Academic journal article Education

Pulling out All the Stops

Academic journal article Education

Pulling out All the Stops

Article excerpt

Students not majoring in mathematics and sciences often perceive mathematics as an abstract, rigid field that has little or no application in daily life. Mathematics teachers, on the other hand, are increasingly dissatisfied by student achievement and lack of conceptual understanding. Thus, current mathematics education leaves both parties discontent. Still, in many secondary schools and college mathematics courses, lecturing remains the most common form of instruction (Wilson, 1996). In this form of teaching, the students are mostly passive (Wilson, 1994; Roth, 1994). This pedagogy assumes that a transfer of knowledge from an expert to a passive learner is possible; however, research indicates that this kind of instruction causes students to learn facts in isolation, often forgetting the reasoning behind the explanations (Roth, 1994). Research indicates that this approach neither encourages nor enhances learning that fosters conceptual understanding (Wilson, 1994; Thorton & Sokoloff, 1989; Hestenes, Wells, & Swackhamer, 1992). Brownell (1987) points out that majority of mathematics instruction is based on giving an algorithm and later asking student to practice it, making mathematics education similar to following a recipe, where the reasoning behind a procedure is often lost. As instructors, we want students to make connections between mathematical ideas, but we do not always provide them with opportunities to do so.

With the publications of NCTM Standards (1989) and AMATYC Standards (1995) there has been an increased emphasis on students discovering the mathematics they are learning, making hypotheses and conjectures and then testing them. Countryman (1992) states that students can construct mathematics "only by exploring, justifying, representing, discussing, using, describing, investigating, predicting, in short by being active in the world" (p. 2). The need to teach mathematics through real-life applications, strengthening problem-solving skills, using collaborative learning as a tool, increasing communication skills in the area of mathematics and alternative assessment strategies have also been stressed frequently in recent literature (NCTM Standards, AMATYC Standards, 1995).

Despite these recommendations, the predominant form of education in many high schools and community colleges remains lectures. Although, collaborative work is often incorporated, what is typically discussed in collaborative groups is a reiteration of the steps to a procedure already outlined by the instructor. Students work on examples identical to those the instructor has previously solved, simply using different numbers. Even if the NCTM and AMATYC recommendations are followed, not all the recommendations are followed in the same course all of the time.

Approach

This paper discusses how the NCTM and AMATYC suggestions were utilized in an urban community college and a high school to teach a prealgebra course that included arithmetic, basic geometry and introductory algebra topics. In both settings, students had seen the topics repeatedly, but had not sufficiently mastered them.

The first assertion of our teaching philosophy was that students would learn what they perceived as valuable and get motivated if they saw the relevance of the concepts in daily life; therefore, the approach used must first make a connection between the mathematics to be learned and its application to a real situation. Most textbooks and classroom instruction start with an abstract treatment of the topic followed by drills; only at the end do they discuss its applications. We switched the order, first giving an example of a situation, whose solution required the mathematics we wanted students to learn. We used a textbook grounded in this philosophy. Each activity depicted a real-life scenario and data (on such problems, since real-life data can be cumbersome to manipulate, students were allowed to use calculators). …

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