Structure of Pupils` Analytical Competence for Quality Development in Learning of Mathematics

Author(s):

Andra Fernate(presenting / submitting)Rudite Andersone(presenting)Irina Maslo Manuel Fernandez

Conference:

ECER 2012

Network:

11. Educational Effectiveness and Quality Assurance

Format:

Paper

Session Information

11 SES 06 B, Curriculum Subjects Assessment to Promote Educational Effectiveness

Parallel Paper Session

Time:

2012-09-19

15:30-17:00

Room:

FCT - Aula Magna

Chair:

Guenter L. Huber

Contribution

The present research has been conducted during the implementation of a cross-country joint comparative study.

Research question: What is a structure of pupils` analytical competence like to promotes improvement of the quality in learning of mathematics?

Purpose of the research: According to the international investigation framework developed by L. Lindenskov (2009) (Danish School of Education, Aarhus University, Denmark) the research on the relationship between pupils’ performances in mathematics and their beliefs and positioning as doers of mathematics in lower-secondary classrooms in Latvia has been conducted. An additional objective is to describe the structure of pupils` analytical competence for quality development in learning of mathematics in Latvia as a starting point for the future joint comparative study.

Theoretical framework of this research, uses the following main categories: “analytical competence”, “beliefs” and “positioning”. Comprehension of these categories is based on the ideas of education researchers in mathematics (Schoenfeld 1985; Goldin 2002; Goldin et al. 2009; Leder et al. 2002; Maass and Schlöglmann 2009; Perrenet & Taconis 2009), and the positioning theory (Ron Harré & Luke van Langenhove’s, 1999; Wagner & Herbel-Eisenmann, 2009).

In this study, the term ‘analytical competence’ refers to being a doer of mathematics (Cobb, Gressalfi & Hodge 2009) within many different contexts inside and outside of school. In accordance with significant tendencies in many post-Lave-and-Wenger research communities, the proposal is based on the assumption that a complex relationship exists between the development of competences and the development of learners’ behaviour as doers inside the domains in which the specific competences are expected or demanded.

References to the notion of beliefs have become increasingly common in the field of the research of mathematical education, especially in the last twenty years. Most of this research is focused on teachers’ and pre-service teacher pupils’ beliefs but pupils’ beliefs are also investigated by the researchers of mathematical education (Schoenfeld 1985; Goldin 2002; Goldin et al. 2009; Leder et al. 2002; Maass and Schlöglmann 2009; Perrenet & Taconis 2009). Several issues on pupils’ beliefs have been explored, e.g. relationship between beliefs and other constructs such as, pupils’ motivation, interest, performance, problem-solving behaviour, meta-cognition, self-efficacy, and the use of mathematical conceptions. However, the notion of beliefs is still disputed among researchers and one of the main points of contention concerns whether beliefs should be regarded as a phenomenon or as a situated process and action.

The term positioning is a relatively new concept in educational research. It is rooted in socio-psychological theory, and refers to the ways in which individuals relate to each other when interacting in different kinds of discursive practice. The term discursive practice is used in accordance with Bronwyn Davies and Ron Harré. According to the positioning theory, human identity should be seen as a combination of, or interplay between, a continuous personal identity and a dynamic and discontinuous personal diversity that is realised through the many different discursive practices in which an individual takes part.

Method

The research methods: analysis of theoretical literature, sources and analysis of the curricullum of mathematics in Latvia, empirical methods – qualitative data collection, data processing and analysis methods (descriptive statistics; secondary data processing – Kolmogorov-Smirnov Z test, Spearman’s rank correlation coefficient, Pearson correlation). The sample: voluntary participants of different types of urban schools - 343 pupils from 16 classrooms (grade 9; 231 girls, 112 boys). The teachers of mathematics divided all their pupils into three groups: high-performing pupils, middle-performing pupils and low-performing pupils. According to the specific objectives and criteria of joint investigation the research includes three stages 1) the respondents were asked to write down their reflections on three questions What is mathematics? What is mathematical thinking? How to solve a mathematical problem?; 2) 2 pupils from each group were interviewed; 3) the pupils’ statements were analysed and the structure of pupils` analytical competence was described. The statements were coded applying the categories “beliefs” and “positioning” and “analytical competence”. Linkages among the categories were created, analyzed. The linkages between metacodes and sub-codes were constructed and analyzed applying AQUAD software and validated applying SPSS software.

