Skip to main content
SpringerLink
Log in

Assessing Mathematical Deductive Reasoning Competence of Eighth-Grade Students from China

  • Published:
Canadian Journal of Science, Mathematics and Technology Education Aims and scope Submit manuscript

Abstract

This study aims to develop an evaluation framework to assess the mathematical deductive reasoning competence (MDRC) of eighth-grade students in China based on Program for International Student Assessment (PISA) and Trends in International Mathematics and Science Study (TIMSS). The framework includes four dimensions of MDRC: cognitive level, reasoning context, reasoning form, and reasoning content. A sample of 58,532 students took the test entitled MDRC Assessment in 90 min. Their MDRC was classified into four levels, and the percentages of students who were at level 1 to level 4 are 17.3%, 25.2%, 26.7%, and 30.8%, respectively. Girls performed significantly better than boys in total and in each of the dimensions of the evaluation framework, but the differences were at a low practical level. Students from urban schools outperformed students from rural schools at a significant level and a higher percentage of students in rural areas were at level 1 (poorest performance) than of students in urban areas. This research proposed a framework for assessing MDRC levels of students and used it with Chinese as well as international studies. Implications of gender and geographical inequalities in this performance were also discussed.

Résumé

Cette étude a pour but l’élaboration d’un cadre d’évaluation de la compétence en raisonnement déductif mathématique (CRDM) des élèves de huitième année en Chine en s’inspirant des enquêtes PISA (programme international pour le suivi des acquis des élèves) et TEIEMS (la Troisième Enquête Internationale sur l’Enseignement des Mathématiques et des Sciences). Le cadre comprend quatre dimensions de la CRDM: le niveau cognitif, le contexte de raisonnement, la forme de raisonnement et le contenu de raisonnement. On a fait passer le test intitulé « évaluation en 90 min de la CRDM» à un échantillon de 58 532 élèves. Leurs résultats en CRDM ont été classés en quatre niveaux, les pourcentages d’élèves se situant du niveau 1 à 4 étant respectivement de 17,3%, 25,2%, 26,7% et 30,8%. Les filles ont bien mieux réussi que les garçons à la fois en ce qui a trait au total des dimensions du cadre d’évaluation ainsi que dans chacune de ces dimensions, cependant les différences se situent à un niveau pratique très bas. Les élèves des écoles en milieu urbain ont obtenu de meilleurs résultats que ceux et celles des écoles rurales et cela s’est montré de façon marquée et un pourcentage plus élevé d’élèves en milieu rural se situait au niveau 1 (qui correspond à la performance la plus faible) que celui des élèves en zones urbaines. Dans cette étude, on a proposé un cadre pour évaluer les niveaux de CRDM des élèves et on a utilisé ce cadre de concert avec des études chinoises et internationales. Les implications des inégalités géographiques et de genre dans ces performances ont également été abordées.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2

Similar content being viewed by others

Data Availability

The data used in this research are from the Regional Education Assessment Project 2020 of the Collaborative Innovation Centre of Assessment toward Basic Education Quality.

References

  • Australian Education Council. (1990). A National Statement on Mathematics for Australian Schools. Curriculum Corporation.

  • Ayalon, M., & Even, R. (2008). Deductive reasoning: in the eye of the beholder. Educational Studies in Mathematics, 69(3), 235-247. https://doi.org/10.1007/s10649-008-9136-2

    Article  Google Scholar 

  • Bal-İncebacak, B., & Ersoy, E. (2016). Analysis of mathematical reasoning ability of the grade 7 students according to TIMSS. Journal of International Social Research, 9(46), 474-481.

    Google Scholar 

  • Baye, A., & Monseur, C. (2016). Gender differences in variability and extreme scores in an international context. Large-scale Assessments in Education, 4(1), 1-16. https://doi.org/10.1186/s40536-015-0015-x

    Article  Google Scholar 

  • Brady, S. R. (2015). Utilizing and adapting the Delphi method for use in qualitative research. International Journal of Qualitative Methods, 14(5), 1609406915621381.

    Article  Google Scholar 

  • Cheng, J., Zheng, X., & Zhu, Y. (2021). Chinese Eighth Graders’ Competencies in Mathematical Reasoning. In Beyond Shanghai and PISA: Cognitive and Non-cognitive Competencies of Chinese Students in Mathematics (pp. 187-207). Cham: Springer International Publishing.

    Chapter  Google Scholar 

  • Chianson, M. M. (2012). School location as a correlate of mathematics students’ achievement in a cooperative learning class. Journal of Education and Leadership Development, 4(1), 42-46.

    Google Scholar 

  • Clauser, B. E., Baldwin, P., Margolis, M. J., Mee, J., & Winward, M. (2017). An experimental study of the internal consistency of judgments made in bookmark standard setting. Journal of Educational Measurement, 54(4), 481-497.

