M.Ed Mathematics Student No: 15m8814 May 2017 Proposal Journey Rhodes university Mr Ben Munichinga M.Ed Mathematics Student No: 15m8814

Provisional title…….. A critical analysis of teaching geometry at van Heile’s visualisation level to facilitate learners’ attainment to level 2 and beyond.

Background and Theory My Experience in teaching geometry (8-10) My experience in teaching geometry is similar to that of the Dutch mathematics educator and researcher Van Heile (1986 Grade 8 and beyond struggle with some, recognising plane figures, describing properties of plane figures, worse to construct appropriate proofs. Studies done by Mateya (2008), Nikoludakis (2009), Atebe & Schafer (2011) revel the under-perfomance of learners

Research Questions 1. What visual materials do teachers use to teach geometry to grade 7 learners? 2. How does the visual materials help learners attain to van Heile’s level 2 of geometrical thought?

Conceptual focus Visualisation in mathematics:Arcavi (2003) defines visualization in mathematics as the ability, the process and product of creation, interpretation, use of and reflection upon pictures, images, diagrams, in our minds, on paper or with technological tools, with the purpose of depicting and communicating information, thinking about and developing previous known and advancing understanding. Visualisation & Van Heile level 1:Assisted by appropriate instructional experiences, the model asserts that the learner moves sequentially from the initial, or basic, level (visualization), where space is simply observed-the properties of figures are not explicitly recognized, through the sequence listed above to the highest level (rigor)

Focus cont….. Primary mathematics: On completion of the senior primary phase(grade 7), all learners are expected to be able to: geometry; understand the properties of shapes in two- and three dimensional space, classify and draw lines and angles and determine position and movement (mathematics Syllabus grade 4-7, NIED 2014 p.4). Transition- Level 1 to level 2 and beyond: Similarly by the end of junior secondary phase, learners are expected to be able to: Geometry; develop the ability to visualize, describe and represent lines, angles, two-dimensional and three-dimensional shapes, and their properties.

Interpretive paradigm Qualitative study Case study Research Design Interpretive paradigm Qualitative study Case study Intervention with two grade 7 and two grade 8 teachers