodology, continuous motion, screen capture and audio recordings of seven high-school AP Calculus students were made while each used five Maplets for Calculus applets developed for continuity concepts. Audio and screen capture recordings were transcribed and analyzed to determine increases in understanding of continuity concepts using a rubric based on Tall\u27s Three Worlds model of mathematics understanding. Using Drijvers and Trouché\u27s Instrumental Approach theory this evidence was also analyzed to determine the features of the Maplets and strategies used by the students that contributed to the increases in understanding. The findings relevant to teachers of mathematics included: evidence about the features of and strategies used by the students with the Maplets that developed students\u27 embodied and symbolic understanding of left and right continuity; evidence for how the proceptual-symbolic understanding of the definition of continuity is developed; evidence of students using the concepts of left and right continuity to develop a formal `rule\u27 for determining the overall continuity of a function; evidence of formal thinking in the embodied world for epsilon-delta continuity; and evidence that supports the contributions of Maplets in developing procedural understanding. A finding of relevance to applet developers included recommendations based on evidence for the sequencing of Maplets along with features and learner strategies that contribute to understanding of continuity in the symbolic world