# Can Mathematics Achievement Be Predicted? The Role of Cognitive–Behavioral–Emotional Variables

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

#### Affect and Mathematics

## 2. Materials and Methods

#### 2.1. Participants

#### 2.2. Instruments

#### 2.3. Procedure

#### 2.4. Data Analysis

^{2}, for the effect size or the intensity of the differences. Values of eta-squared lower than 0.1 mean a small difference, between 0.1 and 0.3 mean a moderate one, and above 0.5 mean a high difference [57]; rurality and type of school were included as covariates. Thus, the results are presented by taking into account the categorical variable created for mathematics achievement as the dependent variable.

## 3. Results

^{2}= 0.06), in emotional control (F = 15.184, p < 0.001, η

^{2}= 0.05), and in critical and creative thinking (F = 12.176, p < 0.005, η

^{2}= 0.04) LS, with all of them showing small effect sizes.

_{Spearman}> 0.5, while it is negative and moderate for mathematics achievement and attitude towards mathematics. The relationship between mathematics achievement and the attitude towards science is much weaker than with the previous attitude, although it is even with statistical significance.

^{2}= 101.130, p < 0.001. Moreover, our model showed good performance in classifying participants accurately into the correct achievement group (see Table 4), with 82.6% of the participants correctly classified overall.

