Pushing the Boundaries of the Teaching Profession

By Dylan Kane, Math Teacher

“All learning begins when our comfortable ideas turn out to be inadequate.” — John Dewey

I don’t know what it’s like to be an artist, but I imagine painting has a few things in common with teaching. Trying to take different perspectives while unifying them in a common experience. Considering both the surface level and the deeper connections happening behind the scenes. I want to take my boring old lesson on graphing polynomials and make it into something perplexing and fascinating for students, the same way a painter looks at a scene thousands of others have looked at and tries to extract something profound.

When Paul Cezanne reimagined Impressionism with his brushstrokes and unique use of color, his ideas created a paradigm shift for a new generation of painters, reimagining what was possible and what art could be. In the same way, the art of teaching moves forward when new ideas and perspectives expand teachers’ ideas of what teaching and learning can become and what rich classroom experiences can look like.

Teaching and Mental Models

Every teacher has a mental model of the type of teacher they aspire to be. When I first started teaching, I had an idea of what I wanted my classroom to look like, based on classes I’d observed, my ideas of effective teaching, and my own school experiences. My improvement in the classroom was largely based on trying to move toward my mental model of effective teaching, happening in fits and starts with occasional breakthroughs. The real improvement came as I expanded my mental model of what great teaching is. As my paradigm for the potential of classroom teaching and learning became more ambitious, my efforts to improve became more purposeful and more effective.

Improving my teaching practice is largely a process of transforming my mental model of great teaching in more and more sophisticated ways. I think that expanding mental models of great teaching are what can distinguish the profession in the year 2017. Many talking heads in education talk about 21st century learning — the essential skills and habits of mind that students need in the modern world. I’m much more interested in 21st century teaching — taking what teachers, teacher leaders, and academics learn around the world, and communicating it in ways that make sense to teachers. I have changed my perspectives on how students learn with knowledge from cognitive science, new strategies for formative assessment, unique perspectives on exactly what it means to think critically, more robust techniques to get students engaged and thinking about what I want them to reason about, and many more.

I don’t believe in any one idea that will transform teaching for teachers or learning for learners. Instead, I believe in the incremental elevation of the teaching profession as new ideas are spread and enrich more and more classrooms. That spread of ideas is uniquely possible in today’s profession, and I believe it will be the reason that tomorrow’s teachers are able to create more and more powerful learning experiences for their students. My advice to teachers: Embrace the art of teaching. Stay humble. Avoid dogma. And always seek out new perspectives and experiences that will enrich your mental model of what great teaching can be.

Works Cited

Liljedahl, P. (2016). Building Thinking Classrooms: Conditions for Problem Solving. In Posing and Solving Mathematical Problems (pp. 361–386). Retrieved from https://www.researchgate.net/publication/275953429_Building_Thinking_Classrooms_Conditions_for_Problem_Solving


Dylan is a high school math teacher in Leadville, Colorado, and previously taught middle school math in Boston. He earned his master’s degree from the Sposato Graduate School of Education. He writes regularly on math education and the intersection of research and practice in teaching on his blog, Five Twelve Thirteen.


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