    Article  Google Scholar 

  • Çoban, H., & Tezci, E. (2020). Developing the mathematical reasoning skills assessment scale. OPUS International Journal of Society Researches, 15(24), 28052837. https://doi.org/10.26466/opus.610197

  • Cocchi, L., Halford, G. S., Zalesky, A., Harding, I. H., Ramm, B. J., Cutmore, T., ... & Mattingley, J. B. (2014). Complexity in relational processing predicts changes in functional brain network dynamics. Cerebral Cortex, 24(9), 2283–2296.

  • Durand-Guerrier, V., Boero, P., Douek, N., Epp, S. S., & Tanguay, D. (2012). Argumentation and proof in the mathematics classroom. Proof and proving in mathematics education: The 19th ICMI study, 349–367.

  • Embretson, S. E., & Reise, P. E. (2000). Item response theory for psychologists. Mahwah (NJ): Lawrence Earlbaum Associates. Inc.[Google Scholar].

  • Evans, J. S. B. (2008). Dual-processing accounts of reasoning, judgment, and social cognition. Annu. Rev. Psychol., 59, 255-278.

    Article  Google Scholar 

  • Fennema, E., & Sherman, J. (1977). Sex-related differences in mathematics achievement, spatial visualization, and affective factors. American Educational Research Journal, 14, 51–71.

    Article  Google Scholar 

  • Foltz, C., & Overton, W. F. (1995). Proof construction: Adolescent development from inductive to deductive problem-solving strategies. Journal of Experimental Child Psychology, 59(2), 179-195.

    Article  Google Scholar 

  • Forgasz, H. J., & Hill, J. C. (2013). Factors implicated in high mathematics achievement. International Journal of Science and Mathematics Education, 11(2), 481-499. https://doi.org/10.1007/s10763-012-9348-x

    Article  Google Scholar 

  • Friedman, L. (1989). Mathematics and the Gender Gap: A Met-Analysis of Recent Studies on Sex Differences in Mathematical Tasks. Review of Educational Research, 59(2), 185-213. https://doi.org/10.3102/00346543059002185

    Article  Google Scholar 

  • Ganley, C., & Lubienski, S. (2016). Current research on gender differences in math. Teaching Children Mathematics. http://www.nctm.org/Publications/Teaching-Children-Mathematics/Blog/Current-Research-on-GenderDifferences-in-Math/

  • Graham, S. E., & Provost, L. E. (2012). Mathematics Achievement Gaps between Suburban Students and Their Rural and Urban Peers Increase over Time. Issue Brief No. 52. Carsey Institute.

  • Griggs, R. A., & Cox, J. R. (1982). The elusive thematic‐materials effect in Wason’s selection task. British journal of psychology, 73(3), 407-420.

    Article  Google Scholar 

  • Grissmer, D. W. (1994). Student achievement and the changing American family. Lilly Endowment, Inc.

  • Halford, G. S., Wilson, W. H., Andrews, G., & Phillips, S. (2014). Categorizing cognition: Toward conceptual coherence in the foundations of psychology. MIT Press.

  • Halpern, D. F., Benbow, C. P., Geary, D. C., Gur, R., Hyde, J. S., & Gernsbacher, M. A. (2007). The science of sex differences in science and mathematics. Psychological Science in the Public Interest, 8, 1–51.

    Article  Google Scholar 

  • Hanna, G. (1990). Some pedagogical aspects of proof. Interchange, 21(1), 6–13.

    Article  Google Scholar 

  • Hanushek, E. A. (1997). Assessing the Effects of School Resources on Student Performance: An Update. Educational Evaluation and Policy Analysis, 19(2), 141-164. https://doi.org/10.3102/01623737019002141

    Article  Google Scholar 

  • Harel, G., & Weber, K. (2020). Deductive Reasoning in Mathematics Education. In S. Lerman (Ed.), Encyclopedia of Mathematics Education (pp. 183–190). Springer International Publishing. https://doi.org/10.1007/978-3-030-15789-0_43

  • Hyde, J. S., Fennema, E., & Lamon, S. J. (1990). Gender differences in mathematics performance: a meta-analysis. Psychological Bulletin, 107(2), 139. https://doi.org/10.1037/0033-2909.107.2.139

    Article  Google Scholar 

  • Ibrahim, N. N., Ayub, A. F. M., Yunus, A. S. M., & Mahmud, R. (2019). Effects of higher order thinking module approach on pupils’ performance at primary rural school. Malaysian Journal of Mathematical Sciences, 13(2), 211-229.

    Google Scholar 

  • Inglis, M. J., & Simpson, A. (2008). Conditional inference and advanced mathematical study. Educational Studies in Mathematics, 67, 187–204.