## 4. Discussion

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

- European Commission Directorate General for Communications Networks. Content & Technology Mathematics for Europe. 2016. Available online: https://ec.europa.eu/futurium/en/system/files/ged/finalreport_maths.pdf/ (accessed on 8 June 2021).
- Chiu, M.M.; Klassen, R.M. Relations of Mathematics Self-Concept and Its Calibration with Mathematics Achievement: Cultural Differences among Fifteen-Year-Olds in 34 Countries. Learn Instr.
**2010**, 20, 2–17. [Google Scholar] [CrossRef] - Algarabel, S.; Dasi, C. The Definition of Achievement and the Construction of Tests for Its Measurement: A review of the Main Trends. Psicologica
**2001**, 22, 43–66. [Google Scholar] - Guo, M.; Leung, F.K. Achievement Goal Orientations, Learning Strategies, and Mathematics Achievement: A Comparison of Chinese Miao and Han Students. Psychol. Sch.
**2020**, 58, 107–123. [Google Scholar] [CrossRef] - House, J.D. Mathematics Beliefs and Achievement of Elementary School Students in Japan and the United States: Results from the Third International Mathematics and Science Study. J. Genet. Psychol.
**2006**, 167, 31–45. [Google Scholar] [CrossRef] [PubMed] - Tsui, M. Gender and mathematics achievement in China and the United States. Gend. Issues
**2007**, 24, 1–11. [Google Scholar] [CrossRef] - Preininger, A.M. Embedded Mathematics in Chemistry: A Case Study of Students’ Attitudes and Mastery. J. Sci. Educ. Technol.
**2017**, 26, 58–69. [Google Scholar] [CrossRef] - Lee, C.Y.; Kung, H.Y. Math Self-Concept and Mathematics Achievement: Examining Gender Variation and Reciprocal Relations among Junior High School Students in Taiwan. Eurasia J. Math. Sci. Technol. Educ.
**2017**, 14, 1239–1252. [Google Scholar] - Niepel, C.; Brunner, M.; Preckel, F. Achievement Goals, Academic Self-Concept, and School Grades in Mathematics: Longitudinal Reciprocal Relations in above Average Ability Secondary School Students. Contemp. Educ. Psychol.
**2014**, 39, 301–313. [Google Scholar] [CrossRef] - Biggs, J.; Kember, D.; Leung, D.Y. The Revised Two-Factor Study Process Questionnaire: R-SPQ-2F. Br. J. Educ. Psychol.
**2001**, 71, 133–149. [Google Scholar] [CrossRef] - Pitsia, V.; Biggart, A.; Karakolidis, A. The Role of Students’ Self-Beliefs, Motivation and Attitudes in Predicting Mathematics Achievement: A multilevel Analysis of the Programme for International Student Assessment data. Learn. Individ. Differ.
**2017**, 55, 163–173. [Google Scholar] [CrossRef] [Green Version] - Hann, T. Investigating the Impact of Teacher Practices and Noncognitive Factors on Mathematics Achievement. Res. Educ.
**2020**, 108, 22–45. [Google Scholar] [CrossRef] - Bassey, S.W.; Joshua, M.T.; Asim, A.E. Gender Differences and Mathematics Achievement of Rural Senior Secondary Students in Cross River State, Nigeria. Math. Connect.
**2011**, 10, 56–60. [Google Scholar] - Else-Quest, N.M.; Hyde, J.S.; Linn, M.C. Cross-National Patterns of Gender Differences in Mathematics: A Meta-Analysis. Psychol. Bull.
**2010**, 136, 103–127. [Google Scholar] [CrossRef] [PubMed] - Isiksal, M.; Cakiroglu, E. Gender Differences Regarding Mathematics Achievement: The case of Turkish Middle School Students. Sch. Sci. Math.
**2008**, 108, 113–120. [Google Scholar] [CrossRef] - Michaluk, L.; Stoiko, R.; Stewart, G.; Stewart, J. Beliefs and Attitudes about Science and Mathematics in Pre-Service Elementary Teachers, STEM, and Non-STEM Majors in Undergraduate Physics Courses. J. Sci. Educ. Technol.
**2018**, 27, 99–113. [Google Scholar] [CrossRef] - McLeod, D.B. Research on Affect and Mathematics Learning in the JRME: 1970 to the Present. J. Res. Math. Educ.
**1994**, 24, 637–647. [Google Scholar] [CrossRef] - De Bellis, V.A.; Goldin, G.A. Aspects of Affect: Mathematical Intimacy, Mathematical Integrity. In Proceedings of the 23rd Conference of the International Group for the Psychology of Mathematics Education, Haifa, Israel, 25–30 July 1996; Zalavsky, O., Ed.; pp. 249–256. [Google Scholar]
- Philipp, R.A. Mathematics Teachers’ Beliefs and Affect. In Second Handbook of Research on Mathematics Teaching and Learning; Lester, F.K., Ed.; Information Age: Charlotte, NC, USA, 2007; pp. 257–315. [Google Scholar]
- Han, S.Y.; Carpenter, D. Construct Validation of Student Attitude towards Science, Technology, Engineering and Mathematics Project-Based Learning: The Case of Korean Middle Grade Students. Middle Grades Res. J.
