Session Information
24 SES 16 A, Problem-Solving and Posing in Mathematics Education
Paper Session
Contribution
The importance of problem-solving in mathematics education has been emphasized in numerous studies (Olivares, Lupiáñez & Segovia, 2021; Schoenfeld, 1985; Sidenvall, Granberg, Lithner & Palmberg, 2024). While problem-solving is an indispensable tool for mathematics instruction, it is also regarded as a fundamental goal of lifelong learning. Among the various types of mathematical content, word problems are among the most challenging for students (Verschaffel, Greer & De Corte, 2000). Many students struggle even with mathematical word problems they consider easy. According to the PISA 2022 results, which heavily assess word problems, an average of 31% of students across OECD countries performed below level 2 in mathematics, placing them in the "low performer" category (OECD, 2023). In the context of the European Education Area, the EU has set a target based on PISA results: by 2030, the proportion of 15-year-olds failing to reach the minimum proficiency level in mathematics should be below 15%. However, recent results indicate that this goal is becoming increasingly difficult to achieve. The EU average for underperformance in mathematics was 22.5% in PISA 2018, but it has now risen to 29% in PISA 2022 (Montanari, 2024; OECD, 2023).
As complex problem-solving exercises, word problems require not only cognitive strategies (heuristics) but also metacognitive (or self-regulatory) strategies (Verschaffel, Schukajlow, Star, & Van Dooren, 2020). Metacognition helps students understand problems, select appropriate problem-solving paths, and use their knowledge, cognitive capacity, and skills more effectively (Aşık & Erktin, 2019; Wang et al., 2021). Successful students plan, monitor, evaluate, and regulate their problem-solving processes more efficiently and consistently than weaker students (Aşık, 2015; Van de Walle, 2003). Being aware of these steps is a hallmark of successful problem solvers and indicates the presence of metacognitive skills (He, Chen, Lin, & Su, 2024). In this regard, it is crucial to enhance both students' mathematics achievement and their metacognitive skills, which are essential for lifelong learning.
The use of online learning platforms and technology in education has evolved from being a facilitator to an integral part of modern education (Drijvers & Sinclair, 2024). The recent pandemic and the increasing prevalence of AI-powered tools have further accelerated the development of applications catering to these needs (Engelbrecht & Borba, 2024).
In response to these needs, the Metatips (Metacognitive Training in Problem Solving) online learning platform was developed over three years to enhance primary and middle school students' mathematical achievement and metacognitive skills. Metatips is designed for students aged 10-16 to assess, evaluate, and improve their mathematical and metacognitive abilities. One of the platform's key features is the virtual learning assistants (agents) that support students throughout their learning process. When solving curriculum-aligned mathematical word problems on Metatips, students can seek assistance from five different virtual learning assistants, such as the Narrator, Planner, and Monitor, if they struggle or need help. On Metatips platform, if students answer a question incorrectly without seeking help from a learning assistant, they must consult at least one assistant before attempting to answer the question again. These assistants support students by asking questions about the problem, providing relevant topical information, or offering solution hints. The platform presents students with four-option multiple-choice problems, while the learning assistants can ask multiple-choice, multiple-select, true/false, and short open-ended questions requiring numerical responses (e.g., "60"). All student interactions on Metatips are recorded as data and presented in detailed reports.
Method
This study analyzes students' responses to mathematical problems on the Metatips Online Learning Platform, their frequency of using learning assistants, and their correct/incorrect response rates. The data was collected from the Metatips platform and analyzed primarily through descriptive statistics. The study follows a descriptive survey model, a quantitative research design aimed at depicting the current situation by collecting data from a specific group at a given time. A total of 5,625 responses to different mathematics questions from 375 students aged 11-13 were examined. Among these responses, 68% (n = 3,827) were correct, while 32% (n = 1,798) were incorrect. That means, despite students getting help from at least one learning assistant, 32% of the answers were incorrect. In 22% (n = 825) of the correct responses, students solved the problems without any assistance, while in 78% (n = 3,002), they received support from at least one learning assistant. The Metatips learning assistants provide support specific to the question at hand by asking related questions, offering explanations, or giving hints. The data reveal that students sought assistance from learning assistants 6,169 times. In nearly half of these cases (n = 3,090), the Metatips system asked questions to the users; while in the other half (n = 3,079), students received direct guidance and content information. Of the questions posed by the learning assistants, 59% were answered correctly, while 41% were answered incorrectly. This suggests that students struggle significantly with understanding, planning, performing mathematical operations, and applying strategies correctly. When analyzing responses to questions specifically aimed at problem comprehension, a total of 1,099 questions were asked. Of these, 48% were answered correctly, while 52% were incorrect. These descriptive statistics highlight the difficulties students face in understanding mathematical word problems. During the presentation, additional findings primarily based on descriptive statistics regarding students' metacognitive awareness and skills in comprehending and solving mathematical word problems will be shared and discussed.
