Geometry

Geometry and why it Should Be Physical

Geometry is one aspect of mathematics that should be made as physical as possible for the students. Having physical manipulatives will allow students to become more comfortable with the 2D and 3D shapes and have a better understanding of key concepts such as symmetry, congruency, and similarity. One of the main fundamental aspects of geometry is visualization, a study conducted in 2004 states, “visual reasoning as ‘seeing to think’” (Whiteley 2004). Since visualization is such an important aspect of geometry allowing students to use physical manipulatives will help them improve on their own visual thinking. Below is an example of an activity that presents geometry to the students in a physical form.

Important Terms

When learning about geometry this week three key terms became apparent. These terms are essential to teaching geometry and if the student is unable to understand these terms then they will have a difficult time throughout the geometry unity.

Similar: A shape is described as similar if they have the same shape with sides in proportion to another. Similar shapes are an enlargement or reduction of the other

Congruent: shapes are said to be congruent if one can be transformed into the other through a series of flips slides and/or turns. Congruence can also be used to describe specific components of shapes. An example of this is if the angle or side length are the same then the shapes are said to have congruent sides or angles. Congruency can be explained as a shape having equal properties, which could be the whole shape is equal to another or just a side or angle.

Symmetry: There are two types of symmetry, reflective and rotational. Reflective is when a shape is divided by a line or plane and the opposite side are mirror images of each other. Reflective symmetry is easily explained as being the same on both sides of the shape. Reflective symmetry is how many times a shape can fit over itself when it is rotated.

These terms should be a starting point for teachers who are introducing geometry to their students. With these words students will be able to have a foundation for the geometry unit. For more definitions in the geometry strand of mathematics, Geometry definitions  is a great resource that students can utilize to help them remember some more important terms.

The Use of Children’s literature

The story that was used to introduce shapes to our class this week was ‘The Greedy Triangle.’ This book was not only an overview of the properties of shapes and what they are called but also gave real life scenarios for what the shapes are used for. The story was about a triangle who was not happy and always wanted another side which transformed it into another shape. The story then told of all the different jobs that this shape could do in the world. I felt that this story was a great way to present the information for students. The storyline allowed the students a refresher on what certain shapes are called and how many sides they have. Most importantly this story allowed students to visualize how shapes are used in real life. By being able to have concrete examples of the use of shapes students can better relate to the geometry strand in mathematics.

It was yet another great week in math class. I was able to learn valuable lessons to how to teach geometry and even gained another children’s literature resource that can be used within mathematics.