**2014**, 9, 27–41. [Google Scholar] - Chacón, I.M.G. Matemática Emocional. Los Afectos en el Aprendizaje Matemático; Narcea: Madrid, Spain, 2000. [Google Scholar]
- Rodríguez, A.; Fernández, A. Propiedades Psicométricas del Cuestionario de Autoconcepto Dimensional AUDIM. In Educación, Aprendizaje y Desarrollo en una Sociedad Multicultural; Román, J.M., Carbonero, M.A., Valdivieso, J.D., Eds.; Ediciones de la Asociación Nacional de Psicología y Educación: Madrid, Spain, 2011; pp. 999–1113. [Google Scholar]
- Goldin, G.A. Affect, Meta-Affect, and Mathematical Belief Structures. In Beliefs: A Hidden Variable in Mathematics Education? Leder, G.G., Pehkonen, R., Törner, G., Eds.; Springer: Dordrecht, The Netherlands, 2002; pp. 59–72. [Google Scholar]
- Di Martino, P.; Zan, R. The Construct of Attitude in Mathematics Education. In From Beliefs to Dynamic Affect Systems in Mathematics Education; Springer: Cham, Switzerland, 2015; pp. 51–72. [Google Scholar]
- Hemmings, B.; Grootenboer, P.; Kay, R. Predicting Mathematics Achievement: The Influence of Prior Achievement and Attitudes. Int. J. Sci. Math. Educ.
**2011**, 9, 691–705. [Google Scholar] [CrossRef] - Jansen, B.R.; Schmitz, E.A.; Van der Maas, H.L. Affective and Motivational Factors Mediate the Relation between Math Skills and Use of Math in Everyday Life. Front. Psychol.
**2016**, 7, 481–513. [Google Scholar] [CrossRef] [Green Version] - Parker, P.D.; Marsh, H.W.; Ciarrochi, J.; Marshall, S.; Abduljabbar, A.S. Juxtaposing Math Self-Efficacy and Self-Concept as Predictors of Long-Term Achievement Outcomes. Educ. Psychol.
**2014**, 34, 29–48. [Google Scholar] [CrossRef] - Pekrun, R.; Lichtenfeld, S.; Marsh, H.W.; Murayama, K.; Goetz, T. Achievement Emotions and Academic Performance: Longitudinal Models of Reciprocal Effects. Child Dev.
**2017**, 88, 1653–1670. [Google Scholar] [CrossRef] - Ramírez, G.; Chang, H.; Maloney, E.A.; Levine, S.C.; Beilock, S.L. On the Relationship between Math Anxiety and Math Achievement in Early Elementary School: The Role of Problem Solving Strategies. J. Exp. Child Psychol.
**2016**, 141, 83–100. [Google Scholar] [CrossRef] [Green Version] - Ocak, G.; Yamac, A. Examination of the Relationships between Fifth Graders’ Self-Regulated Learning Strategies, Motivational Beliefs, Attitudes, and Achievement. Educ. Sci. Theory Pract.
**2013**, 13, 380–387. [Google Scholar] - Auzmendi Escribano, E. Las Actitudes Hacia la Matemática-Estadística en Las Enseñanzas Medias y Universitaria. Características y Medición; Ediciones Mensajero: Bilbao, Spain, 1992. [Google Scholar]
- Peiró-Signes, Á.; Trull, Ó.; Segarra-Oña, M.; García-Díaz, J.C. Attitudes Towards Statistics in Secondary Education: Findings from fsQCA. Mathematics
**2020**, 8, 804. [Google Scholar] [CrossRef] - Palacios, A.; Hidalgo, S.; Maroto, A.; Ortega del Rincón, T. Causas y Consecuencias de la Ansiedad Matemática Mediante un Modelo de Ecuaciones Estructurales. Enseñ. Cienc.
**2013**, 31, 93–111. [Google Scholar] - Berger, N.; Mackenzie, E.; Holmes, K. Positive Attitudes towards Mathematics and Science are Mutually Beneficial for Student Achievement: A Latent Profile Analysis of TIMSS 2015. Aust. Educ. Res.
**2020**, 47, 409–444. [Google Scholar] [CrossRef] - Marsh, H.W. Academic Self-Concept: Theory Measurement and Research. In Psychological Perspectives on the Self; Suls, J., Ed.; Erlbaum: Hillsdale, NJ, USA, 1993; pp. 59–98. [Google Scholar]
- Obilor, I.E. Relationship between Self-Concept and Mathematics Achievement of Senior Secondary Students in Port Harcourt. Educ. Plus
**2012**, 8, 186–197. [Google Scholar] - Ercikan, L.; McCreith, T.; Lapointe, V. Factors Associated with Mathematics Achievement and Participation in Advanced Mathematics Courses: An Examination of Gender Differences from an International Perspective. Sch. Sci. Math.
**2005**, 105, 5–14. [Google Scholar] [CrossRef] - Kung, H.Y.; Lee, C.Y. The longitudinal Reciprocal Effects Model of Junior High School Students’ Mathematics Self-Concept and Mathematics Achievement: The Perspectives of Gender and Urban/Rural Differences. Chin. J. Sci. Educ.
**2016**, 24, 511–536. [Google Scholar] - Bofah, E.A.T. Reciprocal Determinism between Students’ Maths Self Concept and Achievement in an African Context. In Proceedings of the Ninth Congress of the European Society for Research in Mathematics Education, Prague, Czech, 4–8 February 2015. [Google Scholar]
- Pinto, N.S.; Martínez, A.I.M.; Jiménez-Taracido, L. Learning Strategies, Reading Comprehension and Academic Achievement in Secondary Education. Psicol. Esc. E Educ.
