Enablers and obstacles in teaching and learning of mathematics: A systematic review in LUMAT journal

Fatma Kayan Fadlelmula

doi:10.31129/LUMAT.10.2.1627

Authors

Fatma Kayan Fadlelmula Core Curriculum Program, Deanship of General Studies, Qatar University, Qatar https://orcid.org/0000-0001-9309-9756

DOI:

https://doi.org/10.31129/LUMAT.10.2.1627

Keywords:

mathematics education, mathematics learning, mathematics teaching, systematic review, PRISMA

Abstract

This paper presents results of a systematic review of papers published at the LUMAT journal on the current issues positively and negatively affecting teaching and learning in mathematics, in concurrence with the Preferred Reporting Items for Systematic Reviews and Meta-Analyses (PRISMA) guidelines. The analysis also offers insight into the most studied topics in mathematics education research, including key demographic and methodological characteristics such as year of publication, participants, education level, research methodologies, and research focus. Data was gathered from the studies published in the LUMAT: International Journal on Math, Science and Technology Education, starting from its first volume in 2013. So far, 225 articles were published in this journal, with 133 studies written in English and 51 studies related to mathematics. Although earlier studies support the notion that mathematics education is mostly traditional, this review suggests current research has thorough and positive outcomes, such that mathematics educators are likely to implement non-traditional approaches, encouraging student engagement, peer collaboration, and mathematical discourse. Certainly, in such learning environments, students tend to feel more motivated and less anxious about learning mathematics. They may also be more active and responsible in their learning, collaborate with peers, and get into mathematical discussions. Yet, there are also a number of difficulties and obstacles highlighted both in teaching and learning of mathematics. The findings might inspire several instructional implications for mathematics educators, curriculum developers, and researchers. Recommendations are given to add into what the existing literature claims and offer greater empirical evidence to support the verdicts.

References

Studies included in the systematic review are indicated by an asterisk (*).

*Alfaro Viquez, H., & Joutsenlahti, J. (2020). Promoting learning with understanding: Introducing languaging exercises in calculus course for engineering students at the university level. LUMAT: International Journal on Math, Science and Technology Education, 8(1), 229–251. https://doi.org/10.31129/LUMAT.8.1.1412

*Ambrus, A., & Barczi-Veres, K. (2015). Using open problems and cooperative methods in mathematics education. LUMAT: International Journal on Math, Science and Technology Education, 3(1), 3–18. https://doi.org/10.31129/lumat.v3i1.1048

Boaler, J. (2015). Parents’ Beliefs about Math Change Their Children’s Achievement. Retrieved from https://www.youcubed.org/think-it-up/parents-beliefs-math-change-childrens-achievement/

Boud, D., Keogh, R., & Walker, D. (1985). Reflection: Turning experience into learning. Kogan Page.

Bransford, J. D., Brown, A. L., & Cocking, R. R. (2002). How People Learn: Brain, Mind, Experience, and School. The National Academies Press.

Brenneman, K., Lange, A., & Nayfeld, I. (2019). Integrating STEM into pre-school education; designing a professional development model in diverse settings. Early Childhood Education Journal, 47(1), 15–28. https://doi.org/10.1007/s10643-018-0912-z

*Cabello, V. M., Martinez, M. L., Armijo, S., & Maldonado, L. (2021). Promoting STEAM learning in the early years: “Pequeños Científicos” Program. LUMAT: International Journal on Math, Science and Technology Education, 9(2), 33–62. https://doi.org/10.31129/LUMAT.9.2.1401

*Cardino Jr., J. M., & Ortega-Dela Cruz, R. A. (2020). Understanding of learning styles and teaching strategies towards improving the teaching and learning of mathematics. LUMAT: International Journal on Math, Science and Technology Education, 8(1), 19–43. https://doi.org/10.31129/LUMAT.8.1.1348

*Chapman, O. (2015). Mathematics teachers’ knowledge for teaching problem solving. LUMAT: International Journal on Math, Science and Technology Education, 3(1), 19–36. https://doi.org/10.31129/lumat.v3i1.1049

Chiwiye, T. (2013). Assessment of mathematics and science subjects in Zimbabwe: ZIMSEC Perspective. ZIMSEC.

