Probability Concepts: A Systematic Literature Review of Students’ Learning Difficulties, Errors and Misconceptions

Emmanuel Appoh Andam; Francis Kwadwo Awuah; William Obeng-Denteh

doi:10.37284/eajass.8.2.3008

Emmanuel Appoh Andam Kwame Nkrumah University of Science and Technology
Francis Kwadwo Awuah Kwame Nkrumah University of Science and Technology
William Obeng-Denteh Kwame Nkrumah University of Science and Technology

DOI: https://doi.org/10.37284/eajass.8.2.3008

Keywords: Probability, Problem-Solving, Misconceptions, Difficulties, Errors, Mathematics Education

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Abstract

Human thinking development depends heavily on mathematics, especially when it comes to reasoning and problem-solving skills. Despite the fact that mathematics is currently used to solve problems in many disciplines, including science, it possesses unique characteristics known as probability and, more precisely, probability concepts. The review revealed that most students find probability concepts very difficult to learn and conceptualize. This study presents a systematic literature review on students learning difficulties on probability concepts in relation to the misconceptions and errors they encounter. The review analyses 32 empirically relevant studies published from 2014 to 2023, using the inclusion and exclusion search strategy. The 32 publications for this systematic review were chosen through an organised search process that made use of multiple databases, including EBSCO Academic Search Premier, Education Resources Information Centre (ERIC), SCOPUS, and Google Scholar. The findings from the systematic review revealed a number of misconceptions and errors which result in students’ learning difficulties and their probability problem-solving. By recognizing these common errors, misconceptions and leveraging visual representations, educators can create targeted interventions to improve students' mastery of probability problem-solving skills and enhance their overall learning outcomes.

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References

Abdullah, A. H., Abidin, N. L. Z., & Ali, M. (2015). Analysis of students’ errors in solving Higher Order Thinking Skills (HOTS) problems for the topic of fraction. Asian Social Science, 11(21), 133-142.

Adu, E., Assuah, C. K., & Asiedu-Addo, S. K. (2015). Students’ errors in solving linear equation word problems: Case study of a Ghanaian senior high school. African Journal of Educational Studies in Mathematics and Sciences, 11, 17-30.

Álvarez-Carrasco, D. A., Barahona-Rivera, N. Y., & Godoy-Ponce, O. A. (2021). Teachers' affective mastery in solving mathematical problems. Electronic Journal of Knowledge, Knowledge and Practice, 4(1), 70-85.

Ang, L. H., & Shahrill, M. (2014). Identifying students’ specific misconceptions in learning probability. International Journal of Probability and Statistics, 3(2), 23-29.

Anggara, B., Priatna, N., & Juandi, D. (2018). Learning difficulties of senior high school students based on probability understanding levels. In Journal of Physics: Conference Series (Vol. 1013, No. 1, p. 012116). IOP Publishing.

Arum, D. P., Kusmayadi, T. A., & Pramudya, I. (2018). Students’ difficulties in probabilistic problem-solving. In Journal of Physics: Conference Series (Vol. 983, No. 1, p. 012098). IOP Publishing.

Asberger, J., Thomm, E., & Bauer, J. (2021). On predictors of misconceptions about educational topics: a case of topic specificity. Plos one, 16(12), e0259878.

Astuti, D., Anggraeni, L., & Setyawan, F. (2020). Mathematical probability: Student’s misconception in higher education. In Journal of Physics: Conference Series (Vol. 1613, No. 1, p. 012009). IOP Publishing.

Astuti, R., &; Haryadi, R. (2023). Analysis of Student Difficulties in Solving Mathematical Understanding Problems in the Probability Theory Course. AXIOM: Journal of Education and Mathematics, 11(2), 218-227.

Aziz, A. M., & Rosli, R. (2021). A systematic literature review on developing students’ statistical literacy skills. In Journal of Physics: Conference Series (Vol. 1806, No. 1, p. 012102). IOP Publishing.

Baltaci, S. (2016). Examination of Gifted Students' Probability Problem Solving Process in Terms of Mathematical Thinking. Malaysian Online Journal of Educational Technology, 4(4), 18-35.