**2016**, 20, 447–456. [Google Scholar] [CrossRef] [Green Version] - Forehand, M. Bloom’s Taxonomy. Emerg. Perspect. Learn. Teach. Technol.
**2010**, 41, 47–56. [Google Scholar] - Beltrán, J. Procesos, Estrategias y Técnicas de Aprendizaje; Síntesis: Madrid, Spain, 1993. [Google Scholar]
- Beltrán, J.A.; Pérez, L.F.; Ortega, M.I. Cuestionario de Estrategias de Aprendizaje, CEA; TEA Ediciones: Madrid, Spain, 2006. [Google Scholar]
- Verschaffel, L.; Torbeyns, J.; De Smedt, B.; Luwel, K.; Dooren, W.V. Strategy Flexibility in Children with Low Achievement in Mathematics. Educ. Child Psychol.
**2007**, 24, 16–27. [Google Scholar] - Baroody, A.J.; Dowker, A. The Development of Arithmetic Concepts and Skills: Constructing Adaptive Expertise; Erlbaum: Mahwah, NJ, USA, 2003. [Google Scholar]
- Clements, D.H.; Dumas, D.; Dong, Y.; Banse, H.W.; Sarama, J.; Day-Hess, D.A. Strategy Diversity in Early Mathematics Classrooms. Contemp. Educ. Psychol.
**2020**, 60, 101834. [Google Scholar] [CrossRef] - Brunkalla, K. How to Increase Mathematical Creativity-an Experiment. Math. Enthus.
**2009**, 6, 257–266. [Google Scholar] - Hidayat, D.; Nurlaelah, E.; Dahlan, J.A. Rigorous Mathematical Thinking Approach to Enhance Students’ Mathematical Creative and Critical Thinking Abilities. J. Phys. Conf. Ser.
**2017**, 895, 012087. [Google Scholar] [CrossRef] [Green Version] - Liu, Z.K.; He, J.; Li, B. Critical and Creative Thinking as Learning Processes at Top-Ranking Chinese Middle Schools: Possibilities and Required Improvements. High Abil. Stud.
**2015**, 26, 139–152. [Google Scholar] [CrossRef] - Aru, S.A.; Kale, M. Effects of School-related Factors and Early Learning Experiences on Mathematics Achievement “A Multilevel Analysis to Analyse the TIMSS Data”. J. Educ. Train. Stud.
**2019**, 7, 259–272. [Google Scholar] [CrossRef] - Acelajado, M.J. Students’ Mathematical Experiences and Perceptions: Key to Improving Their Attitudes, Anxiety and Achievement in Mathematics. In Proceedings of the 2014 International Conference of the Korean Society of Mathematical Education, Seoul, Korea, 4–5 April 2013. [Google Scholar]
- Arellano, M.; Zamarro, G.; The Choice between Public and Private Schools with or without Subsidies in Spain. Preliminary and Incomplete Preprint. 2007. Available online: https://www.cemfi.es/~arellano/schoolchoice-tr-26Sep2007.pdf (accessed on 8 June 2021).
- Garreta-Bochaca, J.; Macia-Bordalba, M.; Llevot-Calvet, N. Religious Education in State Primary Schools: The Case of Catalonia (Spain). Brit. J. Relig. Educ.
**2019**, 41, 145–154. [Google Scholar] [CrossRef] - Fernández-Cézar, R.; Garrido, D.; Solano-Pinto, N. Do Science, Technology, Engineering and Mathematics (STEM) Experimentation Outreach Programs Affect Attitudes towards Mathematics and Science? A Quasi-Experiment in Primary Education. Mathematics
**2020**, 8, 1490. [Google Scholar] [CrossRef] - Jiménez, C.; Peinado, J.E.; Solano-Pinto, N.; Ornelas, M.; Blanco, H. Relaciones Entre Autoconcepto y Bienestar Psicológico en Universitarias Mexicanas. Revista Iberoamericana. Rev. Iberoam. Diagn. Eval. Aval. Psicol.
**2020**, 55, 59–70. [Google Scholar] - Álvarez Méndez, J.M. La Evaluación del Rendimiento Académico de los Alumnos en el Sistema Educativo Español. In Teoría y Desarrollo del Currículum; Angulo, J.F., Blanco, N., Eds.; Aljibe: Málaga, Spain, 1994; pp. 313–342. [Google Scholar]
- Cohen, J. Statistical Power Analysis for the Behavioral Sciences; Routledge: New York, NY, USA, 2013. [Google Scholar]
- Weber, H.; Loureiro De Assunção, V.; Martin, C.; Westmeyer, H.; Geisler, F.C. Reappraisal Inventiveness: The Ability to Create Different Reappraisals of Critical Situations. Cogn. Emot.
**2014**, 28, 345–360. [Google Scholar] [CrossRef] [PubMed] - Hadar, L.L.; Tirosh, M. Creative Thinking in Mathematics Curriculum: An Analytic Framework. Think. Skills Creat.
**2019**, 33, 100585. [Google Scholar] [CrossRef] - Hasanah, M.A.; Surya, E. Differences in the Abilities of Creative Thinking and Problem Solving of Students in Mathematics by Using Cooperative Learning and Learning of Problem Solving. Int. J. Sci. Basic Appl. Res.
**2017**, 34, 286–299. [Google Scholar] - Fatah, A.; Suryadi, D.; Sabandar, J. Open-Ended Approach: An Effort in Cultivating Students’ Mathematical Creative Thinking Ability and Self-Esteem in Mathematics. J. Math. Educ.
**2016**, 7, 11–20. [Google Scholar] [CrossRef] [Green Version] - Sitorus, J. Students’ Creative Thinking Process Stages: Implementation of Realistic Mathematics Education. Think. Skills Creat.
**2016**, 22, 111–120. [Google Scholar] [CrossRef] - Schoevers, E.M.; Leseman, P.P.; Slot, E.M.; Bakker, A.; Keijzer, R.; Kroesbergen, E.H. Promoting Pupils’ Creative Thinking in Primary School Mathematics: A Case Study. Think. Skills Creat.
**2019**, 31, 323–334. [Google Scholar] [CrossRef]