Çiftçi, A, Topçu, M.S., & Foulk, J.A (2020). Pre-service early childhood teachers' views on STEM education and their STEM teaching practices. Research in Science and Technological Education. https://doi.org/10.1080/02635143.2020.1784125

Drake, K. N., & Long, D. (2009). Rebecca’s in the dark: A comparative study of problem-based learning and direct instruction/experiential learning in two fourth grade classrooms. Journal of Elementary Science Education, 21(1), 1–16. https://doi.org/10.1007/BF03174712

*Ekstam, U., Linnanmäki, K., & Aunio, P. (2017). The Impact of Teacher Characteristics on Educational Differentiation Practices in Lower Secondary Mathematics Instruction. LUMAT: International Journal on Math, Science and Technology Education, 5(1), 41–60. https://doi.org/10.31129/LUMAT.5.1.253

Fritz, A., Haase, V. G., & Rasanen, P. (2019). International handbook of mathematical learning difficulties. Springer.

*Fülöp, E. (2015). Teaching problem-solving strategies in mathematics. LUMAT: International Journal on Math, Science and Technology Education, 3(1), 37–54. https://doi.org/10.31129/lumat.v3i1.1050

Schoenfeld, A. H. (1985). Mathematical problem solving. Academic Press.

*Sterner, H. E. K. (2019). Teachers as actors in an educational design research: What is behind the generalized formula?. LUMAT: International Journal on Math, Science and Technology Education, 7(3), 6–27. https://doi.org/10.31129/LUMAT.7.3.403

Sun, K. L. (2018). The role of mathematics teaching in fostering student growth mindset. Journal for Research in Mathematics Education, 49(3), 330–355. https://doi.org/10.5951/jresematheduc.49.3.0330

*Sunzuma, G., Chando, C., Gwizangwe, I., Zezekwa, N., & Zinyeka, G. (2020). In-service Zimbabwean teachers’ views on the utility value of diagrams in the teaching and learning of geometry. LUMAT: International Journal on Math, Science and Technology Education, 8(1), 1–18. https://doi.org/10.31129/LUMAT.8.1.1316

*Suriakumaran, N., Hannula, M. S., & Vollstedt, M. (2019). Investigation of Finnish and German 9th grade students’ personal meaning with relation to mathematics. LUMAT: International Journal on Math, Science and Technology Education, 7(2), 110–132. https://doi.org/10.31129/LUMAT.7.2.411

*Tomperi, P., Ryzhkova, I., Shestova, Y., Lyash, O., Lazareva, I., Lyash, A., Kvivesen, M., Manshadi, S., & Uteng, S. (2020). The three-factor model: A study of common features in students’ attitudes towards studying and learning science and mathematics in the three countries of the North Calotte region. LUMAT: International Journal on Math, Science and Technology Education, 8(1), 89–106. https://doi.org/10.31129/LUMAT.8.1.1369

*Tossavainen, T., Gröhn, J., Heikkinen, L., Kaasinen, A., & Viholainen, A. (2020). University mathematics students’ study habits and use of learning materials. LUMAT: International Journal on Math, Science and Technology Education, 8(1), 252–270. https://doi.org/10.31129/LUMAT.8.1.1317

*Viholainen, A., Tossavainen, T., Viitala, H., & Johansson, M. (2019). University mathematics students’ self-efficacy beliefs about proof and proving. LUMAT: International Journal on Math, Science and Technology Education, 7(1), 148–164. https://doi.org/10.31129/LUMAT.7.1.406

*Viitala, H. (2015). Two Finnish girls and mathematics: Similar achievement level, same core curriculum, different competences. LUMAT: International Journal on Math, Science and Technology Education, 3(1), 137–150. https://doi.org/10.31129/lumat.v3i1.1056

