VAN HIELE GEOMETRICAL THINKING 

The van Hiele geometrical thinking is the widely used model to understand and categorizing learners’ (pupils and students) geometrical thinking. The model’s main idea is that learners progress through a sequence of discrete, qualitively different levels of geometric thinking for a particular topic that they confront. To help learners to elevate from one level of geometric thinking to the next level of geometric thinking, phase-based instruction is being used to so. Both the model and instruction were developed by Pierre and Dina van Hiele to help teachers to guide their pupils and students in learning geometry. 

PHASE-BASED INSTRUCTION 

Phase-based instruction consist of five phases of learning which include Phase 1 (Inquiry), Phase 2 (Guided orientation), Phase 3 (Explicitation), Phase 4 (Free orientation) and Phase 5 (Integration). 

TOOLS INCORPORATED WITH PHASE-BASED INSTRUCTION 

There are many pedagogical tools that can be used as mediator to implement phase-based instruction in helping learners to elevate from one level of geometrical thinking to another level of geometrical thinking. 

1.   Learning video       

By using video, learners can make a mental representation from the semantic understanding of geometry lesson and helps them in remembering symbols or pictures naturally. There are some other features of video that make it practical to be used in teaching geometry such as: 

1. The learning video can be played repeatedly
2. The learning video can be fast forwarded or slowed down 
3. The is no specific requirements for space
4. Its operation is relatively easy 

2.   GeoGebra 

GeoGebra is a dynamic geometry software that has been designed to be used to teach geometry topics. GeoGebra can be incorporated with phase-based instruction as this software can demonstrate 3-dimentional and 2-dimentional objects. 

3. Geometer’s Sketchpad (GSP) 

Geometer’s Sketchpad (GSP) is another dynamic geometry software was created by Nicholas Jackiw in 1991. This software has the ability to draw, measure, calculate, and script geometric shapes and figures. By using GSP learners can construct and explore the object by dragging the object with mouse. Learners also can easily create, edit, and manipulate accurate geometrical constructions on the computer screen. 

4. Lesson study 

Lesson study is where teachers collaboratively work on geometry lesson. These are some of the steps in implementing lesson study:

1. Identify the same goal between teachers 
2. The teachers plan the lesson 
3. Observe the lesson that is taught by one teacher
4. The teachers revise the lesson 
5. Observe the lesson that is being taught a second time by the teacher 
6. Repeat the process if necessary

By using lesson study, teachers can design suitable activities by using phase-based instruction to elevate learner’s van Hiele geometrical thinking. 

Reference:

• Abu, M. S. and Abidin, Z. Z. (2013). Improving the levels of geometric thinking of secondary school students using geometry learning video based on van hiele theory. International Journal of Evaluation and Research in Education (IJERE), 2(1), 16–22.
• Adulyasas, L. (2016). Enhancing Secondary Students’ Geometric Thinking and Teachers’ TPACK Through Lesson Study Incorporating Phas-Based Instruction Using GSP. PhD thesis, Universiti Sains Malaysia, Penang.  
• Mazlan, Z. Z., Meng, C. C., and Abd. Hamid, M. F. (2019). Achievement of Dual Language Learners in The Study of Nets. North American GeoGebra Journal, 8(1), 69–93.