August  2021, 1(3): 157-169. doi: 10.3934/steme.2021012

Frustration in mathematical problem-solving: A systematic review of research

1. 

Department of Mathematics, University of Auckland, Auckland, New Zealand

* Correspondence: krie235@aucklanduni.ac.nz

Academic Editor: Christopher Tisdell

Received  May 2021 Revised  July 2021 Published  August 2021

Emotions are an integral part of problem-solving, but must emotions traditionally conceptualised as "negative" have negative consequences in learning? Frustration is one of the most prominent emotions reported during mathematical problem-solving across all levels of learning. Despite research aiming to mitigate frustration, it can play a positive role during mathematical problem solving. A systematic review method was used to explore how frustration usually appears in students during mathematical problem-solving and the typical patterns of emotions, behaviours, and cognitive processes that are associated with its occurrence. The findings are mixed, which informs the need for further research in this area. Additionally, there are theories and qualitative findings about the potential positive role of frustration that have not been followed up with empirical investigations, which illuminate how our findings about negative emotions may be limited by the questions we ask as researchers. With the support of research, I consider how educators may directly or indirectly address rethinking the role and consequences of frustration during problem-solving with their students.

Citation: Kaitlin Riegel. Frustration in mathematical problem-solving: A systematic review of research. STEM Education, 2021, 1 (3) : 157-169. doi: 10.3934/steme.2021012
References:
[1]

Hannula, M., Emotions in problem solving, in Selected Regular Lectures from the 12th International Congress on Mathematical Education, S.J. Cho Ed. 2015, pp. 269-288, Springer. 10.1007/978-3-319-17187-6_16.

[2]

R. Zan, Affect in mathematics education: An introduction, Educational Studies in Mathematics, 63 (2006), 113-122.  doi: 10.1007/s10649-006-9028-2.

[3]

McCleod, D.B., The role of affect in mathematical problem solving, in Affect and Mathematical Problem Solving: A New Perspective, D.B. Mcleod and V.M. Adams Ed. 1989, pp. 20-36, Springer. 10.1007/978-1-4612-3614-6_2.

[4]

S. D'Mello and A. Graesser, Dynamics of affective states during complex learning, Learning and Instruction, 22 (2012), 145-157.  doi: 10.1016/j.learninstruc.2011.10.001.

[5]

G.A. Goldin, Affective pathways and representation in mathematical problem solving, Mathematical Thinking and Learning, 2 (2000), 209-219.  doi: 10.1207/S15327833MTL0203_3.

[6]

Pekrun, R. and Stephens, E.J., Achievement emotions in higher education, in Higher Education: Handbook of Theory and Research, J.C. Smart Ed. 2010, 25: 257-306, Springer. 10.1007/978-90-481-8598-6_7.

[7]

E.A. Linnenbrink, Emotion research in education: Theoretical and methodological perspectives on the integration of affect, motivation, and cognition, Educational Psychology Review, 18 (2006), 307-314.  doi: 10.1007/s10648-006-9028-x.

[8]

B. KoichuE. Katz and A. Verman, Stimulating student aesthetic response to mathematical problems by means of manipulating the extent of surprise, The Journal of Mathematical Behaviour, 46 (2017), 42-57.  doi: 10.1016/j.jmathb.2017.02.005.

[9]

O. Marmur and B. Koichu, Surprise and the aesthetic experience of university students: A design experiment, Journal of Humanistic Mathematics, 6 (2016), 127-151.  doi: 10.5642/jhummath.201601.09.

[10]

V.A. DeBellis and G.A. Goldin, Affect and meta-affect in mathematical problem solving: A representational perspective, Educational Studies in Mathematics, 63 (2006), 131-147.  doi: 10.1007/s10649-006-9026-4.

[11]

Leo I. Di, Curiosity...Confusion? Frustration! The role and sequencing of emotions during mathematics problem solving, Contemporary Educational Psychology, 58 (2019), 121-137.  doi: 10.1016/j.cedpsych.2019.03.001.

[12]

K.R. Muis, The role of epistemic emotions in mathematics problem solving, Contemporary Educational Psychology, 42 (2015), 172-185.  doi: 10.1016/j.cedpsych.2015.06.003.

[13]

Leo I. Di and K.R. Muis, Confused, now what? A Cognitive-Emotional Strategy Training (CEST) intervention for elementary students during mathematics problem solving, Contemporary Educational Psychology, 62 (2020), 101879.  doi: 10.1016/j.cedpsych.2020.101879.

