Identifying difficulties in problem solving: Contributions of a pedagogical tool for educators

Authors

  • Sofia Rézio Instituto Superior de Contabilidade e Administração de Lisboa; Centro de Estudos Interdisciplinares em Educação e Desenvolvimento (CeiED) | Portugal https://orcid.org/0000-0002-0687-8231

DOI:

https://doi.org/10.48489/quadrante.41852

Keywords:

mathematical problem solving, mathematical language, difficulties in problem solving, teacher training

Abstract

Numerous education specialists contend that problem-solving constitutes a fundamental mathematical competence that should be cultivated by students from elementary through higher education. The efficacy of problem-solving instruction is influenced, among other factors, by educators’ capacity to critically examine the errors that occur throughout problem-solving processes. Within the context of a training course with educational psychologists and teachers, a pedagogical tool was conceived and implemented to facilitate the identification of students' difficulties in problem-solving. The study sample comprised educators in training, and a qualitative research methodology was employed. The findings underscore several potentialities. According to these educators, the tool enables more targeted interventions, aiding in the determination of whether difficulties stem from deficiencies in language comprehension, an inability to execute calculations, insufficient conceptual understanding, or impediments in decoding mathematical language. Although, applying the model to an entire class was considered challenging, the benefit of focusing on students with greater difficulties was highlighted.

References

Adami, M., & Kiger, A. (2005). The use of triangulation for completeness purposes. Nurse researcher, 12, 19-29. https://doi.org/10.7748/nr2005.04.12.4.19.c5956

CORE (2013). Problem solving in elementary math: Participant handout (Version 1.0). Consortium on Reaching Excellence in Education. https://www.corelearn.com

Davies, R. (2017, 16 august). Teaching math problem solving: 6 research-based approaches that work. Differentiated Teaching. https://www.differentiatedteaching.com/build-math-problem-solving-skills/

Fuchs, L. S., Bucka, N., Clarke, B., Dougherty, B., Jordan, N. C., Karp, K. S., & Woodward, J. (2021). Assisting students struggling with mathematics: Intervention in the elementary grades (Practice Guide). National Center for Education Evaluation and Regional Assistance, Institute of Education Sciences, U.S. Department of Education. https://ies.ed.gov/ncee/wwc/PracticeGuide/26

Given, L. M. (2008). The SAGE encyclopedia of qualitative research methods (2 vols.). SAGE Publications.

Hadi, S., Herman, T., & Hasanah, A. (2018). Students' difficulties in solving mathematical problems. International Journal of Educational Science and Research, 8(1), 55-63. https://scispace.com/pdf/students-difficulties-in-solving-mathematical-problems-50m6iro8rx.pdf

Irenika, I., Susanti, E., Hiltrimartin, C., Hapizah, H., & Meryansumayeka, M. (2019). Design of problem-solving questions for measuring student’s mathematical thinking type representation. Journal of Physics: Conference Series, 1318, 012102. https://doi.org/10.1088/1742-6596/1318/1/012102

Kirkland, P., & McNeil, M. (2021). Question Design Affects Students’ Sense-Making on Mathematics Word Problems. Cognitive Science, 45(4), 1-29. https://doi.org/10.1111/cogs.12960

Kojo, A., Laine, A., & Näveri, L. (2018). How did you solve it? – Teachers’ approaches to guiding mathematics problem solving. LUMAT: International Journal on Math, Science and Technology Education, 6(1), 22–40. https://doi.org/10.31129/LUMAT.6.1.294

Kusumadewi, C. A., & Retnawati, H. (2020). Identification of elementary school students’ difficulties in mathematical problem-solving. Journal of Physics: Conference Series, 1511(1), 12-31. https://doi.org/10.1088/1742-6596/1511/1/012031

Mahmud, M., Yunus, A., Ayub, & A. F. M., Sulaiman, T. (2020). Enhancing Mathematical Language through Oral Questioning in Primary Schools. International journal of Learning, Teaching and Educational Research, 19(5). https://doi.org/10.26803/ijlter.19.5.24

Martaningsih, S. T., Maryani, I., Prasetya, D. S., Purwanti, S., Sayekti, I. C., Abdul Aziz, N. A., & Siwayanan, P. (2022). STEM Problem-Based Learning Module: a solution to overcome elementary students’ poor problem-solving skills. Pegem Journal of Education and Instruction, 12(4), 340–348. https://www.pegegog.net/index.php/pegegog/article/view/1856

Marzano, R. (2004). Building background knowledge for academic achievement. Association for Supervision and Curriculum Development.