Mathematics Achievement | ||
---|---|---|

Fail | Pass | |

N | 159 | 193 |

Age (years) | 10.80 (1.08) | 10.53 (1.09) |

Sex (M/F) | 78:81 | 94:99 |

School environment (R/U) | 85:74 | 99:94 |

School type (SFS/SS) | 55:104 | 58:135 |

Science achievement | 6.70 (1.60) | 8.07 (1.44) |

Attitudes | ||

Towards Mathematics | 24.73 (7.10) | 19.92 (6.41) |

Towards Science | 37.31 (80.07) | 36.25 (72.98) |

Self-concept | ||

Academic | 30.51 (4.51) | 32.56 (4.11) |

Social | 30.77 (4.36) | 31.52 (3.89) |

Physical | 31.22 (4.94) | 31.74 (4.62) |

Personal | 23.54 (3.15) | 23.68 (3.09) |

General | 16.94 (2.63) | 18.91 (2.35) |

Learning strategies | ||

Emotional control | 17.10 (4.27) | 18.71 (4.19) |

Critical and creative thinking | 40.52 (6.24) | 43.50 (5.75) |

Metacognition: Planning and evaluating | 25.72 (5.22) | 25.52 (4.65) |

Metacognition: Regulation | 12.30 (3.63) | 12.34 (3.51) |

**Table 2.**Spearman’s correlations between mathematics achievement and other variables of interest (* p < 0.05, ** p < 0.001; bilateral test).

1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | ||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

1. Mathematics achievement | − | |||||||||||||||

2. Science achievement | 0.504 ** | − | ||||||||||||||

3. Previous mathematics achievement | 0.783 ** | 0.447 ** | − | |||||||||||||

4. Previous science achievement | 0.565 ** | 0.726 ** | 0.631 ** | − | ||||||||||||

Attitude | 5. Towards Mathematics | −0.488 ** | −0.057 | −0.360 ** | −0.186 ** | − | ||||||||||

6. Towards Science | 0.115 * | 0.104 * | 0.014 | 0.177 ** | −0.064 | − | ||||||||||

Self-concept | 7. Academic | 0.366 ** | 0.101 | 0.282 ** | 0.181 ** | −0.291 ** | 0.169 ** | -- | ||||||||

