Introducing a measure of perceived self-efficacy for proof (PSEP): Evidence of validity

Benjamin Shongwe(1*), Vimolan Mudaly(2)

(1) Department of Mathematics Education, University of KwaZulu-Natal, South Africa
(2) Department of Mathematics Education, University of KwaZulu-Natal, South Africa
(*) Corresponding Author


It is widely recognized that students encounter difficulties with proof across all grades and beyond, yet standardized instruments related specifically to students’ perceived self-efficacy for mathematical proof have not been readily available. The purpose of this study was to develop and investigate preliminary validity evidence for a new instrument for measuring self-efficacy for mathematical proof that can be of importance to the field. The new Perceived Self-Efficacy for Proof (PSEP) questionnaire is a self-administered, 8-item questionnaire that quantifies experimentation, conjecturing, inductive reasoning, justification, and validation. To validate the PSEP, two studies with 260 eleventh grade students—recruited from three Dinaledi schools in EThekwini metropolitan area, South Africa—were conducted. In Study 1 (n=128), face and content validity were evaluated, and an exploratory factor analysis (EFA) was performed. In Study 2 (n=132), a confirmatory factor analysis (CFA) was conducted and external validity was investigated. In both samples, the PSEP was found to possess good internal consistency reliability with relatively high factor loadings on a single component. Although the findings in this report represent preliminary validation evidence, it can be concluded that the PSEP is a valid, reliable and sensitive measure of 11th grade students’ perceptions of their ability to construct a proof and may serve as a meaningful outcome in mathematical proof research and classroom proof education.


Calibration, factor analyses, instrument development, self-efficacy for proof

Full Text:



Adelson, J. L., & McCoach, D. B. (2011). Development and psychometric properties of the Math and Me Survey: Measuring third through sixth graders’ attitudes toward mathematics. Measurement and Evaluation in Counseling and Development, 44(4), 225-247.

Alexander, P. A. (2013). Calibration: What is it and why it matters? An introduction to the special issue on calibrating calibration. Learning and Instruction, 24, 1-3.

Bandalos, B. (1996). Confirmatory factor analysis. In J. Stevens (Ed.), Applied multivariate statistics for the social sciences (3rd ed., pp. 389-420). Mahwah, NJ: Lawrence Erlbaum Associates.

Bandura, A. (1986). Social foundations of thought and action: A social cognitive theory. Englewood Cliffs, NJ: Prentice Hall.

Bandura, A. (1997). Self-efficacy: The exercise of control. New York: WH Freeman.

Bandura, A. (2014). Social cognitive theory of moral thought action. In W. M. Kurtines, & J. L. Gewirtz (Eds.), Handbook of moral behavior and development (pp. 69-128). Hillsdale, NJ: Psychology Press.

Baron, J., Gürçay, B., & Metz, S. E. (2017). Reflective thought and actively open-minded thinking. In M. E. Toplak, & J. Weller (Eds.), Individual differences in judgment and decision making from a developmental context (pp. 107-126). New York, NY: Routledge.

Betz, N. E., & Hackett, G. (1993). Mathematics self-efficacy scale. (Mental Measurements Yearbook 14, No. 14081939). Abstract retrieved from Mental Measurements Yearbook.

Boateng, G. O., Neilands, T. B., Frongillo, E. A., Melgar-Quiñonez, H. R., & Young, S. L. (2018). Best practices for developing and validating scales for health, social, and behavioral research: A primer. Frontiers in Public Health, 6:149.

Bong, M., & Skaalvik, E. M. (2003). Academic self-concept and self-efficacy: How different are they really? Educational Psychology Review, 15, 1-40.

Brown, T. (2014). Confirmatory factor analysis for applied research. New York, NY: Guilford Press.

Charness, G., Rustichini, A., & Van de Ven, J. (2018). Self-confidence and strategic behavior. Experimental Economics, 21(1), 72-98.

Chiua, M. M., & Klassen, R. M. (2010). Relations of mathematics self-concept and its calibration with mathematics achievement: Cultural differences among fifteen-year-olds in 34 countries. Learning and Instruction, 20, 2-17.

Creswell, J. W. (2018). Educational research: Planning, conducting, and evaluating quantitative and qualitative research (6th ed.). Boston, MA: Pearson.

Daher, W., Gierdien, F., & Anabousy, A. (2021). Self-efficacy in creativity and curiosity as predicting creative emotions. Journal of Research and Advances in Mathematics Education, 6(2), 86-99.

de Villiers, M. D. (1990). The role and function of proof in mathematics. Pythagoras, 24, 17-24.

Department of Basic Education [DBE]. (2009). The Dinaledi Schools Project: Report from a strategic engagement between the national department of education and business on increasing support for mathematics and science in education in schools. Pretoria: Department of Basic Education.

Dreyfus, T., & Hadas, N. (1987). Euclid may stay—and even be taught. In M. M. Lindquist, & A. P. Shulte (Eds.), Learning and teaching geometry, K-12 (pp. 47-58). Reston, VA: National Council of Teachers of Mathematics.

Efklides, A. (2011). Interactions of metacognition with motivation and affect in self-regulated learning: The MASRL model. Educational Psychologist, 46, 6-25.

Felbrich, A., Kaiser, G., & Schmotz, C. (2012). The cultural dimension of beliefs: An investigation of future primary teachers' epistemological beliefs concerning the nature of mathematics in 15 countries. ZDM Mathematics Education, 44, 355-366.

