Response from learner three, Polly

Polly is a learner who shows many of the signs of someone suffering from mathematical anxiety such as avoidance strategies, spending excessive time working on neatness, writing out the full question into her book before answering it and being absent on assessment days. Prior to the research beginning I was made aware of Polly’s fear of mathematics and how she would often end up crying at home because she was unable to do something. A discussion with her history teacher suggested that Polly is a resilient learner in history but in mathematics she is not. Here, she prefers to focus on revision of work covered previously and enjoying working on consolidation tasks when she has to complete many similar questions. She is expected to gain a C in mathematics despite most of her other subjects predicting an A or above.

In the first discussion, her response was she was making ‘very little’ progress in mathematics. She said she tried really hard and always read through class notes and revision guides but felt it made no difference to her ability in mathematics. She was frustrated because she was using the same strategies to progress her

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learning in mathematics that were successful in other subjects. Her response during the second discussion was very similar. During the third discussion, she said she felt she had made excellent progress when we looked at the history of mathematics. She had chosen to research and write about Pythagoras and she said that following this, she understood Pythagoras’ theorem for the first time. She said she found writing the theorem in her own words helped and she liked the visualisation of the theorem she found on the internet. In this visualisation, there was a square drawn on each side of the right-angled triangle and the two smaller squares were broken down so that they fitted exactly into the larger squares showing that the sum of their areas was the same as the large one. She did comment that she remembered doing something similar in class when we cut up the squares to show they were equal but she admitted that at the time she did not see the link between this and the theorem. This ability to visualise can help develop mathematical thinking (Cuoco et al., 1996).

From early in the research project, I had suspicions that she tried to learn mathematics through developing an instrumental understanding of the topics. Evidence of this came out in all three of the discussions I had with her. When asked what style of lesson she felt allowed her to make the most progress, she described consolidation lessons where transmission teaching was used (Swan, 2005) and they were given lots of examples, then given a worksheet to complete with many similar questions. She said by getting the answer correct she knew that she was making good progress. When asked what style of activity resulted in her not making much progress, she mentioned investigation work and questions when they had to make use of more than one topic, especially one that we had not

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covered for a while. This discussion added evidence that she preferred to gain an instrumental understanding of the topic through rote learning. It also gave evidence to support my observation that she enjoyed being in the Comfort Zone. When she left the Comfort Zone, she felt very uneasy, perhaps entering the Anxiety Zone almost immediately, which resulted in her becoming anxious about the work.

In a follow up question, I asked her if she felt rote learning helped her understand topics better. She commented that it helped her make good progress in lessons but admitted that when she came to do homework or revise for a test on the topics she would look back at her class notes and they would not make sense to her. Further questioning indicated that in her other subjects she would carry out research online to deepen her understanding and synthesise different sources together to give her a good understanding of the concept or theory. She did admit that it would be better to do this in mathematics but she did not know how; this is something we have been aiming to address in this research project. Although she knew her method of learning mathematics was not effective, she appeared scared to try to change it. She knew that her method of learning mathematics would usually allow her to succeed in her class work, so stuck with it, even though she suspected it was holding her back in the long term.

Polly knew that her grade in mathematics was important but did not appear to understand how she would use mathematics in the future. She often mentioned that she needed a C in GCSE mathematics to study A-levels and get into university

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but seemed unaware about the usefulness of the skills developed by studying mathematics.

When asked about ‘getting stuck’, she became quite nervous. In the first discussion, she talked about the strategies she used. As mentioned earlier, she was unaware of why these strategies worked in others subjects but not in mathematics. During the second discussion, she talked about the ‘Stuck Poster’ we had on the wall of the classroom and said she had tried quite a few of them. She found working with a peer to be the most effective way to get through a problem. She did mention she found it easier when she worked with someone who is not in her group of friends. Observations of her group of friends and looking at their exercise books and assessments showed that many of them worked and thought in the same way to Polly and faced similar levels of mathematical anxiety.

In the final discussion, she referred to the lesson on the history of mathematics and said that it did give her a confidence boost and she would quite like to try writing about key topics in this way to help her understand what the topic is saying. I suggested she tried this with other topics although I saw no evidence of this happening.

Throughout the research period, I could clearly see that Polly was frustrated that she was not attaining as well in mathematics compared to her other subjects. Although she often joked about this, often referring to the fact that her mother was also ‘rubbish’ at mathematics, she seemed frustrated by her lack of progress. However, what I have observed and heard during the research indicated that her

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fear of failing was stopping her from changing the way she has always worked even though she felt it was not effective. My hypothesis was that her methods were likely to get her the grade C she needed for her future. Any change could have put this at risk, which was not something she was willing to do.

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