Teachers Talking About Teaching Mathematics

1. Teachers Talking About Teaching Mathematics Dave Hewitt Senior Lecturer in Mathematics Education University of Birmingham Evaluator of NCETM small grant project – The Economy of Teaching Mathematics

2. Collaborative workingandshifting from teacher hatto researcher hat Dave Hewitt School of Education, University of Birmingham

3. Overview • Working on practice as a teacher in a disciplined way; • Shifting from teacher hat to researcher hat; • Beginning a research project; • Importance of collaborative working.

4. Working on practice in a disciplined way: lesson ideas • Each teacher brought a lesson idea for teaching an aspect of algebra which had worked well in their classroom. • Eight ideas were selected. • For each of these eight ideas, there was a group of about 4 teachers who then did the following: • discussed within the group the lesson idea including ways in which it might be developed or adapted; • used the lesson idea with a class in their own school; • returned to report to the group how they had adapted the idea and their reflections upon the way the ideas had worked along with evidence for any comments made. • The group then discussed the idea further and repeated the cycle once more of using it again with another class in their school.

5. Shifting from:teacher hat to researcher hat • Mini-research tasks: • Interviewing two students about thoughts on algebra; • Video record a starter and analyse video; • Analyse students’ written work; • Combination of research methods, including a questionnaire.

6. Task 1:Interviewing • Interview two students about their thoughts concerning algebra. • Pre-interview decisions taken regarding students, organisation, focus and questions; • Interviews to be tape recorded and 10 minutes transcribed from one interview; • Analyse key points from both interviews (‘account of’ and ‘account for’) concerning issues relating to the teaching and learning of algebra. Also reflect upon the interviewing process; • Reflections fed back in the next session at university.

7. Task 2:Video recording • Video a lesson when teaching an algebra topic. • Following the lesson, analyse the video in terms of the approach taken to the mathematics and students’ engagement. • A copy of the video was brought to the next meeting, with a one minute extract to be showed to the whole group along with what mathematical and pedagogic issues were raised from this extract.

8. Task 3:Analysing students’ written work • Teach a lesson on a particular topic of algebra which involves students doing some written work. • Following the lesson, look at the written work produced by the students. Photocopy work which you feel provides evidence for issues relating to: • the understanding a student has of algebra; • the approach you have taken to the mathematics; or • some other focus which you feel is relevant. Note that part of a student’s work might relate to more than one of these categories. • Although you are likely to have collected evidence from more students, write up an analysis of work from just three students which show some contrast in relation to an issue or issues. Note what criteria you may have used to select these students. • In your writing, consider what implications you feel can be drawn from the written work. Be careful to consider what the extracts are evidence of, and whether alternative interpretations could be made.

9. Task 4:Combination of methods • Teach three lessons (or parts of lessons) with the same class on an algebra topic, using one of the approaches from your 'ideas' groups. • There will be four methods used to collect data connected with these lessons: • One lesson is to be video recorded; • At least one lesson will involve students recording their work on paper; • One questionnaire is to be given to the class after all three lessons have been taught. This questionnaire is to gather information about the students’ understanding of the mathematics and the impact of the approach taken; • Two students are to be interviewed to gather in-depth information following the questionnaires. • Your writing of this task should include selected evidence from data gathered and is to address the following: • the thinking which led to you choosing the teaching approach to this algebra topic; • analysis of the data in relation to the learning of mathematics and the teaching approach taken; • a brief commentary on, and comparison between, research methods used and their value in contributing to your conclusions.

10. Assignments • Literature • summarise four articles relating to the teaching and learning of algebra and analyse themes across these. • Portfolio • write up of the four mini-research activities • Analysing of issues relating to the teaching and learning of algebra supported by evidence from your research and from research literature. • Research methods • revisiting portfolio and critically analyse different research methods. • Link in with literature on research methods.

11. Beginning a research project • Previous discussions within the group helped to raise awareness of issues relating to teaching and learning algebra; • This, in turn, helped each teacher identify an area of research interest; • Small groups of teachers help each other turn an area of research interest into focused research questions; • Experience of using different research methods in the mini-research tasks help teachers consider what research methods might produce data which would be useful in trying to answer their research questions; • Shift into more individual work supported by individual tutorials with occasional group ‘check-in’ meetings.

12. Importance of collaborative working • Common focus: • being with others who share a common interest, in our case it was teaching and learning algebra. • Raising awareness: • becoming open to new ideas and listening to other points of view; • Shared work on reading research literature: • the need for evidence to support statements; • use of big words! (e.g. methodology, constructivism, qualitative, empirical,…); • conventions on how to cite references. • Supporting others and being supported yourself: • Critical friends to help: • question statements made; • articulating research question(s); • academic writing.