ACTION RESEARCH: PUPIL EVALUATIONS OF TEACHING AND LEARNING: AUTUMN 2017
Researcher: J Weinberger Minchinhampton
Context: Year 5 Maths
Developing lesson design in maths that based on problems and ensures a growth mindset
Desired Outcomes: Pupils who enjoy maths. Pupils who see themselves as mathematicians
Pupils complete PERTS academic mindsets questionnaire.
Repeat questionnaire and draw conclusions re impact based on qualitative differences at start and end of process; interview children.
The quantitative results from this research have shown a positive shift in attitude towards maths and growth mindset in the sample group interviewed. Beginning a maths objective with some kind of problem solving has not only given all children the chance to experience a deeper applied level of mathematical thinking, but also given their maths learning a purpose. This has made the children more enthusiastic in the way identified by Jo Boaler in Mathematical Mindsets. In addition to the quantitative results, there have been general shifts towards a more positive attitude towards maths. The SEND boy who showed least change in the data at the beginning and in the middle of this research – both in terms of his thinking that maths was relevant to him and that he could improve at maths – began to show much greater positivity in the second half of the project. On a continuum of ‘How I feel about maths’, he moved himself from very negative to very positive; when absent from school due to sickness, he continued lots of the maths learning we had been doing (about multiplying and dividing by powers of 10, 100 and 1000) at home and very proudly presented it to me and the class upon his return.
One of the key challenges of this approach has been in finding, adapting or creating activities that fit a particular learning intention and are low-threshold / high ceiling. Carefully-thought-about maths resources for children who are finding an activity hard are crucial scaffolding for ensuring that all children can get over the threshold – off the first base – of any activity.
Through further thought and discussion with colleagues, the initial direction of this research has led to similar but different approaches to the initial teaching of a learning intention: it could begin with problem solving, but equally could be a maths game, number talk or a maths enquiry that gets the children thinking, exploring and talking about the concepts involved. A mixture of these approaches, according to activities that work best with particular learning intentions, still gives the children a hook. It is useful to use a range of different ‘hooks’ in order to prevent the learning process from becoming stale. For the same reason, every learning intention needn’t be approached using a problem, game or number talk, and instead could go straight to a more traditional fluency activity.
When approaching an objective through one of the ‘purposeful’ ways above, opportunities arise to talk about children’s questions, ideas or misconceptions – their ‘marvellous mistakes’. Shared with the class just verbally or using a visualizer, these are valuable ways to delve into the children’s understanding from their point of view and enables the learning to be led and informed by them.
In a similar way to trying to make the maths purposeful and relevant through problem solving, I have found it useful to begin each particular topic (place value, addition and subtraction, multiplication and division etc) with a discussion about how and when this maths is used in our lives. It has led to interesting ideas that come from the children, and give a broader purpose to the mathematical learning.
All of these ways of approaching a learning intention have meant that the subsequent ‘Shanghai’ stages of teaching and learning – fluency, followed by reasoning then further problem solving – have taken a longer time, however that has not proved to be particularly problematic. In fact, the additional time spent on a learning intention can only to help the children to gain a greater depth of understanding.
Though an evaluation partner interviewed the four sample children at the end of this research process, the opportunity was missed for a lesson study from them; that would still be useful next term as I am encouraged by the results so far. There was a good opportunity for the Academy Development Partner (ADP) to do a lesson study. He identified ways in which the practice could be developed: more explicitly teaching problem solving skills (using a table, trial and improvement, acting out etc), further drawing out the children’s own ideas and conceptual understanding, and teaching the children to know which maths resources to choose to use.
1. Beginning a maths objective with some kind of problem solving, number talk, game or maths enquiry does make the children’s learning more purposeful and they are more enthusiastic / positive as a result.
2. It ensures that all children are regularly encountering reasoning and problem solving activities.
3. Using a ‘hook’ at the beginning of a learning sequence enables the learning to be led and informed by the children’s own thoughts and understanding.
4. Careful, creative thought needs to be given to these activities to make sure that they are low-threshold, high ceiling, and will generate a fruitful exploration of the key concept/s of a learning intention; maths resources such as number lines and multiplication squares are also crucial to ensure all children can get over the threshold, and children need to be taught which resources could be useful, and which not for particular activities.