[14]

B. Munzar, Elementary students' cognitive and affective responses to impasses during mathematics problem solving, Journal of Educational Psychology, 113 (2021), 104-124.  doi: 10.1037/edu0000460.

[15]

Sinclair and N, The roles of aesthetic in mathematical inquiry, Mathematical Thinking and Learning, 6 (2004), 261-284.  doi: 10.1207/s15327833mtl0603_1.

[16]

Galán, F.C. and Beal, C.R., EEG estimates of engagement and cognitive workload predict math problem solving outcomes, in 20th International Conference on User Modeling, Adaptation, and Personalization, 2012, pp. 51-62, Springer. 10.1007/978-3-642-31454-4_5.

[17]

O. Gómez, Achievement emotions in mathematics: Design and evidence of validity of a self-report scale, Journal of Education and Learning, 9 (2020), 233-247.  doi: 10.5539/jel.v9n5p233.

[18]

Chen, L., et al., Riding an emotional roller-coaster: A multimodal study of young child's math problem solving activities, in Proceedings of the 9th International Conference on Educational Data Mining, T. Barnes, M. Chi and M. Feng Ed. 2016, pp. 38-45.

[19]

G. A. Goldin, Beliefs and engagement structures: Behind the affective dimension of mathematical learning, Zentralblatt für Didaktik der Mathematik, 43 (2011), 547-560.  doi: 10.1007/s11858-011-0348-z.

[20]

G. A. Goldin, Problem solving heuristics, affect, and discrete mathematics, Zentralblatt für Didaktik der Mathematik, 36 (2004), 56-60.  doi: 10.1007/BF02655759.

[21]

D.B. McCleod, Affective issues in mathematical problem solving: Some theoretical considerations, Journal for Research in Mathematics Education, 19 (1988), 134-141.  doi: 10.2307/749407.

[22]

K. Weber, The role of affect in learning Real Analysis: A case study, Research in Mathematics Education, 10 (2008), 71-85.  doi: 10.1080/14794800801916598.

[23]

G. A. Goldin, Representational systems, learning, and problem solving in mathematics, Journal of Mathematical Behavior, 17 (1998), 137-165. 

[24]

R. Bjuland, Student teachers' reflections on their learning process through collaborative problem solving in geometry, Education Studies in Mathematics, 55 (2004), 199-225.  doi: 10.1023/B:EDUC.0000017690.90763.c1.

[25]

C. VoicaF.M. Singer and E. Stan, How are motivation and self-efficacy interacting in problem-solving and problem-posing?, Educational Studies in Mathematics, 105 (2020), 487-517.  doi: 10.1007/s10649-020-10005-0.

[26]

DeBellis, V.A. and Goldin, G. A., Interactions between cognition and affect in eight high school students' individual problem solving, in Proceedings of the 13th Annual Meeting of PME-NA, R.G. Underhill Ed. 1991, pp. 29-35. Virginia Polytechnic University, Division of Curriculum and Instruction.

[27]

M.P. Carlson and I. Bloom, The cyclic nature of problem solving: An emergent multidimensional problem-solving framework, Education Studies in Mathematics, 58 (2005), 45-75.  doi: 10.1007/s10649-005-0808-x.

[28]

N.C. Presmeg and P. E. Balderas-Cañas, Visualization and affect in nonroutine problem solving, Mathematical Thinking and Learning, 3 (2001), 289-313.  doi: 10.1207/S15327833MTL0304_03.

[29]

O'Dell, J.R., The interplay of frustration and joy: Elementary students' productive struggle when engaged in unsolved problems, in Proceedings of the 40th annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education, T.E. Hodges, G.J. Roy and A.M. Tyminski Ed. 2018, pp. 938-945. University of South Carolina & Clemson University.

[30]

H.K. Warshauer, Productive struggle in middle school mathematics classrooms, Journal of Mathematics Teacher Education, 18 (2015), 375-400.  doi: 10.1007/s10857-014-9286-3.

[31] J. Piaget, The Psychology of Intelligence, Routledge, London, 1960. 
[32]

Vygotsky, L.S., The collected works of L. S. Vygotsky: Problems of general psychology including the volume thinking and speech, Ed. by R.W. Rieber and A.S. Carton. 10.1007/978-1-4613-1655-8

[33]

Pekrun, R., A social-cognitive, control-value theory of achievement emotions, in Motivational Psychology of Human Development, J. Heckhausen, Ed. 2000, pp. 143-163, Elsevier.

