I didn’t become a teacher with the intention of doing it forever.  My original goal was to design educational video games, but I felt it would be presumptuous of me to build such technology without ever having set foot in a classroom.  Becoming a math teacher seemed like the fastest way for me to find out what kinds of tools schools actually needed. Now I’m not even sure I’m the same person.  

I made countless mistakes during the twelve years I spent teaching, but the one thing I think I got right was approaching it with a “here-to-learn attitude”.  Learning can only take place with the learner’s consent.  Opening one’s self up to learning a new skill means allowing oneself to be vulnerable to mistakes.  Teaching is about creating an environment where multiple learners feel comfortable with the risks of engaging in that process together. The first step is to establish a relationship of trust.

In all honesty, relationship building has never been one of my strengths so I had to make an active effort to improve on it as a teacher.  I found that the most powerful method for facilitating a student’s learning is to simply ask what they need and listen to what they say.  Really listen and trust them.  It’s incredibly difficult to learn when you’re tired, hungry, or stressed. Sometimes “taking a break” is a necessary stage in the learning process. Treating people with kindness is a prerequisite for any meaningful learning to take place.   

One of the most difficult challenges for me as a teacher was learning how to navigate spaces of trauma.  For me, mathematics is something that evokes feelings of joy but my experiences are both highly abnormal and shaped by privilege.  More often a student’s experiences with mathematics are shaped by structural forms of oppression including racism, sexism, and ableism.  Learning how to openly reflect on how I was complicit in these systems was a key factor in my growth as a teacher.  I believe students should be able to see themselves in mathematics, so I tried to actively seek out and integrate the stories of mathematicians from diverse backgrounds into the curriculum.  The self-work continues to be an ongoing process.

My goal as a teacher was to construct an environment where my students could freely “play” with mathematics.  I feel learners are entitled to the opportunity of exploring mathematics and discovering new knowledge on their own.  Often the play comes with a set of constraints that help direct it towards a specific objective, but the important qualities are that the task has a low skill floor and high skill ceiling.  There should be both an easy way for everyone to engage and the depth to encourage further exploration.  Too often we fall into a trap of erroneously thinking there’s “one right answer” in mathematics, so I make it a point to include questions with “no wrong answer”.  I found this helped to foster a culture of collaboration in the classroom because everyone’s input is of equal value in the discussion.

Exploration has limited effectiveness when you’re obligated to address very specific learning objectives, so I usually follow up with some form of direct instruction to fill in the gaps. It’s not quite as engaging, but sometimes students need a concrete example of the behavior they’re expected to model. Our brains are very efficient at mirroring actions.  I’ve found that “worked examples” can also provide a valuable resource afterwards when the student is attempting to replicate the process on their own.  As the number of examples grows, the metacognitive process of learning how to organize this information can reveal insights into its structure.

The next phase of the learning process is to engage in a cycle of formative assessment and feedback known as “practice”.  Any new skill must be practiced to be maintained.  This is one area where I think educational technology excels, because it can enable nearly instantaneous feedback to learners.  While my students often enjoyed the “gamification” of practice, it’s important to select such products carefully.  I’ve learned it’s important for developers to remember that “accuracy is more important than speed” and “some skills cannot be assessed through multiple-choice”.  As our technology improves, so will our automated feedback.  I’m particularly excited about the potential applications of “Large Language Models” in this area, but the application of Artificial Intelligence will also require a great deal of testing before it meets the ethical criteria necessary for use in the classroom.

In the reality of schooling, there’s likely to be a summative assessment stage in the learning process as well, but I tend to think this distinction is artificial.  As far as my class policies were concerned, all assessments are treated as formative where possible.  I tried to allow my students the opportunity to retake assessments as often as needed to the extent I was able. This is another aspect of teaching I found heavily supported by technology.  The combination of algorithmic question generation with automated feedback made it possible for me to focus on the broader picture provided by the data over time.  

If anything, I tend to look at summative assessment data as a tool for self-reflection.  As a student, summative assessments provide me with a form of external validation that I have in fact learned what I set out to learn.  As a teacher, the relation between assessment data and my own performance was always a little bit fuzzy but the process of looking back at that data and asking questions about what I could do differently was an essential part of my personal self-improvement.  I think it’s important to not put too much stock in any one assessment and instead use multiple data sources like observations and interviews to help triangulate areas for growth.  

The final stage in the learning process is to teach what you have learned to someone else.  I think we sometimes overlook this stage because it starts a new cycle of learning, but there are subtle differences between having a skill and being able to teach that skill to others.  Through attempting to teach math, I often found myself seeing old concepts in a new light.  My knowledge of geometry and data analysis grew deeper each time a student asked me “why?”.   Sometimes the most powerful phrase in the classroom is “I don’t know. How can we find out?”.  Likewise, I’m thankful that I had co-workers that were more knowledgeable about teaching than myself and capable of sharing that expertise.  I’m hopeful that I’ll be able to use what I’ve learned about teaching to help others as well.

I’m not necessarily looking for another “teaching job” but the act of teaching has become inseparable from how I learn.   Even if no one reads what I write, the act of putting my thoughts into words has power in it.  No matter where I go or what I do, I will learn new things and attempt to teach them to others.  We face a critical moment in society where we need to recognize the true value of the skills that teachers can bring to an organization. Every organization must learn to grow and teachers are experts on learning how to learn.