Session Information
24 SES 09 A, Exploring Perspectives and Approaches in Mathematics Education: From Students to Pre-service Teachers
Paper Session
Contribution
Problem-solving has been a part of school mathematics for a long time (Stanic & Kilpatrick, 1988), but problem-posing research (Cai & Hwang, 2002; Kilpatrick, 1987; Silver, 1994; Silver & Cai, 2005) is fairly new. Since educational research is done to help students learn better, research on problem-posing is no different. Researchers and curricula have mentioned how important it is for elementary school students to be able to pose mathematical problems. Researchers have suggested that problem-posing activities are good for students' creativity (Silver, 1997) and help them get better at solving problems (Brown & Walter, 2005).
On the other hand, reading comprehension research has a longer history than problem-posing research. Reading comprehension research has shown that getting students to pose problems can help them understand their reading much better. Rosenshine, Meister, and Chapman (1996) found gains in students’ reading comprehension when the students were engaged in problem-posing, with a 0.36 effect size measured by standardized tests and 0.86 when using researcher-designed tests. Yu (2011) mentioned that posing problems could be a good way to get students to do higher-order thinking instead of just trying to memorize and understand the learning content. This could help students figure out what the key ideas are while they are learning. Other researchers have also mentioned that when teachers help students with problem-solving activities, it can strengthen their understanding of the course material, improve their learning outcomes, and improve their ability to understand what they are reading (Sung, Hwang, and Chang, 2013). Studies have shown that those who are very good at reading comprehension point out that they are the most effective readers in constant contact with the text (Duke and Pearson, 2002; Cartwright, 2009; Brassell and Rasinski, 2008). Despite this interest in integrating mathematical problem-posing into classroom practice, little is known about the cognitive processes involved when students generate their problems and how problem-posing relates to other cognitive processes in students, like their reading ability.
Even though the research is limited, these quantitative results show that problem-posing should be used in math classrooms because it helps students understand what they are reading and solve problems. Even though it makes sense, in theory, to give students problem-solving tasks to help them understand and improve their learning, more research is needed to show the link between these two ideas. The research in reading comprehension can be used as a model for a systematic study of how mathematical exploration and problem-posing activities affect how well students learn math. This study addresses some of these questions by investigating students' problem-solving abilities and reading comprehension skills. Therefore, this study aimed to examine the relationship between problem-posing and reading comprehension skills.
Method
This study is part of a larger project funded by Kirikkale University's Scientific Research Projects Coordination Unit, where the researchers work as academics in the Elementary School Teacher Education Department. The study aimed to investigate the relationship between 4th-grade students' problem-posing skills and their reading comprehension abilities; therefore, correlational research was used to understand the relationship between two different abilities. (Tabachnick & Fidell, 2013). The study was conducted in three fourth-grade classrooms at two public elementary schools in a city located in Central Anatolia, Turkey. There are 92 students whose teachers have over fifteen years of teaching experience. The current study's participants are the students in both classrooms. Three different tools were used to collect research data. (1) Personal Information Form; (2) Reading Comprehension Test; (3) Problem Posing Questionnaire Personal Information Form: This form includes information such as students' grade level, gender, and preschool education status. Also, they were requested to evaluate themselves as readers, like do they see themselves as good readers. The Reading Comprehension Test was developed by Karasu, Girgin, and Uzuner (2013). It included the "Non-Formal Reading Inventory," consisting of 10 open-ended questions with open, closed, and knowledge-experience textual questions about a narrative text. The total score that can be obtained from this test is 100. The evaluation criteria of the reading comprehension test are as follows: (i)90-100 points; Independent level, (ii) 75–89 points; Instructional Level, (iii) 74-51 points transitional instructional level, and (iv) difficulty (anxiety) level for 50 points or less. The problem-posing questionnaire consists of three types of problem-posing context mentioned by Kopparla, Mahati, et al. (2019): (1) informal context-based problem posing; (2) visual representation-based problem posing; and (3) symbolic representation-based problem posing. The students’ work was evaluated for aspects of understanding and mathematical fluency using a rubric with three bases: (i) problem structure or context, (ii) mathematical expression, and (iii) appropriateness of the problem-posing design. The data were collected in two separate phases. In the first session, the students read the story more than twice, aloud and silently, and then answered questions about this text on a reading comprehension test. The second phase of the problem-posing questionnaire consisted of three different problem-posing activities, each of which was applied on different days in each week, and the whole set of data was collected in four weeks.
