Well, we only have two chapters left and our book study of * Teaching Student-Centered Mathematics PreK-2* by Van de Walle, Lovin, Karp, and Bay-Williams comes to an end. To read past posts, you can visit our

**book study archive**. Now for chapter 16…

**Chapter 16 – Developing Geometric Reasoning and Concepts**

I think many people believe that geometry is just knowing shapes…especially at the pre-k-2 level. But after reading this chapter, I am discovering that it is so much more, and I have learned ways to teach my primary students geometry using best practices. This chapter was crammed full of activities to do with children in the classroom. I learned a lot from reading it. As always, I am going to give the “gist” of the chapter, but I highly encourage you to read it fully!

The chapter begins by giving content goals across the grades based on the Common Core Standards. They are as follows:

- In kindergarten, children are expected to identify and describe various two- and three-dimensional shapes and describe their relative position using everyday language. They should also draw and build shapes as well as compose larger shapes from smaller ones.
- In first grade, children should be able to distinguish between a shape’s defining attributes and irrelevant attributes. They also work on composing shapes to create new shapes and begin to decompose shapes into smaller shapes.
- Second graders are expected to be able to recognize and draw shapes given specific attributes. They continue to work on decomposing shapes into smaller shapes.

Geometry involves a number of aspects that apply to all grade levels. This chapter includes all features, but more attention is given to shapes and properties. These aspects include:

- Shapes and properties
- Transformation
- Location
- Visualization

The chapter then went on to describe the van Hiele levels of geometric thought. The van Hiele model is a hierarchy of ways of understanding spatial ideas. The model is as follows:

Pre-recognition: **This level was not orginially part of the van Hiele levels of geometric thought, but it was added later.

Level 0: Visualization

Level 1: Analysis (Description)

Level 2: Informal Deduction

Level 3: Deduction

Level 4: Rigor

Most students at the pre-K-2 level will be at the pre-recognition level or level 0 with some children moving to level 1. It was emphasized, multiple times, that students need to have experiences. They need to explore, talk about, and interact with shapes in order to move to the next level. Also, when instruction is at a higher level, students will have difficulty understanding the concept being developed. When picking activities to do with your students, they say to keep in mind four features of effective instruction.

- Show and compare diverse examples and nonexamples.
- Facilitate discussions about shapes and their attributes.
- Examine a wider variety of shape classes.
- Challenge students with a wide range of geometric tasks.

While there is no assessment to determine which level students are at, the teacher can listen as students are engaged and answer some questions: *Can they identify common shapes? Do they understand that shapes do not change when the orientation or size changes? Do they use properties in their descriptions and discussions of shapes? Can they talk about shapes as classes?*

Then readers go on to learn about shapes and properties. Children are finding out what makes shapes alike and different, and in the process they will begin to discover properties of the shapes, including the conventional names for these properties. As I mentioned before, many activities are given to aide in this learning process.

Also, it is important that students use appropriate materials and mainpulatives as they explore. Examples are geoboards, pattern blocks, and tangrams. When building shapes, the following are approaches to making handmade models…

- plastic coffee stirrers with modeling clay
- plastic drinking straws with flexible joints
- rolled newspaper

Through building and drawing, children can focus on the properties and defining the features of shapes.

Activities are also suggested to give students more experiences when learning about transformations, location, and visualization.

Please feel free to leave your thoughts in a comment and stop back Wednesday for chapter 17, the final chapter, about helping your students use data.

Until then, enjoy your week!

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