Updated: Mar 14, 2020
ENJOY THE MATHEMATICAL MUSINGS OF OUR PMA COLLEAGUES AS THEY START A CONVERSATION ABOUT MATHEMATICAL LEARNING AND TEACHING ISSUES THAT MATTER TO THEM.
Mike Chartres has been in education in South Australia for the last forty years. In this time he has worked extensively as a classroom teacher, in school leadership, as a curriculum officer and writer and for the last two decades as an academic in teacher education with the University of South Australia. He brings passion and enthusiasm for his areas of expertise and an outstanding breadth of knowledge and understanding about how to put them into practice in a classroom setting
“We need a common maths language across our school!” comes the cry.
I have been privileged to work with numerous talented colleagues and mathematically passionate schools over the last few years. Much of this time has focussed on making sense of the mathematics curriculum, developing effective classroom practices and mapping out learning programs. A small portion of this time has been looking at school numeracy or mathematics agreements. One of the common statements across all of this is the need for a common maths language. From my conversations this appears to be more about having common words and terms rather than a language. Which I find perplexing.
What underpins this perceived need for a common language? From my conversations with classroom colleagues and school leaders there appears to be two underlying themes, the view that mathematics is a language, particularly if you know the words then you know the mathematics, and the range of professional development programs schools access, many having their own language embedded within them.
Firstly, mathematics as a language. Yes, Galileo is often attributed to have said, “Mathematics is the language in which God has written the universe.” and scientists view mathematics as the language of science. While this may be the case it does not mean simply knowing the mathematics words. I can use a mathematics dictionary and even the glossary attached to the Australian curriculum: mathematics, but simply restating the definitions may not help. If mathematics is language then there is more to it than just the words, there are mathematical equivalents for the grammar, rules, symbols and structures for communication.
Secondly, the language of a string of mathematics professional learning programs. South Australian primary schools have accessed many mathematics professional learning programs offered by a various providers over the last few years. It is fair to say that schools and teachers use the sometimes idiosyncratic language some of these programs offer, particularly when it comes to number. So when teachers are directly or indirectly involved in a variety of such programs they readily identify there appears to be many different “labels” or words for what appears to be the same thing. “Which labels are the correct ones?” and “Which labels should be used across the school?” are common questions as a result of this.
For me the common language question is pretty simple to answer but this answer has significant implications for the focus of classroom mathematics program. Mathematics can be seen as a language but it also one lens we use to make sense of, interact with and influence the world around us. Like any language mathematics has many key attributes. From one point of view an early years and primary context the language of mathematics has two key components, nouns and verbs. The nouns are invariably mathematical concepts and the verbs are either ways of thinking and working mathematically or are how we go about applying conventions, skills and algorithms. From this point of view the Australian curriculum mathematics and the numeracy continuum give us the common mathematical language. We don’t need to generate more words for the same ideas or actions.
Let’s take a simple notion of a noun. Young children build their concept of a dog by their direct and indirect experiences with and conversations about dogs. Their concept of what makes a dog a dog grows and becomes more refined as the number of experiences mount. In a way the same can be said for mathematical concepts, for example the concept of 3, number, numeral, circle, pattern fraction, equivalent, add, commutative law of addition, part part whole model benchmark numbers, …. Simply looking up the refined mathematical definition often doesn’t help. For example, for you “What makes a circle a circle?” Would telling you the mathematical definition for a circle help unless you already had developed concept of your own to compare it with? Is the circle the disc or is it the boundary of the disc? Teaching implication, learners need many and varied experiences to build their mathematics concepts rather than recite the mathematicians’ definition or remember the word.
You could present a similar argument for the verbs of mathematics. The thinking and working mathematically verbs can be found in the Australian curriculum: mathematics through key ideas or what were called the proficiencies. For example, sort, compare, describe, identify, classify, justify, generalise, investigate, model … Teaching implication, learners need many and varied opportunities to develop their capability with each aspect of thinking mathematically.
A final point I find intriguing with the discussion about common language is this is hardly a point of controversy when speaking about English language programs. As teachers, do we make up or offer our learners new labels for noun, verb, sentence, blend, genre, …. or do we use these across the school from the beginning? Why would mathematics, if it is in part a language, be any different?
The views expressed in this blog are those of the named writer and do not represent any official position/comment by PMA