Chapter 17: "Developing Geometric Thinking and Concepts"
Whether you are a kindergarten teacher or an eighth-grade teacher, you are teaching a handful of geometric concepts. Geometry-based instruction is found within all grade levels, which exemplifies its developmental progressions. Students learn a set of geometric concepts in kindergarten that are further built upon in first-grade. Then, the geometric concepts they learned in first-grade are built upon in second-grade. As students cognitively mature, this building process continues. You may worry that some students will not properly progress in their geometric abilities. You may worry that the activities that you implement are not effectively teaching the concepts. Considering the differing learning needs amongst students, that is a valid concern. However, according to Van de Walle et al. (2014), “All learners in your classroom are capable of growing and developing in the ability to think and reason in geometric contexts” (p. 346). So, do not be so hard on yourself. Your students will learn their geometric concepts. And, to ease your worries, I am providing you with some helpful teaching tips. These do not cover every concept that every grade covers. But, they can easily be adapted to fit your particular instruction.
- Shapes and Properties: Two-dimensional and three-dimensional shapes are the earliest concepts taught. Students must have a deep understanding of a variety of shapes and their corresponding attributes, in order to develop more complex geometric reasoning (Van de Walle et al., 2014). If you search Pinterest, you will find hundreds of activities that are supposed to teach students about shapes. Although it can be fun to scroll through the crafty projects and cutesy sayings, you must be cautious. Many of those Pinterest activities do not show shapes in multiple forms. For instance, a triangle is always shown with three equal sides and the vertex on top. Rectangles are always shown horizontally, instead of vertically. Shapes should not be shown in the same position for every activity (Van de Walle et al., 2014). Switch it up! Turn the triangle upside down. Turn the rectangle vertically. It is beneficial for student to see two-dimensional and three-dimensional shapes in their multiple forms. Instead of labeling them from rote memorization, they must pay close attention to the shapes’ attributes. Consequently, this strengthens their ability to reason geometrically.
- Visualization: Van de Walle et al. (2014) explained, “Visualizations might be called ‘geometry done with the mind’s eye.’ It involves being able to create mental images of shapes and then turn them around, thinking about how they look from different viewpoints- in some cases predicting the results of various transformations” (p. 370). That seems complicated, right? How are young students supposed to mentally manipulate shapes? Well, do not panic! Development of visualization skills will naturally progress as students cognitively develop. However, regardless of cognitive ability, their ability to mentally manipulate shapes is dependent on their familiarity with shapes’ attributes (Van de Walle et al., 2014). If you want to support students’ visualization skills, you must implement activities that require them to physically manipulate shapes. They need that foundation to scaffold their ability to perform mental manipulation tasks. I suggest providing students with shape tiles and instructing them to create a new shape from them. They will have to flip and turn the shapes, in order to fit them all together (Van De Walle et al., 2014). While they are physically manipulating them, they are simultaneously manipulating the shapes in their minds. Eventually, with more practice and cognitive maturity, students will visualize shapes without physical models.
"Caution: Venn Diagrams Ahead!"
Do you use Venn diagrams with your students? I am willing to bet that your answer is yes. Venn diagrams are popular graphic organizers, which most teachers implement for students to record information in a concise way. Typically, these graphic organizers are used to enhance students’ reading comprehension. They can compare and contrast characteristics within stories, by writing contrasts in the nonoverlapping portions and comparisons in the overlapping portions (Kimmins & Winters, 2015). But, Venn diagrams can be used for another instructional purpose. Have your students had difficulties classifying shapes by certain attributes? Well, Venn diagrams can help! Kimmins and Winters (2015) explained:
- In the subject area of mathematics, the circles typically represent not things, but their attributes or characteristics. The things are typically mathematical objects, such as numbers or geometric figures. The objects themselves, or representations of the objects, are placed in the circles instead of characteristics of the objects being placed in the circles. In this case, the Venn diagram is used to sort the objects into sets, or in other words, to classify the objects according to whether they possess the characteristics represented by the circles. (p. 487)
Classroom Activity: Kinesthetic Angles
According to Common Core State Standard (2010) 4.G.A.1, fourth-graders should be able to draw right, acute, and obtuse angles. To practice this skill, students are typically instructed to draw the various angles on worksheets. Although the repetitive worksheets are intended to help students refine their angle-drawing skills, they are not overly engaging. As we all know, fourth-graders are full of energy. They like to move and groove! If the worksheets do not engage the students, they will struggle to truly master this geometric skill. Therefore, I have created two angle activities that embody kinesthetic learning. When students are kinesthetically engaged in a learning activity, they are more likely to master the skill being practiced. The fun, kid-friendly nature of the activity makes it much more memorable. Students have an easier time recalling a skill that they practiced with physical motions, instead of writing on a worksheet. In my first example, I demonstrate how to combine this geometric skill with dancing. Break out the music! In my second example, I demonstrate how students can practice drawing angles in the great outdoors. Do not be afraid to trade in pencils for some colorful chalk. Your students are going to have a lot of fun with these activities. Yet, most importantly, they will master drawing right, acute, and obtuse angles.
Independent Practice: Magical Shape Hunt
Early childhood learning lays the foundation for the geometric concepts that upper-elementary students learn. According to Common Core State Standard (2010) K.G.A.2, by the end of kindergarten, students should be able to identify two-dimensional and three-dimensional shapes. That seems simple enough, right? Unfortunately, identifying these shapes is not a simple skill for some kindergarteners. It is difficult for them to transition from the two-dimensional terminology to the three-dimensional terminology. It is even more difficult for them to differentiate between the different types of shapes. Kindergartens must be explicitly taught the different attributes between two-dimensional and three-dimensional shapes. Additionally, they must have a plethora of opportunities to practice identifying each shape with its correct name. "Magical Shape Hunt" is the perfect independent practice for identifying three-dimensional shapes! This online game is designed for young children, so it is developmentally appropriate for kindergarteners. They are provided with auditory directions and vivid visuals. Students are responsible for helping Peg and Cat find Mermaid's lost jewels. But, these jewels are different three-dimensional shapes, such as cubes, spheres, and cylinders. Prior to finding the jewels, the game provides the students with a picture of the shape and an explanation of its attributes. This reinforces the information you explicitly teach in the whole-group setting. Then, they must scoop the proper jewels with their net. If they accidently scoop the wrong-shaped jewel, the game indicates the mistake with a specific sound effect. Additionally, the narrator says, "Uh oh. That's a ______." So, even when they scoop the wrong jewel, they are reminded of that jewel's shape. This game will be intriguing for your kindergartens, which will help them pay close attention to the mathematical component. Click on "Independent Practice" to access this awesome resource.