Developing the Teaching of Fractions with Non-Specialist Teachers in a Primary Setting Primary Researcher: Jen Law Supervisor: Dr Jenni Ingram

Rationale September 2016, Primary Mathematics Achievement Lead. Utilise the specialist knowledge of a secondary mathematics teacher in developing mathematics teaching and learning in the primary school. Initial meetings with Senior Leadership identified Fractions as an area which would benefit from targeted intervention.

RQ1: What are the current perceptions of teachers regarding their own practice in the teaching and learning of fractions, and how do these relate to the literature? RQ2: How do teachers in this context plan for the teaching and learning of fractions? RQ3: What constitutes effective or useful training on the topic of fractions for teachers in this setting? RQ4: How do teachers in this setting interpret and evaluate pupils’ developing understanding of fraction concepts?

Sequence Training intervention - Directed time. - 2 twilights; 3.25 hours in total. Questionnaires - Self-Evaluation of Confidence; Subject Knowledge. - Background information; teaching experience. - Evaluation of the training. Observations - In person. - IRIS video-capture. Interviews - Stimulated recall from video capture. - Pupil books. - Lesson artefacts. Throughout the research period, I have kept a research journal which contains notes from observations, emerging ideas, and comments from informal conversations.

The Rational Number Concept Charalambous, C. Y. & Pitta-Pantazi, D. Revisiting a theoretical model on fractions: Implications for teaching and research Proceedings of the 29th Annual Conference of the International Group for the Psychology of Mathematics Education July 2005

RQ1: What are the current perceptions of teachers regarding their own practice in the teaching and learning of fractions, and how do these relate to the literature? In self-evaluation of confidence, all topics had a mean score >2.47 (maximum score 3, n = 17). “How do you feel about teaching fractions?” Before training: mean = 3.765 (maximum 5, n = 17); After training: mean = 3.950 (maximum 5, n = 20). Several teachers commented that fractions was a topic that they enjoyed teaching. Teachers identified strengths of their pupils as: Definitions of key words/use of vocabulary Identifying what fraction is shaded Splitting things into equal groups/equal sharing Adding fractions with the same denominator

RQ1: What are the current perceptions of teachers regarding their own practice in the teaching and learning of fractions, and how do these relate to the literature?

RQ2: How do teachers in this context plan for the teaching and learning of fractions?

RQ2: How do teachers in this context plan for the teaching and learning of fractions? Planning across the week as a sequence; not always pinning down the specifics. “I kept it very simple” ; “I haven’t overcomplicated it.” Appropriate extension material is not always available.

RQ3: What constitutes effective or useful training on the topic of fractions for teachers in this setting? Fractions specific input during training gave a mean score of 1.941 (maximum 5, n = 17). Only 3/17 teachers had received additional CPD on fractions. 2/17 have done their own research. 3/17 ticked collaboration with a colleague.

RQ3: What constitutes effective or useful training on the topic of fractions for teachers in this setting? “I think it was great to think of a topic in that much detail,… But in terms of what we got from it, was just having that time... we would never, even in PPA… this came out of discussions that we had at the INSET because we understood like, well, S asked me how we going to do… we’ve done fractions of a number, how are we then going to teach percentages of a number? And percentage increase and decrease? And looking at the objectives and thinking ‘well, all of this is linked to fraction knowledge, all of it comes from that same understanding.’ And it’s only when you have that time, and you know, to discuss it in so much detail, that you can think about a better or more interesting approach than just saying to them that, you know, that 25% = ¼, don’t ask me why, but it just equals 1/4… and you divide by your denominator, so get on with it… kind of thing.”

RQ4: How do teachers in this setting interpret and evaluate pupils’ developing understanding of fraction concepts? Books show pupils dividing as equally as they can – have connected the fraction concepts with equality of portion/share. “They all just seemed to get it, you could tell they got it I think”… “they’ve remembered it… remembering after a weekend is really good to see.” “you can see the different levels of who completely understood, and who didn’t understand what was happening. Who had just drawn groups of pictures for the sake of it.” “This one here… she’s done hers in rows, but she’s circled individual cubes to show the quarter… the one who’s done all three in one group shows a definite understanding of ‘this is a quarter, that is one part’ as opposed to ‘I have three cubes’.” Lack of connection for pupils about division and sharing.

Exploring Halves in Year 1 “I was sat at a table with a lot of the low attainers and the language assistance and it was more a discussion-based sharing… he literally just circled one for you one for you… with the pizza he literally shared it in half… with the cupcakes he’s drawn a line down the middle and he’s tried to cut the apple in half… and his problem was with the tomatoes because they weren’t in a uniform arrangement.”

Exploring Halves in Year 1 ‘one for you, one for you’ (connecting to persons sharing) vs ‘how many of each’ (in the share)

Implications for the Future Connections between different concepts need to be developed more thoroughly, earlier. Mastery curriculum from September for Years 1 – 3. Collaborative planning with a topic focus could be a highly beneficial use of directed time during CPD/meetings. Prioritise weaker topics eg. multiplying fractions. Discussed as part of the implementation of the new Mastery curriculum approach. Planning for greater depth or extension is an area for development. Use collaborative planning time to develop these. Stimulated recall using IRIS gave focus to discussion during interview, and allowed the teacher to reflect in advance on specific aspects of the lesson if they so wished. Continue to use IRIS as a tool for developmental observation/discussion/coaching, particularly with NQTs, Associate Teachers and interns.