Month: August 2023

Learning to Play with Math

This is the first in a series of posts about learning to think like a mathematician. This is my first memory of playing with numbers, questioning my own thinking, and making sense of new ideas. As my brother Peter said, when I shot the video clip below, “and this is how it all began!”

When I was around 5 years, my older sister showed me an adding machine that was in my grandmother’s closet. It was large (to a fiver year old) and very heavy. It was completely mechanical and had 81 numbered hexagonal keys – 9 rows of 9 keys (see image, above). Each column of keys was numbered with the digits 1-9. Pressing a digit in a given column would display that digit in a corresponding window along the bottom row. There was also a lever on the right side that could be pulled to reset all of the column windows to zero.

My first experience with this incredible machine, thanks to my sister, Susie, was to press the “1” in the lower right corner (the ones place) continuously.  The tenth press felt different and the display at the bottom returned to zero, but the place just to the left turned to display a “1.” Pressing the same “1” button felt the same again for 9 presses, then on the tenth press if felt different again, and again the window below turned to a “0.” And the window to the left turned to a 2. I could make the second window count to ten, too? By only pressing the one button? This was fascinating! After a long time, and lots of presses of the same key, when all of the bottom windows displayed nines, I would press that same “1” button and it would “feel a little different” and something amazing and extremely satisfying happened. Watch what happened. 

All of the 9s would alternately flip to 0s, like a row of dominoes flipping over. It was a sensory explosion! I could hear the dials flipping. I could see them flipping, and I could feel when it should happen. It seemed magical at the time. 

I (we) were told not to play with this because it was an antique and I (we) might break it. I was a pretty good rule follower, but the allure of this machine was too much. I would sneak into my grandmother’s closet and lug that heavy machine out to play with it – a lot – even when I was a little older, just to get to see, feel, and hear that domino-like effect of numbers flipping over. Even now, it makes me smile to think about it. 

I would spend a lot of time pressing that “1” key until it got to 9, then press it one more time and a “1” would pop up in the place to the left and a zero was in the spot below the key I was pressing. It never got old. I kept pressing that key, not just to see what I had come to know would happen, but to figure it out. I began to make predictions and ask myself questions, like when the display read “249” one more press and the digit in the place to the left of my key changed to a 5. “I bet it changes to a six next time.” When it did, I was hooked. This continued and every time the next column got to a 9, I’d quickly press my “1” key one more time to get it to click over. What I noticed, though, is that it took a lot longer to get each row to 9, but that wasn’t enough. I wanted to know how much longer. I kept going because the more nines I had, the cooler it sounded when they all flipped over! Eventually, I figured out that it took ten presses of that “1” key to make the next column change, and that column had to change 10 times to make the next column change. I discovered a pattern of tens. 

What I didn’t realize, initially, was that I didn’t have to keep adding ones to get the full row of nines (I was still only about 5). I could just press each of the nine “1” keys 9 times, then add 1 more by pressing the far right “1” key. Then, satisfaction and amazement came much sooner! Once I figured this out, it was a much quicker experience but, frankly, a little less satisfying. After a while, I really took note of the other keys and realized that I could use some of them to my advantage as well. For example, I could press the “9” key in each column once and then press the far right “1” key. Still satisfying and much more efficient to get to the end result, but not as enjoyable as seeing this one button do so much. Watch the video below to see and hear what I loved so much.

This was one of my first experiences with playing with mathematics and the effects it can have in the sense-making and building deep understandings of mathematical ideas. I believe it is one of my earliest mathematics learning experiences, and I believe it had a huge impact in how I think, mathematically.

My hope is that this and some future posts may cause you to reflect on some of your own, similar, experiences. If so, please share. I’d love to hear your experiences. Stories like this, I think, have the potential to bring to light just how beautiful mathematics can be and the connections that can be made by studying this amazing subject! 