[34]

A.J. CrumP. Salovey and S. Achor, Rethinking stress: The role of mindsets in determining the stress response, Journal of Personality and Social Psychology, 104 (2013), 716-733.  doi: 10.1037/a0031201.

[35]

A.J. Crum, The role of stress mindset in shaping cognitive, emotional, and physiological responses to challenging and threatening stress, Anxiety, Stress, & Coping, 30 (2017), 379-395.  doi: 10.1080/10615806.2016.1275585.

show all references

References:
[1]

Hannula, M., Emotions in problem solving, in Selected Regular Lectures from the 12th International Congress on Mathematical Education, S.J. Cho Ed. 2015, pp. 269-288, Springer. 10.1007/978-3-319-17187-6_16.

[2]

R. Zan, Affect in mathematics education: An introduction, Educational Studies in Mathematics, 63 (2006), 113-122.  doi: 10.1007/s10649-006-9028-2.

[3]

McCleod, D.B., The role of affect in mathematical problem solving, in Affect and Mathematical Problem Solving: A New Perspective, D.B. Mcleod and V.M. Adams Ed. 1989, pp. 20-36, Springer. 10.1007/978-1-4612-3614-6_2.

[4]

S. D'Mello and A. Graesser, Dynamics of affective states during complex learning, Learning and Instruction, 22 (2012), 145-157.  doi: 10.1016/j.learninstruc.2011.10.001.

[5]

G.A. Goldin, Affective pathways and representation in mathematical problem solving, Mathematical Thinking and Learning, 2 (2000), 209-219.  doi: 10.1207/S15327833MTL0203_3.

[6]

Pekrun, R. and Stephens, E.J., Achievement emotions in higher education, in Higher Education: Handbook of Theory and Research, J.C. Smart Ed. 2010, 25: 257-306, Springer. 10.1007/978-90-481-8598-6_7.

[7]

E.A. Linnenbrink, Emotion research in education: Theoretical and methodological perspectives on the integration of affect, motivation, and cognition, Educational Psychology Review, 18 (2006), 307-314.  doi: 10.1007/s10648-006-9028-x.

[8]

B. KoichuE. Katz and A. Verman, Stimulating student aesthetic response to mathematical problems by means of manipulating the extent of surprise, The Journal of Mathematical Behaviour, 46 (2017), 42-57.  doi: 10.1016/j.jmathb.2017.02.005.

[9]

O. Marmur and B. Koichu, Surprise and the aesthetic experience of university students: A design experiment, Journal of Humanistic Mathematics, 6 (2016), 127-151.  doi: 10.5642/jhummath.201601.09.

[10]

V.A. DeBellis and G.A. Goldin, Affect and meta-affect in mathematical problem solving: A representational perspective, Educational Studies in Mathematics, 63 (2006), 131-147.  doi: 10.1007/s10649-006-9026-4.

[11]

Leo I. Di, Curiosity...Confusion? Frustration! The role and sequencing of emotions during mathematics problem solving, Contemporary Educational Psychology, 58 (2019), 121-137.  doi: 10.1016/j.cedpsych.2019.03.001.

[12]

K.R. Muis, The role of epistemic emotions in mathematics problem solving, Contemporary Educational Psychology, 42 (2015), 172-185.  doi: 10.1016/j.cedpsych.2015.06.003.

[13]

Leo I. Di and K.R. Muis, Confused, now what? A Cognitive-Emotional Strategy Training (CEST) intervention for elementary students during mathematics problem solving, Contemporary Educational Psychology, 62 (2020), 101879.  doi: 10.1016/j.cedpsych.2020.101879.

[14]

B. Munzar, Elementary students' cognitive and affective responses to impasses during mathematics problem solving, Journal of Educational Psychology, 113 (2021), 104-124.  doi: 10.1037/edu0000460.

[15]

Sinclair and N, The roles of aesthetic in mathematical inquiry, Mathematical Thinking and Learning, 6 (2004), 261-284.  doi: 10.1207/s15327833mtl0603_1.

[16]

Galán, F.C. and Beal, C.R., EEG estimates of engagement and cognitive workload predict math problem solving outcomes, in 20th International Conference on User Modeling, Adaptation, and Personalization, 2012, pp. 51-62, Springer. 10.1007/978-3-642-31454-4_5.

