The Australian Educational Researcher

, Volume 45, Issue 4, pp 533–551 | Cite as

Personal Best (PB) goal-setting enhances arithmetical problem-solving

  • Paul Ginns
  • Andrew J. Martin
  • Tracy L. Durksen
  • Emma C. Burns
  • Alun Pope


Personal Best (PB) goals are defined as specific, challenging, and competitively self-referenced goals involving a level of performance or effort that meets or exceeds an individual’s previous best. Much of the available research underpinning arguments for PB goal-setting is self-report-based; thus, the causal effect of PB goals on learning outcomes remains in question. The present experiment examined the impact of PB goal-setting (against a no-goal condition) on 68 Year 5 and 6 schoolchildren’s problem-solving during an arithmetic fluency-building activity, SuperSpeed Math. Equivalence of the two conditions was established across a range of prior ability and self-report motivational variables, including prior mathematical ability; Personal Best, Mastery, and Performance goal orientations at the individual and classroom level; mathematics self-concept; and valuing of and interest in mathematics. Controlling for initial problem-solving performance, students who set PB goals in subsequent rounds showed a small but reliable advantage over students in the control condition. These results suggest PB goals may provide a way for students to experience both challenge and success in a range of classroom activities. Suggestions for future research based on these initial findings are made.


Goal setting Personal Best (PB) goals Mathematics Problem-solving 



The present study was supported by Discovery Research Project Grant DP140104294.