Batanero, C., Chernoff, E. J., Engel, J., Lee, H. S., & Sánchez, E. (2016). Research on Teaching and Learning Probability. The Proceedings of the 12th International Congress on Mathematical Education. New York, NY: Springer.

Begolli, K. N., Dai, T., McGinn, K. M., & Booth, J. L. (2021). Could probability be out of proportion? Self-explanation and example-based practice help students with lower proportional reasoning skills learn probability. Instructional Science, 49, pp.441-473.

Beitzel, B. D., & Staley, R. K. (2015). The efficacy of using diagrams when solving probability word problems in college. The Journal of Experimental Education, 83(1), 130-145.

Bílek, J., Nedoma, J., & Jirásek, M. (2018). Representativeness heuristics: A literature review of its impacts on the quality of decision-making. Scientific papers of the University of Pardubice. Series D, Faculty of Economics and Administration. 43/2018.

Blanco, T. F., Gorgal-Romarís, A., Núñez-García, C., & Sequeiros, P. G. (2022). Digital Education to Approach the Affective Domain in Mathematics Learning. In Inclusive Digital Education (pp. 47-69). Cham: Springer International Publishing.

Bramley, N. R., Jones, A., Gureckis, T. M., & Ruggeri, A. (2022). Children’s failure to control variables may reflect adaptive decision-making. Psychonomic Bulletin & Review, 29(6), 2314-2324.

Brückler, F. M., & Šipuš, Ž. M. (2023). Pre-service mathematics teachers’ understanding of conditional probability in the context of the COVID-19 pandemic. European Journal of Science and Mathematics Education, 11(1), pp.89-104.

Budgett, S., & Pfannkuch, M. (2019). Visualizing chance: tackling conditional probability misconceptions. Topics and trends in current statistics education research: International perspectives, 3-25.

Bulut, A. S. (2023). Mathematics Teachers' Knowledge on Misconceptions and Solution Suggestions: Ratio-Proportion Topic. International Journal of Educational Research Review, 8(3), 596-609.

Bursalı, G. G., & Gökkurt-Özdemir, B. (2019). Instructional explanations of mathematics teachers and preservice teachers on misconceptions: The subject of probability. Journal of computer and education research, 7(14), 642-672.

Çetin, B. (2017). The Influence of Pintrich's Self-Regulated Learning Model on Elementary Teacher Candidates in a Life Science Course. Journal of Education and Training Studies, 5(8), 30-36.

Dayal, H., & Sharma, S. (2021). Secondary Pre-Service Teachers' Views on Using Games in Teaching Probability: An International Collaboration. Mathematics Education Research Group of Australasia.

Djam'an, N., Sahid, S., & Auliyah, F. (2022). Analysis of Student Errors in Solving Statistics Problems in terms of Mathematical Ability. SAINSMAT: Journal of Applied Sciences, Mathematics, and Its Education, 11(2), 96-104.

Estrada, A., & Batanero, C. D. (2020). Prospective primary school teachers’ attitudes towards probability and its teaching. International Electronic Journal of Mathematics Education, 15(1), 1-14.

Estrada, A., Batanero, C., & Díaz, C. (2018). Exploring teachers’ attitudes towards probability and its teaching. Teaching and learning stochastics: Advances in probability education research, 313-332.

Evidence for Policy and Practice Information and Coordinating Centre (EPPI-Centre) (2016). Terms of reference for Systematic reviews. Institute of Education, Department for International Development, EPPI Centre.

Fang, Z., Tan, K., & Wang, Z. (2023). Fundamental results in probability theory. Highlights in Science, Engineering and Technology, 49, 464-469.

Fardah, D. K., & Palupi, E. L. W. (2023). Misconceptions of Prospective Mathematics Teacher in Linear Equations System. Prima: Journal of Mathematics Education, 7(1), 100-111.

Farhat, N., Tsaioun, K., Saunders-Hastings, P., Morgan, R. L., Ramoju, S., Hartung, T., & Krewski, D. (2022). Systematic review in evidence-based risk assessment. ALTEX-Alternatives to animal experimentation, 39(3), 463-479.

