Interactive Vectors For Model-based Reasoning

Abstract

Reasoning about the structure and behavior of physical phenomena using abstract and concrete models (model-based reasoning, MBR) is a key thinking skill in science and engineering practice. One Of the key areas MBR is introduced in the curriculum, particularly the use of abstract models, is applications of trigonometry, such as calculating heights and distances. In India, high school and pre-college (9-12 Grades) trigonometry curricula include three broad MBR cases: i) heights and distances (ratios in right triangles), ii) resolution and addition of vector quantities (projections in a unit circle to give the rectangular components), and iii) periodic systems (represented as sinusoidal functions). Students find trigonometry and its MBR applications difficult to understand, possibly because reasoning in this domain requires handling cognitive (internal/abstract) operations and symbolic (external/concrete) operations simultaneously, in different and complex ways, across these three MBR cases. A particular source Of difficulty is the relationships between these trigonometric operations, which are not clear across the three cases. We are developing an interactive new media system to help students learn model-based reasoning, based on MBR applications of trigonometry. Here we on vector resolution and addition, a key application supporting MBR. In the existing curricula, trigonometric and other concepts related to vectors are scattered across 4 textbooks, and students find it hard to integrate these scattered concepts. We report a study outlining how the new media tool helped students integrate the concepts involved in vectors, and the insights from the study for redesign, particularly to support MBR-