Session Information
24 SES 13, Mathematical Thinking and Achievement
Paper/Poster Session
Contribution
Problem-solving and posing are closely related to each other (Kilpatrick, 1987) and despite the long history of problem solving in the school mathematics; problem-posing is relatively new in mathematics classrooms and curricula (Cai & Hwang, 2002; Silver & Cai, 1996).
Researchers and school curricula have been underlining the importance of primary school students’ mathematical problem-posing skills. It has been suggested that problem-posing activities contribute positively to students' creativity (Silver, 1997) and help to improve their problem-solving skills (Brown & Walter, 2005). Furthermore, problem-posing enables students to generate more diverse and flexible thinking in mathematics (Lowrie, 2002). For early grade level students to generate problems, they should be given meaningful, realistic and relevant contexts, in which they can establish connections to mathematical ideas (English, 1997; Lowrie, 1999; Silver, 1997).
There have been efforts around the world to incorporate problem-posing into mathematics classrooms. For instance, National Council of Teachers of Mathematics (NCTM, 2000) called for an increased emphasis on problem-posing activities in the school mathematics. Thus, problem-posing abilities of students and the benefits of it have been investigated thoroughly in the context of different school curricula and cultures in the world.Chai and Hwang (2002) compared Chinese and US students’ problem-solving and posing abilities and gave a perspective from these two countries about the relationship between problem-solving and posing skills. On the other hand, much earlier, in Netherlands and USA, instructional experiments were done by the researchers in which students generate problems and also solve them for future students or for their classmates (Van den Brink, 1987; Healy, 1993).Despite all, most of these studies have focused on students at upper-primary level or secondary school level. The studies with younger students like pre-school or first graders seem to be limited (Lowrie, 2002).Tertemiz (2017) analyzed the mathematical problems generated by students of grades 1 to 4 and found that the problems posed by students were similar to the types of word problems present in school textbooks. One the one hand, this might indicate students’ adequacy in problem-posing, but on the other hand, this might also be an indication of the limited use of students’ imagination or flexibility in problem posing.
In Turkey, problem-posing activities were added for all grade levels and all content areas in mathematics classes since the year 2005 (MoNE, 2015, 2017). Thus, problem posing is seen an important intellectual activity in school mathematics and supported by national school curricula in Turkey. However, students in schools have difficulties in problem-posing and solving skills (Arıkan & Ünal, 2013).
Although an emphasis is given to problem-posing in mathematics learning, research know little about young students’ thought processes during problem-posing. In this sense, it can be said that one important line of research in problem-posing process is to see how students generate problems and what kind of difficulties they experience during the problem-posing processes. Therefore, the purpose of the present study was to investigate the first-grade students’ problem posing experiences and also their difficulties during problem-posing process regarding the addition and subtraction operations.
This research is a part of a long-term project funded by The Scientific and Technological Research Council of Turkey (TUBITAK). The overarching goal of the parent project was to develop a learning trajectory for Turkish first grade mathematics on “numbers and operations”. English (1997) pointed out that children with strong number sense were more likely to be able to pose much more accurate problems than children with limited number sense, since they had a better understanding of problem structure. Problem-solving and posing are parts of the hypothetical learning trajectory (HLT) which intends to promote various dimensions of number sense in the project.
Method
The Design of the Study & Participants This study was a part of a long-term project based on an educational design research approach, involving cycles of design experiments. The study is conducted in two first-grade classrooms of a small public school in the capital of Turkey. There are 34 students in total and their teachers having over 20 years of teaching experience. The participants of the current study are the students of both the classrooms and the 8 selected students for the interviews (four students from each classroom). Data Collection & Data Analysis The data will be collected during problem-posing activities in the classroom, as well as through clinical interviews with 8 selected students, with an aim to elicit their number sense, understanding of addition and subtraction, as well as approaches in problem-posing. The data will be consisted of classroom video-recordings, observation notes during the problem-posing activities held in the classroom, and the transcripts of the interviews with the selected students. In this study, daily life situations will be used as a context in developing students’ problem-posing skills. Three problem-posing activities will be involved showing a picture to the students that intended to help them imagine the addition situation. Based on these pictures, the students will be asked to pose problems requiring addition operation. Considering the grade level of the students; the contexts will be designed for posing one-step typical word-problems and the students will be asked to provide their answers orally, since at the time of the data collection, students will not yet be fluent in writing. Each activity will take about less than one class hour and after generating the problems, the students will be asked to solve the generated problems. The problem-posing activities will be implemented after students have gained experience with problem-solving tasks in the classroom. The data of subtraction operation will also be collected in the same way with addition operation. In total 6 problem-posing activities (3 for addition operation and 3 for subtraction operation) will be performed as classroom activities. Additionally, semi-structured interviews will be conducted with 9 selected students. The first interview will be conducted after they complete the learning trajectory for the addition operation and the second interview will be conducted after the subtraction operation. All data will be analyzed with qualitative methods. Students’ articulations of problems and also their difficulties will be coded and thematized by the research team.
