Improving Measurement and Geometry in Elementary Schools

Teaching Strategies

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Cluster concepts

Research shows that when students learn concepts and relationships in isolation, they often forget these ideas or are slow in making the connections between them. A thinking process called "clustering," used to group, unify, integrate, and/or make connections between concepts, is something that students and adults use routinely, often without even realizing it. A teacher can use this approach to cluster mathematical ideas, concepts, relationships, and objects in order to reveal common characteristics. This presentation in turn helps students to categorize and classify those ideas or objects and to remember properties and attributes, which makes the learning more meaningful.

Clustering Quadrilaterals

Some students can best understand quadrilaterals when the teacher presents them as a unifying concept. Under the process of clustering, a teacher guides students in studying, comparing, and classifying all quadrilaterals according to their attributes--not only the square and the rectangle, but the plain quadrilateral, the rhombus, the parallelogram, the trapezoid, and the isosceles trapezoid. This approach enables students to have a better sense of four-sided figures, their properties, and characteristics, so that they can eventually internalize the idea and even develop a hierarchy of quadrilaterals based on properties.

Other ideas for clustering in geometry

and measurement

· special lines in triangles such as medians, perpendicular bisectors, altitudes, and bisectors of angles

· special lines of circles

· the classification of Platonic Solids

· the relationship of various types of tessellations

· proportionality

· Archimedean Solids

· inscribed and circumscribed geometric figures

· the classification of angles

· nets of specific solids, such as cubes, pyramids, etc.

· the relationship between area and perimeter of quadrilaterals, triangles, circles, etc.

· concepts of symmetry of geometric figures in two and three dimensions

· the similarity and congruency of polygons

· the relationship between surface area and volume.