Side note: I really wanted to take this amazing contraption apart to see how it worked. My parents are thankful that I never did, but I still wonder what the inner workings of this adding machine look like. Unfortunately, I never got to find out, but I am still very curious. Perhaps there’s a video out there that I can watch so I don’t ruin this antique with my tinkering. 

Impact On Those Around You

Back after a long time away!

I’ve been very lax in posting for a while! In the past 5-6 years, I completed my specialist degree in K-8 Mathematics from UGA, began working as the Elementary Mathematics Program Specialist at the GaDOE, and had two kids graduate from high school. 

This post, which has been sitting in my drafts for 3.5 years, is the beginning of the next phase. I have just recently retired from the GaDOE and am now working independently to deepen everyone’s (students, parents, teachers, schools, and districts) understanding of what it means to teach and learn mathematics. So, many more posts and resources are on the way! 

Two Back-to-Back Events

I’ve been a teacher/coach/mathematics specialist for 30+ years and sometimes we never really know the impact we have.  Sometimes we hear from current even former students and they thank us. Sometimes we get emails from parents thanking us for our work and dedication with their children.  Sometimes we even get nominated and/or chosen for a teaching award.  All of these are amazing and I think they keep us going. They help us get through some of the negativity that, unfortunately, can be a part of teaching.

I’ve received the thank-yous from students (current and former), which are always appreciated.  I’ve received the emails from parents – often even more appreciated. I’ve even been nominated for teacher of the year a few times which was humbling in itself, but also appreciated, for sure. But that’s not why I feel humbled.  Sometimes there’s more in the bigger picture of your teaching career that you didn’t know was there – something that is bigger than you could imagine.  Sometimes you don’t realize the impact you have.  And sometimes it hits you in the face all at once (or at least it seems like it’s all at once)!

As I mentioned, I finished my degree and graduated in December 2019. The night before graduation we had a dinner reception on campus. This was a time when all graduates from multiple programs could bring their families and show them where they’ve been spending the last two years of their lives working on the degree they’d receive the following day. After the meal, a professor from each program would say a few words about each graduate. Dr. Robyn Ovrick @RobynOvrick  is our amazing professor at UGA Griffin and her words about me as a student and a teacher were enough to almost bring me to tears. I learned during her words that she had heard of me before I knew her, which I still find unbelievable. I don’t have her exact words to share but I will never forget their impact on me. When someone you respect and admire, as I do Robyn, reflects that back to you… out loud… in front of everyone, it’s very difficult to not be humbled!  I barely held it together.  

The next happened at graduation. But first a little back story. One of my classmates in our degree program was actually one of my former students. I taught Heather Kelley @heathermjkelley as a fifth grade student a long time ago. She has become an amazing teacher, friend, and colleague. Heather’s organizational skills helped me stay on track through all the research and weekly assignments in this program. It’s safe to say that, without her help, I might still be writing my literature review!

Prior to graduation, we were asked to nominate someone as a student speaker. Heather nominated me, but I threw it back to her. I’ve spoken a lot at conferences and workshops over the years and it was time for someone else’s voice to be heard. I had no idea that her speech would contain thoughts about her former fifth grade teacher. I was super humbled by her message! I still get choked up thinking about the wonderful things she said. Things that I had not even considered might have made a difference in her life.

My wife and father-in-law who were able to attend in person along with my parents and siblings who were able to tune in on-line, were surprised and overjoyed to hear this young woman include me in her speech. The video of her speech is below, if you’d like to hear it. And if you need someone to speak at an event, Heather would be a great choice.

At the dinner the night before, Heather joked that she was going to hand her speech to me to give. That would have been interesting, for sure! 

It’s true that sometimes we never know the impact we may have, but sometimes – usually when we need to hear it – we have the pleasure to hear that we have made a positive impact in the lives of those around us.

The takeaway here, I think, is that no matter what you do in life, it all boils down to what Heather said in her speech (I’m paraphrasing here): “Find someone who nudges you out of your comfort zone, challenges you to be better, and encourages you to be the best person you can be in life. Better yet, be the one who encourages others to do their best and share it with the world!”