We are the ones who must create narratives for mathematics in teaching. And the need for such narratives begins as soon as a teacher has a responsibility for a student. High school, middle school are too late. The students need to know a mathematical narrative exists and is meaningful the moment they walk into a school.
We are the ones who have to develop the stories that will engage our students and that will attempt to answer their questions about how the world is. We will not always succeed. We will be heartened by the simple observation that life’s meaningful moments are not always found while succeeding, but in striving.
To be honest with our students is paramount. We should always be able to answer a thoughtfully-posed question, or be honest in saying that we do not know the answer. The students are smart, and they know when we dissimulate.
We should have, as a goal, to never hear the question “why are we learning this?” again. No one asks why we learn to read. The same should be true for basic mathematics. Once students go beyond the basics, they should learn what their natural interests require of them. The job of a mathematics teacher, once a student achieves basic mathematical fluency, should be to shine light on where mathematics lives in the world, and to point the curious student in the direction that they wish to go. And then to stand aside.
The teachers, the engineers, the musicians, the artists, the scientists – all of us need to demonstrate – not EXPLAIN – how the quantitative complements the qualitative; the reasons that knowing why is as important as knowing how. Or what. Or when. Or who.
If all of this means to scrap the existing mathematical curriculum, then so be it.
If all of this means to walk away, damning the consequences, from the ridiculous idea of “one-size-fits-all” testing, then so be it.
If all of this means to think critically about what we teach, and why, and when, and how, then so be it.
If all of this means to subvert the dominant paradigm, then so be it.
We must justify our existence as teachers of mathematics – or society will justify it for us. Or not.