Expected Outcomes
This study is conducted during the fall semester of the 2022–2023 academic year in Turkey. The participants utilized the reading comprehension test; however, two of three problem-posing activities could be applied. The last item will be utilized in the spring semester of the 2022-2023 academic year. Therefore, preliminary analyses were done with the collected data from the students’ written answers. Based on the early results, the current study's expected results could be changed; however, the preliminary findings indicated a significant positive moderate correlation between the students’ problem-posing abilities and reading comprehension skills. Also, it was seen that students got better scores in visual representation-based problem-posing than informal context-based problem-posing activities. Students at the “difficulty and anxiety level” for reading comprehension also got low scores in informal context-based problem-posing activities. After analyzing the data, findings will be updated and expanded, and conclusions and recommendations will be made according to the study's results.
References
Brassell, D., Rasinski T. (2008). Comprehension that's work. Huntington Beach: Shell Education Brown, S. I., and M. I. Walter. 2005. The Art of Problem Posing. 3rd ed. Hillsdale, NJ: Erlbaum. Cai, J., & Hwang, S. (2002). Generalized and generative thinking in U.S. and Chinese students' mathematical problem solving and problem posing. Journal of Mathematical Behavior, 21(4), 401–421. Cartwright, K. (2009). The role of cognitive flexibility in reading comprehension. S.E. Israel ve G.G. Duffy (Edt.) Handbook Of Research on Reading Comprehension (1. Baskı) içinde (s.115-139) New York: Routledge. Duke, N.K., Pearson, P.D. (2002) Effective Practices for Developing Reading Comprehension. International Reading Association. Karasu, H.P., Girgin, Ü., Uzuner, Y.(2013). Formel olmayan okuma envanteri. (1. Baskı) Ankara: Nobel Akademik Yayıncılık. Kilpatrick, J. (1987). Where do good problems come from? In A. H. Schoenfeld (Ed.), Cognitive science and mathematics education (pp. 123–148). Hillsdale, NJ: Lawrence Erlbaum. Kopparla, M., Bicer, A., Vela, K., Lee, Y., Bevan, D., Kwon, H., ... & Capraro, R. M. (2019). The effects of problem-posing intervention types on elementary students’ problem-solving. Educational Studies, 45(6), 708-725. Rosenshine, B., C. Meister, and S. Chapman. 1996. “Teaching Students to Generate Questions: A Review of the Intervention Studies.” Review of Educational Research 66 (2): 181–221. doi:10.3102/ 00346543066002181. Silver, E. A. (1994). On mathematical problem posing. For the Learning of Mathematics, 14(1), 19–28. Silver, E. A., & Cai, J. (2005). Assessing students’ mathematical problem posing. Teaching Children Mathematics, 12(3), 129– 135. Stanic, G., & Kilpatrick, J. (1988). Historical perspectives in problem-solving. Research Agenda for Mathematics Education: The Teaching and Assessing of Problem Solving. Reston: National Council for Teachers of Mathematics. Taylor, S. & Bogdan. Sung, H. Y., Hwang, G. J., & Chang, Y. C. (2013). Development of a mobile learning system based on a collaborative problem-posing strategy. Interactive Learning Environments, 24(3), 1–16. Tabachnick B.G. and Fidell, L.S. (2013). Using Multivariate Statistics (sixth ed.) Boston: Pearson. Yu, F. Y. (2011). Multiple peer-assessment modes to augment online student question-generation processes. Computers & Education, 56(2), 484–494.
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