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Examining relations between math anxiety, prior knowledge, hint usage, and performance of math equivalence in two different online learning contexts

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Abstract

Prior research has shown negative relations between math anxiety and math performance. We posit that one potential pathway through which math anxiety influences performance of math equivalencies is through help seeking behavior during learning. Here, we examine whether middle school students’ behavior, specifically the frequency of hint requests, within educational technologies mediates the association between math anxiety and performance of math equivalence. Students completed a pretest measuring their performance of math equivalence and math anxiety prior to the intervention, and a posttest measuring their performance of math equivalence. We examine mediation in two online math learning technologies: From Here to There (FH2T) and ASSISTments. In both FH2T and ASSISTments, students can request hints that provide just-in-time support during problem solving. We examined whether the frequency of hint requests mediates the effects of math anxiety on performance in both conditions. Using multi-group mediation analyses, we found that math anxiety was not a predictor of hint usage in either condition when controlling for pretest performance. Further, we found that students with lower performance at the pretest used more hints in the problem set condition, and using more hints was associated with lower performance of math equivalence at the posttest. This relation was not significant in the FH2T condition, suggesting a fundamental difference in hint usage between the two technologies. These findings have implications for designing educational technologies that simultaneously promote math performance and productive help seeking behaviors in middle school students.

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References

  • Aleven, V., & Koedinger, K. R. (2000). Limitations of student control: Do students know when they need help? Lecture notes in computer science (Including subseries lecture notes in artificial intelligence and lecture notes in bioinformatics) (Vol. 1839, pp. 292–303). https://doi.org/10.1007/3-540-45108-0_33

  • Aleven, V., & Koedinger, K. R. (2001, May). Investigations into help seeking and learning with a cognitive tutor. Papers of the AIED-2001 workshop on help provision and help seeking in interactive learning environments.

  • Aleven, V., Elmar, S., Schworm, S., Fischer, F., & Wallace, R. (2003). Help seeking and help design in interactive learning environments. Review of Educational Research, 73(3), 277–320. https://doi.org/10.3102/00346543073003277

    Article  Google Scholar 

  • Anderson, J., Corbett, A., Koedinger, K., & Pelletier, R. (1995). Cognitive tutors: Lessons learned. The Journal of the Learning Sciences, 4(2), 167–207. https://www-jstor-org.ezpxy-web-p-u01.wpi.edu/stable/1466690?sid=primo&seq=4#metadata_info_tab_contents

  • Ashcraft, M. H. (2002). Math anxiety: Personal, educational, and cognitive consequences. Current Directions in Psychological Science, 11(5), 181–185. https://doi.org/10.1111/1467-8721.00196

    Article  Google Scholar 

  • Beilock, S. L., & Maloney, E. A. (2015). Math anxiety. Policy Insights from the Behavioral and Brain Sciences, 2(1), 4–12. https://doi.org/10.1177/2372732215601438

    Article  Google Scholar 

  • Chan, J. Y. C., Lee, J. E., Mason, C., Sawrey, K. B., & Ottmar, E. R. (2021). From Here to There!: A digital algebraic notation system impacts understanding of equivalence in middle school students. Journal of Educational Psychology. https://doi.org/10.1037/edu0000596

    Article  Google Scholar 

  • Choe, K. W., Jenifer, J. B., Rozek, C. S., Berman, M. G., & Beilock, S. L. (2019). Calculated avoidance: Math anxiety predicts math avoidance in effort-based decision-making. Science Advances, 5(11), eaay1062. https://doi.org/10.1126/sciadv.aay1062

    Article  Google Scholar 

  • Chou, C.-Y., & Chang, C.-H. (2021). developing adaptive help-seeking regulation mechanisms for different help-seeking tendencies. Educational Technology & Society, 24(4), 54–66.

