Proceedings of the Day Conference held at the University of Nottingham on 19 Jun 2010 and the New Researchers’ Day held at the University of Leicester on 18 Jun 2010
01 Using video for professional development: a case study of effective practice in one secondary mathematics department in the UK
University of Bristol, Graduate School of Education
The use of video recordings of lessons for teacher professional development is under-researched (Hall and Wright 2007, 9). There have been conflicting recommendations related to viewing videos of similar or different contexts (e.g., Hall and Wright 2007, 11 and, Clarke and Hollingsworth 2000, 40). It has been reported that it can be hard or take time to establish norms for discussion of video (Van E’s and Sherin 2008, Jaworski 1990). This paper reports on evidence from the use of video recordings in one secondary school, where teachers commented on finding video watching in a group more useful than lesson observation, with no evidence of this taking time to develop. I report on the practice of using video in this school, which drew on Jaworski (1990), finally offering speculations based on Rosch (1999) as to why it is effective.
University of Leicester
In the summer of 2008, I worked with a small group of primary PGCE students and discovered that a brief taught session on mental calculation strategies had a significant impact on their final teaching placement (Davis 2009). In order to evaluate whether there was any longer term impact, I have revisited some of those students who are now approaching the end of their second year of teaching. These initial findings of this ongoing research show that all of these teachers have taught a significant amount of mental calculation methods, and all have a strong belief in the importance of discussion of children’s strategies.
03 A study of the effectiveness of a Dynamic Geometry Program to support the learning of geometrical concepts of 2D shapes
School of Education, University of Leicester
The study described in this paper aims to investigate 12-13 year old students’ geometrical reasoning in a Dynamic Geometry environment in order to answer the question: “In what ways do the affordances of Dynamic Geometry Software act to mediate the learning of geometrical concepts of 2 dimensional shapes?” Two theories which shed light on how humans conceptualise geometric figures and how this sometimes leads to misconceptions will be described. Dynamic Geometry Software may hold some of the answers to the problems students have with conceptualising shapes in geometry, and support the development of geometrical reasoning and the correct use of mathematical language. The importance of designing a task which is seen by the students as having a purpose is also mentioned. The research project will be described and findings from early data will be discussed.
University of Manchester
We consider here the use of a particular type of mathematics workshop in some schools, colleges and universities. This is a preliminary qualitative study, focusing largely on the factors that would appear to have an influence on the success, or otherwise, of such events. Several examples of these workshops are provided, and a number of the perceived educational benefits that arise as a result of running them, particularly the impact on student learning, are highlighted. We also discuss some of the issues that may be encountered. Finally, potential research questions in this regard are mooted.
Martin A. Jones
Havant Sixth Form College, Hampshire, UK.
As part of an attempt to track the influence of culture on mathematical activity Paul Ernest’s two categories of ‘traditionalist’ and ‘fallibilist’ images of mathematics was used to analyse students’ perceptions of mathematics. Perceptions were gauged from written answers to a questionnaire from groups of students in England, South Africa and Botswana; these were mapped to the characteristics identified by Ernest. To reflect the complexity of responses the various characteristics were split into groups and the students’ views were mapped onto a number of grids. I suggest that the mapping enables some patterns to be identified as well as illustrating the variety of views within classrooms. While the responses indicate implications for my own teaching, improvements are needed to this first attempt so that these tools might provide a robust means to clarify the different ‘mathematical cultures’ that we each, whether student or teacher, adhere to and contend with.
Marie Joubert and Rosamund Sutherland
University of Bristol
The National Centre for Excellence in Teaching Mathematics funds teachers of mathematics to undertake small-scale enquiry projects. Underpinning this strategy is research evidence which suggests that involvement in teacher enquiry will have an influence on the learning practice of teachers. This paper reports on a study which aimed to understand the range and influence of these projects. The study found that the enquiry projects ranged in scope and focus, reflecting the wide interests and concerns of teachers and those involved with the CPD of teachers. Teachers reported that that taking part in the projects had a positive impact in terms of their own learning, changes in their classroom practice and improved student learning.
