Students For Whom Mathematics Is Not The Bogeyman- The European Perspective

Author(s):

Jelena Radišic(presenting / submitting)Aleksandar Baucal(presenting)Marina Videnović

Conference:

ECER 2016

Network:

09. Assessment, Evaluation, Testing and Measurement

Format:

Paper

Session Information

09 SES 01 A, Findings from PISA: Students' Attitudes, Perceptions and Performance

Paper Session

Time:

2016-08-23

13:15-14:45

Room:

NM-F101

Chair:

Ronny Scherer

Contribution

In the age of lifelong learning perspective it is no longer enough for the students to attain high achievement in mathematics at the end of the compulsory education. Rather they are also expected to develop a positive pattern of self-related mathematics beliefs – e.g. to have positive perception of own mathematics efficacy, self-concept and intrinsic motivation for a specific domain. A student who develops the positive pattern of self-related mathematics beliefs will be ready to learn and excel her/himself throughout the life.

In the light of that mathematics related anxiety is observed as a state during which a student experiences negative reactions when coming across different mathematical concepts (e.g. numbers, geometry). The same goes when one is placed in situation of math knowledge evaluation (Cates & Rhymer, 2003).

At the same time, mathematics related anxiety is not observed as a merely psychological construct related only to the actual situation of solving math problems. Students who suffer from it also report on experiencing feeling of pressure, inadequacy and unease (Bai, Wang, Pan, & Frey, 2009; Zeidner and Matthews, 2011). Even more so if a student has had bad experiences early in school, math anxiety may continue to reappear later in life (Jackson & Leffingwell, 1999) and students may avoid future encounters with mathematics, related courses and even career paths (Ashcraft and Ridley, 2005; Haraekiewitz, Barron, Tauer, Carter, & Elliot, 2000; Lyons and Beilock, 2012; Wigfield, Battle, Keller, & Eceles, 2002).

In general poor performance in mathematics is associated with high mathematics anxiety (Ma and Xu, 2004) and results in so far confirm that students who experience anxiety tend to underperform in tasks compared to students with no or low levels of anxiety (Ma, 1999). Results of the PISA study in 2003 and 2012 (both cycles focused on mathematics) confirm strong association between mathematics anxiety and students’ performance. Across OECD countries, higher mathematics anxiety is associated with a 34-point lower score in maths. This is the equivalent of almost one year of school (OECD, 2013). As a whole some 30% of students reported that they feel helpless when doing mathematics problems. 24% were found among the advantaged and 35% among the disadvantaged students, while cross country variations remain high.

Focus of this study is to identify subgroups of students with different pattern of math achievements and math related beliefs (students’ perception of own mathematics efficacy, self-concept in mathematics and intrinsic motivation), to compare distribution of these subgroups in selected European countries as well as to identify factors differentiating students with the optimal pattern of high math achievement and positive self-related math beliefs. The comparison between different European countries will be the main concern of this paper. First results of an ongoing study are being reported.

Method

17 European regions (countries) were chosen for the analysis based on their intake at PISA 2012 in mathematics and observed mathematics related anxiety. The aim was to include different countries according to combination of the level of anxiety (below average, above average) and achievement at mathematics literacy scale. These included Germany, Austria, the Netherlands, Switzerland, Finland, Belgium–Flemish Community, Belgium–French & German Regions, Ireland, Hungary, Sweden, Slovakia, Norway, Serbia, Croatia, Romania and Bulgaria. Taking into account how the PISA study organizes questions in the students’ questionnaires the missing values analysis (using EM algorithm) was performed for all non-cognitive variables of interest. As a first step of the analysis hierarchical cluster analysis (Ward method) was performed on 10% of randomly chosen student sample (around 9300 students age fifteen). Variables in focus were math anxiety (a composite comprised of five items relating to various aspects of mathematics anxiety), students’ achievement (operationalized through score at PISA math literacy scale) and from the non-cognitive spectrum students’ perception of mathematics efficacy, self-concept in mathematics and intrinsic motivation. Four groups of students were singled out and the results were replicated and confirmed using K-means cluster procedures for the whole sample. In the second step, students’ profiles were analysed at the country level. The profile of the ‘successful’ student (described in the results section) was analysed against non-cognitive set of predictors related to the class and school surrounding. Student socio-economic status (SES) was also included in the analysis. All predictors were observed for the whole sample and each of the 17 selected European regions.

