مسئله های باز-پاسخ: پیوند دهنده دانش ریاضی و زندگی واقعی (مقاله علمی وزارت علوم)
درجه علمی: نشریه علمی (وزارت علوم)
آرشیو
چکیده
پژوهش حاضر باهدف بررسی نقش سؤال های باز-پاسخ در ایجاد پیوند بین دانش ریاضی و زندگی واقعیِ دانش آموزان پایه هشتم انجام گرفت. زمان اجرای این پژوهش، سال تحصیلی 1401-1400 بود و شرکت کنندگان، 10 دانش آموز پایه هشتمِ در یکی از شهرهای شمالی ایران بودند و نویسنده اول، معلم ریاضی شان بود. داده های پژوهش شامل حل مسئله انفرادی و گروهی دانش آموزان، مصاحبه های نیمه ساختاریافته و مشاهده ها و یادداشت های بازتابی معلم/نویسنده اول بود. جمع آوری داده ها ازطریق برگه های حل مسئله های باز-پاسخ به صورت فردی و گروهی، یادداشت های نویسنده اول و مصاحبه های فردی انجام شد. در حل مسئله انفرادی، شرکت کنندگان به 10 سؤال پاسخ دادند و برای حل مسئله گروهی، دانش آموزان چهارمسئله از بین آن 10 مسئله، به همراه یک مسئله زمینه مدار جدید را حل کردند که دراین مقاله، نتایج تجزیه وتحلیل پاسخ ها به سه مسئله، ارائه می گردد. مصاحبه ها بارضایت دانش آموزان، ضبط شنیداری شد. برای تحلیل داده ها، از پاسخ های دانش آموزان، متن پیاده شده مصاحبه ها و یادداشت های بازتابیِ پژوهشگران، استفاده شد. یافته ها نشان دادند که «زمینه»های زندگی واقعی، نقش با اهمیتی در مسئله های باز-پاسخ دارند و علاقه مندی دانش آموزان را برای حل آن ها، بیشتر می کند. همچنین تنوع راه حل ها و پاسخ ها، فرصتی برای درگیرکردن دانش آموزان با مسئله به وجود می آورد که کمک می کند تا میان دانش ریاضی و زندگی واقعیِ دانش آموزان، پیوند برقرار شود.Open-ended Problems: connecting mathematics knowledge and real world
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.
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