07 It’s good to talk! English as an additional language as a medium for teaching and learning in primary mathematics lessons
Department of Primary Education, Canterbury Christ Church University, UK
This study analyses Malaysian Primary Teacher Trainees’ perceptions of their experiences of learning through the medium of English. These learning experiences include their practical engagement with alternative pedagogical practices for teaching mathematical concepts and their engagement with mathematics education research-based literature. The students reflected on how the use of English throughout the course had affected their learning, their ability to develop conceptual understanding and how this had impacted on their own practice in primary classrooms.
Department of Education and Professional Studies, King’s College London
Abstract: An exploratory investigation is reported, aimed at discovering possible evidence relevant to reform of A-level mathematics content. The investigation focussed on the many undergraduates in quantitative subject courses with only GCSE maths. Typically they get a pure maths “top-up” module in their first year to build up their foundational maths knowledge. Comparing its content with A-level indicates how well these students would have been prepared if they had actually taken A-level maths. The comparison covers top-up in three subjects at two differently ranked universities. Very clear patterns are evident: economics, business and finance top-ups overlap AS-level content moderately well. However, Matrices are important in all these courses and are not covered in A-level. The most striking result however is that computer science top-up is entirely in the area of Discrete Mathematics with no content overlap with A-level or with the other three subjects. These clear patterns seem to validate the method of investigation, which consumed only modest resources, and justify further investigation. Possible implications of the patterns are discussed.
Learning Development Centre, Aston University.
This preliminary research showed that the use of an eye tracker gave an insight into how mathematics is parsed. The results indicated that an expert mathematician is able to identify and process relevant information quickly compared to non-experts. The fixation times of the expert support the idea of an asemantic processing mechanism whereas the fixation times of the non-experts indicate the need for explicit semantic processing. The fixation times and gaze trail data support the notion of a first parse to identify relevant information and subsequent parsing to encode the information into working memory.
10 The influence of teacher candidates’ spatial visualization ability on the use of multiple representations in problem solving of definite integrals: A qualitative analysis
Eyup Sevimli and Ali Delice
University of Marmara
This study aims to investigate the influence of spatial visualization ability in representations used in definite integral subject. In this sense, a case study has been carried out on 45 mathematics teacher candidates. Multi- method approach was adopted by using more than one research techniques. Tests, Document analysis and semi-structured interviews are the research instruments and inferential & descriptive statistics are used for the data analysis. Findings showed that spatial visualization ability of the teacher candidates is low. In parallel to these findings, it was determined that the candidates, who have low spatial visualization ability, used predominantly algebraic representation. The development of spatial visualization ability, which may influence the relationship between graphical representations and the other representations, increases the performance of solving definite integral problems. Moreover, the candidates are advised to develop their spatial visualization abilities to improve their abilities of interpretation of visual information.
Notes by Anne Watson
Department of Education, University of Oxford
These notes report key ideas in a discussion about the impact of practice on research and research on practice.
University of Southampton
It remains the case the the geometry component of the school mathematics curriculum is viewed as providing key opportunities for teachers to develop learners’ capacity for deductive reasoning and proving (as well as their spatial and visualisation capabilities). Nevertheless international research consistently shows that teaching the key ideas of proof and proving to all students is not an easy task. Through a consideration of an example of classroom teaching, this paper scrutinises a selection of theoretical frameworks that may afford greater insight into, and greater explanatory power on, the role of the teacher in the teaching of proof and proving in geometry. The brief sketches provided of three relevant theoretical frameworks (the theory of socio-mathematical norms, the theory of teaching with variation, and the theory of instructional exchanges) illustrate the fact that there is much scope for further suitably-designed research studies.
Notes by Anne Watson
Department of Education, University of Oxford
These notes record the discussion at the fifth meeting of this working group. The focus was on reading two research reports and considering the future of this group.