  1. Alschuler, A. S. (1969). The effects of classroom structure on achievement motivation and academic performance. Educational Technology, IX, 19–24.Google Scholar
  2. Ames, C. (1992). Classrooms: Goals, structures, and student motivation. Journal of Educational Psychology, 84, 261–271.CrossRefGoogle Scholar
  3. Anderman, E. M., Gimbert, B., O’Connell, A. A., & Riegel, L. (2015). Approaches to academic growth assessment. British Journal of Educational Psychology, 85, 138–153. Scholar
  4. Beady, C. H., Slavin, R. E., & Fennessey, G. M. (1981). Alternative student evaluation structures and a focused schedule of instruction in an innercity junior high school. Journal of Educational Psychology, 73, 518–523.CrossRefGoogle Scholar
  5. Biffle, C. (2007a). SuperSpeed math. Yucaipa: Crafton Hills College.Google Scholar
  6. Biffle, C. (2007b). SuperSpeed letters and phonics. Yucaipa: Crafton Hills College.Google Scholar
  7. Boomsma, A., & Herzog, W. (2013). R function swain: Correcting structural equation model t-statistics and indexes under small-sample and/or large-model conditions. Retrieved March 28, 2017, from
  8. Bratina, T. A., & Krudwig, K. M. (2003). Get it right and get it fast! Building automaticity to strengthen mathematical proficiency. Focus on Learning Problems in Mathematics, 25, 47–63.Google Scholar
  9. Breaugh, J. A. (2003). Effect size estimation: Factors to consider and mistakes to avoid. Journal of Management, 29, 79–97.CrossRefGoogle Scholar
  10. Dweck, C. S. (2012). Mindsets and human nature: Promoting change in the Middle East, the schoolyard, the racial divide, and willpower. American Psychologist, 67, 614–622. Scholar
  11. Edgington, E., & Onghena, P. (2007). Randomization tests. Boca Raton, FL: CRC Press.Google Scholar
  12. Elliot, A. J. (2005). A conceptual history of the achievement goal construct. In A. J. Elliot & C. Dweck (Eds.), Handbook of competence and motivation (pp. 52–72). New York, NY: Guilford Press.Google Scholar
  13. Elliot, A. J., & McGregor, H. A. (2001). A 2 × 2 achievement goal framework. Journal of Personality and Social Psychology, 80, 501–519.CrossRefGoogle Scholar
  14. Elliot, A. J., Murayama, K., & Pekrun, R. (2011). A 3 × 2 achievement goal model. Journal of Educational Psychology, 103, 632–648. Scholar
  15. Graham, J. W., & Hoffer, S. M. (2000). Multiple imputation in multivariate research. In T. D. Little, K. U. Schnable, & J. Baumert (Eds.), Modeling longitudinal and multilevel data: Practical issues, applied approaches, and specific examples (pp. 201–218). Mahwah, NJ: Erlbaum.Google Scholar
  16. Hattie, J. (2009). Visible learning: A synthesis of over 800 meta-analyses relating to achievement. New York: Routledge.Google Scholar
  17. Hayes, A. F. (2017). Introduction to mediation, moderation, and conditional process analysis: A regression-based approach (2nd ed.). New York: Guilford Publications.Google Scholar
  18. Herzog, W., & Boomsma, A. (2009). Small-sample robust estimators of noncentrality-based and incremental model fit. Structural Equation Modeling, 16, 1–27. Scholar
  19. Huitema, B. (2011). The analysis of covariance and alternatives: Statistical methods for experiments, quasi-experiments, and single-case studies (2nd ed.). Hoboken, NJ: Wiley.CrossRefGoogle Scholar
  20. Kanfer, R., & Ackerman, P. L. (1989). Motivation and cognitive abilities: An integrative/aptitude-treatment interaction approach to skill acquisition. Journal of Applied Psychology, 74, 657–690.CrossRefGoogle Scholar
  21. Keselman, H. J., Othman, A.R., & Wilcox, R.R. (2013). Preliminary testing for normality: Is this a good practice? Journal of Modern Applied Statistical Methods, 12(2), 2. Retrieved from CrossRefGoogle Scholar
  22. Klein, H. J., Wesson, M. J., Hollenbeck, J. R., Wright, P. M., & DeShon, R. P. (2001). The assessment of goal commitment: A measurement model meta-analysis. Organizational Behavior and Human Decision Processes, 85, 32–55. Scholar
  23. Kratochwill, T. R., & Levin, J. R. (Eds.). (2014). Single-case intervention research: Methodological and statistical advances. Washington, DC: American Psychological Association.Google Scholar
  24. Latham, E. A., & Locke, G. P. (2013). Goal setting theory, 1990. In E. A. Locke & G. P. Latham (Eds.), New developments in goal setting and task performance (pp. 3–15). New York: Routledge.Google Scholar
  25. Liem, G. A. D., Ginns, P., Martin, A. J., Stone, B., & Herett, M. (2012). Personal best goals and academic and social functioning: A longitudinal perspective. Learning and Instruction, 22, 222–230. Scholar
  26. Locke, E. A., & Latham, G. P. (2002). Building a practically useful theory of goal setting and task motivation: A 35-year odyssey. American Psychologist, 57, 705–717.CrossRefGoogle Scholar
  27. Marsh, H. W. (1990). Self description questionnaireI (SDQ I). Manual. Macarthur, NSW. Australia: University of Western Sydney.Google Scholar
  28. Marsh, H. W., Balla, J. R., & Hau, K. T. (1996). An evaluation of incremental fit indices: A clarification of mathematical and empirical processes. In G. A. Marcoulides & R. E. Schumacker (Eds.), Advanced structural equation modeling techniques (pp. 315–353). Hillsdale, NJ: Erlbaum.Google Scholar
  29. Marsh, H. W., Hau, K. T., & Wen, Z. (2004). In search of golden rules: Comment on hypothesis-testing approaches to setting cutoff values for fit indexes and dangers in overgeneralizing Hu and Bentler’s (1999) findings. Structural Equation Modeling, 11, 320–341. Scholar
  30. Martin, A. J. (2006). Personal bests (PBs): A proposed multidimensional model and empirical analysis. British Journal of Educational Psychology, 76, 803–825. Scholar
