Looking Back and Moving Forward

I probably couldn’t even list, let alone discuss, all the things that I have learned this semester. I have gotten so many opportunities to push myself, to fail, to succeed, and to grow as a teacher. I’ve had some of the best times as an educator and some of the worst and I walked out of this semester feeling more passionate and excited about teaching than ever. These are some of the most important things I’ve learned about myself as a teacher.

This semester, I taught two sections of Honors Geometry and two sections of Honors Algebra II. As I moved forward, I found myself teaching a different lesson to my second section than my first. I chalked it up to having different students. But, that wasn’t the case. I realized that I was evaluating myself in the first section and noting things that I should change for the next class. Before this semester, I had not really known the benefits of reflection. The next time I would be teaching a class would be next semester and I would have time to improve it. I realized that the best time to improve lessons and to make changes is right after you teach it. I made little changes, like the order of activities or the way I worded something, in order to increase the opportunities for student learning. That’s a piece of advice that I will be sharing with others and taking with me in the future. Reflect, change, improve, alter, and better your lessons each day. Ensure that every time you teach it, it gets better. We shouldn’t move forward as teachers teaching the same lessons day in, day out, year after year. We should be constantly improving. The best way to do this is reflection.

Teaching an honors class was hard. There’s no way to hide that. It is. The pace is faster, the material more difficult, and the expectations more steep. The freshman students I had were doing math that I, and most people, didn’t see until junior year or later. I had these assumptions about freshman students and what they could or couldn’t handle in terms of mathematical challenge. I was wrong. I taught lessons that, by the time I reached the middle, I realized I needed a bigger challenge for them. These students thrive through challenging tasks and I wasn’t doing them justice. I wasn’t challenging them. Over the course of the semester, I improved on this. I learned how to find where my students were at with material and what types of challenges to throw at them. By the end of the semester, every time that I wrote a lesson, I went back and made it a little more difficult. The benefits of this were amazing. My students were coming up with solutions, explanations, and mathematical conversations that blew me away. As freshman they were thinking more critically than I had until college. From this, I learned an important lesson. We’re teaching for the students, so we should be creating lessons for the students. I should be making lessons that challenge my students every single day, whether they are low-achieving students or honors students. Challenges are what create rich mathematical learning.

One of the best strategies I have used this semester is implementing technological demonstrations. During a unit on angle theorems for circles (chord-chord, inscribed, etc.), I used Geogebra Tube to illustrate to students the concepts. These technology applets allow me to spend less time constructing examples for students, give students the opportunity to discover ideas,  provide the opportunity for increased engagement, and give more accurate depictions of concepts. Before this semester, I was tired of hearing about implementing technology. I felt like it was just people talking just to talk, who didn’t have any evidence that implementing technology would actually benefit student learning. In my own classroom, I was proved so wrong. I felt like my students gained a deep understanding of the concepts and some even wanted to continue playing with the programs at home! New teachers, especially student teachers, should use technology in their classrooms. Try certain programs to see if they work in your classroom.

Finally, I have found that think-pair-share works great for me. I really want students to be able to convey mathematical ideas to one another, both through writing and discussion. When there were conversations that I wanted to have with students, I always asked them to do a continuous write for 2-3 minutes to get their ideas solidified. Then, they would get into table groups and each share. Finally, we would discuss the ideas as a class. I love this strategy for many reasons. First, students are able to write about math. Students don’t get to do that very often, and they should. Second, the solidifying of ideas before class discussion really helps students to have something to say. At times when I have just tried to start a discussion, very few students would contribute. After a think-pair-share, I usually had to stop conversation or it would last all class. Finally, I think that it allows for group collaboration. Once students shared their ideas, many groups would discuss different ideas and build on them. The think-pair-share just elicits so many characteristics that I want my students to have.

Overall, I can’t imagine trading this experience for the world. I’ve learned countless lessons, met some amazing mentors, made connections with students that will last forever, and found myself as a teacher. I love this career and I can’t wait to move forward.

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