*Viro, E., & Joutsenlahti, J. (2020). Learning mathematics by project work in secondary school. LUMAT: International Journal on Math, Science and Technology Education, 8(1), 107–132. https://doi.org/10.31129/LUMAT.8.1.1372

*Wadanambi, G. M., & Leung, F. K. S. (2019). Exploring the influence of pre-service mathematics teachers’ professed beliefs on their practices in the Sri Lankan context. LUMAT: International Journal on Math, Science and Technology Education, 7(2), 133–149. https://doi.org/10.31129/LUMAT.7.2.405

Walker, D.A., Smith, M.C. & Hamidova, N.I. (2013). A structural analysis of the attitudes toward science scale: Students' attitudes and beliefs about science as a multi-dimensional composition. Multiple Linear Regression Viewpoints, 39(2), 38–48.

*White, D., & Delaney, S. (2021). Full STEAM ahead, but who has the map? – A PRISMA systematic review on the incorporation of interdisciplinary learning into schools. LUMAT: International Journal on Math, Science and Technology Education, 9(2), 9–32. https://doi.org/10.31129/LUMAT.9.2.1387

Wirkala, C., & Kuhn, D. (2011). Problem-based learning in K–12 education: Is it effective and how does it achieve its effects? American Educational Research Journal, 48(5), 1157–86. https://doi.org/10.3102/0002831211419491

Woodcock, S., & Reupert, A.E. (2016). Inclusion, classroom management and teacher efficacy in an Australian context. In S. Garvis, & D. Pendergast (Eds.), Asia-Pacific Perspectives on Teacher Self-Efficacy (pp. 87–102). Sense Publishers.

*Yeşilyurt- Çetin, A., & Dikici, R. (2021). Organizing the mathematical proof process with the help of basic components in teaching proof: Abstract algebra example. LUMAT: International Journal on Math, Science and Technology Education, 9(1), 235–255. https://doi.org/10.31129/LUMAT.9.1.1497

García-Holgado, A., Díaz, A. C., & García-Peñalvo, F. J. (2019, October). Engaging women into STEM in Latin America: W-STEM project. In Proceedings of the Seventh International Conference on Technological Ecosystems for Enhancing Multiculturality (pp. 232-239). https://doi.org/10.1145/3362789.3362902

*Gorgorió, N., Albarracín, L., Laine, A., & Llinares, S. (2021). Primary education degree programs in Alicante, Barcelona and Helsinki: Could the differences in the mathematical knowledge of incoming students be explained by the access criteria?. LUMAT: International Journal on Math, Science and Technology Education, 9(1), 174–207. https://doi.org/10.31129/LUMAT.9.1.1468

Gough, D., Oliver, S., & Thomas, J. (2012). An introduction to systematic reviews. SAGE.

*Grundén, H. (2020). Planning in mathematics teaching – a varied, emotional process influenced by others. LUMAT: International Journal on Math, Science and Technology Education, 8(1), 67–88. https://doi.org/10.31129/LUMAT.8.1.1326

*Haataja, E., Laine, A., & Hannula, M. (2020). Educators’ perceptions of mathematically gifted students and a socially supportive learning environment – A case study of a Finnish upper secondary school. LUMAT: International Journal on Math, Science and Technology Education, 8(1), 44–66. https://doi.org/10.31129/LUMAT.8.1.1368

*Haataja, E., Toivanen, M., Laine, A., & Hannula, M. S. (2019). Teacher-student eye contact during scaffolding collaborative mathematical problem-solving. LUMAT: International Journal on Math, Science and Technology Education, 7(2), 9–26. https://doi.org/10.31129/LUMAT.7.2.350

*Hannula, J. (2019). Characteristics of teacher knowledge produced by pre-service mathematics teachers: the case of open-ended problem-based learning. LUMAT: International Journal on Math, Science and Technology Education, 7(3), 55–83. https://doi.org/10.31129/LUMAT.7.3.391

