Ah! Now I see: the literacy demands of mathematics problems in the early years
Dr Beryl Exley is a lecturer in language and literacy education, Queensland University of Technology. Keiran Abel is a recent graduand from Queensland University of Technology.
There is widespread acceptance in the teaching community that each subject has its own content focus and ways of representing that content. Wyatt-Smith and Cumming (2003) refer to the specialised forms of representation as literacies. Importantly, the emphasis is on the plural form: literacies. They advocate that there is no single set of literacy knowledge or skill that covers the demands of all school subjects. While it is fair to say that all school subjects share some commonality of literacy knowledge and skill, each subject has its own peculiarities and makes idiosyncratic literacy demands of its students.
Mathematics is no exception. Each state and territory mathematics syllabus recognises the important link between mathematics content and literacy or literacies. Each affirms the need for all students to become citizens who are mathematically literate. Yet no state or territory syllabus explicates what the particular literacies of mathematics might be or what teaching strategies provide the necessary scaffolding for students. In other words, these documents lack a metalanguage, both for teachers to consider the literacies of mathematical representations, and also as a point of study for students.
Recent research undertaken at the Queensland University of Technology in Brisbane explored the literacies of mathematics problems in the early years. Dr Beryl Exley, lecturer in language and literacy education, and Keiran Abel, a recent QUT graduand, used Halliday’s (1990) functional grammar to analyse the literacies of mathematics problems in the early years. Their study was undertaken in two parts: firstly, an examination of six worded mathematical problems; and, secondly, an examination of the reading alternatives of the accompanying pictures. The worded problems and visuals were taken from the Primary Mathematics series from RIC Publications in Western Australia (Way 2004, p 87). The figure, below, shows the first three problems that students working at Level C (Year 2 in Queensland) had to ‘read, choose an operation to use, set out a number sentence and answer it’ (Way 2004, p 87).
Figure 1: ‘Number Stories. Which Sign?’ (Way 2004, p 87)
Our examination of the worded mathematics problems revealed seven complex grammatical devices. We identified these devices as ‘complex’ because when we examined the English syllabus for this age group (Queensland Studies Authority 2005), the devices were not considered to be part of the learning outcomes for this student group (refer to Abel & Exley 2008 for a detailed discussion).
A further instruction at the top of this worksheet told students, ‘You may wish to use the pictures or counters to help you’ (Way 2004, p 87). The second part of the research examined the possibilities for making meaning from these accompanying pictures. We again drew on Halliday’s (1990) functional grammar and the practical work of Hart (1999) to consider the field (the actions, setting and participants of an art work), tenor (the form and construction of an art work, or put another way, the elements and principles of design) and mode (how the visual journey unfolds for the viewer) of each. We noted four ambiguities that left the meaning of the supporting pictures unclear.
This examination of the written and picture representations of mathematical operations brings into focus the task faced by young students. Students need to learn to decipher some complex written and picture codes. Our findings raise two questions: Where is it that the complex written and pictorial representations of maths are carefully scaffolded for these young students? Is it happening in maths instruction? In conclusion, we strongly suggest it is important that those who teach maths also explicitly prepare students with the essential skills necessary for carefully and appropriately dealing with the written and pictorial demands of mathematical problems.
Abel, K & Exley, B 2008 (forthcoming October), ‘Using Halliday’s functional grammar to examine early years worded mathematics texts’, Australian Journal of Language and Literacy.
Halliday, MAK 1990, An Introduction to Functional Grammar, Hodder & Stoughton, Melbourne.
Hart, P 1999, ‘The practised eye: Ways of seeing in visual arts’ in J Callow (Ed.) Image Matters: Visual texts in the classroom, Primary English Teaching Association, Newtown, New South Wales, pp 75–84.
Queensland Studies Authority 2005, Years 1 to 10 English Support Materials: Elaborations for Levels 1 to 6 outcomes. Retrieved February 12, 2007 from http://www.qsa.qld.edu.au/yrs1to10/kla/english/support.html
Way, C 2004, Primary Mathematics. Book C, RIC Publications, Western Australia.
Wyatt-Smith, C & Cummings, J 2003, ‘Curriculum literacies: Expanding domains of assessment’, Assessment in Education,10 (1), 47–49.
Key Learning AreasMathematics