Research Study for the Specialist Schools and Academies Trust & the European Union (Marie Curie Actions)

Principal Investigator: Professor Jo Boaler
Researchers: Lori Altendorff and Geoff Kent

Introduction
The aim of the research was to investigate the impact of the BTEC Mathematical Applications course - both with and without an accompanying pedagogy in 'complex instruction' upon students' learning of Mathematics. The research aimed to include both a large-scale quantitative component involving all of the BTEC schools in phases one and two, and a more detailed and focused component with a smaller number of schools. The first phase of the research aimed to inform the impact of the BTEC experience on achievement and Mathematical attitudes. The second phase aimed to provide more nuanced information about the experiences of the students, the culture of their Mathematics classrooms and the ways that their experiences with this new Mathematics approach changes their relationships with Mathematics and their future with the subject.

The Large-Scale Component
Each school taking part in the large-scale component (hopefully 100 schools) will be asked to provide a matched group of students who are similar in their prior Mathematics achievements to those taking the BTEC course but not involved in the BTEC course. These students will be comparison groups. Investigations will then be conducted into the impact of the BTEC course upon students' achievement, using GCSE mathematics as the outcome measure and a range of data as measures of prior achievement. Such measures will be developed with the schools, but are likely to include school assessments and Key Stage Three assessments. A statistical comparison will be made of the two student samples. In the 50 schools that were in phase one of the pilot, questionnaires will be issued to all students in the sample and the matched groups which will measure students' attitudes towards Mathematics, probe other important aspects of their broader relationship with Mathematics and record their reflections on their different Mathematics experiences. This will be another comparative study. In the 50 schools entering phase two of the pilot, questionnaires will be issued to all students before undertaking the BTEC course. The completion of further questionnaires will be required as the students progress through the course. These questionnaires will measure changes in the students' attitudes and beliefs about Mathematics and learning and their relationships with Mathematics. All data collected from assessments and questionnaires will be subject to statistical analysis.

The Focused Study
In addition to work with the larger sample of the BTEC Mathematical Applications schools, a focused study will be conducted of approximately eight schools trained to use complex instruction. In the focus schools we will conduct detailed explorations at three levels: teachers, students and the classroom:

Teachers:
One of the most important research questions in Mathematics education currently concerns teacher change - specifically, how teachers are encouraged to adopt more effective approaches and this case provides a rare opportunity to learn this. A range of questions will be considered, including:

• What are the challenges faced by teachers as they work to implement a new approach?
• How do teachers' actions relate to their beliefs about learning?
• What are the most important supports that can be provided to teachers when adopting more effective approaches?
• How do the teachers' practices develop and change over the implementation period?
• How do teachers' practices vary according to the students they are teaching?
• How do teachers beliefs about learning relate to their actions in the classroom?

Other questions will be developed and researched in response to the teachers' particular situations.

Students:
The most important questions for the students concern the ways their new Mathematics approach changes their relationship to the subject. How and what they are learning will be considered alongside the nature and depth of their learning and whether they are able to transfer their learning to new situations such as those in the workforce. Their beliefs about mathematics and their own capability will also be considered. Possible research questions include:

• How much do students learn in relation to the BTEC approach with and without the complex instruction pedagogy?
• How deep is the students' understanding?
• How effective are the students at transferring their knowledge to new situations?
• How much do students enjoy Mathematics?
• What do students believe about the nature of Mathematics and its usefulness?
• What do students believe about their own Mathematical capabilities?
• Are there any differences in the suitability of the approach for girls and boys, and for students of different ethnicities and class backgrounds?

In all cases, the way students compare to those in the same school who are not learning Mathematics through the BTEC / Complex instruction approach will be considered. In addition to investigating the ways students change, some of the same questions we asked about teachers, involving the challenges faced by different students, will be considered. Moving to a new teaching and learning approach can be difficult for students as well as teachers, so exploration will also be made into:

• What are the challenges faced by students in adapting to a new way of learning?
• Are some students more able to work in the new approaches than others?
• What are the main supports needed by students?

The Classroom:
The third level of investigation concerns the nature of the classroom environment. Important questions will be considered including:

• How is the culture of the BTEC classroom different from a more traditional Mathematics environment?
• How are classrooms organised?
• How are students engaging in the work?
• How does the culture of the classroom relate to other Mathematical environments - in higher level study and in the workplace?
• How does the culture of the classroom impact students' learning?

These different, nuanced questions concerning the students, teachers and classroom environments will be answered through a combined set of classroom observations which will include videos of the classrooms, student focus groups, individual student interviews and teacher interviews. Data collection will begin as soon as teachers begin the complex instruction training (summer 2008) and extend through the 2008-2009 school year. Data analysis and writing will be completed in autumn 2009. In addition to using classroom videos as an important research tool, some may be developed for use in future professional development and wider dissemination of the methods.