Fırat, S., & Gürbüz, R. (2022). Evaluation of the Probability Teaching-Learning Process Based on Mathematics Teachers' Views. Abant İzzet Baysal University Faculty of Education Journal, 22(4), 1621-1641.

Gallagher, K. (2023). Overcoming misconceptions about probability a review of David J. hand’s the improbability principle. The Mathematics Enthusiast, 20(1), 217-224.

Gorgoz, S., & Tican, C. (2020). Investigation of Middle School Students' Self-Regulation Skills and Vocabulary Learning Strategies in Foreign Language. International Journal of Educational Methodology, 6(1), 25-42.

Gorgun, G., & Botelho, A. F. (2023). Enhancing the Automatic Identification of Common Math Misconceptions Using Natural Language Processing. In International Conference on Artificial Intelligence in Education (pp. 302-307). Cham: Springer Nature Switzerland.

Goulding, B. W., Stonehouse, E. E., & Friedman, O. (2022). Causal knowledge and children’s possibility judgments. Child Development, 93(3), 794-803.

Hendricks, W., & Olawale, B. E. (2023). Mathematical Probability: Learner's misconception in a selected South African School. Infinity Journal, 12(1), 165-178.

Hokor, E. K., Apawu, J., Owusu-Ansah, N. A., & Agormor, S. (2022). Preservice Teachers' Misconceptions in Solving Probabilistic Problems. Pedagogical Research, 7(1), 1 – 16.

Huang, Y., Zhou, Y., & Li, Y. (2021). Analysis of Students' Error in Solving Probability Problem: A Case Study in Guangxi. INOMATIKA, 3(1), 1-15.

Hull, M. M., Jansky, A., & Hopf, M. (2021). Probability-related naïve ideas across physics topics. Studies in Science Education, 57(1), 45-83.

Ibrahim, B. H., & Asiedu-Addo, S. (2019). Effect of problem-based learning on Colleges of Education students’ achievement in probability and attitude towards solving probability related problems. African Journal of Educational Studies in Mathematics and Sciences, 15(2), pp.155-168.

Julio, A. B. (2023). The General Theory of the Probability. Journal of Modern Physics, 14(08), 1157-1166.

Kingston, M., & Twohill, A. (2022). Young children’s use of subjective thinking in response to probabilistic tasks. Statistics Education Research Journal, 21(3), 5-5.

Lian, L. H., Yew, W. T., & Meng, C. C. (2022). Assessing Lower Secondary School Students' Common Errors in Statistics. Pertanika Journal of Social Sciences & Humanities, 30(3).

Lim, S. L., & Yeo, K. J. (2021). A systematic review of the relationship between motivational constructs and self-regulated learning. Int. J. Eval. Res. Educ. ISSN, 2252, 8822.

Malaterre, C., Javaux, E. J., & López-García, P. (2023). Misconceptions in Science. Perspectives on Science, 31(6), 717-743.

Memnun, D. S., Ozbilen, O., & Dinc, E. (2019). A Qualitative Research on the Difficulties and Failures about Probability Concepts of High School Students. Journal of Educational Issues, 5(1), 1-19.

Morsanyi, K., & Szucs, D. (2015). Intuition in mathematical and probabilistic reasoning. Oxford library of psychology. The Oxford handbook of numerical cognition, 180-200.

Mutara, L., & Makonye, J. (2016). Learners’ use of probability models in answering probability tasks in South Africa. In Promoting understanding of statistics about society, Proceedings of the 13th International Conference of Mathematical Education, July (pp. 24-31).

Nadelson, L. S., Heddy, B. C., Jones, S., Taasoobshirazi, G., & Johnson, M. (2018). Conceptual Change in Science Teaching and Learning: Introducing the Dynamic Model of Conceptual Change. International Journal of Educational Psychology, 7(2), 151-195.

Olgun, B., & Isiksal-Bostan, M. (2019). The influence of the context of conditional probability problems on probabilistic thinking: A case study with teacher candidates. Eleventh Congress of the European Society for Research in Mathematics Education (CERME11), Utrecht University, Utrecht, Netherlands. ffhal-02412821f.

Paul, M., & Hlanganipai, N. (2014). The nature of misconceptions and cognitive obstacles faced by secondary school mathematics students in understanding probability: A case study of selected Polokwane secondary schools. Mediterranean Journal of Social Sciences, 5(8), 446-455.

