PROCEEDINGS OF THE 17TH ANNUAL CONFERENCE ON RESEARCH IN UNDERGRADUATE MATHEMATICS EDUCATION
2014
Denver, Colorado
Implied and Empirical Readers of Newton’s Method
Page: 933
The ability to translate a text into a mathematical process is a key goal of mathematics education. Knowing when students have the prerequisite knowledge to understand such a process is a perennial concern for instructors. Here we use Newton’s method to evaluate reader oriented theory as a means to illuminate these issues. Through clinical interviews with twelve first semester calculus students, we determined that knowledge of both tangent lines and roots is required for students to understand and apply Newton’s method. Analysis was done from the perspective of the empirical, implied, and intended readers and was examined for the extent to which the empirical and implied readers aligned. It was found that although the alignment of the empirical and implied readers was helpful in determining the success of the students, it was not in itself a deciding factor.