Procedural and conceptual knowledge among upper secondarystudents : the case of second degree polynomials

Abstract

This study is concerned with conceptual and procedural knowledge of second degree polynomials. I try to give an account of a group of students’ knowledge of this topic The research questions I pose are the following:

- How fluent are the students with respect to the algorithms for problem solving where quadratic polynomials are involved?

- Can one find indications that the students possess any conceptual knowledge of the subject?

I provide an overview of the relevant literature, with a focus on how these knowledge types relate to each other, how they influence one another, which instructional strategies are suited to instill them (also with the use of computer software), and how they can be assessed. The participants in this study belong to the first grade of an upper secondary school in Norway. The students are taking a course called mathematics 1T, which is the most theoretically oriented course in this grade of upper secondary. I have gathered data in the form of students’ answers on a test, and the interviews of students selected on the basis of their performances on the test. The qualitative analysis of the data reveals that the students have a varying grasp of the relevant procedures, and that few of them are able to use procedures effectively. Some of the mistakes made on the test could possibly be avoided if the students had greater conceptual knowledge of the subject matter. Some students show a superficial degree of conceptual knowledge