    Article  Google Scholar 

  • Inglis, M. J., & Simpson, A. (2009). Conditional inference and advanced mathematical study: Further evidence. Educational Studies in Mathematics, 72, 185-198.

    Article  Google Scholar 

  • Israel Ministry of Education and Culture. (1990). The mathematics curriculum in grades. Israel Ministry of Education and Culture.

  • Leahey, E., & Guo, G. (2001). Gender differences in mathematical trajectories. Social forces, 80(2), 713-732. https://doi.org/10.1353/sof.2001.0102

    Article  Google Scholar 

  • Leder, G. C. (2019). Gender and mathematics education: An overview. Compendium for early career researchers in mathematics education, 289–308.

  • Lewis, D. M. (1996). Standard setting: A bookmark approach. In IRT-based standard setting procedures utilizing behavioral anchoring, DR Green (Chair), Symposium conducted at the Council of Chief State School Officers National Conference on Large-Scale Assessment, Phoenix, AZ, 1996.

  • Lindberg, S. M., Hyde, J. S., Petersen, J. L., et al. (2010). New trends in gender and mathematics performance: a meta-analysis. Psychological Bulletin, 136(6), 1123-1135. https://doi.org/10.1037/a0021276

    Article  Google Scholar 

  • Loong, E., Vale, C., Widjaja, W., Herbert, S., Bragg, L. A., & Davidson, A. (2018). Developing a Rubric for Assessing Mathematical Reasoning: A Design-Based Research Study in Primary Classrooms. Mathematics Education Research Group of Australasia.

  • Ministry of Education of the People’s Republic of China. (2012). Mathematics Curriculum Standards for Compulsory Education (2011 version). Beijing Normal University Press.

  • Ministry of Education of the People’s Republic of China. (2020). Mathematics Curriculum Standards for Senior Secondary Schools (2017 version 2020 revised). People’s Education Press.

  • Ministry of Education of the People’s Republic of China. (2022). Compulsory Education Mathematics Curriculum Standards (2021 Version). Beijing Normal University Press.

  • Morsanyi, K., Devine, A., Nobes, A., & Szűcs, D. (2013). The link between logic, mathematics and imagination: Evidence from children with developmental dyscalculia and mathematically gifted children. Developmental science, 16(4), 542-553.

    Article  Google Scholar 

  • Morsanyi, K., Kahl, T., & Rooney, R. (2016). The link between math and logic in adolescence: The effect of argument form. In Individual Differences in Judgement and Decision-Making (pp. 176–195). Psychology Press.

  • Morsanyi, K., McCormack, T., & O’Mahony, E. (2018). The link between deductive reasoning and mathematics. Thinking & Reasoning, 24(2), 234-257.

    Article  Google Scholar 

  • Mullis, I. V. S., Martin, M. O., & Loveless, T. (2016). International Trends in Mathematics and Science Achievement, Curriculum, and Instruction: Trends in International Mathematics and Science Study. Paris: IEA, 90.

    Google Scholar 

  • Mullis, I. V., Martin, M. O., Foy, P., Kelly, D. L., & Fishbein, B. (2020). TIMSS 2019 international results in mathematics and science. Retrieved from Boston College, TIMSS & PIRLS International Study Center website: https://timss2019.org/reports

  • Mullis, I.V.S. & Martin, M.O. (Eds.) (2013). TIMSS 2015 Assessment Frameworks. Retrieved from Boston College, TIMSS & PIRLS International Study Center website: https://timssandpirls.bc.edu/timss2015/frameworks.html

  • National Academy of Sciences. (2006). Beyond bias and barriers: Fulfilling the potential of women in academic science and engineering. Washington, DC: National Academies Press.

    Google Scholar 

  • National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics. National Council of Teachers of Mathematics

  • New Zealand Ministry of Education. (1991). The New Zealand Curriculum Framework. Retrieved September 19, 2022, from http://www.tki.org.nz/r/maths/curriculum/statement/p8_e.php

  • Ni, Y. J., Cai, J., Hau, K. T., & Li, Q. (2009). Has curriculum reform made a difference: looking for change in classroom practice. RGC Grant Report.

  • Niss, M. A., & Højgaard, T. (2011). Competencies and mathematical learning: Ideas and inspiration for the development of mathematics teaching and learning in Denmark. http://pure.au.dk/portal/files/41669781/THJ11_MN_KOM_in_english.pdf

  • Nosek, B. A., Smyth, F. L., Sriram, N., Lindner, N. M., Devos, T., Ayala, A., . . . Greenwald, A. G. (2009). National differences in gender–science stereotypes predict national sex differences in science and math achievement. Proceeding of the National Academy of Sciences, 106(26), 10593– 10597. https://doi.org/10.1073/pnas.0809921106

  • OECD. (2003). The PISA 2003 assessment framework: Mathematics, reading, science and problem-solving knowledge and skills. OECD Publishing.

