Exploration of teaching mathematics in a foreign language (research paper)

Palmer, P. (2014). Exploring Synergies between the teaching of mathematics and modern foreign languages. Proceedings of the BSRLM November 2014.

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.

Palmer says:

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!

Quick post: Why aren’t all penguins criminals?

I was sent this link a while ago, and on the webpage is a video of a maths teacher, Mr Ben Davies, who talks about his favourite lesson. The lesson he talks about is designed by Simple @ Complex (a group of research students at UCL) and is titled “Why aren’t all penguins criminals?” It is a mathematical modelling (50 minute) lesson aimed at year 9 pupils and makes use of videos from the BBC’s Frozen Planet series.

I haven’t yet used the resource but, after flicking through my iPad this evening and coming across the lesson plan, I thought I would share it. I have added the lesson plan to a new Dropbox folder for resources that I come across and will add the rest of the resources tomorrow.

Lesson plan

Online resources provided via Simple @ Complex

It looks like an exciting lesson and I would be interested to know if anyone else has used this resource and found it successful.

Introduction to university mathematics: Coding Theory

Last year I visited a selection of schools in Cheshire in the lead up to my PGCE course so as to gain some experience in schools following the completion of my degree. One of the schools I visited was where I had been taught and the department were incredibly supportive in me venturing into the teaching profession. They offered me the opportunity to teach a lesson to the A Level Further Maths class and said I could do anything I wanted. As I have mentioned I had just completed my degree (in mathematics), and it struck me as an ideal opportunity to try and present them with some university level mathematics.

Within the time frames I had to both plan and deliver the lesson I needed to ensure the content I presented was accessible to the students. I chose to arrange a lesson based on one of my third year pure mathematics courses, coding theory, which required some prerequisite knowledge of very basic set theory notation and also modular arithmetic before introducing the core material. One of the most interesting aspects (for me) are the questions based on the ISBN-10 code which was used for book identification until the introduction of the ISBN-13 code.

The content which I delivered to the class was well received both by students and their teacher and I have recently reformatted the content into a PowerPoint presentation with an accompanying student worksheet and ‘Take it home…’ sheet. Due to time being tight at A Level anyway, this type of lesson would be most effectively used in some sort of after school session or as a one-off lesson when year 12 students return from exams in June (or when ahead of schedule). The links to these documents follow:

Coding Theory lesson – PowerPoint (notes for each slide are included)

Coding Theory lesson – Student Worksheet

Coding Theory lesson – Student Take it home… sheet

Please feel free to provide me with any feedback regarding the materials and I shall update them accordingly if there are any problems – I hope that they can be of use!

In time I hope to make further use of the notes and materials I have from my mathematics degree in order to create more ‘one-off’ lessons like this which provide accessible university material to (sixth form) students. I hope that they might spark interest in pupils to take mathematics to higher levels, or at the very least provide an enjoyable ‘alternative’ lesson.

Credit: Y. Bazlov, lecturer of MATH32031 Coding Theory at The University of Manchester 2013-2014.

First blog post

I am strongly in support of sharing ideas and resources and believe it to be an important factor in developing as a teacher. I also think that making use of research can help to inform our practice and widen our mind sets and ideologies. As such I hope to make use of this blog (irregularly) as a way of sharing some of my ideas, discussions and resources for use in mathematics education.

I am only entering my NQT year in September, so I don’t claim to know all (or in fact much!) about mathematics education, or teaching in general. I am, however, constantly expanding my knowledge and developing my practice and so I hope some of my ideas will be well received and made use of. I will be open to comments and feedback on all of my posts and hope it is useful!

In the meantime here are a list of some of the mathematics education blogs I have recently come across via Twitter:

These are all excellent and there are so many more out there too!!