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Prediction of elementary mathematics grades by cognitive abilities

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Abstract

In the present study, the relationship between the mathematics grade and the three basic cognitive abilities (inhibition, working memory, and reasoning) was analyzed regarding possible alterations during elementary school. In a sample of N = 244 children, the mathematics grade was best predicted by working memory performance in the second grade and by reasoning in the third and fourth grades. Differentiation of these abilities during elementary school was considered as a cause for this pattern but discarded after the analysis of structural equation models. Thus, with respect to output-orientated curricula, scholastic standards, and a large inter-individual heterogeneity of students, it is implied for teachers to account for different cognitive strengths and weaknesses of their students, using adequate tasks and teaching strategies like self-differentiating tasks and adaptive explorative learning.

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Notes

  1. The questions were not related to the number of smiley faces. Exemplary questions are “Did the faces look happy?” and “Did the faces have different sizes?”

  2. The first group contained children between 8 and 9 years of age, the second group children between 9 and 10 years, and the third group children between 10 and 11 years.

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Author information

Authors and Affiliations

  1. Faculty of Psychology, Educational Science, and Sport Science, University of Regensburg, Universitätsstraße 31, 93053, Regensburg, Germany

    Sven Hilbert

  2. School for Teacher Education, Institute for Primary Education, University of Applied Sciences Northwestern Switzerland, Liestal, Switzerland

    Georg Bruckmaier

  3. Faculty of Mathematics, Department of Mathematics Education, University of Regensburg, Universitätsstraße 31, 93053, Regensburg, Germany

    Karin Binder & Stefan Krauss

  4. Department of Psychology, Psychological Methods and Assessment, LMU Munich, Leopoldstraße 13, 80802, Munich, Germany

    Markus Bühner

Authors
  1. Sven Hilbert
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  2. Georg Bruckmaier
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  3. Karin Binder
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  4. Stefan Krauss
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  5. Markus Bühner
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Correspondence to Sven Hilbert.

Additional information

Prof. Dr. Sven Hilbert. Faculty of Psychology, Educational Science, and Sport Science, University of Regensburg, Universitätsstraße 31, 93053 Regensburg, Germany. E-mail: sven.hilbert@ur.de. Tel: +49 (0) 941/943–7444

Current themes of research:

Learning in mathematics. Multi-level modeling for longitudinal data. Working memory strategies and training.

Most relevant publications in the field of Psychology of Education:

Binder, K., Krauss, S., Hilbert, S., Brunner, M., Anders, Y. & Kunter, M. (2018). Diagnostic Skills of Mathematics Teachers in the COACTIV study. In T. Leuders, K. Philipp & J. Leuders (Eds.) Diagnostic Competence of Mathematics Teachers—Unpacking a complex construct in teacher education and teacher practice (pp. 33–53). Cham: Springer.

Hilbert, S., Schwaighofer, M., Sarubin, N., Zech., A. & Bühner, M. (2017). Working memory tasks train working memory but not reasoning: A material- and operation-specific investigation of transfer from working memory practice. Intelligence, 61, 102–114.

Hilbert, S., Nakagawa, T. T., Puci, P., Zech, A. & Bühner, M. (2015). The Digit Span Backwards Task: Verbal and Visual Cognitive Strategies in Working Memory Assessment. European Journal of Psychological Assessment, 31(3), 174–180.

Dr. Georg Bruckmaier. Faculty of Mathematics, Department of Mathematics Education, University of Regensburg, Universitätsstraße 31, 93053 Regensburg, Germany. E-mail: georg.bruckmaier@ur.de. Tel: +49 (0) 941/943–2786

Current themes of research:

Mathematics education. Pedagogical content knowledge. Probability and eye tracking.

Most relevant publications in the field of Psychology of Education:

Binder, K., Krauss, S., & Bruckmaier, G. (2015). Effects of visualizing statistical information—An empirical study on tree diagrams and 2 x 2 tables. Frontiers in Psychology, 6(1186).

Bruckmaier, G., Krauss, S., Blum, W., & Leiss, D. (2016). Measuring mathematical teachers’ professional competence by using video clips (COACTIV video). ZDM—The International Journal on Mathematics Education, 48(1-2). doi: 10.1007/s11858-016-0772-1 (online first).