Ferla, J., Valcke, M., & Cai, Y. (2009). Academic self-efficacy and academic self-concept: Reconsidering structural relationships. Learning and Individual Differences, 19, 499-505.

Field, A. (2017). Discovering statistics using IBM SPSS statistics (5th ed.). London: Sage.

Hair, J. F., Black, W. C., Babin, B. J., & Anderson, R. E. (2019). Multivariate data analysis (8th ed.). New Jersey, NJ: Pearson.

Hayton, J. C., Allen, D. G., & Scarpello, V. (2004). Factor retention decisions in exploratory factor analysis: A tutorial on parallel analysis. Organizational Research Methods, 7, 191-205.

Hofstede, G. (1986). Cultural differences in teaching and learning. International Journal of Intercultural Relations, 10, 301-320.

Hofstede, G. (2011). Dimensionalizing cultures: The Hofstede model in context. Online Readings in Psychology and Culture, 2(1), 26 pages.

Hughes, A., Galbraith, D., & White, D. (2011). Perceived competence: A common core for self-efficacy and self-concept? Journal of Personality Assessment, 93, 278-289.

Jackson, M., Khavenson, T., & Chirkina, T. (2020). Raising the stakes: Inequality and testing in the Rtussian education system. Social Forces, 98(4), 1613-1635.

Kim, Y., & Silver, R. E. (2016). Provoking reflective thinking in post observation conversations. Journal of Teacher Education, 67(3), 203-219.

Lau, Y., Fang, L., Cheng, L. J., & Kwong, H. K. (2019). Volunteer motivation, social problem solving, self-efficacy, and mental health: A structural equation model approach. Educational Psychology, 39(1), 112-132.

Lawson, D. M. (2015). Family violence: Explanations and evidence-based clinical practice. New York: Wiley.

McCoach, D. B., Gable, R. K., & Madura, J. P. (2013). Instrument development in the affective domain. School and corporate applications (3rd ed.). New York, NY: Springer.

Moore, D. A., & Healy, P. J. (2008). The trouble with overconfidence. Psychological Review, 115(2), 502-517.

Morony, S., Kleitman, S., & Lee, Y. P. (2012). Predicting achievement: Confidence vs self-efficacy, anxiety, and self-concept in Confucian and European countries. International Journal of Educational Research, 58, 79-96.

Oriol, X., Amutio, A., Mendoza, M., Da Costa, S., & Miranda, R. (2016). Emotional creativity as predictor of intrinsic motivation and academic engagement in university students: The mediating role of positive emotions. Frontiers in Psychology, 7:1243.

Pajares, M. F. (2006). Self-efficacy during childhood and adolescence. In M. F. Pajares, & T. Urban (Eds.), Adolescence and education: Self-efficacy and adolescence (Vol. 5, pp. 339-367). Greenwich, Connecticut: Information and Age.

Pajares, M. F., & Kranzler, J. (1995). Self-efficacy beliefs and general mental ability in mathematical problem-solving. Contemporary Educational Psychology, 20, 426-443.

Pett, M. A., Lackey, N. R., & Sullivan, J. J. (2003). Making sense of factor analysis: The use of factor analysis for instrument development in health care research. Thousand Oaks, CA: Sage.

Raykov, T., & Marcoulides, G. A. (2011). Introduction to psychometric theory. New York, NY: Routledge.

Schoenfeld, A. H. (1983). Beyond the purely cognitive: Beliefs systems, social cognitions, and metacognitions as driving forces in intellectual performance. Cognitive Science, 7, 329-363.

Seegers, G., & Boekaerts, M. (1996). Gender-related differences in self-referenced cognitions in relation to mathematics. Journal for Research in Mathematics Education, 27(2), 215-240.

Shen, C., & Tam, H.-P. (2008). The paradoxical relationship between student achievement and self-perception: A crossnational analysis based on three waves of TIMSS data. Educational Research and Evaluation, 14(1), 87-100.

Stankov, L., Lee, J., Luo, W., & Hogan, D. J. (2012). Confidence: A better predictor of academic achievement than self-efficacy, self-concept and anxiety? Learning and Individual Differences, 22, 747-758.

Stylianides, A. J., & Stylianides, G. J. (2018). Addressing key and persistent problems of students' learning: The case of proof. In A. J. Stylianides, & G. Harel (Eds.), Advances in mathematics education research on proof and proving: An international perspective (pp. 99-113). Cham, Switzerland: Springer.

Triandis, H. C. (1989). The self and social behaviour in differing cultural contexts. Psychological Review, 96, 506-520.

Vancouver, J. B., & Kendall, L. N. (2006). When self-efficacy negatively relates to motivation and performance in a learning context. Journal of applied psychology, 91(5), 1146-1153.

Wilkins, J. L. (2004). Mathematics and science self-concept: An international investigation. The Journal of Experimental Education, 72(4), 331-346.

Willis, G. B. (2005). Cognitive interviewing: A tool for improving questionnaire design. Thousand Oaks, CA: Sage.

Zimmerman, B. J. (2009). Self-efficacy and educational development. In A. Bandura (Ed.), Self-efficacy in changing societies (pp. 202-231). Cambridge, UK: Cambridge University Press.

Article Metrics

Abstract view(s): 367 time(s)
PDF: 294 time(s)


  • There are currently no refbacks.