4.1 The reconnaissance stage
As discussed in section 3.5, I had been teaching the research group for a term before I started the cycles of interventions for my action research. The aim of waiting a term before starting the study was to give me the opportunity to gain an insight into what barriers to learning I needed to address through the interventions to support these learners. The first term was my reconnaissance stage.
In line with school policy, the research group sat a baseline assessment during their second week of year 10 at the school. This baseline assessment was a GCSE
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examination paper from a previous year. I marked these papers using the official mark scheme issued by the examination board and analysed them to get an insight into their current mathematical attainment. Looking at the marks achieved for different topics, I found that particular of strengths of the group were addition, subtraction and multiplication of positive integers, calculating simple probabilities as fractions and interpreting simple bar charts and pictograms. The topics for development included algebra (all elements), percentages, fractions and area. I also looked at the different styles of questions, and found that the learners were more successful with the short one or two mark questions, especially those that made it easy to see what they were required to do. Those questions that contained a lot of text or involved multi-step problems were not answered well and often were not attempted. When I spoke to some of the learners afterwards, they said that they did not attempt a question if it looked difficult. During a discussion with one of these learners, I was able to get them to correctly explain the steps involved in solving such a question verbally even though they did not attempt it.
During these initial weeks, I also asked the class to complete a mini-investigation based on investigating how many squares were on a chessboard. Although many learners could see that there were more than sixty-four squares, I observed that they found it difficult to get an accurate answer for the number of squares because they were approaching the problem without a plan. This resulted in them missing many squares and counting some twice. When they did get the correct answers, the majority did not present their work in a way that aided them in finding a pattern. From these observations, I knew that I needed to focus on approaching
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investigations in a systematic way and encouraging them to present their findings in a format that would support them in generalising their findings.
The second term started with a focus on number work. During this unit, I saw many examples of student lacking the confidence to persevere when the structure of the question changed. For example, when looking at column subtraction they were able to confidently subtract two positive integers of any size but as soon as I asked them to use the same technique with decimals, they were reluctant to attempt that question because they said it looked different. During the discussions I had with them following this, they mentioned that they did not want to attempt the different question in case they got it wrong. I came across more evidence of this happening during the remainder of the first term.
Following the reconnaissance stage, I found that this particular group of learners lacked confidence in their mathematical ability and preferred to remain within their comfort zone, focussing on routine questions that were all very similar. As soon as they came across something that looked slightly different, they felt as though they could not do it, despite discussion with me afterwards revealing that they could do it. I also observed that they were poor at reading the information given to them in questions and that they would use avoidance techniques to avoid having to work on questions they felt looked challenging. The only way I saw them accessing support when stuck was by asking the teacher for help with the hope that the teacher would do it for them. During discussion with learners, I also found that they did not see mathematics as a subject that develops skills they will
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require for their future. I aimed to address these barriers to learning through the interventions.
During this stage, I also spoke to the learners about their learning in their previous school. They revealed that their previous education in mathematics followed the same routine. Each lesson began with the teacher introducing the topics followed by a number of examples. Following this, they would work from a textbook or worksheet attempting many similar questions, progressively getting more difficult. Each question was similar to that of the example. Although the textbooks often had problem solving questions in each exercise, the learners told me that they often missed them out ‘because they looked difficult’. This style of lesson is what I witnessed when I went to visit them in their previous school as part of our transition visits. Observations during the reconnaissance phase indicated that the learners had become encultured into practices of rote learning, procedural competency and the idea of there either being a correct or wrong answer. In order to address their lack of resilience I needed to carefully consider how I would change this culture of learning.
4.2 Intervention one: plotting coordinates
The first intervention lesson was based around plotting coordinates in all four quadrants. For this lesson, split-screen objectives were used, as explained in the literature review section 2.8. One objective related to the learning of a mathematical technique and the other related to a Building Learning Power outcome. For this lesson the mathematical objective was to be able to plot