Warning: You are about to read the second installment of my #mathconfession series. It is my intent through sharing and reflecting on math confessions, we can work together to grow our math practice together.
As a math coach, I reflect back on my classroom teaching years and cringe at some of the decisions I made in math class. Some of these practices included lengthy and unneccsary quantitites of homework, teaching with abstract numbers and not attending enough to the concrete and representational work of mathematics, and engaging to “test prep”, just to name a few. However, the one decision that I made year in and year out that has been weighing heavily on my mind recently is the way in which I treated the domain of geometry in my classroom and in my mind. I perceived geometry as the domain that we did “for fun” (unlike all the other mathematics that I taught?) and therefore it didn’t seem as important to teach. In addition, because geometry was not as heavily tested on our annual assessments, it was often taught at the end of the year and rarely taught to completion.
This practice got me thinking…Can geometry be fun and important? How important is it to teach geometry as something more than just the “fun” end of the year activity?
Moreover, the 6th NAEP (National Assessment of Educational Progress) indicated that students in grades 4, 8, and 12 appeared to be performing at the Visualization Level of geometric thought. This level is considered “level 0” in Van Hiele’s Level of Geometric Thought and it is considered necessary for students to have achieved a minimum of “level 2” geometric thought (Informal Deduction) by the end of middle school. (Read more about Van Hiele Levels of Geormetric Thought here)
Could these findings be in part due to the fact that I, and likely many others, did not see geometry as important? How can we begin to see the geometric connections to the major work of the grade and bring geometry back to math class?
One of the major connections I see is between the work of
- Operations & Algebraic Thinking (OA)/Numbers & Operations Fractions (NF)
- Geometry (G).
The major connection between these domains is the work with composing and decomposing. Just as we put together and take apart numbers (whole and otherwise), we also put together and take apart shapes. For example, consider the work we do with combining fractions. When using the concrete tools of pattern blocks, students can more easily see how the combination of these shapes can relate to the combination of fractional parts.
These representations can also apply to the inverse work of fraction subtraction and/or division in relation to shape decomposition.
In the earlier grades, when students are engaging in the beginning concepts of part-whole models, the use of geometric tools can perhaps demonstrate the equality of the parts to the whole better than using digits in a number bond can, especially for students who are still functioning in the concrete level of understanding with these part-whole relationships.
They say that hindsight is 20/20. While I can’t go back and undo these decisions I made about geometry in my past, I can move forward and support others in clearly seeing that geometry CAN be both fun and important. These examples are just the tip of a much larger iceburg that I hope we can reveal together.
What opportunities do you see for integrating geometric instruction into other mathematical domains?