    Google Scholar 

  • Foley, A. E., Herts, J. B., Borgonovi, F., Guerriero, S., Levine, S. C., & Beilock, S. L. (2017). The math anxiety-performance link. Current Directions in Psychological Science, 26(1), 52–58. https://doi.org/10.1177/0963721416672463

    Article  Google Scholar 

  • Ganley, C. M., & McGraw, A. L. (2016). The development and validation of a revised version of the math anxiety scale for young children. Frontiers in Psychology. https://doi.org/10.3389/fpsyg.2016.01181

    Article  Google Scholar 

  • Heffernan, N. T., & Heffernan, C. L. (2014). The ASSISTments ecosystem: Building a platform that brings scientists and teachers together for minimally invasive research on human learning and teaching. International Journal of Artificial Intelligence in Education, 24(4), 470–497. https://doi.org/10.1007/s40593-014-0024-x

    Article  Google Scholar 

  • Hulse, T., Daigle, M., Manzo, D., Braith, L., Harrison, A., & Ottmar, E. (2019). From here to there! Elementary: A game-based approach to developing number sense and early algebraic understanding. Educational Technology Research and Development, 67(2), 423–441. https://doi.org/10.1007/s11423-019-09653-8

    Article  Google Scholar 

  • Hung, C.-M., Huang, I., & Hwang, G.-J. (2014). Effects of digital game-based learning on students’ self-efficacy, motivation, anxiety, and achievements in learning mathematics. Journal of Computers in Education, 1(2–3), 151–166. https://doi.org/10.1007/s40692-014-0008-8

    Article  Google Scholar 

  • Inventado, P. S., Scupelli, P., Ostrow, K., Heffernan, N., Ocumpaugh, J., Almeda, V., & Slater, S. (2018). Contextual factors affecting hint utility. International Journal of STEM Education, 5(1), 1–13. https://doi.org/10.1186/s40594-018-0107-6

    Article  Google Scholar 

  • Iossi, L. (2007). Strategies for reducing math anxiety in post-secondary students. In S. M. Nielsen & M. S. Plakhotnik (Eds.), Proceedings of the sixth annual college of education research conference: urban and international education section (pp. 30–35).

  • Kaput, J. (2008). What is algebra? What is algebraic reasoning? In J. Kaput, D. Carraher, & M. Blanton (Eds.), Algebra in the early grades (pp. 5–17). Lawrence Erlbaum Associates.

    Google Scholar 

  • Karabenick, S. A., & Berger, J.-L. (2013). Help seeking as a self-regulated learning strategy. In H. Bembenutty, T. J. Cleary, & A. Kitsantas (Eds.), Applications of self-regulated learning across diverse disciplines: A tribute to Barry J. Zimmerman (pp. 237–261). IAP Information Age Publishing.

    Google Scholar 

  • Karabenick, S. A., & Knapp, J. R. (1988). Help seeking and the need for academic assistance. Journal of Educational Psychology, 80(3), 406–408. https://doi.org/10.1037/0022-0663.80.3.406

    Article  Google Scholar 

  • Karabenick, S. A., & Knapp, J. R. (1991). Relationship of academic help seeking to the use of learning strategies and other instrumental achievement behavior in college students. Journal of Educational Psychology, 83(2), 221–230. https://doi.org/10.1037/0022-0663.83.2.221

    Article  Google Scholar 

  • Kazelskis, R., Reeves, C., Kersh, M. E., Bailey, G., Cole, K., Larmon, M., et al. (2000). Mathematics anxiety and test anxiety: Separate constructs? The Journal of Experimental Education, 68(2), 137–146.

    Article  Google Scholar 

  • Kehrer, P., Kelly, K., & Heffernan, N. (2013). Does immediate feedback while doing homework improve learning? www.aaai.org

  • Kelly, K., Heffernan, N., Heffernan, C., Goldman, S., Pellegrino, J., & Soffer-Goldstein, D. (2013). Estimating the effect of web-based homework. CEUR Workshop Proceedings, 1009, 824–827. https://doi.org/10.1007/978-3-642-39112-5_122

    Article  Google Scholar 

  • Knuth, E. J., Stephens, A. C., McNeil, N. M., & Alibali, M. W. (2006). Does understanding the equal sign matter? Evidence from solving equations. Journal for Research in Mathematics Education, 37(4), 297–312.

