What does it mean to go Back to the Basics?
There has been a lot of conversation around the idea of
teaching effectiveness and the choices that teachers make about how they teach,
particularly teaching mathematics. A
recent editorial in the Calgary Herald draws attention to the widening gap that
students in Alberta and North America are experiencing. What is at the heart of
this discussion, discovery math and bringing math teaching back to the basics.
To engage in this conversation about teaching mathematics I
would like to clarify some terminology for those that are not familiar with
discourse around math teaching.
Inquiry (Constructivism) is not Equivalent to Discovery Learning
The apparent connection, which has been made between these two
different ideas is false and unproductive. Firstly, the term “inquiry” is a
stance, a way of being, not an approach to teaching. To inquire means to ask
questions, to gather information about the world and use that to help answer
those questions. However, there are three main ways of knowing through inquiry
that Friesen et. al. (2015) highlight in their comprehensive review of inquiry:
Minimally Guided Inquiry (discovery learning), Universal Inquiry Models (the
discipline does not matter) and Discipline Based Inquiry. Of these three
approaches, discipline based inquiry is a way to know our world that is
authentic, personally meaningful, relevant beyond school and connects to real
work. It is a way to thoughtfully and intentionally design learning experiences
for students. As teachers, it is our job to provide authentic learning
experiences for students. This comes from designing lessons, which are inspired
by the disciplines which we have learned the information from in the first
place. Students must experience the teaching of mathematics in ways that are
authentic to the discipline of mathematics.
The False Dichotomy of Back to the Basics
The discourse in math has created a false dichotomy in the
teaching of mathematics. Back to the basics, I believe, must mean back to the way we
understand the world through the discipline of mathematics. Mathematics is not
unlike any performance-based discipline. Yes we need to know basic facts in
mathematics, like this “=” means equivalent. Yes we need to know the fundamental
results found in our multiplication tables. We must practice these such that
they are easily recalled. However, it is equally important that we understand
how mathematics works. If students are merely learning algorithms to solve problems,
and applying these algorithms repeatedly, again and again, they will not
understand. Students must be given the opportunity to think like a
mathematician. Students must learn to recognize the information that is
necessary to solve a problem, that there are multiple ways to solve those
problems and that all problems have with them assumptions that must be
acknowledged. Otherwise, we are simply asking them to do math mindlessly and
not to think.
My recommendation is that we embrace the idea that "Back to
the Basics" means back to the ways of knowing in mathematics. It's not this way
verses that, memorization verses conceptual understanding. It's "Yes" to
practice and "Yes" to thinking, it's a resounding “Yes!” to foundational principles
and a “Yes!” to deep conceptual understanding. We cannot abandon our learners
in their quest to become literate in mathematics. Nor can we teach them that
math is just a series of algorithms to solve problems in a textbook. To teach
mathematics in that way would be a disservice to the learning of our students.
We must embrace teaching math, authentic to the discipline and ignore the false dichotomy
that plagues the discourse around teaching mathematics.
References
Calgary Herald Editorial Board. (2015). Editorial: Back to the Basics. Retrieved from:
Galileo Educational Network. (2015). Focus on Inquiry, What is Inquiry. Retrieved from: http://inquiry.galileo.org/ch1/what-is-inquiry/
Inspired by the words of Dr. Sharon Friesen at the Werlund
School of Education, University of Calgary and conversations with colleagues at
the Galileo Educational Network.
For further understanding about the conceptual teaching of
mathematics visit Dan Meyer’s blog: http://blog.mrmeyer.com