Expected Outcomes
The findings of this study suggest that online learning platforms like Metatips can serve as valuable support mechanisms for improving students' mathematical success by guiding them through problem-solving processes. For mathematical tasks requiring cognitive and metacognitive skills, such as word problems, students who receive support from learning assistants show higher accuracy rates. However, the findings also indicate that students should not solely rely on external assistance but should also receive guidance in developing metacognitive strategies such as planning, monitoring, and evaluating their problem-solving processes. The support provided by learning assistants can help students adopt a more conscious and systematic approach to problem-solving. Online learning platforms can offer teachers detailed analyses of students' difficulties in problem-solving, enabling the design of tailored interventions to enhance metacognitive skills. By tracking the types of problems students struggle with and the learning strategies they frequently use, teachers can plan their instruction in a more data-driven manner. Additionally, supplementary instructional materials and teacher-guided activities aimed at fostering metacognitive skills can strengthen students' independent problem-solving abilities (Sidenvall et al., 2024). These findings suggest that online learning platforms should not be viewed as alternatives to traditional teaching methods but rather as complementary tools. When virtual learning assistants support students' individual learning processes and are combined with teacher-led classroom guidance, they can contribute to the development of a holistic learning ecosystem that fosters metacognitive skills. Therefore, the design of digital learning tools should emphasize features that not only lead students to the correct answer but also encourage them to reflect on their thinking processes.
References
Aşık, G. (2015). Üstbiliş odaklı problem çözme destek programı tasarım çalışması [A design study on metacognitive training in problem solving], [Unpublished doctoral dissertation], Marmara University, Turkey. Aşık, G., & Erktin, E. (2019). Metacognitive experiences: Mediating the relationship between metacognitive knowledge and problem solving. Education and Science, 44(197), 85-103. Drijvers, P., & Sinclair, N. (2024). The role of digital technologies in mathematics education: Purposes and perspectives. ZDM–Mathematics Education, 56(2), 239-248. Engelbrecht, J., & Borba, M. C. (2024). Recent developments in using digital technology in mathematics education. ZDM–Mathematics Education, 56(2), 281-292. He, G., Chen, S., Lin, H., & Su, A. (2024). The association between initial metacognition and subsequent academic achievement: a meta-analysis of longitudinal studies. Educational Psychology Review, 36(3), 81. Montanari, M. (2024, March 7). PISA 2022 and the EU: three thought-provoking trends. European Commission: European School Education Platform. https://school-education.ec.europa.eu/en/discover/expert-views/pisa-2022-and-eu-three-thought-provoking-trends OECD (2023), PISA 2022 Results (Volume I): The State of Learning and Equity in Education, PISA, OECD Publishing, Paris, https://doi.org/10.1787/53f23881-en Olivares, D., Lupiáñez, J. L., & Segovia, I. (2021). Roles and characteristics of problem solving in the mathematics curriculum: a review. International Journal of Mathematical Education in Science and Technology, 52(7), 1079-1096. Schoenfeld, A. H. (1985). Mathematical problem solving. New York: Academic Press. Sidenvall, J., Granberg, C., Lithner, J., & Palmberg, B. (2024). Supporting teachers in supporting students’ mathematical problem solving. International Journal of Mathematical Education in Science and Technology, 55(10), 2389-2409. Verschaffel, L., Greer, B., & De Corte, E. (2000). Making sense of word problems. Lisse, The Netherlands: Swets & Zeitlinger Publishers. Verschaffel, L., Schukajlow, S., Star, J., & Van Dooren, W. (2020). Word problems in mathematics education: A survey. ZDM, 52, 1-16. Wang, M. T., Binning, K. R., Del Toro, J., Qin, X., & Zepeda, C. D. (2021). Skill, thrill, and will: The role of metacognition, interest, and self‐control in predicting student engagement in mathematics learning over time. Child Development, 92(4), 1369-1387.
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