*Hatisaru, V. (2019). Lower secondary students’ views about mathematicians depicted as mathematics teachers. LUMAT: International Journal on Math, Science and Technology Education, 7(2), 27–49. https://doi.org/10.31129/LUMAT.7.2.355

Hazari, Z., Sonnert, G., Sadler, P. M., & Shanahan, M. (2010). Connecting high school physics experiences, outcome expectations, physics Identity, and physics career choicer: A gender study. Journal of Research in Science Teaching, 47(8), 978–1003. https://doi.org/10.1002/tea.20363

*Heikkinen, H., Hästö, P., Kangas, V., & Leinonen, M. (2015). Promoting Exploratory Teaching in Mathematics: A Design Experiment on a CPD course for Teachers. LUMAT: International Journal on Math, Science and Technology Education, 3(6), 905–924. https://doi.org/10.31129/lumat.v3i6.1007

Higgins, J.P.T., Thomas, J., Chandler, J., Cumpston, M., Li, T., Page, M.J.& Welch, V.A. (2021). Cochrane Handbook for Systematic Reviews of Interventions (version 6.2). Cochrane. Retrieved from www.training.cochrane.org/handbook

Holzberger, D., Philipp, A., & Kunter, M. (2013). How teachers’ self-efficacy is related to instructional quality: A longitudinal analysis. Journal of Educational Psychology, 105(3), 774–786. https://doi.org/10.1037/a0032198

*Kaarakka, T., Helkala, K., Valmari, A., & Joutsenlahti, M. (2019). Pedagogical experiments with MathCheck in university teaching. LUMAT: International Journal on Math, Science and Technology Education, 7(3), 84–112. https://doi.org/10.31129/LUMAT.7.3.428

King-Sears, M. & Baker, P. H. (2014). Comparison of teacher motivation for mathematics and special educators in middle schools that have and have not achieved AYP. ISRN Education, 24, 1–12. https://doi.org/10.1155/2014/790179

*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

*Koponen, M. (2015). Teacher’s instruction in the reflection phase of the problem solving process. LUMAT: International Journal on Math, Science and Technology Education, 3(1), 55–68. https://doi.org/10.31129/lumat.v3i1.1051

*Kuzle, A. (2015a). Problem solving as an instructional method: The use of open problems in technology problem solving instruction. LUMAT: International Journal on Math, Science and Technology Education, 3(1), 69-86. https://doi.org/10.31129/lumat.v3i1.1052

*Kuzle, A. (2015b). Nature of metacognition in a dynamic geometry environment. LUMAT: International Journal on Math, Science and Technology Education, 3(5), 627–646. https://doi.org/10.31129/lumat.v3i5.1010

*Kuzle, A. (2019). Design and evaluation of practice-oriented materials fostering students’ development of problem-solving competence. LUMAT: International Journal on Math, Science and Technology Education, 7(3), 28–54. https://doi.org/10.31129/LUMAT.7.3.401

*Laine, A., Ahtee, M., Näveri, L., Pehkonen, E., & Hannula, M. S. (2018). Teachers’ influence on the quality of pupils’ written explanations – Third-graders solving a simplified arithmagon task during a mathematics lesson. LUMAT: International Journal on Math, Science and Technology Education, 6(1), 87–104. https://doi.org/10.31129/LUMAT.6.1.255

*Laine, A., Ahtee, M., Näveri, L., Pehkonen, E., Koivisto, P. P., & Tuohilampi, L. (2015). Collective emotional atmosphere in mathematics lesson based on finnish fifth graders’ drawings. LUMAT: International Journal on Math, Science and Technology Education, 3(1), 87–100. https://doi.org/10.31129/lumat.v3i1.1053

*Lake, E. (2019). ‘Playing it safe’ or ‘throwing caution to the wind’: Risk-taking and emotions in a mathematics classroom. LUMAT: International Journal on Math, Science and Technology Education, 7(2), 50–64. https://doi.org/10.31129/LUMAT.7.2.335

Larmer, J., Mergendoller, J., & Boss, S. (2015). Setting the standard for project-based learning: A proven approach to rigorous classroom instruction. ASCD.