Expected Outcomes

The results of the cluster analysis single out 4 different groups of students. The first group (uninterested achiever) is marked by low mathematics related anxiety and intrinsic interest in the domain and higher scores at PISA mathematics scale. Second groups of students receives highest achievement scores in mathematics, is interested in the subject and perceives own mathematics self-concept and efficacy as high (the successful group). Third group can be described as an anxious student, who is interested in mathematics, however fails in the domain and perceives own math-efficacy and self-concept as low (the anxious group). Final group of students (the underachievers) is marked by high anxiety, low interest in mathematics, low achievement and perceives own math-efficacy and self-concept as low. Countries differ in respect to frequency of each of the extracted clusters (χ²=7909.582, df=48, p=0.000). For example ‘the successful group’ is significantly more frequent among the group of countries like Germany, Austria, Switzerland and Finland, characterized by higher achievement in mathematics and lower anxiety at the country level. Switzerland and Germany also have significantly less students belonging to the fourth group. The Netherlands, similarly positioned, is however characterized by significantly higher number of students in group one, and less in group three. Analysis of predictors contributing frequency of students in the successful group shows significant positive relationship with SES (exp(β) from 1.299 for Switzerland to 2.325 Romania), discipline in the classroom (exp(β) from 1.165 for Finland to 1.765 Bulgaria) and experience with pure mathematics tasks at school (exp(β) from 1.372 for Romania to 2.021 Finland) across all countries. The results suggested that the relationships between experience with applied mathematics tasks and pure mathematics tasks at school are in the form of inverse square function. Teacher practices related to formative assessment are significant predictors only in Austria and Finland.

References

Ashcraft, M.H. and K.S. Ridley (2005), Math anxiety and its cognitive consequences, in J.I.D. Campbell (ed.), Handbook of Mathematical Cognition, (pp. 315-327) Psychology Press, New York. Bai, H., Wang, L.S., Pan, W. and Frey, M (2009). Measuring mathematics anxiety: psychometric analysis of a bidimensional affective scale. Journal of Instructional psychology, 36(3), 185-193. Harackicwitz, J.M., Barron, K.E., Tauer, J.M., Carter, S.M., & Elliot, A.J. (2000). Short-term and long-term consequences of achievement goals: Predicting interest and performance over time. Journal of Educational Psychology, 92, 316-330. Cates, G. L., & Rhymer, K. N. (2003). Examining the relationship between mathematics anxiety and mathematics performance: An instructional hierarchy perspective. Journal of Behavioral Education, 12 , 23-34. Jackson, C., & Leffingwell, R. (1999). The role of instructors in creating math anxiety in students from kindergarten through college. Mathematics Teacher, 92(7), 583-587. Lyons, I.M. and S.L. Beilock (2012),“When math hurts: math anxiety predicts pain network activation in anticipation of doing math”, Plus ONE, 7(10), 1-6. Ma, X. and J.M. Xu (2004), “The causal ordering of mathematics anxiety and mathematics achievement: a longitudinal panel analysis”, Journal of Adolescence, 27(2), 165-179. Ma, X. (1999), “A meta-analysis of the relationship between anxiety toward mathematics and achievement in mathematics”, Journal for Research in Mathematics Education, 30(5), pp. 520-540. OECD (2013). PISA 2012 Results: Ready to Learn – Students’ Engagement, Drive and Self-Beliefs (Volume III), PISA, OECD Publishing. Wigfield, A., Battle, A., Keller, L. B., & Eccles, J. S. (2002). Sex differences in motivation, self-concept, career aspiration, and career choice: implications for cognitive development. In A. McGillicuddy-De Lisi & R. De Lisi (Eds.), Biology, society, and behavior: The development of sex differences in cognition (pp. 93-124). Westport, CT: Ablex. Zeidner, M. and G. Matthews (2011), Anxiety 101, Springer, New York.

Author Information

Jelena Radišic (presenting / submitting)

University of Oslo

Oslo

Aleksandar Baucal (presenting)

Univ. of Belgrade

Dept. of Psychology

Belgrade

Marina Videnović

Institute of Psychology, University of Belgrade

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