Geometry thinking
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Geometry thinking involves mathematical reasoning within the domain of geometry. It considers the skills students are expected to develop, such as visual, verbal, drawing, logical, and applied thinking. There are five levels of understanding geometry concepts called the van Hiele levels. Level 1 involves recognizing figures by appearance. Level 2 sees figures as collections of properties but not relationships between properties. Level 3 understands relationships between properties and figures and can create definitions. Level 4 can construct proofs using axioms and definitions. Level 5 comprehends the formal aspects of deduction across mathematical systems.
Geometry thinking
- 1. Geometry thinking •is a form of mathematical thinking within a specific domain •Considers what the students are expected to be able to do in geometry and accordingly model and understand their thinking
- 2. Geometry thinking skills • Visual: • Verbal • Drawing • Logical • applied
- 3. What are the van Hiele levels of geometry understanding? A . There are five levels, which are sequential and hierarchical. They are: Level 1 (Visualization): Students recognize figures by appearance alone, often by comparing them to a known prototype. At this level, students make decisions based on perception, not reasoning. Level 2 (Analysis): Students see figures as collections of properties. They can recognize and name properties of geometric figures, but they do not see relationships between these properties. When describing an object, a student operating at this level might list all the properties the student knows, but not discern which properties are necessary and which are sufficient to describe the object.
- 4. Level 3 (Abstraction): Students perceive relationships between properties and between figures. At this level, students can create meaningful definitions and give informal arguments to justify their reasoning. Logical implications and class inclusions, such as squares being a type of rectangle, are understood. Level 4 (Deduction): Students can construct proofs, understand the role of axioms and definitions, and know the meaning of necessary and sufficient conditions. At this level, students should be able to construct proofs such as those typically found in a high school geometry class.
- 5. Level 5 (Rigor): Students at this level understand the formal aspects of deduction, such as establishing and comparing mathematical systems. Students at this level can understand the use of indirect proof.