Marcus Witt and Jill Mansergh School of Education Bath Spa University

1. This collection of powerpoint slides and the accompanying audio clips are intended as a companion to the more formal written report on the study undertaken at Bath Spa University looking at the mathematics anxiety of primary teacher trainees on a one year PGCE course. They are intended to give an introduction to the findings and to be a starting point for discussion and further thoughts. To this end, we would welcome comments, feedback and suggestions. Our contact details are given on the final slide.We would like to express our gratitude to the hundreds of dedicated and hardworking trainee teachers that we have worked with over the past few years and who gave up their time to take part in the project. We would also like to thank ESCalate whose funding enabled the project to continue. We hope that you find the contents interesting. Marcus and Jill.

2. Breaking the anxiety spiral: the impact of innovations in teacher trainees' subject knowledge instruction. Marcus Witt and Jill Mansergh School of Education Bath Spa University

3. Breaking the Spiral There is strong evidence that primary school teachers who are anxious about mathematics can inadvertently transmit this anxiety to their pupils. Many children who are anxious about mathematics choose to become primary school teachers, despite the need to teach some maths. Without intervention, it is likely that they will become anxious teachers.

4. Introduction There are many anxious trainee teachers (e.g. Hogden and Askew, 2007). Poor planning and teaching (Goulding et al., 2002). but... Attitudes towards mathematics can and do change during the course of the PGCE year (Brown et al., 1999).

5. What we did A more detailed discussion of the methodology is available in the written report. We collected quantitative data about our trainees’ levels of anxiety about mathematics and their attitudes towards the subject at three points during their PGCE year. This allowed us to track their changing attitudes. We also conducted small group interviews with a number of trainees. The audio clips that accompany this presentation are taken from those interviews and seek to illustrate the findings. Clearly we have had to be selective here. We have tried to choose clips that best illustrate the big ideas that were discussed and expressed.

6. Exploration of the themes and issues raised in the interviews with trainees. • Trainees’ initial anxieties about mathematics • Closer understanding of a link between subject knowledge and pedagogy • Links between trainees’ own pedagogy and their own experience of learning mathematics. • Changing/emerging views about the nature of mathematics.

7. Initial Views and Feelings about Mathematics Some of the anxiety expressed by our trainees as they joined the course related to teaching mathematics rather than their own understanding of the subject. They were aware that they had been taught how to get an answer, but were equally aware that they needed a deeper understanding in order to be able to teach effectively. Others were more aware of the very clear link between teaching and their own level of subject knowledge.

8. Initial Views and Feelings about Mathematics Interestingly, the majority of the trainees who were anxious about mathematics having had bad experiences as learners, expressed a very strong determination not to repeat the mistakes that had been made with them. The majority were clear about the negative points in their own experiences as learners. A few found it difficult to envisage teaching mathematics in a way that wasn’t dry and repetitive.

9. Changes in Attitude During the PGCE Course Many trainees’ views about the nature of mathematics seemed to change during the course. Many had moved away from the idea that mathematics is all about simply getting the right answer. They were aware that part of the primary teacher’s role is to try and engender positive attitudes towards mathematics in the children.

10. Changes in Attitude During the PGCE Course • The trainees identified a number of university-based factors that had led to changes in attitudes about mathematics. • Among these were: • The attitude of tutors • A growing awareness of the link between subject knowledge and pedagogy • Having fun while doing mathematics and therefore no longer seeing maths as something to be feared. • Subject knowledge provision.

11. Subject Knowledge Provision As part of our subject knowledge provision, we decided that our main aim was not to try and ‘teach’ our trainees a lot of mathematics. Rather, we wanted them all, irrespective of their confidence with the subject, to spend some time actually doing some mathematics and (hopefully) being successful with it. We wanted to model a way of teaching mathematics that was possibly not what they had done in school themselves, so that they could experience it. In order to do this, we spent the first three subject knowledge sessions engaged primarily in mathematical investigations that the trainees could tackle at a level that was comfortable for them.

12. Subject Knowledge Provision The three sessions looked at: Mathematical reasoning and communication Shape and Space Calculations For example, the first session contained an investigation of number chains. If the number in the chain is even – divide by 2 If the number in the chain is odd – multiply by 3 and add 1

13. Comments about the investigative subject knowledge sessions. • Re-engagement with mathematics (Rachel) • Establishing an ethos (Matt/Kat) • The importance of collaboration (Eirian/Mina) • Reducing anxiety • Uncovering latent understanding (Caroline) • Taking risks with mathematics; establishing a low-anxiety environment. (Gwen)

14. Comments about the investigative subject knowledge sessions. A great many trainees, particularly those who had expressed some anxiety at the beginning of the course, or who had had negative experiences of learning mathematics in school, saw the investigative sessions as a way drawing a line under their bad experiences and of re-engaging with the subject. There was a sense in which those trainees who were engaging with mathematics in a new way were doing so along with the children they were teaching. Many saw the powerful pedagogical advantages of this.

15. Comments about the investigative subject knowledge sessions. The initial investigative sessions also helped to establish a positive and non-threatening environment in which to learn. Several of the trainees who were less confident with mathematics to begin with found it gratifying that they were able to engage with this investigative way of doing mathematics. Some of the trainees who had been more ‘successful’ with mathematics in a more traditional way, were more reticent about the investigative mathematics, possibly as they had more to ‘lose’.

16. Comments about the investigative subject knowledge sessions. For many of our more anxious trainees, the feeling that they were on their own exacerbated their anxiety. Being open about their feelings about mathematics and discovering that they were not alone in feeling that way was helpful. The investigative sessions encouraged a collaborative approach to mathematics; something that we hoped the trainees would take with them into the classroom. The collaborative nature of the investigations meant that the more anxious trainees felt a degree of reassurance.

17. Comments about the investigative subject knowledge sessions. One of the main objectives of the subject knowledge provision was to promote a more confident approach to mathematics and to reduce anxiety. These first investigations were intentionally designed with an easy entry, so that all the trainees were able to make a start. It was hoped that they would be able to feel a degree of success.

18. Comments about the investigative subject knowledge sessions. Taking risks with maths Some of our trainees who were originally anxious about mathematics and were afraid of ‘getting things wrong’ seemed more willing, by the end of the course, to have a go and to take risks with their own mathematics. This was particularly gratifying, as we felt that it was getting to the heart of our messages about mathematics and was what we hoped our trainees would take with them into their own classrooms.

19. The Way Ahead • We are very aware that what we do for our trainees is by no means perfect. Many come to the course with such low expectations of mathematics that they would be positive almost whatever we do. • We are left with a number of difficult decisions: • Should we seek to differentiate the investigative sessions, or conduct them in groups based on the trainees’ levels of confidence? • What should we do about those trainees whose confidence does not really improve during the year • Are we making adequate provision for the more confident trainees.

20. The Way Ahead We hope that you have found the thoughts and ideas generated by our study interesting. If you are involved in initial teacher education we would be very interested to hear about how you deal with trainees who are anxious about mathematics. We are looking at ways of extending the research and would be interested in hearing from anyone who might like to get involved in the project, by conducting some research in their own institution. Please contact Marcus at: m.witt@bathspa.ac.uk or by phone on 01225 875837.