Factors involved in making post-performance judgments in mathematics problem-solving

  1. Trinidad García Fernández 1
  2. Evelyn Kroesbergen 2
  3. Celestino Rodríguez Pérez 1
  4. Paloma González Castro 1
  5. Julio González Pienda 1
  1. 1 Universidad de Oviedo
    info

    Universidad de Oviedo

    Oviedo, España

    ROR https://ror.org/006gksa02

  2. 2 Utrech University
Journal:
Psicothema

ISSN: 0214-9915

Year of publication: 2015

Volume: 27

Issue: 4

Pages: 374-380

Type: Article

More publications in: Psicothema

Abstract

Background: This study examines the impact of executive functions, affective-motivational variables related to mathematics, mathematics achievement and task characteristics on fifth and sixth graders’ calibration accuracy after completing two mathematical problems. Method: A sample of 188 students took part in the study. They were divided into two groups as function of their judgment accuracy after completing the two tasks (accurate= 79, inaccurate= 109). Differences between these groups were examined. The discriminative value of these variables to predict group membership was analyzed, as well as the effect of age, gender, and grade level. Results: The results indicated that accurate students showed better levels of executive functioning, and more positive feelings, beliefs, and motivation related to mathematics. They also spent more time on the tasks. Mathematics achievement, perceived usefulness of mathematics, and time spent on Task 1 significantly predicted group membership, classifying 71.3% of the sample correctly. Conclusions: These results support the relationship between academic achievement and calibration accuracy, suggesting the need to consider a wide range of factors when explaining performance judgments.

