In defense of Algebra

Recently I have started reading the book Unknown Quantity: A real and imagined history of algebra by John Derbyshire. For any history (or mathematics) students, the book is a fascinating read, detailing the development of the number system, algebraic notation and use from over four thousand years ago to as we know it today.

From time to time I have shared with my students snippets of what I have read. For example, the ancient Babylonians didn’t have a conceptual understanding of the numbers 1 to 10. Instead they worked with a base 60 notation, which explains why this same notation appears in various instances of our numerate world today. For my students, who were studying trigonometry and the breakdown of degrees into minutes and seconds, this explanation proved helpful.

Derbyshire’s book has highlighted for me how complex the development of algebraic thinking, language and writing has been. Mathematicians struggled over the course of generations trying to figure out how to represent the unknown number (i.e. a pronumeral or variable, often written as ‘x’). Each step of the way, they didn’t know how their findings would be of use to secondary students today, nor did they often know what had immediately preceded them or was being simultaneously discovered somewhere else in the world.

The study of Algebra today gives many students grief. They struggle with its abstractness and the ideas of simplifying an expression or working with a balanced equation.

Alongside these students, however, there are others who enjoy it and who get a sense of achievement when they find that they do understand this new language they are learning.

In response to recent debate over the worthiness of algebra in the classroom, why limit what our students are learning because it is difficult for some? Learning is not intended to be easy. It is intended to set students up to navigate and make sense of our world. And who knows, maybe there is another Diophantus or al-Khwarizmi growing up today, who will in the years to come make some amazing leap forward in mathematical thinking.

A great contribution to this debate can be found here in an article by Judy Bolton-Fasman.

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Learn to Live

It is a fallacy to assume that the school teacher is just an academic educator. If our role was solely to develop lesson plans, teach content, mark assessments and report on students’ ability levels in a subject area, then our job would be relatively easy. As it happens though, students (much like the rest of us) are not Econs, but humans. They are developing, young individuals, prone to error and emotion.

The students who walk into my classroom each day are not just learning how to manipulate linear equations or find an unknown angle in a triangle, but they are learning how to interact with those around them and how to live.

Incidentally, at the first two schools I attended when growing up, the mottos were Learn to Live and Learn and Live. These were an explicit acknowledgement of the holistic teaching that took place to assist in my growth and development.

I began writing this post this morning, and since then have attended a PD on positive behaviour management by Jo Lange. Jo emphasised the important role that teachers have, not in tutoring individual or small groups of students, but in teaching them. This is a careful distinction: for students to succeed in future workplaces and in relationships with their colleagues and their communities, they must be responsible for their behaviour and learning. It is not the role of the teacher to hover, attending to their every need.

Too often, we as teachers are trying to set students up for a tunnel vision ideal of academic success, working to provide the perfect learning conditions. I know that I am guilty of this – unquestionably and without hesitation providing students with pens, for example, so that they at least do not have an excuse for not doing their work. After all, why should a lack of equipment be a reason not to learn?

As the teacher, what I am doing however, is saying that content learning must be given primacy, and as such, I am neglecting some basic life skills that these students must develop (namely, responsibility and organisation). Even in maths classes, I am not teaching maths, I am teaching students. If a student cannot prioritise bringing a pen to class after they have been practising being a student for sometimes over a decade, what use is that algebra equation going to be?