[17]

O. Gómez, Achievement emotions in mathematics: Design and evidence of validity of a self-report scale, Journal of Education and Learning, 9 (2020), 233-247.  doi: 10.5539/jel.v9n5p233.

[18]

Chen, L., et al., Riding an emotional roller-coaster: A multimodal study of young child's math problem solving activities, in Proceedings of the 9th International Conference on Educational Data Mining, T. Barnes, M. Chi and M. Feng Ed. 2016, pp. 38-45.

[19]

G. A. Goldin, Beliefs and engagement structures: Behind the affective dimension of mathematical learning, Zentralblatt für Didaktik der Mathematik, 43 (2011), 547-560.  doi: 10.1007/s11858-011-0348-z.

[20]

G. A. Goldin, Problem solving heuristics, affect, and discrete mathematics, Zentralblatt für Didaktik der Mathematik, 36 (2004), 56-60.  doi: 10.1007/BF02655759.

[21]

D.B. McCleod, Affective issues in mathematical problem solving: Some theoretical considerations, Journal for Research in Mathematics Education, 19 (1988), 134-141.  doi: 10.2307/749407.

[22]

K. Weber, The role of affect in learning Real Analysis: A case study, Research in Mathematics Education, 10 (2008), 71-85.  doi: 10.1080/14794800801916598.

[23]

G. A. Goldin, Representational systems, learning, and problem solving in mathematics, Journal of Mathematical Behavior, 17 (1998), 137-165. 

[24]

R. Bjuland, Student teachers' reflections on their learning process through collaborative problem solving in geometry, Education Studies in Mathematics, 55 (2004), 199-225.  doi: 10.1023/B:EDUC.0000017690.90763.c1.

[25]

C. VoicaF.M. Singer and E. Stan, How are motivation and self-efficacy interacting in problem-solving and problem-posing?, Educational Studies in Mathematics, 105 (2020), 487-517.  doi: 10.1007/s10649-020-10005-0.

[26]

DeBellis, V.A. and Goldin, G. A., Interactions between cognition and affect in eight high school students' individual problem solving, in Proceedings of the 13th Annual Meeting of PME-NA, R.G. Underhill Ed. 1991, pp. 29-35. Virginia Polytechnic University, Division of Curriculum and Instruction.

[27]

M.P. Carlson and I. Bloom, The cyclic nature of problem solving: An emergent multidimensional problem-solving framework, Education Studies in Mathematics, 58 (2005), 45-75.  doi: 10.1007/s10649-005-0808-x.

[28]

N.C. Presmeg and P. E. Balderas-Cañas, Visualization and affect in nonroutine problem solving, Mathematical Thinking and Learning, 3 (2001), 289-313.  doi: 10.1207/S15327833MTL0304_03.

[29]

O'Dell, J.R., The interplay of frustration and joy: Elementary students' productive struggle when engaged in unsolved problems, in Proceedings of the 40th annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education, T.E. Hodges, G.J. Roy and A.M. Tyminski Ed. 2018, pp. 938-945. University of South Carolina & Clemson University.

[30]

H.K. Warshauer, Productive struggle in middle school mathematics classrooms, Journal of Mathematics Teacher Education, 18 (2015), 375-400.  doi: 10.1007/s10857-014-9286-3.

[31] J. Piaget, The Psychology of Intelligence, Routledge, London, 1960. 
[32]

Vygotsky, L.S., The collected works of L. S. Vygotsky: Problems of general psychology including the volume thinking and speech, Ed. by R.W. Rieber and A.S. Carton. 10.1007/978-1-4613-1655-8

[33]

Pekrun, R., A social-cognitive, control-value theory of achievement emotions, in Motivational Psychology of Human Development, J. Heckhausen, Ed. 2000, pp. 143-163, Elsevier.

[34]

A.J. CrumP. Salovey and S. Achor, Rethinking stress: The role of mindsets in determining the stress response, Journal of Personality and Social Psychology, 104 (2013), 716-733.  doi: 10.1037/a0031201.

[35]

A.J. Crum, The role of stress mindset in shaping cognitive, emotional, and physiological responses to challenging and threatening stress, Anxiety, Stress, & Coping, 30 (2017), 379-395.  doi: 10.1080/10615806.2016.1275585.