    Google Scholar 

  • Lyons, I. M., & Beilock, S. L. (2012). When math hurts: Math anxiety predicts pain network activation in anticipation of doing math. PLoS ONE, 7(10), e48076. https://doi.org/10.1371/journal.pone.0048076

    Article  Google Scholar 

  • Ma, X. (1999). A meta-analysis of the relationship between anxiety toward mathematics and achievement in mathematics. Journal for Research in Mathematics Education, 30(5), 520–540. https://doi.org/10.2307/749772

    Article  Google Scholar 

  • Maloney, E. A., Risko, E. F., Ansari, D., & Fugelsang, J. (2010). Mathematics anxiety affects counting but not subitizing during visual enumeration. Cognition, 114(2), 293–297. https://doi.org/10.1016/j.cognition.2009.09.013

    Article  Google Scholar 

  • Marwan, S., Dombe, A., & Price, T. W. (2020, June). Unproductive help-seeking in programming: What it is and how to address it. In Proceedings of the 2020 ACM conference on innovation and technology in computer science education (pp. 54–60). https://doi.org/10.1145/3341525.3387394

  • Newman, R. (2008). The motivational role of adaptive help seeking in self-regulated learning. In D. H. Schunk, & B. J. Zimmerman (Eds.), Motivation and self-regulated learning: Theory, research, and applications. Lawrence Erlbaum Associates Publishers. https://psycnet.apa.org/record/2008-03967-013

  • Newman, R. S. (1990). Children’s help-seeking in the classroom: The role of motivational factors and attitudes. Journal of Educational Psychology, 82, 71–80.

    Article  Google Scholar 

  • Ottmar, E. R., Landy, D., Goldstone, R. L., & Weitnauer, E. (2015a). Getting from here to there: Testing the effectiveness of an interactive mathematics intervention embedding perceptual learning. In D. C. Noelle, R. Dale, A. S. Warlaumont, J. Yoshimi, T. Matlock, C. D. Jennings & P. P. Maglio (Eds.), Proceedings of the thirty-seventh annual conference of the cognitive science society (pp. 1793–1798). Pasadena, CA.

  • Ottmar, E., Landy, D., Weitnauer, E., & Goldstone, R. (2015b). Graspable mathematics: Using perceptual learning technology to discover algebraic notation. In M. Meletiou-Mavrotheris, K. Mavrou & E. Paparistodemou (Eds.), Integrating touch-enabled and mobile devices into contemporary mathematics education (pp. 24–48). Pennsylvania: IGI Global

  • Peeters, A., Robinson, V., & Rubie-Davies, C. (2020). Theories in use that explain adolescent help seeking and avoidance in mathematics. Journal of Educational Psychology, 112(3), 533–550. https://doi.org/10.1037/edu0000423

    Article  Google Scholar 

  • Pizzie, R. G., & Kraemer, D. J. M. (2017). Avoiding math on a rapid timescale: Emotional responsivity and anxious attention in math anxiety. Brain and Cognition, 118, 100–107. https://doi.org/10.1016/j.bandc.2017.08.004

    Article  Google Scholar 

  • Pollack, C., Wilmot, D., Centanni, T. M., Halverson, K., Frosch, I., D’Mello, A. M., et al. (2021). Anxiety, motivation, and competence in mathematics and reading for children with and without learning difficulties. Frontiers in Psychology. https://doi.org/10.3389/fpsyg.2021.704821

    Article  Google Scholar 

  • Price, T. W., Zhi, R., & Barnes, T. (2017). Hint generation under uncertainty: The effect of hint quality on help-seeking behavior. In E. André, R. Baker, X. Hu, M. Rodrigo, & B. Boulay (Eds.), Artificial intelligence in education. AIED 2017. Lecture notes in computer science. (Vol. 10331). Cham: Springer. https://doi.org/10.1007/978-3-319-61425-0_26

