Debates in mathematics education

Book review of the 'Debates in mathematics education', edited by Dawn Leslie and Heather Mendick, London and New York, Routledge, 2014, xx+212 pp., £24.99 (paperback), ISBN 978-0-415-62385-

‘Balancing’ the ‘live’ use of resources towards the introduction of the iterative numerical method

This paper draws on the Knowledge Quartet (Rowland, Huckstep, & Thwaites, 2005) to analyse an introductory to the Iterative Numerical Method Year 13 lesson of a secondary mathematics teacher who uses a range of paper based and electronic resources including Autograph, a mathematics-education software. Data were collected during one lesson observation and a follow up interview with the teacher. Analysis identifies the different aspects of the Knowledge Quartet dimensions: foundation, transformation, connection and contingency, in relation to the introduction to the Iterative method and to the teaching of Year 13 students. Findings demonstrate how the teacher used students’ contributions as resource for his teaching; how he balanced his use of resources; and how he created connections between these resources while he remained attentive to exam requirement

Transforming Aspirations of Future Mathematics Teachers Into Strategies In Context

In this paper I present a collaborative research and development programme, in which we design situation specific tasks and use them to explore, challenge and change knowledge and beliefs of in- and pre-service secondary mathematics teachers. In this work we use practice-based and research-informed tasks in which we invite teachers to consider a mathematical problem and typical student responses (and teacher reactions) to this problem. So far the programme develops in four stands: (1) mathematical knowledge for teaching; (2) classroom management and mathematics learning; (3) disability and inclusion in the mathematics classroom; and, (4) meta-use of tasks and task development. Examples of tasks from these strands will be discussed in the session

Balancing classroom management with mathematical learning: Using practice-based task design in mathematics teacher education

In this paper we present the results from a study conducted in a UK institution in which 21mathematics pre-service teachers engage with two practice-based tasks featuring incidents where classroom management interferes with mathematical learning. We investigate their considerations when they make decisions in classroom situations and how these tasks can trigger their reflections on the teaching and learning of mathematics. In our analysis we used the constructs of social and sociomathematical norms (Cobb & Yackel, 1996) and Teaching Triad (Jaworski, 1994). Results indicate commendable norms pre-service teachers aspire to establish in their classroom, such as peer respect, value of discussion and investigative mathematical learning. However, they often miss the opportunity to engage students with metacognitive discussions and mathematical challenge as they focus on behavioural issues or endorse dichotomous and simplistic views of mathematical learning. We credit these tasks with allowing insight into pre-service teachers’ considerations and we propose their further implementation in teacher education programs

Micro-evolution of documentational work in the teaching of the volume of revolution

In this paper, we draw on the documentational approach to analyse the evolution of one experienced secondary teacher’s work towards the teaching of the topic of “volume of revolution”. He used a range of paper and computer based resources in- cluding the software Autograph. Data were collected in observations of three lessons on this topic taught to two different groups of 16-18 years old students and a follow up interview with the teacher where he was asked to reflect on his choices in these lessons. The findings illustrate teacher’s documentational work with the used resources, and his schemes of use – aims, rules of actions, operational invariants and inferences – and identify the micro-evolution, namely the small changes and the rationale behind these changes, of these schemes across the lessons