Schmeisser, C., Krauss, S., Bruckmaier, G., Ufer, S. & Blum, W. (2013). Transmissive and Constructivist Beliefs of In-Service Mathematics Teachers and of Beginning University Students. In Y. Li & J. N. Moschkovich (Eds.), Proficiency and beliefs in learning and teaching mathematics. Learning from Alan Schoenfeld and Günter Törner. Mathematics teaching and learning, 3 (pp. 51–68). Rotterdam: Sense.

Dipl.-Phys. Karin Binder. Faculty of Mathematics, Department of Mathematics Education, University of Regensburg, Universitätsstraße 31, 93053 Regensburg, Germany. E-mail: karin.binder@ur.de. Tel: +49 (0) 941/943–2786

Current themes of research:

Mathematics education. Diagnostic competence (COACTIV and medicine). Probability and Bayesian reasoning.

Most relevant publications in the field of Psychology of Education:

Binder, K., Krauss, S., Hilbert, S., Brunner, M., Anders, Y. & Kunter, M. (2018). Diagnostic Skills of Mathematics Teachers in the COACTIV study. In T. Leuders, K. Philipp & J. Leuders (Eds.) Diagnostic Competence of Mathematics Teachers—Unpacking a complex construct in teacher education and teacher practice (pp. 33–53). Cham: Springer.

Binder, K., Krauss, S., & Bruckmaier, G. (2015). Effects of visualizing statistical information—An empirical study on tree diagrams and 2 x 2 tables. Frontiers in Psychology, 6(1186).

Binder, K., Krauss, S., Bruckmaier, G. & Marienhagen, J. (under review). Visualizing the Bayesian 2-test case: The effect of tree diagrams on medical decision making. PLoS One.

Prof. Dr. Stefan Krauss. Faculty of Mathematics, Department of Mathematics Education, University of Regensburg, Universitätsstraße 31, 93053 Regensburg, Germany. E-mail: stefan1.krauss@ur.de. Tel: +49 (0) 941/943–2788

Current themes of research:

Teaching and learning. Probability education. Professional knowledge of teachers (COACTIV and FALKO studies)

Most relevant publications in the field of Psychology of Education:

Krauss, S., Brunner, M., Kunter, M., Baumert, J., Blum, W., Neubrand, M., & Jordan, A. (2008). Pedagogical content knowledge and content knowledge of secondary mathematics teachers. Journal of Educational Psychology, 100(3), 716–725.

Brunner, M., Krauss, S., & Kunter, M. (2008). Gender differences in mathematics: Does the story need to be rewritten? Intelligence, 36, 403–421.

Krauss, S., & Bruckmaier, G. (2014). Das Experten-Paradigma in der Forschung zum Lehrerberuf. In E. Terhart, H. Bennewitz & M. Rothland (Hrsg.), Handbuch der Forschung zum Lehrerberuf (2. Aufl.) (S. 241–261). Münster: Waxmann.

Prof. Dr. Markus Bühner. Department of Psychology, Psychological Methods and Assessment, LMU Munich, Leopoldstraße 13, 80802 Munich, Germany. E-mail: buehner@psy.lmu.de. Tel: +49 (0) 89/2180–6257

Current themes of research:

Behavioral data science. Working memory and intelligence. Structural equation models

Most relevant publications in the field of Psychology of Education:

Schwaighofer, M., Bühner, M., & Fischer, F. (2017). Executive functions in the context of complex learning: Malleable moderators?. Frontline Learning Research, 5(1), 58–75.

Zihl J., Fink T., Pargent F., Ziegler M., Bühner M. (2014). Cognitive Reserve in Young and Old Healthy Subjects: Differences and Similarities in a Testing-the-Limits Paradigm with DSST. PLoS One 9(1): e84590.

Krumm, S., Bühner, M. & Ziegler, M. (2008). Intelligence and working memory as predictors of school performance. Learning and Individual Differences, 18 (2), 248–257.

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Hilbert, S., Bruckmaier, G., Binder, K. et al. Prediction of elementary mathematics grades by cognitive abilities. Eur J Psychol Educ 34, 665–683 (2019). https://doi.org/10.1007/s10212-018-0394-9

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