Question 1 / Vraag 1 (8)
Describe an activity that shows how you will teach lenght measurement to pre-scholars developing the following:
a)Transitive reasoning
b)Unit iteration reasoning
Question 2 (10)
The Van Hiele theory of the levels of geometric thought and development is important for teaching geometry. Draw the theory of geometric thought and explain the properties of this theory.
Question 1: To teach length measurement to pre-scholars and promote their development in transitive reasoning and unit iteration reasoning, you can engage them in a hands-on activity such as measuring objects using non-standard units, like their own hands or blocks.
a) Transitive Reasoning: Transitive reasoning involves understanding the relationship between different objects or measurements. In this activity, you can demonstrate transitive reasoning by comparing the lengths of different objects. Start by measuring the length of a few objects using non-standard units, such as blocks. Then, ask the pre-scholars questions like "Is this object longer or shorter than the previous one?" or "How many blocks long is this object compared to the previous one?" This will encourage them to use transitive reasoning to make comparisons and order the objects based on their lengths.
b) Unit Iteration Reasoning: Unit iteration reasoning refers to the understanding that a longer length can be obtained by repeatedly adding or iterating a shorter unit length. To promote unit iteration reasoning during the activity, you can have the pre-scholars measure the lengths of objects using a non-standard unit, like their own hand span. Initially, show them how to measure an object using their hand span and then ask them to measure a longer object by iterating the hand span unit several times. For example, if their hand span measures 4 blocks long, they can measure a longer object by counting how many hand spans it covers. This will encourage them to apply the concept of unit iteration reasoning to determine the length of longer objects.
Question 2: The Van Hiele theory of the levels of geometric thought and development is essential in understanding how students learn and develop geometric concepts.
The theory consists of five levels:
1. Visualization: The first level focuses on recognizing and describing basic geometric shapes and their properties. Students at this level primarily rely on visual observations and can identify shapes based on their appearance.
2. Analysis: At this level, students start to investigate the properties and relationships between geometric figures. They begin to understand the characteristics that define different shapes and make connections between them.
3. Informal Deduction: In this level, students start to justify their geometric conjectures and begin to use deductive reasoning. They form logical arguments based on their observations and develop informal proofs.
4. Deduction: At this level, students work with formal proofs and deductive reasoning. They can derive geometric theorems and justify their claims using deductive arguments.
5. Rigor: The highest level of the Van Hiele theory implies a comprehensive understanding of the formal system of geometry. Students can analyze and prove theorems through formal proofs and abstract reasoning.
The Van Hiele theory emphasizes that students need to progress through each level by building upon their understanding. It is crucial for educators to guide students through appropriate activities and experiences that align with their current level of geometric thought.
By considering the Van Hiele theory, teachers can scaffold their instruction, provide appropriate tasks, and assess students' progress accurately. This theory helps educators understand the developmental stages of geometric learning and supports the transition from visual recognition to formal proofs.