Geometry: Dina Van Hiele-Geldof

Many students find difficulty understanding mathematics beyond the straightforward drills. The concept of a mathematical proof seems to be troublesome for students, but proofs are an important part in mathematics. If a student is presented with a conjecture, the only way that student can safely be sure that it is true, is by constructing a valid mathematical proof. A student who has the ability to write down a valid proof has indicated that they possess a thorough understanding of the problem. Some proofs sometimes require a deeper understanding of the theory in question before there are efforts to prove the conjecture. Unfortunately, the difficulties in understanding the idea of proofs starts from elementary school through the first years

They saw the difficulties that students were facing with understanding geometry, therefore, conducted research with the goal of understanding the children’s levels of geometric thinking. The Van Hieles knew that students needed to have more experience in thinking at lower levels and fully understanding the concepts in order to later be able to write geometric proofs [5]. They developed a model that takes the learner through five levels of understanding, which are not age-dependent but are more related to the experiences of the students. The levels are sequential, therefore, students need to pass through the levels 0 through 4 in order as their understanding increases. Instruction level must not be higher than the level of the student because it will inhibit the student from learning [6]. The five levels are sequential and hierarchical and they start at visualization then to analysis then to informal deduction then to deduction, and finally to rigor (Table 1). This theory is not flawless, but it is a sufficient model of the progress of geometrical

Computers allow the student to interact with manipulations of figures. The students are able to move, reflect, rotate, or stretch a figure. They can observe how the figure is changing along with its properties, and are even able to easily create their own figures for experimentation. Computers provide students with a more manageable, flexible, and a clean manipulative [4]. Students using computers in discovery learning are encouraged to develop conjectures and pose problems. The computers provide a framework for problem solving, help focus student attention, and increase