Preservice secondary school mathematics teachers' knowledge of trigonometry: Subject matter content knowledge, pedagogical content knowledge and envisioned pedagogy.

摘要

The education community recognizes that subject matter content knowledge and pedagogical content knowledge form the basis for effective teaching. The purpose of this study was to assess the subject matter content knowledge, pedagogical content knowledge, and envisioned practice of preservice secondary school mathematics teachers in the area of trigonometry.;Data was collected in two phases. Phase I involved 14 preservice secondary mathematics teachers who had completed at least two methods courses in mathematics education and a practicum course. All participants in phase one of the study completed (1) a test measuring knowledge of trigonometry, (2) a measure of pedagogical content knowledge with respect to trigonometry via two card-sorting activities, and (3) two concept maps.;Five case studies formed the basis for phase two of the study. The five cases were selected after a preliminary analysis of the data from phase one. Individuals were chosen to achieve distinct profiles: (1) high subject matter content knowledge and (2) low subject matter content knowledge. Each case study participant was interviewed twice using semi-structured interviews designed to delve deeply into their trigonometric knowledge and envisioned teaching practice. Interview data were transcribed and analyzed using the qualitative methods of constant comparison and content analysis.;Subject matter content knowledge items were scored for correctness with credit given for partially correct solutions. The card sorting activities and concept maps, and the interview data were analyzed using primarily qualitative methods.;Results indicate that these preservice secondary school mathematics teachers have poorly developed understanding in such areas as: radian measure of angles, inverse trigonometric functions, reciprocal functions, periodicity, and co-functions. Many of the scores on the test of trigonometric knowledge were below the 50 percent correct level. These findings agree with prior research findings that preservice teachers' knowledge of many areas of school mathematics is weak and considerably below what is usually expected. The preservice teachers' concept maps of trigonometric ideas generally focused on either right triangles or notions of function. The sequencing task revealed that these preservice teachers seldom considered prerequisite skills in planning lessons.