Building Mathematical Knowledge for Teaching (MKT) for Pre-Service Mathematics Teachers

Author(s):

Majella Dempsey(presenting / submitting)Dr. Ann O'Shea(presenting)Dr. James Lovette Dr. Brien Nolan

Conference:

ECER 2015

Network:

24. Mathematics Education Research

Format:

Paper

Session Information

24 SES 03, Teachers' Perspectives

Paper Session

Time:

2015-09-08

17:15-18:45

Room:

659.Oktatóterem [C]

Chair:

n.n. n.n.

Contribution

This research concerns the development of Mathematical Knowledge for Teaching with a group of pre-service mathematics teachers. The pre-service teachers were enrolled in the second year of an undergraduate Mathematics Education degree and were studying both Mathematics and Education. Nine students took part in this study. The concept of Mathematical Knowledge for Teaching (MKT) was first introduced by Deborah Ball and her colleagues; building on Shulman’s (1986) notion of pedagogical content knowledge they defined MKT as ‘the mathematical knowledge needed to carry out the work of teaching mathematics’ (Ball, Thames, and Phelps 2008, p 395). Ball et al. (2008, p 403) identified six different dimensions of MKT: Common Content Knowledge; Horizon Content Knowledge; Specialised Content Knowledge; Knowledge of Content and Students; Knowledge of Content and Teaching; and Knowledge of Content and Curriculum. They list some of the situations in which a teacher would need to use MKT, for example: presenting mathematical ideas, choosing an appropriate example, evaluating students’ responses, appraising textbooks, modifying tasks (Ball et al. 2008, p. 400).

The literature on MKT refers repeatedly to the role of MKT in teacher education programmes, noting that it is an aspect of the teacher’s knowledge that must be explicitly built (Delaney 2010). The link between high levels of MKT and richer teaching outcomes has been discussed by Hill, Rowan and Ball (2005) and by Delaney (2010). With this in mind, a team of researchers at two universities in Ireland studied the development of MKT in two groups of pre-service teachers. We will report here on the outcomes of the Maynooth University part of the study only. The project aimed to help students develop their own MKT; in order to do this a series of workshops were designed and delivered by the authors. The students’ awareness of MKT and levels of MKT were investigated using pre- and post-intervention tests, questionnaires and focus group interviews.

Our research questions for this study were:

To what extent are pre-service teachers aware of the variety of mathematical tasks involved in mathematics teaching?
Can pre-service teachers’ levels of MKT be raised through a taught unit that focuses on the reflective study of classroom practice?

Method

The methodology used in this research was that of Design Based Research as described by Plomp (2009) as the systematic study of designing, developing and evaluating educational interventions as solutions for complex problems in educational practice (p.13). It followed a cycle of design, implementation and analysis (Stephan & Cobb, 2013). Phase 1: Assessing students’ knowledge of MKT Student teachers’ knowledge of MKT was assessed using materials developed by the ‘Learning Mathematics for Teaching’ team (LMT Project, 2013), and adapted to the Irish context by Delaney (2010). Noting that MKT has numerous different aspects, the research concentrated on the following five, and applied the work of Ball and colleagues to determine the students’ level of mathematical knowledge in relation to these (Delaney 2010): • Representing mathematical ideas • Eliciting properties of numbers and operations • Following and evaluating pupils’ explanations • Interpreting pupils’ utterances • Connecting mathematics to the pupils’ environment. These five have been selected for a variety of reasons. Some have been identified by Delaney (2010) as areas where primary mathematics teachers show some weakness, while others relate to areas where there is a self-reported lack of confidence among teachers implementing the Project Maths syllabus (Cosgrove, Perkins, Shiel, Fish and McGuinness, 2012). Phase 2: Developing an intervention to develop MKT The intervention was designed around the practice of teaching mathematics and involved (i) the analysis of pupils’ work, (ii) the analysis of videos and (iii) content knowledge development. This element emphasised the importance of critical reflection on the part of the students in terms of the teaching episodes that they reviewed and developed. Phase 3: Post-testing of student teachers The project concluded with an assessment of the gains in MKT that the student teachers made over its course through questionnaire and focus group interviews. Data Analysis Quantitative data were analysed using SPSS. Qualitative data were analysed using MAXQDA software.