Lawson, C. A., Cook, M., Dorn, J., & Pariso, B. (2018). A STEAM-Focused Program to Facilitate Teacher Engagement Before, During, and After a Fieldtrip Visit to a Children's Museum. Journal of Museum Education, 43(3), 236–244. https://doi.org/10.1080/10598650.2018.1474421

*Lehtonen, D., Jyrkiäinen, A., & Joutsenlahti, J. (2019). A systematic review of educational design research in Finnish doctoral dissertations on mathematics, science, and technology education. LUMAT: International Journal on Math, Science and Technology Education, 7(3), 140–165. https://doi.org/10.31129/LUMAT.7.3.399

Lester, F. K., & Kehle, P. E. (2003). From problem solving to modeling: The evolution of thinking about research on complex mathematical activity. In R. A. Lesh & H.M. doer (eds.), Beyond constructivism: Models and modeling perspectives on mathematics problem solving, learning, and teaching (pp. 501–518). Erlbaum.

Linares-Espinós, E., Hernández, V., Domínguez-Escrig, J. L., Fernández-Pello, S., Hevia, V., Mayor, J., & Ribal, M. J. (2018). Methodology of a systematic review. Actas Urológicas Españolas (English Edition), 42(8), 499-506. https://doi.org/10.1016/j.acuro.2018.01.010

*Luoto, J. (2020). Scrutinizing two Finnish teachers’ instructional rationales and perceived tensions in enacting student participation in mathematical discourse. LUMAT: International Journal on Math, Science and Technology Education, 8(1), 133–161. https://doi.org/10.31129/LUMAT.8.1.1329

*Manderfeld, K. A. M., & Siller, H. S. (2019). Pre-Service mathematics teachers’ beliefs regarding topics of mathematics education. LUMAT: International Journal on Math, Science and Technology Education, 7(2), 65–79. https://doi.org/10.31129/LUMAT.7.2.332

Markham, T., Lamer, J., & Ravitz, J. (2006). Project-based learning handbook. Buck Institute for Education.

*Marotto, C. C. F., & Milner-Bolotin, M. (2018). Parental engagement in children’s STEM education. Part II: Parental attitudes and motivation. LUMAT: International Journal on Math, Science and Technology Education, 6(1), 60–86. https://doi.org/10.31129/LUMAT.6.1.293

*Mason, J. (2015). On being stuck on a mathematical problem: What does it mean to have something come-to-mind?. LUMAT: International Journal on Math, Science and Technology Education, 3(1), 101–121. https://doi.org/10.31129/lumat.v3i1.1054

Mayer, R. E., & Wittrock, R. C. (2006). Problem solving. In P. A. Alexander & P. H. Winne (Eds.), Handbook of educational psychology, (pp. 287–304). Erlbaum.

*Meier, A., Hannula, M. S., & Toivanen, M. (2018). Mathematics and outdoor photography experience – exploration of an approach to mathematical education, based on the theory of Dewey’s aesthetics. LUMAT: International Journal on Math, Science and Technology Education, 6(2), 146–166. https://doi.org/10.31129/LUMAT.6.2.317

*Milner-Bolotin, M., & Marotto, C. C. F. (2018). Parental engagement in children’s STEM education. Part I: Meta-analysis of the literature. LUMAT: International Journal on Math, Science and Technology Education, 6(1), 41–59. https://doi.org/10.31129/LUMAT.6.1.292

*Milner-Bolotin, M., Fisher, H., & MacDonald, A. (2013). Modeling Active Engagement Pedagogy through Classroom Response Systems in a Physics Teacher Education Course. LUMAT: International Journal on Math, Science and Technology Education, 1(5), 523–542. https://doi.org/10.31129/lumat.v1i5.1088

Milner-Bolotin, M. (2012). Increasing interactivity and authenticity of chemistry instruction through data acquisition systems and other technologies. Journal of Chemical Education, 89(4), 477–481. https://doi.org/10.1021/ed1008443

