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
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coordinates in all four quadrants and the Building Learning Power objective was about being resourceful, with the emphasis on carefully reading instructions and using different support mechanisms when stuck and therefore not relying on the teacher telling you what to do. These objectives were based on what I perceived to be some of the barriers to learning found during my initial reconnaissance. I had briefed the learning support assistant in advance to not to give direct support but instead to ask questions designed to encourage the learners to think about the different ways they could access support.
Following the sharing of the lesson objectives and a discussion about what the learners were being asked to achieve, I issued each learner with written instructions and a number of questions with a list of coordinates. The instructions were as follows:
‘Plot the points below and join them up in the order shown. Where you see a gap or begin a new line, start a new part of the shape. Do not join this to the previous coordinate.’
These instructions were read out to the class before the task began and I reminded the learners about what they could do if they got stuck. Following these instructions, learners were asked to complete the questions in any order. An example question is given below in Figure 8.
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Figure 8: An example question used in intervention one.
Within two minutes of starting the task, three learners had their hand up asking for help. They all claimed they did not know what they had to do. On speaking to the first learner, it became clear he knew how to plot the coordinates but did not know what he had to do once he had plotted the points. When I suggested that he read the instructions at the top, his response was ‘why can’t you just tell me what to do?’. I asked him what else he could do if he was stuck and he eventually said ‘ask a friend’. He did this and was able to continue but did so stubbornly and without his usual pace.
The other two learners had the same problem. They held the view that it was the teacher’s job to tell them what to do and it was not their job to read the instructions. One learner commented that if I did not tell them what to do then they would not do the task. This attitude towards their learning was also evident in the comments made in their learner journals that each learner completed afterwards. One learner wrote ‘The teacher would not help me when I got stuck and made me ask another student. I wasted lots of time waiting for help so I didn’t get the picture finished. The worksheet was boring and a waste of time because I will never need to use coordinates in real life.’ In this comment, I saw the learner making use of avoidance techniques, perhaps to shield his uncertainty over how to cope when
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outside his Comfort Zone. He was clearly annoyed at not getting the task completed and tried to pass the blame onto someone else. There is also evidence that he did not find the task useful because it seemed to him to lack any obvious real life relevance and he indicated that as a consequence he became demotivated in completing the task. The lack of real life applications is something that Nardi and Steward (2003) suggest is adding to learners’ dislike of mathematics.
One observation I made from this comment that supported me in my future planning of interventions was that I needed to look at ways of managing the change of expectations of these learners. Their past expectation of being able to ask the teacher for help when they became ‘stuck’ was no longer the way I wanted them to operate.
The learners’ journals indicated that many learners appeared to enjoy the challenge of the task. One commented that ‘the rules on the sheet made it a little confusing’ but ‘working with a partner and discussing the task made it easier and helped us understand more and we could compare our work and see where we had done wrong’. My observation records indicated that I did see learners working together and being proactive by dealing with problems themselves instead of asking an adult for help.
By monitoring the requests for help, just over eighty percent of the class were seen to move away from relying on teacher help and instead using peer support when required. Having this as a lesson objective appeared to make a difference. One area that I felt was missing in this task were the links to real life applications of
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mathematics, as mentioned by some of the learners in their journals. The initial reconnaissance indicated that the majority of the class did not see the relevance of mathematics in life so this is something I ensured was more evident in the next intervention.