A Computer-enhanced Package for Learning School Algebra

This proposal is to roll out the outcomes of the ESRC/EPSRC-funded MiGen project, in order to enhance the teaching of early algebra in the secondary school, and thus improve mathematics achievement throughout England. Specifically, we propose to assemble and disseminate to a range of audiences, a polished package of computer and text-based materials for students and teachers based on the MiGen project outputs. The overarching aim is to support the learning of early algebra, in ways that are clearly and explicitly aligned to the National Curriculum and to teachers' practice at Key Stage 3.

MiGen focused on a widespread difficulty that impedes students' ability to learn mathematics in secondary school: namely that they routinely fail to see the point of algebra, a finding that has been discussed thoroughly in the literature (e.g. Küchemann, 2010; Mason et al., 2009; Nunes & Bryant, 2010). As a result, they cannot use algebra as a tool for thinking mathematically, which in turn obstructs their learning about and engagement with STEM subjects more generally. MiGen addressed these challenges by building a technical environment with pedagogical rationale and support, as well as associated activities, so that 11-14 year-old students could appreciate from the outset that algebra is about building and expressing structure and generality and that symbolic rules are the language of this expression. A unique feature of this environment is that the computer system provides support to the students, derived from AI (Artificial Intelligence) techniques, which offer timely and targeted feedback to students on the basis of their actions.

The proposed project has two strands. The first strand will assemble in a coherent package, the outputs of the MiGen project to include student activities, teacher guidance, and 'bridging activities' to assist the transition to paper and pencil. The second strand comprises a series of knowledge-exchange activities, targeted at the teacher and teacher education communities, as well as policy and commercial stakeholders.

Teachers and schools will benefit from a ready-to-use package that fits precisely into their existing teaching practice, and offers a solution to a widespread challenge for teaching mathematics.

Mathematics subject leaders will benefit in fulfilling their responsibilities for programmes of work and ensuring that teachers' activities align with the priorities of the curriculum and the school. In this respect, an easy-to-use and 'non-install' system has already been seen, by a few subject leaders, as a way to involve 'their' teachers in thinking about the pedagogical issues involved in teaching generalization, and a first step in encouraging staff to make productive use of technology.

Pre-service and in-service teachers will benefit from the distribution of the materials, allowing them to enhance their existing teaching of algebra with a unit or module that gets to grips with students' difficulties and misconceptions.

Finally, key stakeholders, policymakers (regional and national) are increasingly aware of the economic and societal value of mathematics, and our existing contacts with government indicate considerable interest in our proposed package. In addition, the artificial intelligence approach we have adopted in MiGen can be seen as a more general pointer to the future use of technologies in educational settings.