Teaching and Learning Practices in Mathematics: Students’ Perception of Teaching Practices at Different Contexts and Educational Levels

Author(s):

Maria Pampaka(presenting / submitting)Julian Williams(presenting)Birgit Pepin Svein Arne Sikko

Conference:

ECER 2013

Network:

24. Mathematics Education Research

Format:

Paper

Session Information

24 SES 05, Mathematics at University Level

Paper Session

Time:

2013-09-11

11:00-12:30

Room:

D-405

Chair:

Birgit Pepin

Contribution

This paper aims to shed more light into the issue of how teaching influences students’ dispositions in mathematics. It is well documented that very few students are well prepared or well-disposed to continue their studies in mathematically-demanding courses in Higher Education (HE) (Roberts, 2002; Smith, 2004) at least in UK, but the problem is global. The so-called STEM (Science, Technology, Engineering and Mathematics) agenda and the significance of secondary school mathematics for this is what drives our current project (www.teleprism.com), building on the results of previous studies (www.transmaths.org).

The theoretical framework of this research programme has been based on the attempt to understand how students can acquire a mathematical disposition and an identity that supports their engagement with mathematical courses such as those in STEM in their pre-university and university education. In particular, we investigated how students’ experiences of mathematics education practices interact with background social factors to shape students’ self-identity, dispositions, learning outcomes and their decision-making in college and in transition into HE. Our focus was on learning outcomes for mathematics because of its importance to STEM as a whole in HE and hence to students’ educational and socioeconomic life opportunities (Boaler & Greeno, 2000). One of the findings of this work in UK demonstrated the damaging effect of ‘transmissionist’ pedagogies in school/college (pre-university) students’ mathematics dispositions (Pampaka et al., 2012).

The paper we propose aims to synthesise results from our previous and current studies: Firstly we draw on our projects on transition to mathematically demanding subjects (TransMaths) in UK HE and an extension of this work in Norway. We also use preliminary data from our ongoing work on ‘Teaching and Learning Practices in Secondary Mathematics’ (TeLePriSM) which aims to map secondary students’ learning outcomes, attitudes and choices regarding mathematics, together with the teaching they are exposed to. The combination of these studies will provide evidence for possible associations between students’ perceptions of pedagogy and how these are affecting their mathematics dispositions in two European countries at different stages of students’ educational progression. The studies made use of students and teachers’ questionnaires aiming to capture among others students’ (and their teachers) perceptions about the teaching they receive as well as their attitudes to mathematics with longitudinal surveys. Our focus in this paper is on ‘teaching practice in mathematics’ across different educational contexts and levels. In particular, we seek to answer the following questions:

(a) How can we measure students’ perceptions of the teaching they receive at pre-university and university courses?

(b) How can we test the comparability of these measures across different educational contexts (e.g. UK and Norway) and levels (different secondary year groups, pre-university and university)?

(c) To what extend are these measures associated with other learning outcomes and dispositions of students during their educational progression?

Method

Our research projects can all be described methodologically as mixed method studies with longitudinal student surveys and case studies of mathematics lessons at different levels. Here we focus on the surveys. In particular, analysis is based on longitudinal surveys of students entering different programmes in five UK universities (N=1778) and two Norwegian Universities (N=721). We also draw on the first data point (out of three) of the Teleprism longitudinal survey of students in Year 7 to 11 (N=13,000+), which took place during the previous academic year. Data include students’ responses regarding their attitudes to mathematics, confidence at various mathematical topics, future aspirations, and their perceptions of the teaching they encounter (our focus here). The first two research questions are approached within the validation of our instruments performed within the Rasch measurement framework (Bond & Fox, 2001). Our analysis seeks validity evidence through item fit statistics and Differential Item Functioning. The latter provides evidence for cross-national and cross-level measure invariance and presents a methodological challenge: its resolution will have implications for our comparisons. Once the measures’ validity is established we use them in further statistical modelling, to demonstrate associations with students’ dispositions and attainment measures, and cross-national comparisons.

Expected Outcomes

With the Rasch modelling approach we were able to construct and consequently add to our datasets valid measures of perceived pedagogical experience for the UK and Norwegian student samples: one for students’ pre-university courses and one for their first year university (maths) courses. Similarly, we have been able to give a score of students’ perception of maths pedagogy from Year 7 to 11 (secondary level). Validation results also gave some interesting insights regarding cross-national comparisons as well as the detail of teaching practices: for example we found that formal presentations and extended investigations become a less frequent practice as students move upwards in Secondary school (i.e. based on differences in items’ functioning between Year groups). Comparative, results also showed that the Norwegian students reported more transmissionist teaching during their pre-university maths courses compared to students in UK (t=11.66,p<0.001). We also found some interesting associations between students’ like/dislike of mathematics with their reported teaching practices. Further results and synthesis will be presented in the paper. Our discussion of these findings is expected to shed light on how mathematics pedagogy relates to learner engagement contributing to (mathematics) education research, policy and practice across Europe.

References

Boaler, J., & Greeno, J. (2000). Identity, Agency and Knowing in Mathematics Worlds. In J. Boaler (Ed.), Multiple Perspectives on Mathematics Teaching and Learning. Westport: Ablex Publishing. Bond, T. G., & Fox, C. M. (2001). Applying the Rasch Model: Fundamental Measurement in the Human Sciences. NJ: Lawrence Erlbaum Associates Inc. Pampaka, M., Williams, J. S., Hutcheson, G., Wake, G., Black, L., Davis, P., & Hernandez - Martinez, P. (2012). The association between mathematics pedagogy and learners’ dispositions for university study. British Educational Research Journal, 38(3), 473-496. Roberts, G. (2002). SET for Success. The supply of people with science, technology, engineering and mathematics skills. London: HM Stationery Office. Smith, A. (2004). Making mathematics count – the report of Professor Adrian Smith’s Inquiry into Post-14 Mathematics Education. London: DfES.

Author Information

Maria Pampaka (presenting / submitting)

The University of Manchester

Education

Manchester

Julian Williams (presenting)

University of Manchester

Education

Manchester

Birgit Pepin

Høgskolen i Sør-Trøndelag

Svein Arne Sikko