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What made a difference for teachers, teaching and students? (details)
In all schools mathematics results were better than other subjects, and in two of the schools significant improvements were made in maths test outcomes. In one school there was dramatic improvement for PLAS. What can we say about how to make a difference both overall and for these students?
There are key features of the ways departments worked which affected the teachers, the teaching, and the students:
- The focus in all schools was on mathematics. Most of the mathematics teachers talked to us about issues that were specific to the subject; very few talked about more generic matters such as assessment for learning or other whole-school policies.
- In all schools mathematics was discussed in department meetings. Teachers discussed the key ideas to be taught and how to teach them, associated language, diagrams and metaphors, what might be misunderstood, how key ideas related across topics, and what examples could be used. In LS there was whole-team agreement on some ways of teaching particular topics; in SP the team worked through a teaching textbook on division together.
- In two schools teachers routinely discussed with each other, in department meetings, how they had taught particular topics, what had gone wrong, and what could be improved in future. In the third school this was not an organised aspect of working together.
- Stability is important. The two schools that did better had the more stable teams, and the school that had outstanding improvement had the most stable student population.
- In all schools planning was primarily about best ways to give all students access to mathematical ideas. All schools shifted from a focus on selecting resources and tasks to a focus on how to help students learn. None adhered to particular lesson structures.
- In LS and FH there were several strong mathematicians who taught the full range of students; in SP there were fewer, but work on personal mathematical knowledge was frequent and open. Mathematics was the focus of all meetings we observed in all schools, and most informal conversations we heard.
- Mixed ability teaching over the first two years in SP was a tool for students and teachers to rethink potential and restructure expectations and enabled a team approach to planning and to discussing teaching at a detailed level. In each school, when setting was introduced it was to create as many parallel groups as possible to maintain open expectations and team planning, with high and low achieving groups identified for special teaching. In LS and FH this happened in year 8, and this sometimes, but not always, resulted in the deployment of less specialised teachers with PLAS.
- The focus on developing mathematical thinking for all students in year 7 in SP and was a contributing factor. The other two schools also focused on mathematical methods to some extent, but also included progression through mathematical content. None of the schools used the strategic tool of squashing KS3 into two years to raise achievement.
- In most lessons there was a strong focus on mathematical concepts, relationships and understanding central ideas. When techniques were taught they were to support the growth of knowledge and not an end in themselves. There were only two out of about 30 observed lesson in which this was not the case.
- Team discussion contributed to a sense of departments learning together. This was most marked at SP in which the HoD herself was open about her weaknesses, and when she messed-up she sought advice from less-experienced colleagues. Most of them also enrolled on an accredited course at the local HEI (n.b. we heard recently that they were told to pull out of this while the school was in special measures). In the other schools there was formal and informal discussion within the teams, especially among the core members, but less open discussion of personal mathematical knowledge.
- The range of influences on practice in all schools was wide and well-informed: ideas were used from research and a range of curriculum projects and materials. All departments included teachers who were members of professional associations and attended courses, seminars and conferences voluntarily. In a few meetings teachers did mathematics together for themselves.
- All schools contained teachers who had pursued voluntary professional development courses and sessions outside school. In SP there was joint enrolment on such a course; in FH the first HoD had a strong PD agenda for the team; in LS significant team members introduced ideas from national initiatives.
- The initial changes in all schools were research-based. That is, mixed-ability teaching is known to benefit lower attaining students and not necessarily to disadvantage for higher achieving students. We are not claiming a general finding from three schools, but notice that the school in which PLAS did best was the one which maintained mixed-ability teaching for longest.
- All schools focused on the development of ways to work and think in mathematics, and many research studies indicate that this is likely to improve learning for all.
- Although we knew that some students were being given maths in year 8 that was much easier than they had been doing in year 7, we are not saying that this was a general effect of using non-specialist teachers. In SP, in which mixed ability teaching continued into year 8, one class was taught by a non-specialist who was openly insecure with mathematics. Nevertheless she worked hard on her knowledge and teaching, was a full member of the team, and taught the full range of attainment in both years. Marginalisation, either institutional or deliberate, and disagreement with department policies and practices, may be a stronger negative influence than merely being non-specialist. However, we did find that even the best non-specialist teachers did not help learners think about the mathematical implications of their work, the mathematical connections, or the ways in which new knowledge can become a tool for future learning.
- Teacher autonomy is unlikely to be a critical factor, since LS had a highly-specified scheme of work. Their philosophy was to have joint and detailed planning and review of tasks so that they could be modified in subsequent use. Special weekly early-morning meetings took place solely for this kind of planning and review. By contrast, teachers in the other schools were free to use their own approaches and tasks, while being provided with some materials, and then contribute them to the team as a whole.
- Decisions about tier of entry do not seem to be a factor. Some teachers enter students who are expected to get level 4 for the 3-5 tier to ensure they get 4 and hope they get 5, which many do. Others enter similar students for the 4-6 tier because the higher level questions depend more on thinking than on calculations. We found no overall effect in the results, so it probably depends on the emphasis on content or reasoning in the teaching.
- Relationship to whole school policy is not a factor. The HoD in SP had to resist many pressures to conform to what she saw as more mediocre practices being adopted to get out of special measures. The HoD at LS, and two other maths teachers, by contrast, were influential in whole-school policies.
- Teaching styles varied, but it is worth reading those parts of the website in detail to find important commonalities, such as listening to students' perspectives and promoting discussion with all students. See the examples of lesson structures.
We have looked at the progression data for higher achieving students and compared these to 2007. Differences are marginal, but appear to be very slightly lower for 2008 than for 2007.
Nothing can be deduced from this data about relationships between mixed-ability teaching and KS3 test results. All schools set in year 9; two school set in year 8.
At the time of writing we have not compared results to national data.