Phonapichat, P., Wongwanich, S., & Sujiva, S. (2014). An analysis of elementary school students’ difficulties in mathematical problem solving. Procedia-social and behavioral sciences, 116, 3169-3174.

Pickering, C., Grignon, J., Steven, R., Guitart, D., & Byrne, J. (2015). Publishing not perishing: How research students transition from novice to knowledgeable using systematic quantitative literature reviews. Studies in Higher Education, 40(10), 1756-1769.

Ren, J., & Wang, H. (2023). Mathematical methods in data science. Elsevier.

Rossi, G. B., Crenna, F., & Berardengo, M. (2023). Probability theory as a logic for modelling the measurement process. Acta IMEKO, 12(2), 1-5.

Ruz, F., Chance, B., Medina, E., & Contreras, J. M. (2021). Content knowledge and attitudes towards stochastics and its teaching in pre-service Chilean mathematics teachers. Statistics Education Research Journal, 20(1), 5-5.

Sadiah, D. S., & Afriansyah, E. A. (2023). Student misconceptions are reviewed from the level of problem solving in fractional operation material. Journal of Mathematics Learning Innovation: PowerMathEdu, 2(1), 31-44.

Salido, A., & Dasari, D. (2019), April. Students’ errors in solving probability problems viewed by learning style. In Journal of Physics: Conference Series (Vol. 1211, No. 1, p. 012067). IOP Publishing.

Salifu, A. S., & Dokurugu, M. E. (2022). The Relationship Between Pre-Service Teachers' Attitude Towards Statistics and Attitude Towards Probability. Infinity Journal, 11(1), 115-132.

Sani, D. N., & Rosnawati, R. (2022). Students’ Error Analysis in Solving Probability Story Questions Based on Revised Newman Theorem. Journal of Mathematics Education (JUPITEK), 5(2), pp.123-131.

Satnarine, T. (2023). Systematic review methodology: conducting high-quality reviews and understanding their significance in evidence-based practice. Journal for International Medical Graduates, 2(1).

Shodiqin, A., & Sukestiyarno, Y. L. (2021). Probabilistic Thinking Profile of Mathematics Teacher Candidates in Problem Solving Based on Self-Regulated Learning. European Journal of Educational Research, 10(3), 1199-1213.

Sihotang, S. F., & Zuhri, Z. (2022). The Effect of Statistics and Probability Learning Model Improvement on Student Learning Outcomes. Alifmatika: Journal of Mathematics Education and Learning, 4(1), 65-81.

Sulfiah, S. K., Cholily, Y. M., & Subaidi, A. (2021). Professional Competency: Pre-Service Mathematics Teachers' Understanding toward Probability Concept. Journal of Research and Advances in Mathematics Education, 6(3), 206-220.

Supply, A. S., Wijns, N., Van Dooren, W., & Onghena, P. (2023). It is probably a pattern: does spontaneous focusing on regularities in preschool predict reasoning about randomness four years later? Educational Studies in Mathematics, 112(1), 3-24.

Triliana, T., & Asih, E. C. M. (2019l). Analysis of students’ errors in solving probability based on Newman’s error analysis. In Journal of Physics: Conference Series (Vol. 1211, No. 1, p. 012061). IOP Publishing.

Yusuf, M., Rahim, S. S. A., & Eu, L. K. (2020). Solving Strategies of Probability Word Problems Among College Students. MOJES: Malaysian Online Journal of Educational Sciences, 8(2), 28-35.

Yusuf, M., Rahim, S. S. A., & Eu, L. K. (2021). Obstacles faced by college students in solving probability word problems. Journal of Mathematics Education, 15(1), 83-90.

Yusuf, M., Rahim, S. S. A., & Eu, L. K. (2022). Challenges Faced by College Students in Solving Probability of Event Problems. MOJES: Malaysian Online Journal of Educational Sciences, 10(3), pp.13-19.

Zorzos, M., & Avgerinos, E. (2023). Research on visualization in probability problem solving. Eurasia Journal of Mathematics, Science and Technology Education, 19(4), em2247.