نظریه و عمل در برنامه درسی

نظریه و عمل در برنامه درسی

مسئله‌های باز-پاسخ: پیوند‌دهنده دانش ریاضی و زندگی واقعی

نوع مقاله : مقاله پژوهشی

نویسندگان
1 کارشناس ارشد آموزش ریاضی و دبیر ریاضی، لاریجان، ایران
2 استاد بازنشسته دانشگاه شهید بهشتی، تهران، ایران
چکیده
پژوهش حاضر باهدف بررسی نقش سؤال‌های باز-پاسخ در ایجاد پیوند بین دانش ریاضی و زندگی واقعیِ دانش‌آموزان پایه هشتم انجام گرفت. زمان اجرای این پژوهش، سال تحصیلی 1401-1400 بود و شرکت‌کنندگان، 10 دانش‌آموز پایه هشتمِ در یکی از شهرهای شمالی ایران بودند و نویسنده اول، معلم ریاضی‌شان بود. داده‌های پژوهش شامل حل مسئله انفرادی و گروهی دانش‌آموزان، مصاحبه‌های نیمه‌ساختاریافته و مشاهده‌ها و یادداشت‌های بازتابی معلم/نویسنده اول بود. جمع‌آوری داده‌ها ازطریق برگه‌های حل مسئله‌های باز-پاسخ به‌صورت فردی و گروهی، یادداشت‌های نویسنده اول و مصاحبه‌های فردی انجام‌شد. در حل مسئله انفرادی، شرکت‌کنندگان به 10 سؤال پاسخ دادند و برای حل مسئله گروهی، دانش‌آموزان چهارمسئله از بین آن 10 مسئله، به‌همراه یک مسئله زمینه‌مدار جدید را حل‌کردند که دراین مقاله، نتایج تجزیه‌وتحلیل پاسخ‌ها به سه‌مسئله، ارائه می‌گردد. مصاحبه‌ها بارضایت دانش‌آموزان، ضبط شنیداری شد. برای تحلیل داده‌ها، از پاسخ‌های دانش‌آموزان، متن پیاده شده مصاحبه‌ها و یادداشت‌های بازتابیِ پژوهشگران، استفاده شد. یافته‌ها نشان دادند که «زمینه»های زندگی واقعی، نقش با اهمیتی در مسئله‌های باز-پاسخ دارند و علاقه‌مندی دانش‌آموزان را برای حل آن‌ها، بیشتر می‌کند. همچنین تنوع راه‌حل‌ها و پاسخ‌ها، فرصتی برای درگیرکردن دانش‌آموزان با مسئله به‌وجود می‌آورد که کمک می‌کند تا میان دانش ریاضی و زندگی واقعیِ دانش‌آموزان، پیوند برقرار شود.
کلیدواژه‌ها

موضوعات


عنوان مقاله English

Open-ended Problems: connecting mathematics knowledge and real world

نویسندگان English

zohreh mahmoudi 1
zahra gooya 2
1 Master of Mathematics Education and Mathematics Teacher, Larijan, Mazandaran, Iran
2 Emeritus Professor of mathematics education, Shahid Beheshti University, Tehran, Iran
چکیده English