Bibliographic References

  • Adelson, J. L., & McCoach, D. B. (2011). Development and psychometric properties of the Math and Me Survey: Measuring third through sixth graders’ attitudes towards mathematics. Measurement and Evaluation in Counseling and Development, 44, 225-247.
  • Boekaerts, M., & Rozendaal, J. S. (2010). Using multiple calibration measures in order to capture the complex picture of what affects students’ accuracy of feeling of confidence. Learning and Instruction, 20(4), 372-382.
  • Bol, L., Hacker, D. J., Walck, C. C., & Nunnery, J. A. (2011). The effects of individual or group guidelines on the calibration accuracy and achievement of high school biology students. Contemporary Educational Psychology, 37, 280-287.
  • Boonen, A. J. H., van der Schoot, M., van Wesel, F., de Vries, M. H., & Jolles, J. (2013). Contemporary Educational Psychology, 38, 271-279.
  • Bouffard, T., & Narciss, S. (2011). Benefits and risks of positive bias in self-evaluation of academic competence. International Journal of Educational Research, 50(4), 205-256.
  • Bull, E., & Lee, K. (2014). Executive functioning and mathematics achievement. Child Development Perspectives, 8(1), 36-41.
  • Cohen, J. (1988). Statistical power analysis for the behavioral sciences (2nded.). New York: Academic Press.
  • Dupeyrat, C., Escribe, C., Huet, N., & Régner, I. (2011). Positive biases in self-assessment of mathematics competence, achievement goals, and mathematics performance. International Journal of Educational Research, 50, 241-250.
  • Finn, B., & Metcalfe, J. (2014). Over-confidence in children’s multi-trial judgments of learning. Learning and Instruction, 32, 1-9.
  • García, T., Álvarez-García, D., Cueli, M., González-Castro, P., & Álvarez, L. (2013). Psychometric properties of the Executive Functions Scale for Families (EFS-F). Manuscript submitted for publication.
  • García, T., González-Pienda, J. A., Rodríguez, C., Álvarez-García, D., & Álvarez, L. (2014). Psychometric characteristics of the BRIEF scale for the assessment of executive functions in Spanish clinical population. Psicothema, 26(1), 47-54.
  • García, T., Rodríguez, C., González-Castro, P., Álvarez-García, D., & González-Pienda, J.A. (In Press). Metacognition and Executive Functioning in Primary School. Anales de Psicología.
  • García, T., Rodríguez, C., González-Castro, P., González-Pienda, J.A., & Torrance, M. (2015). Elementary students’ metacognitive processes and post-performance calibration on mathematical problem-solving tasks. Metacognition and Learning, 10(2).
  • Garner, J. K. (2009). Conceptualizing the relations between executive functions and self-regulated learning. Journal of Psychology: Interdisciplinary and Applied 143, 405-426.
  • González-Pienda, J. A., Cueli, M., García, T., Suárez, N., Fernández, E., Tuero-Herrero, E., et al. (2012). Gender differences in attitudes towards Mathematics in compulsory school. Revista Iberoamericana de Psicología y Salud, 3(1), 55-73.
  • Hacker, D. J., Bol, L., & Keener, M.C. (2008). Metacognition in education: A focus on calibration. In J. Dunlosky, & R. Bjork (Eds.), Handbook of Memory and Metacognition (pp. 429-455). Mahwah, NJ: Erlbaum.
  • Howie, P., & Roebers, C. (2007) Developmental progression in the confidence-accuracy relationship in event recall: New insights provided by a calibration perspective. Applied Cognitive Psychology, 21(7), 871-893
  • Jacobse, A. E., & Harskamp, E. G. (2012). Towards efficient measurement of metacognition in mathematical problem-solving. Metacognition and Learning, 7(2), 133-149.
  • Kolkman, M. E., Hoijtink, H. H., Kroesbergen, E. H., & Leseman, P. P. M. (2013). The role of executive functions in numerical skills. Learning and Individual Differences, 24, 145-151.
  • Montague, M., Enders, G., & Dietz, S. (2011). Effects of cognitive strategy instruction on math problem solving of middle school students with learning disabilities. Learning Disability Quarterly, 34(4), 262-272.
  • Narciss, S., Koerndle, H., & Dresel, M. (2011). Self-evaluation accuracy and satisfaction with performance: Are there affective costs or benefits of positive self-evaluation bias? International Journal of Educational Research, 50, 230-240.
  • Özsoy, G. (2012). Investigation of fifth grade students’ mathematical calibration skills. Educational Sciences: Theory & Practice, 12(2), 1190-1194.
  • Presentación, M. J., Siegenthaler, R., Pinto, V., Mercader, J., & Miranda, A. (2015). Math skills and executive functioning in preschool: clinical and ecological evaluation. Revista de Psicodidáctica, 20(1), 65-82.
  • Rinne, L. F., & Mazzocco, M. M. (2014). Knowing right from wrong in mental arithmetic judgments: Calibration of confidence predicts the development of accuracy. PLoSONE 9(7), e98663.
  • Roebers, C. M., Cimeli, P., Röthlisberger, M., & Neuenschwander, R. (2012). Executive functioning, metacognition, and self-perceived competence in elementary school children: an explorative study on their interrelations and their role for school achievement. Metacognition and Learning, 7, 151-173.
  • Sheldrake, R., Mujtaba, T., & Reiss, M. J. (2014). Calibration of selfevaluations of mathematical ability for students in England aged 13 and 15, and their intentions to study non-compulsory mathematics after age 16. International Journal of Educational Research, 64, 49-61.
  • Stolp, S., & Zabrucky, K. M. (2009). Contributions of metacognitive and self-regulated learning theories to investigations of calibration of comprehension. International Electronic Journal of Elementary Education, 2(1), 3-31.
  • Thorell, L. B., Veleiro, A., Siu, A. F., & Mohammadi, H. (2013). Examining the relation between ratings of executive functioning and academic achievement: findings from a cross-cultural study. Child Neuropsychology, 19(6), 630-638.
  • Welsh, M. C., & Pennington, B. F. (1988). Assessing frontal lobe functioning in children: Views from developmental psychology. Developmental Neuropsychology, 4, 199-230.
  • Van Loon, M. H., de Bruin, A. B. H., van Gog, T., & Van Merriënboer, J. J. G. (2013). Activation of inaccurate prior knowledge affects primaryschool students’ metacognitive judgments and calibration. Learning & Instruction, 24, 15-25.
  • Whimbey, A., & Lochhead, J. (1999). Problem-solving and comprehension. Hillsdale, NJ: Erlbaum.
  • Williams, J. R. (2008). Revising the Declaration of Helsinki. World Medical Journal, 54, 120-125.
  • Zelazo, P. D., & Carlson, S. M. (2012). Hot and Cool Executive Function in Childhood and Adolescence: Development and Plasticity. Child Development Perspectives, 6(4), 354-360.