TIAN Bundle 5 Articles and References (For Teachers) about Geometric Thinking
About van Hiele:
Malloy, C. (2002). The van Hiele Framework. Provides an explanation of van Hiele’s model.
Mason, M. (n.d.) Van Hiele Levels of Geometric Reasoning. Provides some concrete examples of various levels of the van Hiele model.
- Woleck, K.R. (2003). Tricky Triangles: A Tale of One, Two, Three Researchers in Teaching Children Mathematics, (10)1, 40-44.While the researchers focus on first grade, the article illustrates the sort of thinking at van Hiele’s lowest level of geometry.
- Maxwell, S.A. (2006). Measuring Tremendous Trees: Discovery in Action in Mathematics Teaching in the Middle School, (12)3, 132-139. The “shadow” problem comes to life in this article about measuring the height of a tree using a handmade clinometer.
- Reynolds, M.J. (2002). Letting the Cat out of the Bag….to Make Room for a Triangle in Mathematics Teacher, (95)1, 6-7.An interesting activity to introduce the idea of congruence – having groups of students figure out the shape of a triangle in a bag.
About Perimeter and Area:
- Beck, S.A., Huse, V.E., & Reed, B.R. (2007). How Does Your Mathematical Garden Grow? in Mathematics Teaching in the Middle School, (13)2, 69-76.In this article, middle school students move from determining perimeter and area to discovering functional relationships with perimeters and areas.
- Pagni, D.L. (2006). Finding Areas on Dot Paper in Mathematics Teaching in the Middle School, (12)5, 274-278.Students using dot paper to find the area of rectangles, triangles, parallelograms, and trapezoids readily see how the various formulas were derived. Sample worksheets are included.
- Cipoletti, B., & Wilson, N. (2004). Turning Origami into the Language of Mathematics in Mathematics Teaching in the Middle School, (10)1, 26-31.Explains how to effectively use origami in the classroom to teach geometric vocabulary.
- Roberts, S. (2007). On My Mind: Not All Manipulatives and Models Are Created Equal in Mathematics Teaching in the Middle School, (13)1, 6-9.Something to think about as you use readily-available manipulatives in your class.
- Tepper, A.B. (1999). A Journey through Geometry: Designing a City Park in Teaching Children Mathematics, 348-352. The description of an integrated curriculum project that would be applicable to students of all ages.
- Morris, B. (2004). The Beauty of Geometry in Mathematics Teaching in the Middle School, (9)7, 358-361. A hands-on project that allows students to be creative while learning the vocabulary of geometry.