"In the long run, we shape our lives, ...

... and we shape ourselves. The process never ends until we die. And the choices we make are ultimately our own responsibility" (Roosevelt, 1983, Foreword).

Eleanor Roosevelt is my favorite figure in history,

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This has been an insane summer. Six months ago, I was not planning to take summer courses. I figured I'd continue in the PhD program in the Department of Mathematics and Statistics after I wrapped up my master's degree in May and that I'd have the summer off. I was exploring trips to Disney World and the beach, helping my kids plan their summer camp schedules, and mostly looking forward to a well-earned rest after my h̶e̶l̶l̶ intense learning in the math/stats department.

There are innumerable reasons I am grateful that 1) I decided not to reapply to the math PhD program and 2) I applied to the DREAM-Math (Developing, Recruiting, and Empowering Alabama Mathematics Teachers) program for a second master's degree, not the least of which is my health. Within two months of matriculation out of my previous department my blood pressure dropped more than 30 points - it crept up by about 30 points while enrolled there - and I'm back to my historic normal (just below, actually). I knew that I was experiencing mental health impacts which were exacerbated by the mild concussion I experienced in 2018 and two major concussions in 2020 and 2021. To put it simply, my brain was Not Okay. Factor this with other diagnoses, some long-standing and some new, and I'm surprised that I never collapsed (there was that one time I had to dismiss class 20 minutes early on a Friday afternoon because I had "glitter vision" - I was seeing stars that looked like gold glitter floating in the air).

Here I am, at the end of my first semester as a Dreamer - I made it! I didn't do any of the house projects I'd planned, and I didn't get to take my kids to the park or the pool every day, but the summer was far more rewarding than I could have imagined. In my Statement of Intent for my DREAM application, I wrote:

*(Buechner, 2006, p. 111)

Teaching resonates with me on a profound level; I should have listened to the still, small voice inside that told me for decades that I am supposed to be a teacher.

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I loved being a Graduate Teaching Assistant, of course, but I was lacking training on how to teach. I have more than 25 years' experience as a tutor; however, it isn't the same as teaching in a classroom. The two courses our cohort took this summer, Mathematics (MATH) 6850 Functions and Mathematical Modeling for Teachers and Curriculum and Teaching Secondary Education (CTSE) 6040 Technology and Applications in Mathematics Secondary Education, taught me more about teaching than 25 years of tutoring or my tenure as a GTA.

Considering that this reflection is intended to cover what I learned in CTSE 6040, I'll (try) to stick to the impression this course had on me and let this be my grand finalé for the summer.

We covered at least five mathematical action technologies (MATs) during this course: WolframAlpha, spreadsheets (Google Sheets, Microsoft Excel), Desmos, Geogebra, and CODAP (Common Online Data Analysis Platform). I have used the first three before, knew of Geogebra, and had never heard of CODAP. Of these, the only one that I really knew was Excel (click here to read about this in depth!). Taking the time to explore these MATs was a sublime experience. For the technology I'd touched before, I learned new - and more interesting - ways to use them.

In addition to the explorations for the five technologies listed above, we had labs on 3-d printing, robotics, and coding. I'd used TinkerCAD before to make a quadratix for fun/to use at Spring Into Science for a table demonstration. In undergrad, I took an elective on VEX Robotics but that was also just for fun, not for learning or teaching. My kids introduced me to code.org - having this "virtual lab" assignment was especially fun as I was able to show off to my kids the same as they do to me.

This would have been a rewarding course if all we did was ̶p̶l̶a̶y̶ learn the MATs above, but we did so much more! The reading material was intense (see List of Readings for a complete list) but the insights provided should prove to be invaluable. We wrote lesson plans. We started blogs! We had thoughtful discussions about things like "what makes a good resource?"

This course gave me much insight into the how of teaching that I was lacking, and I'm certain that I will continue to make connections with this course throughout my teaching journey.

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References

Roosevelt, E. (1983). You learn by living: Eleven keys for a more fulfilling life. Westminster John Knox Press.

Buechner, F. (2006). Vocation. In M. R. Schwen & D. C. Bass (Eds.), Leading lives that matter: What we should do and who we should be (pp. 111–112). William B. Eerdmans Publishing Company.

List of Readings

Alabama course of study: Mathematics. (2019). Alabama State Department of Education.

Anderson, B. (2019, June 4). Our math curriculum at 5th grade defines trapezoids as having at least one pair parallel sides. Therefore in a hierarchy [Online forum post]. MyNCTM. https://my.nctm.org/communities/community-home/digestviewer/view%E2%80%A67367143&tab=digestviewer#bm04662ec2-3f63-4b40-9aea-68dfaf10ee03

Beigie, D. (2017). Solving Optimization Problems with Spreadsheets. The Mathematics Teacher, 113(3), 27–38.

Cardone, T. (2015). Nix the Tricks.

Dick, T. P., & Hollebrands, K. F. (2011). Focus in high school Mathematics. National Council of Teachers of Mathematics.

Fairley, K. (2015, October 31). I am using the math program called MobyMax for elementary students K-5. It is a online program that is core [Online forum post]. MyNCTM. https://my.nctm.org/communities/community-home/digestviewer/viewthread?MessageKey=215ddaec-c%E2%80%A670-ceb6-4514-ac1c-413a77367143&tab=digestviewer#bm215ddaec-c6ba-4ede-965e-3a73ba5bda8b%23bm0

Meyer, D. D. (2020). Social and Creative Classrooms. The Mathematics Teacher, 113(3), 249–250.

Principles to actions. (2014). National Council of Teachers of Mathematics.

Ronau, R. N., Rakes, C. R., Bush, S. B., Driskell, S., Niess, M. L., & Pugalee, D. (2011). Using calculators for teaching and learning mathematics [Technology Research Brief]. National Council of Teachers of Mathematics.

Shaughnessy, J. M., & Burger, W. F. (1985). Spadework Prior to Deduction in Geometry. The Mathematics Teacher, 78(6), 419–428.

Skemp, R. R. (1978). Relational Understanding and Instrumental Understanding. The Arithmetic Teacher, 26(3), 9–15.