Session Information
99 ERC SES 04 G, Mathematics Education Research
Paper Session
Contribution
Educational assessment studies show that students have difficulties in mathematics, particularly in problem solving. This could be a difficulty in at least one of the four phases (Polya, 1945), namely: understanding the problem, making a plan, carrying out the plan, and looking back. Other studies have also examined the different ways in which students cope with such difficulties. Problem solving is a fundamental skill, both now and in the future. Researchers have long been concerned with its development, and its relevance remains undiminished. The academic study of problem solving emerged in the second half of the 20th century. In the 1970s and 1980s, it focused primarily on elucidating the nature of mathematical problems, students' approaches to solving them, and the salient aspects of problem solving that warrant investigation (Schoenfeld, 1985). More recently, scholarly attention has shifted to educators' perspectives on problem solving and strategies for its improvement (Boaler, 2002; Schoenfeld, 2010, 2014; Stein et al., 2008).
In this study, we have investigated the multifaceted domain of problem solving, with a particular focus on the strategies employed in solving mathematical word problems. Van der Schoot et al. (2009) investigated the factors that differentiate successful and less successful problem solvers in their approach to word problems, highlighting in particular the impact of consistency and markedness. Recognised as a fundamental tool for assessing students' practical application of mathematical knowledge, mathematical word problems are often presented in text form rather than using purely mathematical symbols (Daroczy et al., 2015). In solving these problems, as highlighted by Verschaffel et al. (2000), the solver is required to use mathematical operations on known or inferred numerical values from the problem statement to arrive at a solution. This process, according to Kang et al. (2023), can serve as an indicator of the problem solver's abstract reasoning ability. Recently, the scholarly focus has shifted to exploring educators' perspectives on problem solving and coping strategies to improve it (Boaler, 2002; Schoenfeld, 2010, 2014; Stein et al., 2008). Significantly, not every mathematical word problem is sufficiently challenging for students, highlighting the need for exposure to truly complex tasks that promote mathematical sense making (Marcus & Fey, 2003; NCTM, 1991; van de Walle, 2003). Word problems are a particularly difficult type of problem for mathematics students (Verschaffel et al., 2020). Jacobson (2023) defines dyscalculia as a term for specific learning disabilities that affect a child's ability to do arithmetic and number. The estimated prevalence is 5-7% in primary school children. Mathematics covers a wide range of areas: arithmetic, problem solving, geometry, algebra, probability and statistics. Solving mathematical problems requires students to mobilise a range of skills related to number sense, symbol decoding, memory, visuospatial skills, logic, etc., and may lead to difficulties in any one or a combination of these skills (Karagiannakis et al., 2014). Even if these students have not been diagnosed with a mathematical disorder, they need systematic support to learn mathematics because, according to a study by Nelson and Powel (2017), they are likely to continue to experience mathematical difficulties in the future. This paper aims to construct a model for overcoming mathematics learning difficulties by taking into account the congruent abilities required for problem solving, based on Feuerstein's (2015) mediated learning method and Karagiannakis et al.'s (2014) mathematics learning difficulties.
Method
The Scopus and Web of Science databases were used for the study because of their reputation for providing reliable and comprehensive data, ease of data extraction, and extensive coverage of relevant articles. After automated data screening in both databases, the selected articles were catalogued in Research Information Systems (RIS) format to ensure the compilation of a scientifically rigorous body of evidence. All identified articles were then imported into Zotero. This meticulous curation process was facilitated by assigning codes to the articles and applying exclusion criteria within the Zotero platform. The selected articles were integrated into the MAXQDA program, and the data were coded using an inductive approach. Inductive reasoning, as postulated by Leavy (2017), is often used in qualitative research, where the primary aim is to uncover entirely new and unexplored data, thus promoting the generation of new knowledge rather than reinforcing existing theoretical frameworks. The qualitative codes derived from the data were then analysed within the interpretive paradigm, in line with the principles elucidated by Leavy (2017).
Expected Outcomes
This work is expected to result in a theoretical model that reflects the level of flexibility needed to overcome students' learning difficulties and the potential for teachers to apply this model in schools to improve students' use of problem-solving strategies.
References
1.Boaler, J. (2002). Experiencing school mathematics. In Routledge eBooks. https://doi.org/10.4324/9781410606365 2.Feuerstein, R., Falik, L., & Feuerstein, R. S. (2015). Changing Minds and Brains—The Legacy of Reuven Feuerstein: Higher Thinking and Cognition Through Mediated Learning. Teachers College Press. 3.Karagiannakis, G., Baccaglini-Frank, A., & Papadatos, Y. (2014). Mathematical learning difficulties subtypes classification. Frontiers in Human Neuroscience, 8. https://doi.org/10.3389/fnhum.2014.00057 4.Leavy, P. (2017). Research design: Quantitative, Qualitative, Mixed Methods, Arts-Based, and Community-Based Participatory Research Approaches. Guilford Publications. 5.Schoenfeld, A. H. (2010). How we think. In Routledge eBooks. https://doi.org/10.4324/9780203843000 6.Schoenfeld, A. H. (2014a). Mathematical problem solving. Elsevier. 7.Stein, M. K., Engle, R. A., Smith, M. S., & Hughes, E. K. (2008). Orchestrating Productive Mathematical Discussions: Five practices for helping teachers move beyond show and tell. Mathematical Thinking and Learning, 10(4), 313–340. https://doi.org/10.1080/10986060802229675 8.Van Der Schoot, M., Arkema, A. H. B., Horsley, T., & Van Lieshout, E. (2009). The consistency effect depends on markedness in less successful but not successful problem solvers: An eye movement study in primary school children. Contemporary Educational Psychology, 34(1), 58–66. https://doi.org/10.1016/j.cedpsych.2008.07.002
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