A Teacher’s Journey

by Marcus Elbel

I just finished my 12th year of teaching high school mathematics at the school I graduated from in 2010, Chambersburg Area Senior High School. It has been quite the journey with many highs and lows, but I wouldn’t trade it for anything. I love teaching and plan to stay in education as long as I possibly can. A lot of my success can be traced back to discovering Henri Picciotto’s website, www.mathed.page, at the end of my first year of teaching. I had drifted away from many of the teaching principles that inspired me in college, and Henri’s work helped me rediscover them.

I went to Shippensburg University in south-central Pennsylvania for my undergraduate degree. I had awesome professors who instilled the importance of teaching through rich problem-solving tasks, conceptual understanding, making deep connections, and using hands-on manipulatives as tools. They taught me about the NCTM Process Standards: problem solving, reasoning and proof, communication, connections, and representations. They also taught me the eight Standards for Mathematical Practice. I share all of this because as I entered my first year of teaching, I seemed to forget it all!

I was given an Algebra 1 and Algebra 2 textbook along with notes packets, but they weren’t really aligned with what I had learned in college. Each day consisted of me showing how a micro-mathematical procedure worked, and then students would practice trying to mimic what they saw me doing. I basically resorted to teaching mathematics with an “I do, we do, you do” approach. But months into my first year, more and more of my students started acting out because class was “boring” and they were disinterested. Since my students were not engaged, problems in my classroom began to escalate.

At the end of my first year, I began to reflect on what had gone wrong. I started researching ways to make my classroom more engaging and productive. This was when I came across Henri’s website. Everything I read there reminded me of the NCTM Process Standards and the Standards for Mathematical Practice. I immediately bought his book Algebra: Themes, Tools, Concepts (ATTC), which he co-wrote with Anita Wah. I also bought a set of Lab Gear blocks to use while working through ATTC. I spent that entire summer devouring the book, doing as many lessons as I could and noting which ones I liked best. By the end of the summer, I was ready to purchase a whole class set of Lab Gear for my classroom.

My second year of teaching quickly arrived, but this time I was ready. I began incorporating “lab” lessons that used the Lab Gear blocks to supplement our curriculum. I also added non-Lab Gear lessons from ATTC that were highly engaging and helped transform our curriculum. Not only were students enjoying math class more, but my state test scores dramatically improved as well.

This success eventually led to our school purchasing class sets of Lab Gear for all Algebra 1 classrooms. We also bought Henri’s newer book, Algebra Lab Gear: Algebra 1, which updates many of the key ideas from ATTC. My favorite lessons with the Lab Gear are the perimeter and surface area arrangements, Make a Rectangle, and Make a Box. I also love how intuitive completing the square becomes. As for factoring cubics and higher-degree expressions, I remember several instances where students were teaching me things they were noticing and figuring out. That experience is incredibly humbling and reminds me that meaningful mathematics classrooms should create opportunities for students to make discoveries, not just follow procedures. Lastly, the Lab Gear area model generalizes naturally to the multiplication-table format. This is powerful because students are then able to understand factoring and long division in a way that makes the algorithm feel intuitive rather than mysterious.

I should mention that every year I encounter a few students who push back against using the Lab Gear. They complain that the blocks are “childish,” and I have to remind them that they are simply tools that help make algebra visual and concrete. By no means do they make algebra easy. Rather, they make it more accessible for everyone. Traditionally, algebra is highly abstract, and students commonly mix up expressions such as x + 2, 2x, and x². The Lab Gear is incredibly helpful in making these distinctions visible. In fact, even when students do not have the blocks in front of them, I often find them drawing pictures of the pieces because the visual models are so useful. One other thing I have learned is that if the teacher does not have 100% buy-in, students will not buy in either. By the end of each semester, however, I would say that 99% of my students are on board because they see the power of using the blocks.

Another idea that I have implemented over the years is that my classroom has no downtime. Many times, when students finish practice problems, quizzes, or tests, they are told to read a book or find other classwork to catch up on—but not in my classroom! In Algebra 1, I use Henri’s Working With Pentominoes book whenever students finish early. I absolutely love this book because it reviews many important ideas from grades 4–8 from a fresh perspective. Students explore area, perimeter, triangular numbers, congruence, similarity, and symmetry through pentominoes in a puzzle-like environment. There are many “Problems of the Week” in the book, and they reinforce the idea that these twelve plastic tiles are far from childish. I admit to students that there are still puzzles in the book that I have not solved successfully—and I have two mathematics degrees! At the end of the year, after state testing is complete, I even host a pentomino tournament, and the students absolutely love it.

Each summer, I find my way back to Henri’s website, where I explore something new that I somehow missed before. For example, one type of activity on his website is the “Make These Designs” series using any electronic grapher. I have done his linear, quadratic, polynomial, and exponential versions of these activities. Students spend tremendous amounts of time trying to create each design. They enjoy the artistic nature of the activities, and important mathematical ideas such as slope, y-intercept, and transformations emerge naturally through the process. These activities also remind me of the diversity of learners in my classroom. Some students thrive through explorations, others through hands-on experiences, graphing technology, puzzles, or problem-solving challenges.

It is an understatement to say that Henri Picciotto has revolutionized my classroom. Between his books, website, and blog posts, I learn something new every time I encounter his work. His website is a treasure trove of lessons, investigations, puzzles, and ideas that promote sense-making and deep mathematical thinking. I am forever grateful for all he has done for mathematics education.

Over my 12 years in education, I have gradually discovered educators and resources that build on what Henri Picciotto first introduced in my classroom. Jo Boaler’s ideas (youcubed.org) about productive struggle helped shape my thinking, and Dan Finkel’s Prime Climb chart was the first image I used with the question, “What do you notice and wonder?” The list goes on with Fawn Nguyen’s Visual Patterns and Mary Bourassa’s Which One Doesn’t Belong? Then, when COVID hit, I heard many teachers online talking about Dr. Peter Liljedahl’s book Building Thinking Classrooms, where students work standing up in random groups of three on vertical non-permanent surfaces. Together, these ideas transformed my classroom into a place where students truly interact with one another and engage with meaningful mathematical thinking.

As I head into my 12th summer break, I am preparing to teach AP Calculus. This will be a great challenge as I seek to apply all the teaching techniques I have learned over the years to the highest level of mathematics offered in my high school. Yet the biggest lesson I have learned from the past twelve years is that meaningful mathematics instruction is not about the level of the course—it is about creating opportunities for students to explore, reason, communicate, make connections, and develop genuine understanding. Those ideas transformed my Algebra 1 and Algebra 2 classrooms, and now they will guide me into AP Calculus. Challenge accepted!

———————————————————————

Thanks, Marcus! You inspire me to write about my own teacher’s journey. Maybe in a future blog post!

— Henri