8. Social | 0.148 * | −0.076 | 0.094 | 0.016 | −0.165 ** | 0.091 | 0.447 ** | - | ||||||||

9. Physical | 0.041 | −0.081 | −0.080 | −0.068 | −0.189 ** | 0.119 * | 0.315 ** | 0.278 ** | - | |||||||

10. Personal | −0.009 | 0.060 | −0.004 | −0.063 | −0.168 ** | 0.075 | 0.339 ** | 0.348 ** | 0.344 ** | - | ||||||

11. General | −0.080 | −0.065 | −0.062 | −0.059 | 0.027 | 0.103 * | 0.266 ** | 0.229 ** | 0.142 * | 0.384 ** | - | |||||

Learning Strategies | 12. Emotional control | 0.258 ** | 0.055 | 0.273 ** | 0.161 ** | −0.369 ** | 0.105 * | 0.276 ** | 0.190 ** | 0.177 ** | 0.269 ** | 0.041 | - | |||

13. Critical and creative thinking | 0.205 * | 0.105 | 0.105 | 0.135 * | 0.087 | −0.122 * | 0.421 ** | 0.300 ** | 0.067 | 0.245 ** | 0.082 | 0.105 | −- | |||

14. Metacognition: Planning and evaluating | −0.073 | −0.210 ** | −0.167 ** | −0.227 ** | 0.099 | 0.167 ** | 0.108 | 0.051 | 0.095 | 0.123 * | 0.103 | −0.058 | 0.128 * | - | ||

15. Metacognition: Regulation | −0.013 | −0.049 | −0.065 | 0.015 | 0.055 | 0.033 | −0.003 | 0.126 * | 0.137 * | 0.106 | −0.011 | 0.013 | 0.128 * | −0.018 | - |

Mathematics Achievement | |||
---|---|---|---|

OR | 95% CI | p | |

Science achievement | 1.002 * | 1.000–1.004 | 0.016 |

Previous mathematics achievement | 2.690 * | 1.922–3.763 | <0.001 |

Previous science achievement | 0.997 * | 0.995–1.000 | 0.028 |

Attitude towards Mathematics | 0.949 | 0.889–1.013 | 0.119 |

Attitude towards Science | 1.001 | 0.978–1.025 | 0.926 |

Academic self-concept | 1.090 | 0.978–1.215 | 0.118 |

Social self-concept | 0.968 | 0.862–1.087 | 0.581 |

Emotional control learning strategies | 0.974 | 0.872–1.087 | 0.632 |

Critical and creative thinking | 1.120 * | 1.038–1.209 | 0.004 |

Sex (M/F) | 1.149 | 0.506–1.613 | 0.740 |

School environment (R/U) | 0.215 a | 0.046–1.007 | 0.051 |

School type (SFS/SS) | 0.251 | 0.051–1.230 | 0.088 |

^{a}appears in all the statistically marginal relationships.

Predicted | |||
---|---|---|---|

Fail | Pass | Percentage Correct | |

Fail | 61 | 18 | 77.2% |

Pass | 15 | 96 | 86.5% |

Overall percentage | 82.6% |

Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. |

© 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Fernández-Cézar, R.; Solano-Pinto, N.; Garrido, D.
Can Mathematics Achievement Be Predicted? The Role of Cognitive–Behavioral–Emotional Variables. *Mathematics* **2021**, *9*, 1591.
https://doi.org/10.3390/math9141591

**AMA Style**

Fernández-Cézar R, Solano-Pinto N, Garrido D.
Can Mathematics Achievement Be Predicted? The Role of Cognitive–Behavioral–Emotional Variables. *Mathematics*. 2021; 9(14):1591.
https://doi.org/10.3390/math9141591

**Chicago/Turabian Style**

Fernández-Cézar, Raquel, Natalia Solano-Pinto, and Dunia Garrido.
2021. "Can Mathematics Achievement Be Predicted? The Role of Cognitive–Behavioral–Emotional Variables" *Mathematics* 9, no. 14: 1591.
https://doi.org/10.3390/math9141591