PROCEEDINGS OF THE 21ST ANNUAL CONFERENCE ON RESEARCH IN UNDERGRADUATE MATHEMATICS EDUCATION
2018
San Diego, California
An Instructional Resource for Improving Students’ Conceptual Understanding of Functions through Reflective Abstraction
Page: 1734
It has been widely documented that undergraduate-level students’ understanding of functions is rigid and indicative of an action view which constrains conceptual understanding (Carlson, Jacobs, Coe, & Hsu, 2002). Duval affirms that, “to understand the difficulties that many students have with comprehension of mathematics, we must determine the cognitive functioning underlying the diversity of mathematical processes” (2006, p.103). What are the underlying cognitive skills students need to gain a better conceptual understanding of functions? How should instruction of function content and training in these cognitive skills be combined? We propose the theoretical model “Structural-Schema Development for a Function”, to address these questions. This model defines developmental stages students pass through to form a global view for the function concept, identifies underlying cognitive mechanisms involved in each stage, and develops instructional exercises that combine content with cognitive skills training for these cognitive mechanisms.