The purpose of this study was to increase the student's understanding of the measures of area and perimeter of polygons. The goal of the project was to create a supplemental geometry unit to develop the concept of the area and perimeter of a polygon without the use of formulas and numbers and to measure the effectiveness of this unit on student understanding. Two high school geometry classes with under 28 students each participated in this study.

The purpose of this study is to investigate the role of physical manipulatives in the teaching and learning of measurement in Grade 8. The study focuses on how the use of physical manipulatives promotes learners' mathematical proficiency in relation to the five strands of Kilpatrick, Swafford and Findell (2001). The basis of the research is a case study in the interpretive paradigm involving 18 out of a cohort of 270 Grade 8 learners in the school where I teach. The data was collected using a range of methods including: (i) baseline assessment tasks, first piloted using 7 Grade 8 learners and then given to the target group; (ii) an intervention programme with intervention tasks; (iii) a post-intervention task; (iv) observations during the intervention; and (v) individual interviews. The results of the baseline assessment and the post-intervention tasks were analysed both quantitatively and qualitatively. My research findings indicate an overall improvement of the performance after learners engaged in using physical manipulatives. The average mark of the learners in the baseline assessment task was 23% and after the intervention programme the average mark was 31 %. The responses from the learners interviewed showed that they were motivated and that the use of physical manipulatives assisted them in understanding the concepts of measurement, in particular surface area and volume. The results of my study thus reveal that the use of physical manipulatives in teaching and learning mathematics has a positive role to play in learners' understanding of surface area and volume at the Grade 8 level. The fmdings of this case study support other research regarding the importance of using physical manipulatives in teaching and learning mathematics. They align with other findings that assert that manipulatives are essential mediating tools in the development of the conceptual and procedural understanding of mathematical concepts, clarifying and helping learners to visualize abstract mathematical concepts.