| This research project examined the effect of two different technological curricula on students' understanding of the concept of function. Treatment Group I used a text-based, graphing calculator curriculum. Treatment Group II used a computer-based, graphing calculator curriculum. Treatment Group I participated in graphing calculator activities related to the domain and range of functions that were designed to promote conceptual change via cognitive conflict. Because Treatment Group I instruction was predominately lecture and Treatment Group II used self-paced computer software, the research also explored the effect of students' preferred amount of instruction on their understanding of the concept of function.;The research sample included 281 students in 10 college algebra classes with five classes per treatment group. Function understanding was measured in terms of students' ability to apply domain/range concepts and their ability to identify, define, translate, model, and reify functions. Based on posttest group means, neither students' preferred amount of instruction nor the interaction of students' preferred amount of instruction with the technological curriculum had a significant effect on their understanding of the concept of function.;The text, graphing calculator group demonstrated a significantly stronger understanding of the function concept than the computer, graphing calculator group in terms of their application of domain/range concepts and their ability to identify, define, and translate functions. The abilities to apply the domain/range concepts and translate between algebraic and graphical representations were the major sources of their better understanding.;An analysis of the posttests for both treatment groups revealed difficulties. Students had difficulty (a) considering the domain when translating between algebraic and graphical representations, (b) determining the range of a function in its algebraic and graphical representations, and (c) identifying whether or not algebraic formulas and written descriptions of relationships represent functions.;Students demonstrated a limited concept image of function. The majority of students' concept image of function did not include the definition of function. Students' strongest concept image of function was that a function is an equation. When considering a graphical representation, students demonstrated a concept image of function in terms of the vertical line test and continuity. |