Expected Outcomes
This study will be conducted during the second cycle of design research. From the first cycle, a research has been conducted to figure out problem posing experiences of first graders. The findings of the research is basis for the current study. The expected results of the current study will be expanded on the findings of previous study. The previous study indicated that daily life situations contributed positively to students' problem-posing skills. In addition, difficulties were experienced by students included (i) focusing on doing operations rather than posing problems, (ii) focusing on a story without including numbers (iii) not being able to form question sentence even if they could set up a story based on daily life situations, and (iv) not being able to pose problems differing from the contexts exemplified by the teacher. Based on the research conducted in the first cycle, the data collection tools of the present study have been formed and the data will be collected in the spring semester in 2018-2019 school years. After collecting and analyzing the data, findings will be shared and conclusion and recommendations will be made according to the results of the study.
References
Arıkan, E. E. ve Ünal, H. (2013). İlköğretim 2. sınıf öğrencilerinin matematiksel problem kurma becerilerinin incelenmesi. Amasya Üniversitesi Eğitim Fakültesi Dergisi, 2(2), 305-325. Brown, S. I., & Walter, M. I. (2005). The art of problem posing. Psychology Press. 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. English, L. (1997) Promoting a Problem-posing classroom, Teaching Children Mathematics, 3, 172-179. Healy, C. C. (1993). Creating miracles: A story of student discovery. Berkeley, CA: Key Curriculum Press. Kilpatrick, J. (1987) Problem Formulating: where do good problems come from? In A.H. Schoenfeld (Ed.) Cognitive Science and Mathematics Education, pp. 123-147. Hillsdale: Lawrence Erlbaum. Lowrie, T. (1999) Free Problem Posing: Year 3/4 students constructing problems for friends to solve, in J. Truran & K. Truran (Eds) Making a Difference, pp. 328-335. Panorama, South Australia: Mathematics Education Research Group of Australasia. Lowrie, T. (2002). Designing a framework for problem posing: Young children generating openended tasks. Contemporary Issues in Early Childhood, 3(3), 354-364. Ministry of National Education [MoNE] (2015).İlkokul matematik dersi 1-4 sınıflar öğretim programı [Primary school mathematics curriculum grades 1 to 4]. Ministry of National Education [MoNE] (2015).İlkokul matematik dersi 1-4 sınıflar öğretim programı [Primary school mathematics curriculum grades 1 to 4]. National Council of Teachers of Mathematics (NCTM) (2000). Principals and Standards of School Mathematics. Reston: NCTM. Silver, E. A., & Cai, J. (1996). An analysis of arithmetic problem posing by middle school students. Journal for research in mathematics education, 521-539. Silver, E. A. (1997). Fostering creativity through instruction rich in mathematical problem solving and problem posing. Zdm, 29(3), 75-80. Tertemiz (2017). İlkokul öğrencilerinin dört işlem becerisine dayalı kurdukları problemlerin incelenmesi. Türk Eğitim Bilimleri Dergisi,15(1), 1-25. van den Brink, J. F. (1987). Children as arithmetic book authors. For the Learning of Mathematics, 7, 44–48.
Search the ECER Programme
- Search for keywords and phrases in "Text Search"
- Restrict in which part of the abstracts to search in "Where to search"
- Search for authors and in the respective field.
- For planning your conference attendance you may want to use the conference app, which will be issued some weeks before the conference
- If you are a session chair, best look up your chairing duties in the conference system (Conftool) or the app.