  • OECD. (2013). PISA 2012 Assessment and Analytical Framework. https://doi.org/10.1787/9789264190511-en

  • OECD. (2017). PISA 2015 Mathematics Framework. https://doi.org/10.1787/9789264281820-5-en

  • OECD. (2018). PISA 2021 Mathematics Framework (Draft). Available online: http://www.oecd.org/pisa/pisaproducts/pisa-2021-mathematics-framework-draft.pdf (accessed on 3 December 2022).

  • OECD. (2019a). PISA 2018 Mathematics Framework. https://doi.org/10.1787/13c8a22c-en

  • OECD. (2019b). PISA 2018 Results (Volume I). https://doi.org/10.1787/5f07c754-en

  • Piaget, J., & Ackermann-Valladao, E. (1987). Possibility and Necessity: The Role of Possibility in Cognitive Development.-159 S. University of Minnesota Press.

  • Qualifications and Curriculum Authority. (2006). National curriculum online. Retrieved September 19, 2022, from http://www.tki.org.nz/r/maths/curriculum/statement/p8_e.php

  • Ragni, M., Kola, I., & Johnson-Laird, P. (2017). The Wason Selection task: A Meta-Analysis. In CogSci.

  • Ren, C. R., & Xin, T. (2013). Longitudinal study on predicting effect of social economic status on students’ performance. Educational Research, 34(3), 79-87.

    Google Scholar 

  • Shi, N. Z. (2016). Logicality in the Process of Mathematical Reasoning. Journal of Mathematics Education, 25(4), 1–16, 46.

  • Stylianides, A. L. (2007). Proof and proving in school mathematics. Journal for Research in Mathematics Education, 38(3), 289-321. https://doi.org/10.2307/30034869

    Article  Google Scholar 

  • Stylianides, G. J., & Stylianides, A. J. (2008). Proof in school mathematics: Insights from psychological research into students’ ability for deductive reasoning. Mathematical thinking and learning, 10(2), 103-133. https://doi.org/10.1080/10986060701854425

    Article  Google Scholar 

  • Sumpter, L. (2016). Investigating upper secondary school teachers’ conceptions: Is mathematical reasoning considered gendered?. International Journal of Science and Mathematics Education, 14, 347-362.

    Article  Google Scholar 

  • Wang, L., Li, X., & Li, N. (2014). Socio-economic status and mathematics achievement in China: a review. ZDM Mathematics Education, 46(7), 1051-1060. https://doi.org/10.1007/s11858-014-0617-8

    Article  Google Scholar 

  • Wason, P. C. 1968. Reasoning about a rule. Quarterly Journal of Experimental Psychology, 20, 273-81.

    Article  Google Scholar 

  • Wason, P. C., & Shapiro, D. (1971). Natural and contrived experience in a reasoning problem. Quarterly journal of experimental psychology, 23(1), 63-71.

    Article  Google Scholar 

  • Wilder, G. Z., & Powell, K. (1989). Sex differences in test performance: A survey of literature (Vol. 89). New York: College Entrance Examination Board. https://eric.ed.gov/?id=ED308231

  • Willingham, W. W., Cole, N. S., Bridgeman, B., Dwyer, C. A., Johnson, L. M., Leung, S. W., ... & Wilder, G. Z. (2013). Research on gender differences. In Gender and fair assessment (pp. 17–54). Routledge.

  • Zhang, X. (2000). Welcome the new era of math education: The reading of the mathematical curriculum standards under full-time compulsory education. Beijing Normal University Press.

  • Zhu, Y., Kaiser, G., & Cai, J. (2018). Gender equity in mathematical achievement: the case of China. Educational Studies in Mathematics, 99(3), 245-260. https://doi.org/10.1007/s10649-018-9846-z

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Mathematics and Computer, Jilin Normal University, Jilin, China

    Lianming Hao

  2. Faculty of Education, Beijing Normal University, Beijing, China

    Haili Liang & Chunxia Qi

  3. Faculty of Education, University of Macau, Macao, China

    Chunlian Jiang

Authors
  1. Lianming Hao
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Haili Liang
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Chunxia Qi
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Chunlian Jiang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Chunxia Qi.

Ethics declarations

Conflict of Interest

The authors declare no competing interests.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Hao, L., Liang, H., Qi, C. et al. Assessing Mathematical Deductive Reasoning Competence of Eighth-Grade Students from China. Can. J. Sci. Math. Techn. Educ. (2024). https://doi.org/10.1007/s42330-024-00315-3

Download citation

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s42330-024-00315-3

Keywords

Search

Navigation