*Moate, J., Kuntze, S., & Chan, M. C. E. (2021). Student participation in peer interaction – Use of material resources as a key consideration in an open-ended problem-solving mathematics task. LUMAT: International Journal on Math, Science and Technology Education, 9(1), 29–55. https://doi.org/10.31129/LUMAT.9.1.1470

*Mohamed, R., Ghazali, M., & Samsudin, M. A. (2021). A systematic review on teaching fraction for understanding through representation on Web of Science database using PRISMA. LUMAT: International Journal on Math, Science and Technology Education, 9(1), 100–125. https://doi.org/10.31129/LUMAT.9.1.1449

Moher, D., Liberati, A., Tetzlaff, J., & Altman, D.G. (2009). Preferred Reporting Items for Systematic Reviews and Meta-Analyses: The PRISMA Statement. PLOS Medicine, 6(7): e1000097. https://doi.org/10.1371/journal.pmed.1000097

Møller, A. M. & Myles, P. S. (2016).What makes a good systematic review and meta-analysis?, British Journal of Anesthesia, 117(4), 428–430. https://doi.org/10.1093/bja/aew264

Monkeviciene, O., Autukeviciene, B., Kaminskiene, L., & Monkevicius, J. (2020). Impact of innovative STEAM education practices on teacher professional development and 3-6 year old children's competence development. Journal of Social Studies Education Research, 11(4), 1–27.

*Mononen, R., & Aunio, P. (2013). Early Mathematical Performance in Finnish Kindergarten and Grade One. LUMAT: International Journal on Math, Science and Technology Education, 1(3), 245–261. https://doi.org/10.31129/lumat.v1i3.1104

*Namsone, D., Čakāne, L., & France, I. (2015). How science teachers learn to reflect by analyzing jointly observed lessons. LUMAT: International Journal on Math, Science and Technology Education, 3(2), 213–222. https://doi.org/10.31129/lumat.v3i2.1045

*Nyman, M., & Sumpter, L. (2019). The issue of ‘proudliness’: Primary students’ motivation towards mathematics. LUMAT: International Journal on Math, Science and Technology Education, 7(2), 80–96. https://doi.org/10.31129/LUMAT.7.2.331

Op’t Eynde, P., De Corte, E., & Verschaffel, L. (2006). “Accepting Emotional Complexity”: A Socio-Constructivist Perspective on the Role of Emotions in the Mathematics Classroom. Didactical Studies in Mathematics, 63(2), 193–207. https://doi.org/10.1007/s10649-006-9034–4

Pehkonen, E. (2001). How Do We Understand Problem and Related Concepts? In E. Pehkonen (Ed.), Problem Solving Around the World. Proceedings of the Topic Study Group 11 (Problem Solving in mathematics Education) at the ICME-9 meeting August 2000 in Japan (pp. 11–20). Turun yliopisto.

Polya, G. (1962). Mathematical discovery: On understanding, learning, and teaching problem solving. John Wiley & Sons.

*Pörn, R., Hemmi, K., & Kallio-Kujala, P. (2021). Inspiring or confusing – a study of Finnish 1–6 teachers’ relation to teaching programming. LUMAT: International Journal on Math, Science and Technology Education, 9(1), 366–396. https://doi.org/10.31129/LUMAT.9.1.1355

*Portaankorva-Koivisto, P., & Grevholm, B. (2019). Prospective mathematics teachers’ self-referential metaphors as indicators of the emerging professional identity. LUMAT: International Journal on Math, Science and Technology Education, 7(2), 97–109. https://doi.org/10.31129/LUMAT.7.2.343

*Rossi, M. (2015). Mathematics can be meaningful, easy and fun. LUMAT: International Journal on Math, Science and Technology Education, 3(7), 984–991. https://doi.org/10.31129/lumat.v3i7.981

*Rott, B. (2015). Rethinking heuristics – characterizations and vignettes. LUMAT: International Journal on Math, Science and Technology Education, 3(1), 122–126. https://doi.org/10.31129/lumat.v3i1.1055