A well-received direction towards fruitful use of the problem-solving approach to teaching and learning of school mathematics is to use open-ended problems. Reviewing the history of open-ended mathematics problems show that the problem-solving as a new way to conceptualize school mathematics curriculum started in 1970’s and became the “heart of school mathematics” in 1980’s. However, despite the real effort that was made to teach how to use different problem-solving heuristics, students’ difficulties with mathematics remained almost unsolved. In the early 1970’s, Shimada et al. (1972) developed several open-ended problems like "marble problem" and "water flask problem" for evaluating students’ activities (cited in Nohda, 2000). Later, four mathematics education researchers at the University of Tsukuba in Japan with several elementary teachers, joined Shimada and conducted various studies to shed more light on the ways in which, problem solving could be implemented in mathematics classrooms. The group published their research findings in books titled "The open-ended approach: A new proposal for teaching mathematics" (Shimada, 1977), "The open approach" (Nohda, 1983), "From problem to problem" (Takeuchi & Sawada, 1984) and "Various ways of thinking" (Sawada & Sakai, 1995; Koto, 1992) (all cited in Nohda, 2000). An open-ended problem refers to the problem that has multiple correct answers. Acknowledging the importance of open-ended problems in school mathematics, a study was designed and conducted to explore the role of open-ended problems in enhancing students’ mathematics learning. The study carried out in2019- 2020 (1400-1401 SH) school year in one of the small counties of northern part of Iran. The participants were Grade 8 students at a school located in a small county in northern part of Iran. The number of students was 10 and they all agreed to join the study and gave permission to the researchers to use their data in their study. The authors as well, gave assurance that their data will be used anonymously without referring to their names and identities. To collect the data, 10 open-ended problems were designed using the mathematics content of the first four chapters of the Grade 8 mathematics textbook that was taught before the study. The students solved the problems individually and their written solutions were collected and evaluated by the first author that was the mathematics teacher of that class. Then, the teacher/researcher asked to solve problems in groups. The problems consisted of those that students had more difficulty in solving them, and a new problem with a real-world context. In addition, semi-structured interviews were conducted. The students’ solutions of problems both individually and in the groups, transcripts of the interviews and the teacher’s reflective notes, served the purpose of triangulation and endorsed the confirmability of the findings. The analysis of the data showed that the real-world context plays a crucial role in open-ended problems. A meaningful and rich context has potential to provide opportunities for students to use their mathematical knowledge to solve a real-world problem. As well, a thoughtful and well-developed context can provide an opportunity to implement the mathematics knowledge to solve an open-ended problem.

کلیدواژه‌ها English

Open-ended Problems
Grade 8 Students
Grade 8 Mathematics
Real-life Context
Mathematical Problem Solving
Bingolbali, E. & Bingolbali, F. (2021). An Examination of Open-Ended Mathematics Questions’ Affordances. International Journal of Progressive Education, (17) 4.
Dehghan Naieri, M. & Gooya, Z. (2015). Understanding of the concept of equality in solving first-degree equations by Grade 9 students. Roshd Mathematics Education Journal. 32(4), 4-14. Publication and Teaching Aid Office, Organization for
Research and Educational Planning, Ministry of Education. (In Persian.)
Foong, P.Y. (2002). Using Short Open-ended Mathematics Questions to Promote Thinking and Understanding. Proceedings of the 4 Th International Conference on the Humanistic Renaissance in Mathematics Education. Italy, Palermo. PP.135-140.
Nohda, N. (1986). A study of open-approach method in school mathematics. Tsukuba. Journal of Educational Study in Mathematics, 5, 119-132, Nohda.
Nohda, N. (2000). Teaching by open-approach method in Japanese mathematics classroom. In T. Nakahara, & M. Koyama (Eds.), Proceedings 24th of the Conference of the International Group for the Psychology of Mathematics Education, 1, 39-53.
Rafipour, A. (2019). A strategy for designing real-world problems. Roshd Mathematics Education Journal. 38(2), 16-18.  Publication and Teaching Aid Office, Organization for Research and Educational Planning, Ministry of Education. (In Persian.)
Sanchez, W. B. (2013). Open-ended Questions and the Process Standards. National Council of Teacher Mathematics, 107(3), pp.206-211. The Author.
Savić, D. (2019). The Role of Open-ended Tasks in the Development of Student Activities and Creative Thinking. Croatian Journal of Education,22(1), 287-305
Silver, E. A. (1995). The nature and use of open problems in mathematics education: Mathematical and pedagogical perspectives, ZDM, 27(2), 67-72.
Wiliam, D. (1994). Assessing authentic tasks: alternatives to mark-schemes. Nordic Studies in Mathematics Education 2 (1), 48-68.
Yeo, J. B. W. (2015). Development of a Framework to Characterize the Openness of Mathematical Task. International Journal of Mathematics Education, 15,175-191.