Ministério da Educação. (2021, August 19). Despacho n.º 8209/2021. Diário da República, 2.ª série, n.º 161. https://diariodarepublica.pt/dr/detalhe/despacho/8209-2021-169831748

Ministério da Educação e Ciência (2013). Programa Nacional de Matemática do Ensino Básico. Programa e Metas Curriculares Matemática Ensino Básico. https://www.dge.mec.pt/sites/default/files/Basico/Metas/Matematica/programa_matematica_basico.pdf

Nasrun, Prahmana, R., & Akib, I. (2023). The Students’ Representative Processes in Solving Mathematical Word Problems. Knowledge, 3, 70-79. https://doi.org/10.3390/knowledge3010006

Nurharyanto, D., & Retnawati, H. (2020). The difficulties of the elementary school students in solving the mathematical narrative test items. Jurnal Prima Edukasia, 8(1), 29-39. https://doi.org/10.21831/jpe.v8i1.29969

Nurkaeti, N. (2018). Polya’s strategy: an analysis of mathematical problem solving difficulty in 5th grade elementary school. EduHumaniora|Journal of Basic Education Cibiru Campus, 10(2), 140. https://doi.org/10.17509/eh.v10i2.10868

Palhares, P. (2004). Elementos de matemática para professores do ensino básico. Lidel.

Pólya, G. (1945). How to Solve It: A New Aspect of Mathematical Method. Princeton University Press.

Pólya, G. (1962). Mathematical Discovery: On Understanding, Learning, and Teaching Problem Solving (Vol. 1). Wiley.

Powell, S., Bos, S. & Lin, X. (2021). The assessment of mathematics vocabulary in the elementary and middle school grades. In A. Fritz, E. Gürsoy, & M. Herzog (Eds.), Diversity Dimensions in Mathematics and Language Learning: Perspectives on Culture, Education and Multilingualism (pp. 313-330). De Gruyter. https://doi.org/10.1515/9783110661941-016

Proença, M. (2022). Habilidades matemáticas na resolução de problemas: Análise da compreensão de futuros professores. Bolema, 36(74), 1135–1157. https://doi.org/10.1590/1980-4415v36n74a09

Proença, M., Maia-Afonso, É., Mendes, L., & Travassos, W. (2022). Dificuldades de alunos na resolução de problemas: Análise a partir de propostas de ensino em dissertações. Bolema, 36(72), 262–285. https://doi.org/10.1590/1980-4415v36n72a12

Salimpoor, V. (2018, 7 november). The role of working memory in math processing. Cignition. https://www.cignition.com/blog/the-role-of-working-memory-in-math-processing

Sulisyani, D., Subekti, E. E., Wardana M. S. (2021). Students' Learning Difficulties Review from Mathematics Problem-Solving Ability in Third-Grade Elementary School. Indonesian Journal of Educational Research and Review 4(2), 345-351.http://dx.doi.org/10.23887/ijerr.v4i2.30310

Suseelan, M., Chew, C.M., & Chin, H. (2022). Research on mathematics problem solving in elementary education conducted from 1969 to 2021: A bibliometric review. International Journal of Education in Mathematics, Science, and Technology (IJEMST), 10(4), 1003-1029. https://doi.org/10.46328/ijemst.2198

Yeni, E. M., & Wahyudin, T. H. (2020). Difficulty Analysis of Elementary School Students in Mathematical Problem Solving in Solutions. International Journal of Scientific & Technology Research, 9, 44-47. https://api.semanticscholar.org/CorpusID:216466826

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Published

2026-06-30

How to Cite

Rézio, S. (2026). Identifying difficulties in problem solving: Contributions of a pedagogical tool for educators. Quadrante, 35(1), 126–153. https://doi.org/10.48489/quadrante.41852

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