Date of Award

2010

Thesis Type

PhD

Document Type

Thesis

Divisions

Faculty of Education

Department

Department of Mathematics and Science Education

Institution

Universiti Malaya

Abstract

The purpose of this study was to investigate preservice secondary school mathematics teachers (PSSMTs)' subject matter knowledge (SMK) of perimeter and area. Specifically, this study aimed to investigate PSSMTs’ five basic types of knowledge of perimeter and area, namely conceptual knowledge (CK), procedural knowledge (PK), linguistic knowledge (LK), strategic knowledge (SK), and ethical knowledge (EK). This study also aimed to investigate PSSMTs' levels (low, medium, high) of SMK of perimeter and area. Data of this study was collected using clinical interview technique. Interview sessions were recorded using digital video camera and tape recorder. Subjects of this study consisted of eight PSSMTs enrolled in a Mathematics Teaching Methods course at a public university in Peninsula Malaysia. They were selected based on their majors (mathematics, biology, chemistry, physics) and minors (mathematics, biology, chemistry, physics). With regard to CK, findings of this study showed that all PSSMTs understand the inverse proportion between the number of units and the unit of measure. Six out of eight PSSMTs knew the relationship between area units and linear units of measurement that area units are derived from linear units based on squaring. Nevertheless, most of the PSSMTs did not know that there is no direct relationship between perimeter and area. None of the PSSMTs were able to develop the formula for the area of a rectangle. It was apparent that all of them lack conceptual knowledge underpinning the formula for the area of a rectangle. With respect to PK, findings of this study depicted that at least half of the PSSMTs had adequate procedural knowledge of converting standard units of area measurement. Most of the PSSMTs had adequate procedural knowledge of calculating perimeter and area of composite figures. Five, two, and three PSSMTs were able to develop the formula for the area of a parallelogram, triangle, and trapezium, respectively. Concerning the LK, findings of this study demonstrated that most of the PSSMTs used appropriate mathematical symbols to write the formula for the area of a rectangle, parallelogram, triangle, and trapezium. Most of the PSSMTs used appropriate mathematical terms to justify their selection of shapes that have a perimeter and an area. All the PSSMTs understand the general measurement convention that perimeter is measured in linear units while area is measured in square units. Nevertheless, they had limited knowledge about the conventions pertaining to writing and reading of Standard International (SI) area measurement units. For the SK, findings of this study revealed that three types of strategies were employed by the PSSMTs to compare perimeters as well as areas, namely formal, semi-formal, and informal methods. Two types of strategies used to verify the answers for perimeters and areas were emerged, namely recalculating strategy and alternative method. Three types of strategies used to solve the fencing problem were identified, namely looking for a pattern strategy, trial-and-error strategy, and differentiation method. PSSMTs used the cut and paste strategy, partition strategy, and algebraic method to develop the formula for the area of a parallelogram, triangle, and trapezium, respectively. With respect to EK, findings of this study exhibited that all PSSMTs had taken the effort to justify the selection of shapes that have a perimeter and an area. Several PSSMTs had attempted to examine the possible pattern of the relationship between perimeter and area, to formulate and test generalization pertaining to the relationship between perimeter and area. However, most of the PSSMTs did not check the correctness of the answers for the perimeters and areas. With regard to the overall level of SMK of perimeter and area, only one of the PSSMTs secured a high level of knowledge, six with medium level and one at low level. The findings of this study lead to the conclusion that many PSSMTs do in fact lack SMK of perimeter and area they are expected to teach.

Initial

khm

Additional Information

Thesis (PhD) – Faculty of Education, Universiti Malaya, 2010.

Download

Share

COinS