Thinking about geometry and my tumultuous relationship with it these past few weeks has made me come to realize how much I have grown to love the subject and the added challenge it seems to come with when teaching it to high school students who over the years have heard from upperclassmen that ‘proofs suck’ and ‘geometry is awful’. And while some topics are still a struggle for me to get across to my students, I love the challenge of finding new activities to bring to them to help them appreciate it like I do. One activity I love is at the beginning of our quadrilaterals unit I always have my students begin by creating two columns split 3 times to create 8 boxes on their paper. Then I tell them to fill one box with the name of one quadrilateral that they know. Then they pass their notebook to the next student in their group and they need to come up with a different quadrilateral in the next box, then they pass again, and so on. When it dawns on them that they need to come up with 8 unique quadrilaterals the look of dread sets in, they can only think of a square, or question if a diamond is an acceptable shape. Typically the last 3 turns are torture for them and I get a good little laugh. We then share out and they realize they knew a lot more than they thought and typically we get all 8 (the kite being the real struggle, because ‘how is that a shape when diamond isn’t!?’) I share this story because this week, while working on my Introduction to Trigonometry unit, I was challenged to come up with new pedagogies to bring to this unit by doing a quickfire challenge in my CEP 805 course. I had to set a 15 minute timer, add a pedagogy with a quick description, and then add another, and another until the timer ran out. I felt the torture, much as I’m sure my students do, as the minutes pressed on and I had used all of my go to strategies and was now diving into the uncomfortable unknown. However, I then was able to give and receive feedback from my classmates about my ideas and my confidence grew. I was reminded that trying something new in class, while scary, is usually rewarding. Even if it fails there is a lesson there for your students to see - even as teachers we are not perfect, but we are still trying. Two new strategies I intend to implement in my trigonometry unit that are new to me, in this context, are a Gallery Walk and 3-Act-Math. In my gallery walk I intend to have students visit 12 different stations with 3 of each having a different piece of a right triangle being solved for. Each different missing piece will be color coded and there will be matching color post-it notes at each station. Students will copy the picture and steps for solving onto the post-it, hang on to it and at the end look for the pattern in how each problem is being solved. Hopefully they will see that whenever solving for the adjacent side when given the hypotenuse, for example, you use cosine and follow the same steps. The downside being, they are not actually solving. I have done a 3-Act-Math with my students before in Algebra, so I am excited to bring this to my geometry students as it always goes over really well. Dan Meyer, who pioneered the idea of 3-Act-Math describes how this works in the video below. As students work together, they come to a consensus of ‘how it will end’ and you share the final act that shows them ‘the solution’ or the ending of the video. Students are so invested in figuring it out and knowing how it will end that they are eager to get more information to work through and figure it out. However some students can get frustrated with 'not knowing' or the unstructured style of the lesson. Overall, I’m glad this week reminded me that while challenging my students is good, challenging myself to try something new is also good- and can help my students in the long run as well. Resources:
Tedx Talks. (2010, April 13). Dan Meyer at TEDxNYED [Video]. YouTube. https://youtu.be/BlvKWEvKSi8
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I think the moment I knew I was truly obsessed with mathematics was during my proofs unit during my Integrated Math 4 class. Given a picture and only a few pieces of evidence, figure out what happened. Looking back this makes so much sense to me because of my love of puzzles, I love deduction style board games, and I love a good mystery that I can try to solve. On the flip side of that I remember the unit I was introduced to sine, cosine, and tangent and felt more lost than I had ever felt in math class. This gave me the impression that I would ‘not be able to teach geometry’. So, of course geometry was the class I was placed in for my student teaching. And after I was hired at my current district, I was made lead teacher of the geometry professional learning community (PLC) because no one else in my department liked teaching the class either. After teaching geometry every year of my career thus far, I have grown to love the class so much. There truly is so much room to play with mathematics in that course and that had never really clicked with me until reading up on a few articles this week about incorporating play into teaching and learning geometric concepts. Play in mathematics is so important and students don’t always appreciate how beautiful and playful it can be (Vasilevska 2021). Having my students fold origami cubes on the first day of class to talk about planes, symmetry, shapes, rotations, and so much more lets me gauge how much they already know about these topics and see their skills in patience and perseverance. Folding the pieces and fitting them together is no simple task - if you’d like to try you need 6 pieces of square paper and you can follow along with my instructions below. Later in the year during our unit on transformations, we create an animation flip book and the amount of creativity that my students come up with each year astounds me. Some students will just do a basic 20 page note card flip book, while others take to programming on a computer, stop-motion animation, or videos of their object sliding, rotating and reflecting within the world they have created for them. I feel that this is one of my strengths in regards to six types of MKT, content and teaching (Hill & Ball, 2009) where the material presented and the level of engagement my students felt to the subject area really aligned. However, while my content and teaching shines in our transformation unit it truly needs work in our surface area and volume unit. Making the connection from 2 dimensions to 3 is an important Common Core State Standard that I need to develop with my students at a deeper level. We do these at the end of the school year so it always feels rushed and there is just a formula to fill in if need be. And even after all these years the dreaded trigonometry unit in some ways is still my weakness, another thing to work on to better the specialized content knowledge (Hill & Ball, 2009). While I have found ways to play with ratios and similarity to make sine, cosine, and tangent make more sense to me, bridging the gap for my students who are not always as obsessed with mathematical concepts as I am is where I am lacking. A final thought on playfulness in my geometry classroom is a board game I came across a few years ago called Mental Blocks. It is a cooperative game that has your team creating a 3-dimensional scene where each member only has some of the information about the scene - be it a side view without color, or an overhead view with color, etc. Not only do I love the cooperative aspect to foster working together in my classroom but the 2-dimensional to 3-dimensional views tie into our geometry standards. And I feel like it could also be argued that having some of the information to create the whole is a bit like how we piece together a proof. I was lucky enough to know the publisher so they gifted me 8 copies of the game to use in my classroom but because of the pandemic I haven’t been able to integrate it yet, but I am so excited to try! Resources:
Vasilevska, V. (2021). From playful math explorations to beautiful origami creations. Utah Mathematics Teacher, 14, 8-19. Misura, M. (2020, September 9). Folding/Putting Cube together! [Video]. https://www.youtube.com/watch?v=TFrkiHFJndk Hill, H., & Ball, D.L. (2009). The curious - and crucial - case of Mathematical Knowledge for Teaching. Phi Delta Kappan, 91(2), 68-71. Misura, M. (2019, August 1). Mental Blocks Demo [Image]. |
AuthorMarissa McGregor, high school math teacher extraordinaire. I love my husband, daughter, and family dearly. Archives
August 2022
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