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Frame of Reference effects on values in mathematics: evidence from German secondary school students

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Abstract

Expectancy-value theory of achievement motivation identifies two classes of beliefs that are important predictors of educational choices and achievement: expectancies and values. It is well known that high achieving peers can have a negative impact on self-concept and other measures of expected success: holding individual achievement constant, school or class average achievement negatively predicts self-perceptions of ability, called the Big Fish Little Pond Effect (Marsh, Journal of Educational Psychology 79(3):280–295, 1987). In this paper, research on the Big Fish Little Pond Effect is extended to students’ values in mathematics. Data were drawn from the Transformation of the Secondary School System and Academic Careers study including 2079 secondary school students from 156 randomly selected schools in Baden-Württemberg, Germany. Using multilevel structural equation models, negative contextual effects for utility value, intrinsic/attainment value, and self-concept, and positive contextual effects for cost were found. There was no evidence for gender differences in the BFLPE. Self-concept significantly mediated the effects of individual and average achievement on each of the values.

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Notes

  1. In expectancy-value theory, intrinsic value is concerned with how enjoyable an individual finds an activity, interest theory distinguished between two aspects: situational interest refers to the emotional state related to task and individual interest, the stable orientation towards a certain domain (Renninger and Hidi 2002). Because expectancy-value theory is task-oriented, intrinsic value is more similar to situational interest; however, like individual interest, intrinsic value may facilitate long term engagement (Wigfield and Cambria 2010). Schiefele (2009) distinguished between cognitive and affective aspects of interest, intrinsic value is primarily related to the affect aspect of interest, (i.e., enjoyment). We expect that interest and intrinsic value will relate similarly to the BFLPE.

  2. In general, the German school system has three main tracks, which are Hauptschule, Realschule, and Gymnasium. The tracks tend to offer the same subjects, but at different paces. Hauptschule is for students who do not plan to attend university and had low to average grades in elementary school. Realschule is a middle track and students who perform well can later transfer to professional or general Gymnasium. Gymnasium is the most advanced level, which prepares students to attend university and these were the students used in this study. Students can move up or down one track at a time depending on grades and approval.

  3. Furthermore, results not reported here showed that factor scores for the intrinsic/attainment value factor obtained from two unidimensional factor models with either the original 9 items or the formed 4 item parcels correlated to 0.998 and 0.996 on the within and the between level, respectively.

  4. Technical details on the calculation of the indirect effects and their BFLPE’s are provided in the supplementary electronic appendix.

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Acknowledgements

Jenna Cambria was a member of the Pathways to Adulthood program funded by the Jacobs Foundation. Holger Brandt was a member of the Postdoc Academy of the Hector Research Institute of Education Sciences and Psychology, Tübingen, funded by the Baden-Württemberg Ministry of Science, Education and the Arts. Data are from the TOSCA study, using one of five subsections of the project that was initially began by the Berlin Max Planck Institute for Human Development and is now led by Hector Research Institute of Education Sciences and Psychology.

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  1. Educational Statistics and Research Methods (RHRC), University of Arkansas, 751 W Maple St, Fayetteville, AR, 72701, USA

    Jenna Cambria

  2. University of Kansas, Lawrence, USA

    Holger Brandt

  3. Hector Research Institute of Education Sciences and Psychology, University of Tübingen, Tübingen, Germany

    Benjamin Nagengast & Ulrich Trautwein

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  1. Jenna Cambria
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Cambria, J., Brandt, H., Nagengast, B. et al. Frame of Reference effects on values in mathematics: evidence from German secondary school students. ZDM Mathematics Education 49, 435–447 (2017). https://doi.org/10.1007/s11858-017-0841-0

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  • DOI: https://doi.org/10.1007/s11858-017-0841-0

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