  31. Martin, A. J. (2011a). Personal Best (PB) approaches to academic development: Implications for motivation and assessment. Educational Theory and Practice, 33, 93–99.CrossRefGoogle Scholar
  32. Martin, A. J. (2011b). The Motivation and Engagement Scale. Sydney, Australia: Lifelong Achievement Group.Google Scholar
  33. Martin, A. J. (2015). Implicit theories about intelligence and growth (personal best) goals: Exploring reciprocal relationships. British Journal of Educational Psychology, 85, 207–223. Scholar
  34. Martin, A. J., Anderson, J., Bobis, J., Way, J., & Vellar, R. (2012). Switching on and switching off in mathematics: An ecological study of future intent and disengagement among middle school students. Journal of Educational Psychology, 104, 1–18. Scholar
  35. Martin, A. J., Durksen, T. L., Williamson, D., Kiss, J., & Ginns, P. (2014). Personal Best (PB) goal setting and students’ motivation in science: A study of science valuing and aspirations. The Australian Educational and Developmental Psychologist, 31, 85–96. Scholar
  36. Martin, A. J., & Elliot, A. J. (2016a). The role of personal best (PB) and dichotomous achievement goals in students’ academic motivation and engagement: A longitudinal investigation. Educational Psychology, 36, 1285–1302. Scholar
  37. Martin, A. J., & Elliot, A. J. (2016b). The role of personal best (PB) goal setting in students’ academic achievement gains. Learning and Individual Differences, 45, 222–227. Scholar
  38. Martin, A. J., & Liem, G. A. D. (2010). Academic personal bests (PBs), engagement, and achievement: A cross-lagged panel analysis. Learning and Individual Differences, 20(3), 265–270. Scholar
  39. McDonald, R. P., & Marsh, H. W. (1990). Choosing a multivariate model: Noncentrality and goodness-of-fit. Psychological Bulletin, 107, 247–255.CrossRefGoogle Scholar
  40. Muthén, L.K. & Muthén, B.O. (1998–2010). Mplus user’s guide. Los Angeles: Muthén & Muthén.Google Scholar
  41. Nordstokke, D. W., & Zumbo, B. D. (2010). A new nonparametric test for equal variances. Psicologica, 31, 401–430.Google Scholar
  42. Nordstokke, D. W., Zumbo, B. D., Cairns, S .L., & Saklofske, D. H. (2011). The operating characteristics of the nonparametric Levene test for equal variances with assessment and evaluation data. Practical Assessment, Research & Evaluation, 16. 84. Retrieved from
  43. Prentice, D. A., & Miller, D. T. (1992). When small effects are impressive. Psychological Bulletin, 112, 160–164.CrossRefGoogle Scholar
  44. Schmidt, F. L. (2013). The economic value of goal setting to employers. In E. A. Locke & G. P. Latham (Eds.), New developments in goal setting and task performance (pp. 16–20). New York: Routledge.Google Scholar
  45. Schunk, D. H. (1985). Participation in goal setting: Effects on self-efficacy and skills of learning-disabled children. The Journal of Special Education, 19, 307–317.CrossRefGoogle Scholar
  46. Schunk, D. H., & Rice, J. M. (1989). Learning goals and children’s reading comprehension. Journal of Reading Behavior, 21, 279–293.CrossRefGoogle Scholar
  47. Seijts, G. H., Latham, G. P., & Woodwark, M. (2013). Learning goals: A qualitative and quantitative review. In E. A. Locke & G. P. Latham (Eds.), New developments in goal setting and task performance (pp. 195–212). New York: Routledge.Google Scholar
  48. Slavin, R. E. (1980). Effects of individual learning expectations on student achievement. Journal of Educational Psychology, 72, 520–524.CrossRefGoogle Scholar
  49. Steiner, E. T., & Ashcraft, M. H. (2012). Three brief assessments of math achievement. Behavior Research Methods, 44, 1101–1107. Scholar
  50. Swain, A.J. (1975). Analysis of parametric structures for variance matrices. Unpublished doctoral dissertation, Department of Statistics, University of Adelaide, Australia.Google Scholar
  51. Tallmadge, G. A. (1977). The joint dissemination review panel ideabook. Washington, DC: National Institute of Education & US Office of Education.Google Scholar
  52. Weinberg, R. S. (2002). Goal setting in sport and exercise: Research to practice. In J. L. Van Raalte & B. W. Brewer (Eds.), Exploring sport and exercise psychology (pp. 25–48). Washington, DC: American Psychological Association.CrossRefGoogle Scholar
  53. Whisman, M. A., & McClelland, G. H. (2005). Designing, testing, and interpreting interactions and moderator effects in family research. Journal of Family Psychology, 19, 111–120. Scholar
  54. Williams, K. J. (2013). Goal setting in sports. In E. A. Locke & G. P. Latham (Eds.), New developments in goal setting and task performance (pp. 375–396). New York: Routledge.Google Scholar
  55. Yeager, D. S., & Walton, G. M. (2011). Social-psychological interventions in education: They’re not magic. Review of Educational Research, 81, 267–301. Scholar
  56. Yu, K., & Martin, A. J. (2014). Personal best (PB) and ‘classic’ achievement goals in the Chinese context: their role in predicting academic motivation, engagement and buoyancy. Educational Psychology, 34, 635–658. Scholar
  57. Yuan, K. H. (2005). Fit indices versus test statistics. Multivariate Behavioral Research, 40, 115–148. Scholar

Copyright information

© The Australian Association for Research in Education, Inc. 2018

Authors and Affiliations

  1. 1.Faculty of Education and Social WorkThe University of SydneyCamperdownAustralia
  2. 2.School of EducationUniversity of New South WalesKensingtonAustralia
  3. 3.Eastern Health Clinical School, Faculty of Medicine, Nursing and Health SciencesMonash UniversityBox HillAustralia

Personalised recommendations