Expected Outcomes

Analysis of the data collected in this project is not yet complete. However initial findings indicate that the students’ levels of MKT increased over the course of the study; seven students took both the pre- and post- tests based on the LMT material and the scores of all seven students were higher on the post-test. The quantitative data arising from the questionnaires and the interviews are still being analysed. The questionnaires contained two open-ended questions: 1. What specific knowledge and skills do you think a mathematics teacher needs? 2. List different teaching situations where a teacher uses his or her knowledge of mathematics. It appears from the analysis carried out so far that the group’s view of the mathematical work of a teacher changed over the course of the project. To begin with, the group seemed to hold a naive view of teaching and emphasised content knowledge (in particular knowledge of what topics were on the syllabus) and classroom control. After the intervention, the students spoke about knowledge of students, about being able to ask good questions, and being able to highlight links with different parts of the curriculum and with real-world situations. It seems as though the students’ appreciation of MKT had broadened over the course of the study, perhaps as a result of the intervention or from the students’ own growing experience of working in mathematics classrooms. In any case, the language and the framework associated to MKT gave us tools to identify different aspects of the group’s mathematical and pedagogical knowledge. This research has begun the process of investigating a key aspect of a pre-service teacher’s knowledge in the context of second level teacher education in Ireland. This project was funded by the 3U NStep Initiative.

References

Ball, D. L., Thames, M. H., & Phelps, G. (2008). Content knowledge for teaching: What makes it special? Journal of Teacher Education, 59, 389. Cosgrove, J., Perkins, R., Shiel, G., Fish, R. and McGuinness, L. (2012). Teaching and Learning in Project Maths: Insights from Teachers who Participated in PISA 2012. Dublin: Education Research Centre. Delaney, S. (2010). Knowing what counts. Irish primary teachers’ Mathematical Knowledge for Teaching. Dublin: Marino Institute of Education and Department of Education and Science. Hill, H.C., Rowan, B., & Ball, D.L. (2005). Effects of Teachers’ Mathematical Knowledge for Teaching on Student Achievement. American Educational Research Journal, 42(2), p 371–406. LMT Project (2013). Learning Mathematics for Teaching Project home page. http://sitemaker.umich.edu/lmt/about Cited on 30th May 2013. Plomp, T. (2009). Educational design research: An introduction. In T. Plomp & N. Nieveen (Eds), An Introduction to educational design research (pp. 9-35). Enschede, the Netherlands: SLO. Shulman, L. S. (1986). Those who understand: Knowledge growth in teaching. Educational Researcher, 15(2), 4-14. Stephan, M., & Cobb, P. (2013). Teachers engaging in mathematics design research. In T. Plomp, & N. Nieveen (Eds), Educational design research – Part B: Illustrative cases (pp. 277-298). Enschede, the Netherlands: SLO.

Author Information

Majella Dempsey (presenting / submitting)

Maynooth University

Education

Maynooth, Co. Kildare

Dr. Ann O'Shea (presenting)

Maynooth University, Ireland

Dr. James Lovette

Maynooth University, Ireland

Dr. Brien Nolan

Maynooth University, Ireland

Search the ECER Programme

Search for keywords and phrases in "Text Search"
Restrict in which part of the abstracts to search in "Where to search"
Search for authors and in the respective field.
For planning your conference attendance you may want to use the conference app, which will be issued some weeks before the conference
If you are a session chair, best look up your chairing duties in the conference system (Conftool) or the app.

Session Information

Contribution

Method

Expected Outcomes

References

Author Information

Search the ECER Programme

Navigation

Info for