Educational Philosophy

Mathematics is interesting, deeply beautiful, and has a fascinating dichotomy: it’s both essential to everyday life and it has elements completely abstracted from application. English is a playful language and it interests me equally for effective, persuasive communication as it does for creative writing and emotional exploration. These are the subjects I’m trained to teach. However, my philosophy doesn’t focus on them – I focus on the growth of the youth in my classroom.

Tile Mosaic from the Alhambra in Spain. Image from John Baez

Tile mosaic from the Alhambra in Spain. Image from John Baez

Specifically, I want to develop in youth attributes of leadership, citizenship, and integrity. I believe the most effective way to do so is in a cross-curricular setting where students help to set goals and their passions help to develop programming. This does not come at the cost of academic rigour. Braiding together different subjects allows each strand to illuminate the others; allowing students to help determine a path forward builds curiosity which is foundational to lifelong learning.

Below, there are short descriptions of how I incorporate my philosophy into a mathematics classroom. For more information, and examples, you can look at my Sample Lesson Plans page.

Leadership

It’s fundamental that, before a leader can be effective, she knows how to work in a group someone else is leading. Collaborative, small group activities play a central role in my classroom. These groups allow students to lead, to follow, to support each other, to develop teamwork skills, and to value the skills and abilities of peers. It’s central to building an inclusive, accepting classroom environment. Further, discussion of mathematical concepts often helps with understanding and retention.

Paul Erdős working with a young Terence Tao. Erdős was such a prolific collaborator that a mathematician's Erdős Number is analogous to an actor's Bacon Number

Paul Erdős working with a young Terence Tao. Erdős was such a prolific collaborator that a mathematician’s Erdős Number is analogous to an actor’s Bacon Number. Photo from Wikipedia.

Students also work independently. They research topics that interest them, present the logic of their approach to peers, and spend time tackling challenging mathematical problems. All of these activities build mathematical literacy, personal confidence, and tenacity.

Citizenship

Education prepares students for their adult lives. More and more, teachers are recognizing their own importance to the future of our society in areas outside of traditional academic streams. We no longer have the luxury to pretend that we teach subjects, students learn them and then move on to be competent, socially adjusted adults. Citizenship goes beyond involvement in the democratic process – though that’s part of it. Citizenship involves respecting fellow human beings and being empathetic and collaborative in outlook.

A tweet I sent during the 2016 Saskatchewan provincial election, showing connections between graphing and politics

A tweet I sent during the 2016 Saskatchewan provincial election, showing connections between graphing and politics

Math provides the tools for social interaction. It’s central to logic and problem solving. Data analysis and graphic representations are main tools in journalism, political activity, and activism. Statistics and probability are intertwined with concepts of social justice and equity. Trigonometry and algebra are part of our economic system, from land ownership to commodity pricing to investment and large scale purchases. Tax systems underpin how our country functions. Coding, number systems, and proof based research are part of a scientifically literate society.

As a field, mathematics has two tendencies: abstraction and universalization. Arithmetic formalizes as algebra, which formalizes as group theory, which formalizes as topology. The more abstract and generalized mathematicians can be, often, the happier they are. However, when learning mathematics, all of this rich context does not need to be stripped away immediately. It can help with building cognitive bridges and a thorough understanding and fluency with mathematics. Our world is messy and math class shouldn’t ignore that – it should celebrate and analyze it.

Integrity

Often, grade school mathematics seems very black and white – you can be wrong, you can be right, and people have trouble recognizing middle ground. But as you study more math you realize it’s incredibly fluid and dynamic. There are alternative approaches. Answers can be right, or wrong – it depends on the context. It’s true that proofs in math are absolute, and new results don’t invalidate old. However, mathematics is a field that depends on precise, fastidious definition. When something is proven it is proven for a very specific context – outside of that context, no claims are made.

Gabriel's Horn. An object with infinite surface area and finite volume. Once thought a paradox, and so a kind of grey area of math. Also, there's an integral/integrity joke here somewhere. Photo from Wikipedia.

Gabriel’s Horn. An object with infinite surface area and finite volume. Once thought a paradox, and so a kind of grey area in math. Also, there’s an integral/integrity joke here somewhere. Photo from Wikipedia.

This mixture of rigidity and fluidity perfectly parallels ethical and moral dilemmas. Context matters, but opinions and cultural attitudes are incredibly fixed. Navigating social interaction in an upstanding way is mirrored precisely by navigating the field of mathematics. Integrity arises from following cohesive rules in varied and unfamiliar situations. Understanding and following rules in math can prepare students for leading ethically sound lives – knowing when to question the rules in math helps them to realize when different moral obligations need to be considered and evaluated. Making these connections explicit is part of how I develop integrity in my math students.

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