Table of Contents

## What are the first three van Hiele levels of geometric thought?

Abstract. The van Hiele theory describes how young people learn geometry. It postulates five levels of geometric thinking which are labeled visualization, analysis, abstraction, formal deduction and rigor.

**How many phases of teaching and learning are described by the van hiele?**

To address these issues, the van Hieles proposed five sequential phases of learning: inquiry, directed orientation, explication, free orientation, and integration. They assert that instruction developed according to this se- quence promotes the acquisition of a level (van Hiele-Geldof 1984b).

**What is instructional learning phase of Van hiele?**

Van Hiele (1986) recommends a set of instructional phases that teachers should follow in order to facilitate the students’ movement between the Van Hiele levels of geometric thinking. The phases of instruction are: information, guided orientation, explicitation, free orientation and integration.

### Can a learner skip any of the van hiele levels?

Students cannot “skip” a level. The van Hieles claim that much of the difficulty experienced by geometry students is due to being taught at the Deduction level when they have not yet achieved the Abstraction level. 2. Adjacency: properties which are intrinsic at one level become extrinsic at the next.

**Which level of geometrical thinking begins with nonverbal thinking?**

The main content focus is on two-dimensional (plane) shape. This level begins with ‘nonverbal thinking’. Shapes are judged by their appearance and generally viewed as ‘a whole’, rather than by distinguishing parts.

**What geometrical skills do learners at level 3 formal deduction have?**

Level 3: Formal Deduction At this level students are able of more complex geometric concepts. They can think about properties are related, as well as relationships between axioms, theorems, postulates and definitions.

## What are the stages of pedagogy?

Specifically, these five steps include: preparation, presentation, association, generalization, and application. Herbart suggests that pedagogy relates to having assumptions as an educator and a specific set of abilities with a deliberate end goal in mind.

**What is level of rigor?**

Rigor. For the purpose of this series of modules, rigor is the cognitive complexity of a skill within a standard or of an assessment item. An. assessment has “an appropriate level of rigor” if it includes items that match the level of rigor of the skill or skills you intend. students to master.

**How do learners think about the quadrilateral at Level 2?**

In level 2 the objects of thought are geometric properties the student learnt to connect deductively. learners recognize the relationship between types of shapes thus rectangle is a quadrilateral because it has four sides.

### How do learners think about Quadrilaterals at Level 2?

**How a learner on Level 1 will define a rectangle?**

According to De Villiers (2010), the meaningful definition of a rectangle for a learner operating at level 1 can be called visual definition, where a rectangle is a figure which looks like this (draws or identifies a quadrilateral with all angles 900 and two long and two short sides) and that of a level 2 thinker is …

**What is spatial sense in geometry?**

Spatial sense is an understanding of shape, size, position, direction, and movement – being able to describe and classify the physical world we live in. Later on in school, this is referred to as ‘geometry.

## What are the van Hiele levels?

The Van Hiele levels have helped shaped curricula throughout the world, including a large influence in the standards of geometry in the US ( source ). How do they work? Geometric reasoning starts as soon as we can start processing information and in early schooling.

**What is the van Hiele model?**

The van Hiele model of development of geometric thought. In Learning and Teaching Geometry , K-12, 1987 Yearbook of the National Council of Teachers of Mathematics. Edited by Mary Montgomery Lindquist, 1-16. Reston, VA: National Council of Teacher of

**What do the van Hieles have to do with education?**

As was indicated above, the van Hieles assert that progress through the levels is more dependent on the instruction rrolceived thalr on age or matur- ation. Thus the method and organization of instruaiou, as well as the content and materials used, are important areas of pedagogical concern.

### What did Pierre van Hiele mean by the term plateau?

Pierre van Hiele noticed that his students tended to “plateau” at certain points in their understanding of geometry and he identified these plateau points as levels. In general, these levels are a product of experience and instruction rather than age. This is in contrast to Piaget ‘s theory of cognitive development, which is age-dependent.