QUANTUM RESEARCH GROUP

QUANTUM RESEARCH GROUP

QUANTUM is the name given to a research and development project on quality mathematical education for teachers in South Africa. The development arm of QUANTUM focused on qualifications for teachers underqualified in mathematics (hence the name) and completed its tasks in 2003 (see below).

From 2003, QUANTUM has continued as an NRF-funded collaborative research project, with Professor Jill Adler as Principle Investigator and research leader.

Our problem
The central concern of QUANTUM s research is Mathematics for Teaching (MfT): what it is, how it is constituted across varying sites of practice, and why this is so. Our major empirical focus is MfT as it is constituted in mathematics teacher education. This is being complemented by smaller empirical studies of MfT in school mathematics practice. The goal is that together these will enable the production of a framework for the development of MfT in teacher education i.e. a systematically informed basis for intervention into the content preparation and development of mathematics teachers.

Our findings to date have yielded important results and insights. These have been published (see below) in a significant range of refereed journals and conference proceedings: in general education in South Africa; in the mathematics teaching community; the community of mathematicians, and the mathematics education research community. Briefly:

• In relation to (a) and (b) we found that across mathematics courses specifically offered to teachers in formal in-service teacher education, the mathematical demands in formal assessment was largely restricted to the recall and reproduction of procedures taught in the courses. There was evidence, though limited and infrequent, of assessment of 'unpacking' of mathematical ideas - that specific mathematics teachers need to know and know how to use in practice to make mathematics learnable in school. There is thus a disjuncture between what is valued at the level of intention, and what comes to count as legitimate and valued knowledge in mathematics teacher education. The significance of this research has seen its publication in the Journal for Research in Mathematics Education (the leading journal in the field). See Adler & Davis, 2006. See, also, Adler (2005), Adler & Davis (2003). This initial finding confirms the importance of studying teacher education itself, as argued below. See also Adler, Ball, Krainer, Lin and Novotna (2005).
  
  
• In relation to (c) our in-depth study of selected courses has revealed that different models of teaching are in evidence across courses. We have identified how particular employment of means of identification with mathematics and teaching produce different possibilities for learning MfT. In one case, teachers are offered images of teaching together with symbolic resources that suggest opportunities for developing principled and practical orientation to mathematics and teaching. In the two other cases, the images of teaching came to predominate, resulting in limited orientations to mathematics in particular. These insights are critical in that they identify and describe different models at work. They are suggestive of potentialities, and also the possibilities for the reproduction of disadvantage (in relation to mathematical content development of teachers). Further study of additional and more contrasting sites is needed. This research was presented at the Kenton conference in October 2005, in an invited plenary, and is currently under review in the Journal of Education. It has been accepted for presentation at the peer reviewed Psychology of Mathematics Education conference in 2006. See Davis, Parker & Adler (2005), Adler & Davis (2006).
  
  
• In relation to (d) the two small case studies have yielded important comparative insights. See Kazima & Adler (2006), and Adler & Pillay (forthcoming). The pedagogies in each case were different, with the teaching of functions by and large traditional, and the teaching of probability more aligned with what have come to be called reform-based approaches. The studies show that the mathematical work required of teachers in these two situations differs markedly in relation to the selection and use of learning tasks, interactions with learners? mathematical thinking, and ultimately how mathematical explanations come to be offered in class. MfT is differently shaped in and by these two contexts, suggesting that topic, pedagogy and context matter. Three further studies are currently underway to extend these insights, and so provide a means for relating MfT in teacher education to MfT across topics and classroom contexts. This in turn will inform teacher education across contexts.
  
  
• Overall, our progress to date is also a function the innovative language of description we have developed so far in this research, and described in the various papers noted above.

Our work to date reflects back on the significance of this research for the field of mathematics teacher education in particular, and teacher education more generally. The kind of study of MfT in teacher education that we are undertaking is in its infancy, yet crucially needed. We have made significant progress in QUANTUM to date. Much remains to strengthen our understanding, and to be able to usefully inform intervention into the mathematical education of teachers. This is the work of current project, funded by the NRF from 2007 - 2011, and in focus in doctoral student work;

In 2008, QUANTUM-UK was established and a project is underway focused on prospective teachers who retrain through a mathematics enhancement programme.

The QUANTUM project (2000 - 2003)
(Qualifications on the NQF for teachers underqualified in Mathematics)
The QUANTUM project was set up at Wits University in 2000 under the direction of Prof Jill Adler. There are two arms to QUANTUM - a development arm funded from 2000 - 2003 and a research arm which is ongoing. The overarching development goal of QUANTUM was to intervene stragegically and systematically in the crisis in mathematics education in South Africa by developing a model of appropriate school-focussed mathematics and mathematics educaiton courses for the teaching corps (in Senior Phase of GET and FET), and a selection of systematically evaluated mathematics course materials for teachers. In order to meet this goal, the project:

• conceptualised and developed a set of cumulative, integrated school-focussed mathematics and mathematics educaiton courses for teachers appropriate to the teachers mathematical development in the first instance as well as to curriculum reform in South Africa
• negotiated a partnership relatinoship with the Provincial Education Department for teacher participation
• implemented these courses with teachers in practice

A final report of this project is availaible on request.
The Research arm of QUANTUM was set up to constribute to a practice-based description of mathematical knowledge for teaching.