Spatial sense is an important ability in mathematics. Formula application is very different from spatial concept acquisition. But it is often observed that in schools students learn spatial concepts by memorizing instead of understanding. In the past academic year we had tried out and developed a series of learning activities based on van Hiele’s model for guiding learners to explore the cube and its cut sections. The ideas in origami, and mathematical modelling by manipulative as well as mathematical software are integrated into our study. This paper gives a brief account on our works. We start by presenting a sequence of math-rich learning tasks, followed by some related folding ideas and mathematical background analysis. Finally we round up our paper with a concise discussion on some major elements of our design based on the van Hiele learning phases.

Spatial sense is an important ability in mathematics. Formula application is very different from spatial concept acquisition. But it is often observed that in schools students learn spatial concepts by memorizing instead of understanding. In the past academic year we had tried out and developed a series of learning activities based on van Hiele’s model for guiding learners to explore the cube and its cut sections. The ideas in origami, and mathematical modelling by manipulative as well as mathematical software are integrated into our study. This paper gives a brief account on our works. We start by presenting a sequence of math-rich learning tasks, followed by some related folding ideas and mathematical background analysis. Finally we round up our paper with a concise discussion on some major elements of our design based on the van Hiele learning phases.

Summaries in Afrikaans and English / Outcomes-Based Education forms the foundation of South Africa's revised national education curriculum, known as The Revised National Curriculum Statement Grades R-9. The Van Hiele Model, developed for the teaching and learning of geometry, has already been used successfully in the school curricula of the Netherlands and Russia. Strong support for this theory exists in leading countries like America and Europe. This study has investigated the possible relationship between the Van Hiele theory and the "Revised National Curriculum Statement Grades R-9" and through critical evaluation found a great compatibility between them. Both are giving strong support for the spiral approach to mathematics education. It is recommended that all geometry learning programmes and teaching units be moulded on the Van Hiele Model. / Suid-Afrika se hersiene nasionale onderwyskurrikulum, die "Revised National Curriculum Statement Grades R-9" word deur uitkomsgebaseerde onderwys gefundeer. Die Van Hiele Model vir die onderrig en leer van meetkunde, is suksesvol in skoolkurrikula van Nederland en Rusland toegepas en geniet wye steun in lande soos Amerika en Europa. Hierdie navorsing het die moontlike verband tussen die Van Hiele raamwerk en die nuwe kurrikulum ondersoek en deur kritiese evaluering baie sterk versoenbaarheid tussen die "Revised National Curriculum Statement Grades R-9" en die Van Hiele Model gevind. Verder is ook aangetoon dat beide sterk gebruik maak van die spiraalbenadering in wiskundeonderwys. Aanbevelings in die verband is dat leerprogramme en onderrigeenhede wat die kurrikulum vir meetkunde in skole implementeer op die Van Hiele Model geskoei word. / Mathematical Sciences / M. Sc. (Mathematics Education)

Summaries in Afrikaans and English / Outcomes-Based Education forms the foundation of South Africa's revised national education curriculum, known as The Revised National Curriculum Statement Grades R-9. The Van Hiele Model, developed for the teaching and learning of geometry, has already been used successfully in the school curricula of the Netherlands and Russia. Strong support for this theory exists in leading countries like America and Europe. This study has investigated the possible relationship between the Van Hiele theory and the "Revised National Curriculum Statement Grades R-9" and through critical evaluation found a great compatibility between them. Both are giving strong support for the spiral approach to mathematics education. It is recommended that all geometry learning programmes and teaching units be moulded on the Van Hiele Model. / Suid-Afrika se hersiene nasionale onderwyskurrikulum, die "Revised National Curriculum Statement Grades R-9" word deur uitkomsgebaseerde onderwys gefundeer. Die Van Hiele Model vir die onderrig en leer van meetkunde, is suksesvol in skoolkurrikula van Nederland en Rusland toegepas en geniet wye steun in lande soos Amerika en Europa. Hierdie navorsing het die moontlike verband tussen die Van Hiele raamwerk en die nuwe kurrikulum ondersoek en deur kritiese evaluering baie sterk versoenbaarheid tussen die "Revised National Curriculum Statement Grades R-9" en die Van Hiele Model gevind. Verder is ook aangetoon dat beide sterk gebruik maak van die spiraalbenadering in wiskundeonderwys. Aanbevelings in die verband is dat leerprogramme en onderrigeenhede wat die kurrikulum vir meetkunde in skole implementeer op die Van Hiele Model geskoei word. / Mathematical Sciences / M. Sc. (Mathematics Education)