    Chapter  Google Scholar 

  • Ramirez, G., Shaw, S. T., & Maloney, E. A. (2018). Math anxiety: Past research, promising interventions, and a new interpretation framework. Educational Psychologist, 53(3), 145–164. https://doi.org/10.1080/00461520.2018.1447384

    Article  Google Scholar 

  • Razzaq, L., & Heffernan, N. T. (2010). Hints: Is it better to give or wait to be asked? Lecture notes in computer science (Including subseries lecture notes in artificial intelligence and lecture notes in bioinformatics), 6094 LNCS(PART 1) (pp. 349–358). https://doi.org/10.1007/978-3-642-13388-6_39

  • Renkl, A. (2002). Worked-out examples: instructional explanations support learning by self-explanations. In Learning and instruction (Vol. 12). www.elsevier.com/locate/learninstruc

  • Rittle-Johnson, B., Matthews, P. G., Taylor, R. S., & McEldoon, K. L. (2011). Assessing knowledge of mathematical equivalence: A construct-modeling approach. Journal of Educational Psychology, 103(1), 85–104. https://doi.org/10.1037/a0021334

    Article  Google Scholar 

  • Roschelle, J., Feng, M., Murphy, R. F., & Mason, C. A. (2016). Online mathematics homework increases student achievement. AERA Open, 2(4), 233285841667396. https://doi.org/10.1177/2332858416673968

    Article  Google Scholar 

  • Ryan, A. M., Gheen, M. H., & Midgley, C. (1998). Why do some students avoid asking for help? An examination of the interplay among students’ academic efficacy, teachers’ social-emotional role, and the classroom goal structure. Journal of Educational Psychology, 90(3), 528–535. https://doi.org/10.1037/0022-0663.90.3.528

    Article  Google Scholar 

  • Singh, R., Saleem, M., Pradhan, P., Heffernan, C., Heffernan, N. T., Razzaq, L., Dailey, M. D., O’Connor, C., & Mulcahy, C. (2011). Feedback during web-based homework: The role of hints. Lecture notes in computer science (Including subseries lecture notes in artificial intelligence and lecture notes in bioinformatics), 6738 LNAI (pp. 328–336). https://doi.org/10.1007/978-3-642-21869-9_43

  • Stamper, J., Barnes, T., & Croy, M. (2011). Enhancing the automatic generation of hints with expert seeding. International Journal of Artificial Intelligence in Education, 21, 153–167. https://doi.org/10.3233/JAI-2011-021

    Article  Google Scholar 

  • Star, J. R., Pollack, C., Durkin, K., Rittle-Johnson, B., Lynch, K., Newton, K., & Gogolen, C. (2015). Learning from comparison in algebra. Contemporary Educational Psychology, 40, 41–54. https://doi.org/10.1016/j.cedpsych.2014.05.005

    Article  Google Scholar 

  • Stowell, J., & Bennett, D. (2010). Effects of online testing on student exam performance and test anxiety. Journal of Educational Computing Research, 42(2), 161–171. https://doi.org/10.2190/EC.42.2.b

    Article  Google Scholar 

  • Szczygiel, M. (2020). Gender, general anxiety, math anxiety and math achievement in early school-age children. Issues in Educational Research, 30(3), 1126–1142.

    Google Scholar 

  • Van Mier, H. I., Schleepen, T., & Van den Berg, F. (2019). Gender differences regarding the impact of math anxiety on arithmetic performance in second and fourth graders. Frontiers in Psychology, 9, 2690. https://doi.org/10.3389/fpsyg.2018.02690

    Article  Google Scholar 

  • Whitehill, J., & Seltzer, M. (2016). A crowdsourcing approach to collecting tutorial videos—Toward personalized learning-at-scale. In L@S 2017 - Proceedings of the 4th (2017) ACM conference on learning at scale (pp. 157–160). http://arxiv.org/abs/1606.09610

