A Brief History of the SURF Framework
The increasing emphasis on mental mathematics
Mental math strategies have become increasingly emphasised in the teaching of mathematics, because they help to build mental flexibility, efficient approaches to solving math problems and mathematical fluency (Beishuizen & Anghileri, 1998). Despite its recent prominence, the teaching of mental math strategies appears to lack a clear organisational framework.
There certainly have been texts developed which outline the strategies that may be introduced at various stages of a student’s mathematical development and provide explanations for the teaching of these strategies (e.g., Teaching Mental Calculation Strategies, developed by the Qualifications and Curriculum Authority, QCA, 1999). However, these texts tend to organise strategies in a long linear sequence, without much emphasis on how they build on or relate to each other, or how they connect to different mathematical goals.
Inspiration from Daily CAFE
Over the past several years, many Australian schools have successfully implemented the Daily CAFE approach for reading (Bouchey & Moser, 2009). One of the major strengths of Daily CAFE is its organising framework. There are four reading goals comprising the acronym CAFE: Comprehension, Accuracy, Fluency and Expand Vocabulary. The idea is that these four goals of reading are relevant to readers of all levels and that students will focus on working towards one particular goal in a given reading lesson (or series of lessons). In order to help students work towards achieving a given reading goal, a number of strategies are introduced (Bouchey & Moser, 2009).
In general, the strategies are introduced in order of sophistication, with the least sophisticated (but by no means the least important) strategies introduced first. For example, to improve Comprehension, which is defined as understanding what you read, the reader must initially practise the strategies Check for Understanding and Back-Up and Re-Read. Having mastered these rudimentary strategies, more complex strategies may be introduced, such as Connecting Text to Prior Knowledge and Asking Questions While Reading (Bouchey & Moser, 2009).
Its origins at Belgrave South Primary School
A small-to-medium size public primary school in the Dandenong Ranges region of Melbourne has had some success with implementing Daily CAFE as a whole of school approach to reading since 2011. With a small grant from school council, I initiated a scoping study to explore the feasibility of developing a similar framework for organising and managing the teaching of mental mathematics at the school. It was from these beginnings that the idea of SURF Maths was born. The framework is currently being utilised at the school with students in Foundation, Grade 1 and Grade 2, and there is an intention to extend its application to students in Grades 3 and 4 in the coming years.
References (for the entire website)
Beishuizen, M. and J. Anghileri (1998). "Which mental strategies in the early number curriculum? A comparison of British ideas and Dutch views." British Educational Research Journal 24(5): 519-538.
Boushey, G., & Moser, J. (2009). The CAFE book: Engaging all students in daily literacy assessment and instruction, Stenhouse Publishers.
Cowan, R. (2003) Does it all add up? Changes in children’s knowledge of addition combinations, strategies, and principles. In: The development of arithmetic concepts and skills, ed. A. J. Baroody & A. Dowker. Erlbaum.
Hartnett, J. E. (2007). "Categorisation of mental computation strategies to support teaching and to encourage classroom dialogue." Support Teaching and to Encourage Classroom Dialogue. In Watson, Jane and Beswick, Kim, Eds. Proceedings 30th annual conference of the Mathematics Education Research Group of Australasia: Essential Research, Essential Practice, p. 345-352, Hobart, Tasmania.
Hartnett, J. E. (2008). "Capturing students’ thinking about strategies used to solve mental computations by giving students access to a pedagogical framework." In: Navigating Currents and Charting Directions : 31st Annual Conference of the Mathematics Education Research Group of Australasia, 28 June - 1 July 2008, St Lucia, Brisbane.
QCA (1999). The National Numeracy Strategy: Teaching mental calculation strategies, guidance for teachers at key stage 1 and 2. Q. a. C. Authority. Great Britain.
Threlfall, J. (2009). "Strategies and flexibility in mental calculation." ZDM 41(5): 541-555.
Torbeyns, J., et al. (2009). "Efficiency and flexibility of indirect addition in the domain of multi-digit subtraction." Learning and instruction 19(1): 1-12.