The Path to the Geometry Rabbit Hole

I am a visual learner. Seeing how things physically fit together and can transform helps me retain that information by connecting it to the visual cues given to me. That is why geometry is one of my favorite units in math. The nature of geometry revolving around shapes, spaces, and relationships makes it a great subject for hands-on learning.

In my 6th grade classroom, our geometry unit typically consists of finding the area of polygons, specifically parallelograms, triangles, and trapezoids. Having my students take a break from solving equations, dealing with fractions, or converting decimals while still engaging in content is a great time for everybody in the room. For many of them, it is when they take that step from understanding how something works to why something works. Instead of just showing them formulas to memorize and going through typical equations to solve, geometry allows them to use their hands, minds, and imaginations differently than they usually would. They can draw pictures, they can make shapes using rubber bands and geoboards, and they can test their own hypotheses or challenge themselves to try and find a polygon that doesn’t fit the rule. It gives them a chance to play and allows their instinct and creativity to take over, allowing me to witness the “specializing, conjecturing, representing, generalizing, investigating, analysing, explaining, justifying, refuting, modifying and convincing” that McFeetors and Palfy (2017) witnessed during their study on play.

My greatest tool is using my knowledge of the content and of my students (Hill, 2009) to play to their strengths and curiosities. I want them to ask questions they haven't thought of before. “This is what we’re supposed to do, but why does it work?” or “Have you ever thought about how this formula was created?”. This questioning gets them engaged and intrigued, allowing us to turn math class into a science class where we go through different experiments to try and recreate the formula we have. For example, knowing that a triangle is half of the area of a parallelogram, students would only need to know that relationship between the two shapes and can test finding different triangles with different parallelograms. When they are finally able to replicate the formula using a model, or other methods, then they have cemented that understanding on their own, in their own way, using their own terms, and in a way that is meaningful to them. Not only that, but their confidence is boosted because they were able to discover something that they might not have believed they could do when waking up that morning. This could even lead into a class discussion, which would allow for students to “experience a sense of mutual influence without feeling they had to compete for opportunities to participate in ways they liked.” (Martinez Hinestroza, 2019)

Geometry presents a great opportunity to allow students to witness the inner workings of mathematics, share their findings and observations, and ask other questions that came up during their learning. The visual nature of this branch of mathematics can be the catalyst for student comprehension, engagement, and rational understanding.

References:

Hill, H., & Ball, D. L. (2009). The curious - and crucial - case of Mathematical Knowledge for Teaching. Phi Delta Kappan, 91(2), 68–71

Martínez Hinestroza, J. M. (2019). Connecting reflection and practice: Transforming a mathematics classroom culture of participation. [Doctoral dissertation, Michigan State University]. Electronic Thesis & Dissertations.

McFeetors, P. J. & Palfy, K. (2017). We’re in math class playing games, not playing games in math class. Mathematics Teaching in the Middle School, 22(9), 534–544.

Wix. Eagle Shape [Photograph]. Wix. https://static.wixstatic.com/media/f058f63b89505492af74be9cb1eeac4d.jpg/v1/fill/w_1110,h_737,al_c,q_85,usm_0.66_1.00_0.01,enc_auto/f058f63b89505492af74be9cb1eeac4d.jpg

Wix. Geoboard Game [Photograph]. Wix. https://static.wixstatic.com/media/11062b_3ce26c21b4284ebba173dab556f74ed9~mv2.jpeg/v1/fill/w_525,h_350,al_c,q_80,usm_0.66_1.00_0.01,enc_auto/11062b_3ce26c21b4284ebba173dab556f74ed9~mv2.jpeg

Wix. Mosaic of Woman [Photograph]. Wix. https://static.wixstatic.com/media/11062b_58f0ff67c3f840b0aa2aa2edc966f363~mv2_d_4877_3252_s_4_2.jpg/v1/fill/w_525,h_350,al_c,q_80,usm_0.66_1.00_0.01,enc_auto/11062b_58f0ff67c3f840b0aa2aa2edc966f363~mv2_d_4877_3252_s_4_2.jpg