  • Wood, H., & Wood, D. (1999). Help seeking, learning and contingent tutoring. Computers and Education, 33(2–3), 153–169. https://doi.org/10.1016/S0360-1315(99)00030-5

    Article  Google Scholar 

  • Wu, S. S., Barth, M., Amin, H., Malcarne, V., & Menon, V. (2012). Math anxiety in second and third graders and its relation to mathematics achievement. Frontiers in Psychology, 3(JUN), 1–11. https://doi.org/10.3389/fpsyg.2012.00162

    Article  Google Scholar 

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Acknowledgements

The research reported here was supported by the Institute of Education Sciences, U.S. Department of Education, through Grant R305A180401 to Worcester Polytechnic Institute. The opinions expressed are those of the authors and do not represent views of the Institute or the U.S. Department of Education. We would like to thank the teachers and students for their participation; the Summer Training in Arts and Sciences (STAR) Fellowship for funding our corresponding author for this research, David Brokaw and Graspable Inc. and Neil Heffernan and the ASSISTments Team for programming and data support.

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Authors and Affiliations

  1. Social Sciences and Policy Studies, Worcester Polytechnic Institute, Unity Hall 320, 100 Institute Road, Worcester, MA, 01609, USA

    Alisionna Iannacchione, Erin Ottmar, Vy Ngo, Jenny Yun-Chen Chan, Hannah Smith, Kathryn C. Drzewiecki & Stacy T. Shaw

  2. School of Learning and Teaching, University of Maine, Orono, ME, USA

    Craig A. Mason

  3. Department of Early Childhood Education, The Education University of Hong Kong, Tai Po, Hong Kong SAR, China

    Jenny Yun-Chen Chan

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  1. Alisionna Iannacchione
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Contributions

AI: Conceptualization, Writing, Project leader. EO: Conceptualization, Writing, Supervision, Project administration, Funding acquisition. VN: Writing, Project coordination. CM: External Independent Evaluator, Formal data analysis, Writing, Visualization. JY-CC: Conceptualization, Writing, Visualization, Project administration. HS: Writing, Data analysis. KCD: Writing. STS: Conceptualization, Writing.

Corresponding author

Correspondence to Alisionna Iannacchione.

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Competing interests

Erin Ottmar was a designer and co-developer of From Here to There! The remaining authors have no competing interests to declare.

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Appendix

Appendix

Students’ demographic information by condition, and their pretest scores.

 

All

(N = 466)

FH2T

(n = 225)

Problem set

(n = 241)

 

n

%

n

%

n

%

Gender

      

 Male

255

54.7

125

55.6

130

53.9

 Female

211

45.3

100

44.4

111

46.1

Race

      

 White

159

34.1

80

35.6

79

32.8

 Asian

259

55.6

119

52.9

140

58.1

 Hispanic

21

4.5

10

4.4

11

4.6

 African American

10

2.1

6

2.7

4

1.7

 Native American

5

1.1

1

0.4

4

1.7

 Pacific Islander

1

0.2

1

0.4

0

0.0

 Multi-racial

11

2.4

8

3.6

3

1.2

Grade

      

 Sixth

445

95.5

215

95.6

230

95.4

 Seventh

21

4.5

10

4.4

11

4.6

Class

      

 Advanced

392

84.1

190

84.4

202

83.8

 On-level

33

7.1

14

6.3

19

7.9

 Support

41

8.8

21

9.3

20

8.3

Gifted status

      

 Gifted

243

52.1

118

52.4

125

51.9

 Not gifted

223

47.9

107

47.6

116

48.1

Pretest math scores (M, SD)

3.82

1.61

3.87

1.59

3.76

1.63

Pretest math anxiety (M, SD)

15.67

8.29

15.80

8.05

15.55

8.53

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Iannacchione, A., Ottmar, E., Ngo, V. et al. Examining relations between math anxiety, prior knowledge, hint usage, and performance of math equivalence in two different online learning contexts. Instr Sci 51, 285–307 (2023). https://doi.org/10.1007/s11251-022-09604-6

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