I developed a fascination with the use of mathematical language earlier this year as I studied various research books and papers for my second PGCE assignment. In the assignment (which you can find here) I considered research by Halliday (1978) and Pimm (1987) into the ideas surrounding the difficulties found when using mathematical language, as well as the development of understanding and use of the ‘mathematical register’ which is claimed to be the ‘language’ of mathematics.
So naturally when I came across this paper today I was inclined to read. It is a short paper and I do recommend giving it a quick read through, however below I have posted a brief summary of some parts of the paper.
It is noted in the article that some children already see mathematics as a foreign language, with symbols and expressions forming barriers to understanding certain concepts. Palmer provides a nice quote from Gough (2007):
Mathematics is like a language, although technically it is not a natural or informal human language, but a formal, that is, artificially constructed language. Importantly, we use our natural everyday language to teach the formal language of mathematics. Sometimes we encounter problems when the technical words we use, as formal parts of mathematics, conflict with an everyday understanding or use of the same word, or related words.
[Side note]: Carolyn Lee presents the idea of teaching mathematics as an additional language in her book, Language for learning mathematics (2006), and I talk briefly about this in my assignment (see quote below):
Lee (2006) briefly explores the idea of teaching the mathematical language as an additional language, since it holds many of the features of a natural language. She suggests that teaching mathematics as a foreign language might overcome issues and barriers that occur when pupils are required to use the mathematical register. Pupils might be expected to master words, grammar and syntax of mathematics, along with cultural aspects of people who use it, in order to fully grasp certain ideas. Lee suggested that pupils need to divulge and become engrossed with the social and cultural aspects of mathematics before they can express mathematical ideas and concepts through efficient use of the mathematics register.
The key aim of Palmer’s paper is to consider the pedagogical advantages combining the teaching of MFL and mathematics to see whether or not it would benefit mathematical understanding. It was certainly interesting to read some research into this idea. In the analysis section Palmer notes that the pupils enjoyed learning the language in this way (via another subject), whilst receiving varying responses about their learning of mathematics this way. Tutors themselves had concerns about the speed of their normal content delivery, since they delivered their lesson much slower in Spanish.
If we do consider mathematics to be a language that learners need to understand and use themselves, then there are some key messages that seem to be emerging, in terms of repetition and slowing down the normal speech patterns, possibly removing some of the extraneous detail that may clutter explanations. Moreover, the use of gestures, resources and pictures seemed to be beneficial for this group of learners and parallels may be made with working in a classroom.
She concludes with reservations about teaching the two subjects together in terms of development of mathematical understanding (though it may be of more value for MFL teaching). Her suggestion for further study links back to Lee’s idea of teaching mathematics as a foreign language, in itself, and borrowing strategies from MFL teaching.
Some of the most extensive research into mathematical language was done by David Pimm in his book Speaking Mathematically (1987). I am still making my way through it, but find that the explanations and examples are still relevant today. It is well worth taking a look, especially if mathematical language interests you!