Teaching geometrical concepts of measurement - Essay Example

Teaching Geometrical Concepts of Measurement Teaching common geometrical concepts relating to measurement March Teaching common geometrical concepts relating to measurement Measurement has a number of geometrical concepts behind it that are in common, regardless of whether it involves length, area, volume, weight, angles, time, etc. Teaching students these common geometrical concepts could help them to better understand geometry and acquire the skills and tools necessary to apply it properly. This paper seeks to identify these common geometrical concepts relating to measurement so that they can be given greater attention in class.

It discusses the use of standard units, the use of tools to measure, the importance of precision and accuracy, estimation, and the use of manipulatives and other visual aides. In addition, the van Hiele Levels of Geometric Thinking is also very important in math instruction. It has its foundation in “an appreciation for developmental differences in individuals based on both their experiences and maturation” (Class notes, 2011). Some key points of the van Hiele Levels and their importance when teaching students geometrical concepts are therefore explained as well.

The first point students need to grasp is what measurement actually is and what it involves. Measurement is technically “a number that indicates a comparison between the attribute of the object (or situation, or event) being measured and the same attribute of a given unit of measure” (Van de Walle, 2007, p. 375). They must be able to appreciate that all objects have certain attributes that can be measured before they can learn how to do so. Measurement would also involve making comparisons with other objects with the same kind of attributes.

Although most attributes can be compared directly, some, such as volume, may require using indirect methods. Also, some younger students may need help in grasping how smaller units form larger measures. After knowing what attribute to measure, students would then need to select a unit of measure. It is therefore necessary to also make students familiar with the most frequent units of measure referred to as ‘standard units’. They should be able to recognize and make sense of measurements. With some measures such as capacity, it may help to make the students think of ‘filling’, ‘covering, or ‘matching’ the measure with the attribute.

Furthermore, it would be helpful to point out how some measures are related, such as length, perimeter, area and volume, and hence the concept of basic measures. Besides conceptual knowledge, it is necessary to teach the use of tools so that students become proficient in their use and make meaningful and accurate measurements. This would therefore need to include an understanding of how the instruments work. Also, it is usually necessary to explain how the instrument actually compares to using the units (Van de Walle, 2007, p. 377). Achieving precision and accuracy in measurement may require extra time and effort, but it is important because many functions, processes, experiments, etc.

rely on them to be successful. Once the basic concepts are understood, estimation is another skill that could help students ensure their measurement is sound. It also helps students to focus on the attribute being measured and the measuring process, it provides intrinsic motivation to see how accurate the estimation was, it develops familiarity with the unit, and it promotes multiplicative reasoning (Van de Walle, 2007, p. 378). Manipulatives and other visual aids can also play a useful role as informal units for learning to measure until the student is competent to use standard units.

Virtual manipulatives have also proven useful if concrete manipulatives cannot be obtained (Hancock & Lane, 2010). An understanding of the van Hiele levels of geometric thought helps the teacher to know why differences in thinking on geometry exist and how they develop in students. The model, illustrated below, consists of five hierarchical levels with respect to understanding spatial ideas, each of which describes the thinking processes used. The van Hiele theory of geometric thought (Source: Van de Walle, 2007, p. 412) The five levels beyond precognition are visualization/recognition, analysis/descriptive, informal deduction, deduction and rigor.

Visualization involves identifying, naming, comparing and operating on geometric shapes based on their appearance. Analysis involves descriptions of components and relationships, and the discovery of properties of the shapes. Informal deduction involves logically interrelating these properties using informal arguments and deduction involves proving theorems deductively, establishing interrelationships among networks of theorems in Euclidean geometry, and proving facts inductively. Rigor is achieved when students are able to establish theorems in different postulational systems and compare them.

(Alagic, 2011) This model also highlights the importance of teaching according to the level of conceptual understanding of the student. Also, students who are finding geometry difficult may need to have pass through more basic levels of understanding first, before progressing to a higher level.References Alagic, Mara. (2011). Developing geometric thinking: van Hiele’s levels (presentation). WSU. Class notes. (2011). Understanding geometric principles. WSU. Hancock, Gerry & Lane, Catriona. (2010).

Case study: the effectiveness of virtual manipulatives in the teaching of primary mathematics. University of Limerick. Retrieved March 13, 2011 from http://ulir.ul.ie/handle/10344/450. Van de Walle, John A. (2007). Elementary and Middle School Mathematics: Teaching Developmentally. Sixth Edition. Allynn and Bacon.