Table 1.  Literature search and processing of records
Table 2.  Studies selected for the systematic review and the role of frustration
Author(s) Method Participants Role
Bjuland [24] QL Student teachers positive
Carlson & Bloom [27] QL Mathematicians (N = 12) inconclusive
Chen et al. [18] MM Case study of a 9-year-old boy negative
DeBellis & Goldin [26] QL High school students (N = 8) positive
DeBellis & Goldin [10] T/QL 9-10 year olds (N = 19) both
Di Leo & Muis [13] MM Grade 5 students (N = 57) negative
Di Leo et al. [11] MM Study 1: Grade 5-6 students (N = 138); Study 2: Grade 5 students (N = 79) both
Galán & Beal [16] QN Undergraduate students (N = 16) negative
Goldin [23] T n/a both
Goldin [5] T n/a both
Goldin [20] T n/a both
Goldin et al. [19] T n/a both
Gómez et al. [17] QN Grade 9 students (N = 452) negative
McCleod [21] T n/a negative
Muis et al. [12] MM Grade 5 students (N = 79) negative
Munzar et al. [14] MM Study 1: Grade 3-6 students (N = 136); Study 2: Grade 5 students (N = 80) negative
O'Dell [29] QL Grade 4-5 students (N = 10) positive
Presmeg & Balderas-Cañas [28] QL Graduate students (N = 4) both
Voica et al. [25] MM Pre-service teachers (N = 114) inconclusive
Weber [22] QL Case study of an undergraduate student negative
Note. QL = Qualitative, QN = Quantitative, T = Theoretical, MM = Mixed Methods
Author(s) Method Participants Role
Bjuland [24] QL Student teachers positive
Carlson & Bloom [27] QL Mathematicians (N = 12) inconclusive
Chen et al. [18] MM Case study of a 9-year-old boy negative
DeBellis & Goldin [26] QL High school students (N = 8) positive
DeBellis & Goldin [10] T/QL 9-10 year olds (N = 19) both
Di Leo & Muis [13] MM Grade 5 students (N = 57) negative
Di Leo et al. [11] MM Study 1: Grade 5-6 students (N = 138); Study 2: Grade 5 students (N = 79) both
Galán & Beal [16] QN Undergraduate students (N = 16) negative
Goldin [23] T n/a both
Goldin [5] T n/a both
Goldin [20] T n/a both
Goldin et al. [19] T n/a both
Gómez et al. [17] QN Grade 9 students (N = 452) negative
McCleod [21] T n/a negative
Muis et al. [12] MM Grade 5 students (N = 79) negative
Munzar et al. [14] MM Study 1: Grade 3-6 students (N = 136); Study 2: Grade 5 students (N = 80) negative
O'Dell [29] QL Grade 4-5 students (N = 10) positive
Presmeg & Balderas-Cañas [28] QL Graduate students (N = 4) both
Voica et al. [25] MM Pre-service teachers (N = 114) inconclusive
Weber [22] QL Case study of an undergraduate student negative
Note. QL = Qualitative, QN = Quantitative, T = Theoretical, MM = Mixed Methods
Table 3.  Summary of the findings on the role of frustration in mathematical problem-solving by study participants
Positive Negative Both Inconclusive Total
Primary 1 4 2 - 7
Secondary 1 1 - - 2
Tertiary - 2 1 - 3
Student-teachers 1 - - 1 2
Mathematicians - - - 1 1
Total 3 7 3 2 15
*Note. The exclusively theoretical papers were not applicable so were not included (N = 15)
Positive Negative Both Inconclusive Total
Primary 1 4 2 - 7
Secondary 1 1 - - 2
Tertiary - 2 1 - 3
Student-teachers 1 - - 1 2
Mathematicians - - - 1 1
Total 3 7 3 2 15
*Note. The exclusively theoretical papers were not applicable so were not included (N = 15)
Table 4.  Summary of the role of frustration in mathematical problem-solving by study methods
Positive Negative Both Omitted Total
Qualitative 3 1 1 1 6
Quantitative - 2 - - 2
Mixed-Methods - 4 1 1 6
Theoretical - 1 5 - 6
Total 3 8 7 2 20
*Note. DeBellis & Goldin [10] was included as a theoretical study as this is where the discussion of the role of frustration is dominant.
Positive Negative Both Omitted Total
Qualitative 3 1 1 1 6
Quantitative - 2 - - 2
Mixed-Methods - 4 1 1 6
Theoretical - 1 5 - 6
Total 3 8 7 2 20
*Note. DeBellis & Goldin [10] was included as a theoretical study as this is where the discussion of the role of frustration is dominant.
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