Expected Outcomes

Regarding of the research question on the relation between pupils’ beliefs and positioning and their performance findings allow concluding that: 1. The higher level performing pupils more believe that mathematics is about operating in formal systems and processes; they mention less that mathematics is a school discipline. 2. Internal and external assessment of performance allows concluding that the lack of personal imaginative positioning is characteristic to the lower level performing pupils. The pupils’ position as everyday thinkers in mathematics has significant relationship with low external assessment. 3. The more pupils position themselves as imaginative thinkers or doers having a personal way of understanding or dealing with mathematics, the less they have the belief that mathematics is a school discipline. Analytical competence refers to being a doer of mathematics, it is characteristic for this competence that the pupils believed that mathematics is about operating in formal systems, but not a school discipline, they positioned themselves as imaginative thinkers or doers having a personal way of understanding or dealing with mathematics, they did not express themselves abstractly when speaking about mathematics, but they had practical expressions about how to use mathematics in everyday contexts or in school-related work.

References

Cobb, P.; Gresalfi, M.; Hodge, L.L. (2009). An Interpretive Scheme for Analyzing the Identities That Students Develop in Mathematics Classrooms. Educational Studies in Mathematics, 40, 1, 40-68. Davies, B. & Harré, R. (1990). Positioning: The Discursive Production of Selves. Journal for the Theory of Social Behaviour 20(1), 43-63. Goldin, G. (2002). Affect, meta-affect, and mathematical belief structures. In G. Leder, E. Pehkonen, & G. Törner (Eds.), Beliefs: A hidden variable in mathematics education? (pp. 59–72). Dordrecht: Kluwer. Goldin, G.; Rösken, B.; Törner, G. (2009). Beliefs – No Longer a Hidden Variable in Mathematical Teaching and Learning Processes. In Maass; J.; Schlöglmann, W. (Eds). Beliefs and Attitudes in Mathematics Education. New Research Results, p. 1-18. Rotterdam: Sense Publishers. Harré, R. & Langenhove, L. van (Eds.) (1999). Positioning Theory. Oxford, Malden, Massachusetts: Backwell Publishers. Leder, G.C., Pekhonen, E., Törner, G. (Eds) (2002). Beliefs: A Hidden Variable in Mathematics Education? Dordrecht: Kluwer Academic Publishers. Lindenskov, L., Hetmar, V., Andresen, B. (2009). Beliefs, positionings and the development of analytical competences: Results from a small scale study in 14 years old pupils’ beliefs and positioning in school mathematics, p. 493-503 in: The 10th international conference on education research: Global and Comparative Perspectives in Academic Competence, Evaluation and Quality Assurance. Seoul: Education Research Institute Seoul National University. Maass, J., Schlöglmann, W. (Eds). (2009). Beliefs and attitudes in mathematics Education. New research results. Rotterdam: Sense Publishers. Perrenet, J., Taconis, R. (2009). Mathematical enculturation from the pupils’ perspective: shifts in problem-solving beliefs and behaviour during the bachelor program. Educational studies in mathematics education. 71: 181-198. Schoenfeld, A. H. (1985). Mathematical Problem Solving. Orlando, Florida: Academic Press. Wagner, D., Herbel-Eisenmann, B. (2009) Re-mythologizing mathematics through attention to classroom positioning. Educational Studies in Mathematics 72, 1, 1-15.

Author Information

Andra Fernate (presenting / submitting)

University of Latvia

Institute of Pedagogical Science

Riga

Rudite Andersone (presenting)

University of LatviA

Education, Psychology and Art faculty

Riga

Irina Maslo

University of Latvia, Latvia

Manuel Fernandez