The Van Hiele theory, also known as the Van Hiele model or the Van Hiele levels of geometric thinking, is a theory of mathematical development that was proposed by two Dutch educators, Dina van Hiele-Geldof and Pierre van Hiele. The theory is based on the idea that students progress through a series of levels as they develop their understanding of geometry, and that these levels are hierarchical, with each level building upon the understanding and skills acquired at the previous level.
According to the Van Hiele theory, there are five levels of geometric thinking, each corresponding to a different stage of development. These levels are:
Visualization: At this level, students are able to recognize and draw basic geometric shapes, such as circles, squares, and triangles. They are able to identify these shapes in their environment and distinguish between them based on their characteristics, such as size and number of sides.
Analysis: At this level, students are able to classify shapes based on their properties, such as size, symmetry, and angles. They are also able to recognize and describe the relationships between shapes, such as congruence and similarity.
Deductive: At this level, students are able to use logical reasoning to prove geometric statements and theorems. They are able to apply their understanding of geometric concepts to solve problems and make predictions.
Informal Deductive: At this level, students are able to apply their understanding of geometry in more abstract and formal settings, such as in coordinate geometry and transformations.
Formal Deductive: At this highest level, students are able to apply their understanding of geometry in more complex and abstract settings, such as in non-Euclidean geometries.
The Van Hiele theory suggests that students typically progress through these levels in a linear fashion, with each level building upon the understanding and skills acquired at the previous level. However, the rate at which students progress through the levels can vary greatly, and some students may never reach the highest levels of geometric thinking.
One of the key implications of the Van Hiele theory is that teaching geometry should not be limited to simply memorizing formulas and theorems, but should instead focus on helping students develop their understanding of geometric concepts and their ability to apply them in real-world situations. This can be achieved through activities such as hands-on exploration, problem-solving, and the use of visual aids and manipulatives.
In conclusion, the Van Hiele theory is a valuable framework for understanding the development of mathematical thinking, particularly in the area of geometry. By recognizing the different levels of geometric thinking and the skills and understanding that students acquire at each level, educators can tailor their instruction to meet the needs and abilities of their students, and help them progress through the levels of geometric thinking in a meaningful and effective way.
properties of triangles and quadrilaterals
Second grade Preassess: See comments on first grade. Students can reason with simple arguments about geometric figures. Level 1: Analysis Children learn to analyze specific shapes and groups of shapes to find geometric properties. ERIC Document Reproduction Service No. Children at the visualization level can insepect specific examples of shapes and figure out what properties they have.
The teacher might also give an assignment to remember the principles and vocabulary learned for future work, possibly through further exercises. A teacher might say, "How could you construct a rhombus given only two of its sides? Therefore, the student does not yet have insight into which properties are essential or which ones are sufficient to define a figure. The object of thought is deductive reasoning simple proofs , which the student learns to combine to form a system of formal proofs Level 4. A student can now see how one figure could be described in different ways if it shares the same properties as another figure. Therefore the system of relations is an independent construction having no rapport with other experiences of the child. Neither of these is a correct description of the meaning of "square" for someone reasoning at Level 1.
As it goes with most learning, the earlier the better. Unpublished doctoral Dissertation, University of Georgia. Report on Methods of Initiation into Geometry. The teacher should also teach mathematical vocabulary parallel, equal, right, acute, obtuse in combination with repeated opportunities to sort and describe groups of shapes. . The original Van Hiele levels were numbered from 0 to 4 and Van Hiele claimed that all students were at least at level 0 Senk, 1989. The five levels postulated by the van Hieles describe how students advance through this understanding.
Definitions of special shapes such as rectangles are given as a list of properties that the shapes have. It is important that the teacher not present any new material during this phase, but only a summary of what has already been learned. Definitions involving essential and sufficient conditions are now understood. The objects of thought are classes of shapes, which the child has learned to analyze as having properties. By asking good questions, you help children learn what geometric properties are. The meaning of a linguistic symbol is more than its explicit definition; it includes the experiences the speaker associates with the given symbol.
He has not learned to establish connections between the system and the sensory world. With more research involving elementary students, researchers saw it necessary to classify geometric thinking that was below the Van Hiele introductory first level level 0. When you're trying to think of whether a shape could have two properties at the same time like obtuse and isosceles , it helps a lot if you're seen shapes that have both of those properties before. It helps to include, and have children include, drawings of examples in the set diagrams. In: Grouws D ed Handbook of research on mathematics teaching and learning. Properties are in fact related at the Analysis level, but students are not yet explicitly aware of the relationships.
If a figure is sketched on the blackboard and the teacher claims it is intended to have congruent sides and angles, the students accept that it is a square, even if it is poorly drawn. Deepening level 1 and moving to level 2 understanding: Guess my rule is an activity where children try to guess the rule that produced a particular group or sorting of shapes. A huge challenge can be tackling two-column proofs, which are seemingly detached from practical life applications, for the first time. According to their model and other research, students enter geometry with a low Van Hiele level of understanding. How do they work? Geometry is seen in the abstract with a high degree of rigour, even without concrete examples Khembo, 2011.
The Van Hiele Student Development Levels for Geometry Learners
Geometric reasoning starts as soon as we can start processing information and in early schooling. This should result in squares being included in the rectangle group 4 right angles and rectangles and squares being sorted in the parallelogram group 2 parallel sets of sides etc. Pierre continued to develop and refine the theory that is explored thoroughly in his 1986 book, Structure and Insight. They can identify the properties of figures, for example, they can recognise and describe a square as a figure that has all its sides equal. . How can we incorporate this? This type of activity is much more open-ended than the guided orientation.
Later, children learn properties such as "having straight sides" or " having square corners", and use them to describe shapes. Not to mention the competition we have for students' attention while they are in our classrooms. When a teacher speaks of a "square" she or he means a special type of rectangle. Unpublished doctoral Dissertation, University of Georgia. Distinction: each level has its own linguistic symbols and network of relationships.
In the next few years, elementary teachers will need to think about what they do in geometry at these grade levels, and whether it is robust enough to support what the Common Core is expecting children to learn. Attribute is another word for property in geometry. Third graders are expected to work with relationships between types of shapes. Here is some insight connecting to the Van Hiele levels for learning Geometry. The teacher may give the students an overview of everything they have learned. In this case a is true, so I can conclude that c must be true as well. It can seem like a grueling task to teach and to learn.