The Language of Mathematics

When I first started working at an IB school seven years ago, I quickly became acquainted with the Learner Profile. The grade six students I taught, many of whom had been at the school since Junior Kindergarten, were well-versed in the language of the Learner Profile and were able to identify the attributes that they best demonstrated. Their ongoing reflection about the Learner Profile prompted my own self-evaluation. I made it as far as communicator. The descriptor for that attribute stated that communicators express themselves confidently in more than one language. I speak French, but certainly not confidently. Did that mean I wasn’t a communicator? I reread the descriptor a bit more closely. As I did so, I was relieved to discover that, according to the descriptor, mathematics is considered a language.

While I knew that mathematics had its own vocabulary and notation, I had never thought of it as a language; however, as I continue to explore teaching and learning in mathematics within the context of an IB school, I have come to see it as such. Just as fluency in languages like English, Spanish, and French allow us to express ourselves in multiple ways and access a wider range of information, so does fluency in mathematics expand our options for exploring the world and communicating our discoveries. The value that IB places on mathematics as a language is not limited to the Learner Profile. Indeed, the structure of the IB framework for mathematics promotes the development of communication skills. One of the four criteria against which middle school students are assessed in math is specific to communication. The objectives of criterion C, Communicating, include showing logical lines of reasoning, using mathematical language and notation, as well as an ability to move between forms of representation.

It is the ability to move between different forms of representation that I find particularly inspiring. For example, the grade 4 students at my school , after having studied place-value, created pictures that represented a specific number. They used grid paper and coloured in the exact number of squares in order to creatively represent their number visually as well as numerically. In grade 2, students examined pictures of a plant as it grew, recorded their observations numerically in a table and then plotted their findings visually in a graph. They also discussed their observations verbally before using their graphs and tables to predict what might come next.

Moving between forms of representation appeals to a variety of learning styles, but also lays the foundation for more sophisticated mathematics. When students understand that quantities can be represented in a variety of ways, they are better able to manipulate those quantities in order to solve problems. For example, multiplying 14 x 5 is much easier when you understand that the same quantity can be expressed as 2 x 5 x 7 or 10 x 7. Similarly, being able to describe relationships using graphs, tables, and words establishes a foundation for describing real-life situations algebraically, which, in turn, supports the use of algebra in problem-solving.

Thinking about mathematics as a language has had a significant impact on how I teach math. Very few people enjoy grammar and spelling for their own sake; however, the basic skills required for reading and writing come to life when students delve into a story or prepare a persuasive speech. In the same way, the basic skills of math come to life when they are applied in authentic situations. Out of context, converting fractions, decimals, and percents is boring; however, when students are creating an infographic or pitching a business proposal, the skills are meaningful and relevant. In my mind, the ideal math class consists of authentic tasks and challenges through which students can develop and apply the math skills they need to learn. In this way, mathematics can be learned by inquiry while also being a tool for inquiry.

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