This is a major modification of the proposed Academic Fellowship ‘Constructivist Computing for a Mathematics Learning Environment’ following submission of ‘reflections’ (one from Steve Russ, another from Meurig Beynon in February 2012) on why that did not proceed as planned. This proposed ‘Pedagogic intervention’ nevertheless arises directly out of the Fellowship proposal. We did not appreciate then that our environment is one in which learners build their own understanding (both as an artefact on the computer, and as something personal). It is not one which can be ‘evaluated’ as a typical objective piece of software. Hence the title ‘A personal introduction to linear algebra’.
The objectives and outcomes of the project are therefore very different although the learning objective remains the same.
We have recruited a team of six first year CS students who have been learning (last term) basic theory in the domain of linear algebra by conventional teaching methods (lectures, notes and problem classes). They will have a basic competence in solving standard problems in this domain but their conceptual understanding will probably be quite limited. The Empirical Modelling research project has developed new tools (JS-EDEN) that combine unconventional approaches to modelling with state-of-the-art web-based techniques. The tools are well-suited to an experiential framework for learning that affords a flexible and personal exploration and construction of a domain.
The students are learning about these tools in seven one-hour (unpaid) sessions, of which we have had three last term and will have a further four in the latter part of June after their exams.
The project proper will then consist of the students working intensively with us over the two weeks 2nd - 13th July for which they are paid. The students will follow a course of ‘guided’ construction and discovery which includes freedom for them to explore and gain confidence through personal experiment. The objective here is for the students themselves to engage so much with the software visualisation and interactions (both suggested and chosen) that they effectively chart out their own self-made course in the basics of linear algebra. So the result we hope for will not be a tutorial others can ‘use’, but rather a map of key staging-posts and experiences so that others may traverse a similar, but personal, learning and discovery path. We believe this will be a novel kind of software for a learning environment. The students’ experience of it will be a crucial part of the outcome. We shall ask the students to write a short ‘reflective’ piece and hope that this might demonstrate improved conceptual understanding and confidence.
We also hope to employ the equivalent of one full-time 4th year student over the two weeks (who will have taken the 4th year module (Introduction to Empirical Modelling) as a hands-on Tutor.
The funded project will only involve this group of students (plus possibly some virtual interaction with other researchers helping with technical issues and development).
The legacy we look for from the project is lessons we can learn about the methods in general and their accessibility to non-experts in the tools, and lessons in the particular case of this domain for what are effective points of ‘guided discovery’ for others to benefit from similar learning experiences.