فصلنامه علمی

نوع مقاله: مقاله پژوهشی

نویسندگان

1 گروه ریاضی، دانشکده علوم، دانشگاه تربیت دبیر شهید رجایی، تهران، ایران

2 گروه آموزش و پرورش، دانشکده‌ روان‌شناسی و علوم تربیتی، دانشگاه علامه طباطبائی، تهران، ایران

چکیده

پیشینه و اهداف: توانایی ‌فضایی به دلیل کاربرد آن در زندگی روزمره و جایگاه آن در علوم و مهندسی اهمیتی ویژه دارد. در دهه­های اخیر مطالعات زیادی در مورد توانایی فضایی در حوزه­ آموزش ریاضی صورت گرفته است. بخشی از این مطالعات در حوزه­ی ریاضیات مدرسه­ای بوده و در آن بر اهمیت جایگاه توانایی فضایی در فرآیند آموزش ریاضی مدرسه‌ای تأکید شده‌است. البته لازم به ذکر است که تعداد پژوهش های مرتبط با آموزش ریاضی  در کشور ایران چندان زیاد نیست و بیشتر پژوهش‌ها در حیطه روانشناسی انجام شده است. در اسناد آموزشی نظیر سند اصول و استانداردهای ریاضیات مدرسه‌ای نیز به این نکته اشاره شده است که دانش‌آموزان باید انواع بازنمایی‌های تجسمی را در تحلیل مسأله‌ها و موضوعات ریاضی به‌کار ببرند. تعاریف متعدد و متنوعی از توانایی فضایی ارائه شده و برای توصیف آن، از عبارات مختلفی نظیر تفکر تجسمی، تفکر شهودی و توانایی بصری استفاده شده است. همچنین برای توضیح ماهیت آن، عوامل و مؤلفه‌های گوناگونی بر شمرده شده است. هدف پژوهش حاضر، بررسی توانایی فضایی در دانش‌آموزان، با ملاحظه‌ جنسیت، رشته و پایه‌ تحصیلی آنان و با توجه به عامل‌های تجسم فضایی، دوران‌ذهنی و جهت‌یابی فضایی است.
روش‌ها‌: روش این مطالعه روش پیمایشی است و شرکت­کنندگان آن، 901 دانش‌آموز متوسطه‌ دوم از شهرستان شهریار هستند که در سال تحصیلی 97-1396 در پایه‌ دهم و یازدهم در دو رشته‌ ریاضی و تجربی مشغول به تحصیل بوده­اند. ابزار پژوهش، آزمونی محقق­ساخته است که روایی صوری و محتوایی آن توسط تعدادی از اساتید آموزش ریاضی و نیز معلمان ریاضی، تأیید شد و معیار آلفای کُرونباخ با مقدار تقریبی 83/0، مؤید پایایی آن می‌باشد. به منظور تجزیه و تحلیل داده­ها از آمار توصیفی (میانگین و انحراف استاندارد) و آمار استنباطی (t مستقل) استفاده شد.
یافته‌ها: یافته‌های این مطالعه حاکی از تفاوت معنادار بین عملکرد دانش‌آموزان دختر و پسر در حوزه‌ توانایی‌فضایی است. به­علاوه دانش‌آموزان رشته‌ ریاضی نسبت به دانش­آموزان رشته‌ تجربی و نیز دانش‌آموزان پایه‌ یازدهم نسبت به پایه‌ دهم به­شکل معناداری عملکرد قوی­تری داشته­اند. این تفاوت با توجه به آموزش ضمنی که در پایه‌های تحصیلی و در پایه­ دهم و یازدهم اتفاق می‌افتد و نیز دروسی که دانش‌آموزان دوره‌ یازدهم تا زمان اجرای آزمون در درس هندسه گذرانده‌اند، قابل توجیه است. این یافته­ها نشان می­دهند که رشد توانایی فضایی به آموزش وابسته است و با توجه به جایگاه آن در زندگی روزمره و حرفه­ای نیازمند توجه بیشتری در ریاضیات مدرسه­ای است. یافته­های کیفی این مطالعه حاکی از آن است که تکالیف مرتبط با توانایی فضایی، بستری مناسب برای پرورش تفکر ریاضی و فرآیند های ریاضی نظیر حل مسأله، استدلال و اثبات است. به هر ترتیب به نظر می­رسد آموزش و افزایش پایه­ تحصیلی بر رشد توانایی فضایی و بهبود عملکرد حل مسأله دانش­آموزان تأثیری انکار ناپذیر دارد.
نتیجه‌گیری: هرچند رویکرد حل مسأله در کتاب­های درسی ریاضی ایران در دهه‌ اخیر به‌طور آشکاری حضور خود را تثبیت کرده است؛ اما مطالعات چندانی در مورد جایگاه و نقش توانایی فضایی در آموزش فرآیند حل مسأله ریاضی انجام نشده است و عرصه­ آموزش ریاضی مدرسه­ای نیازمند به پژوهش‌های بیشتری در مورد توانایی فضایی در سطوح مختلف مانند برنامه‌های درسی، آموزش معلمان و یاددهی و یادگیری ریاضی است. یافته‌های این پژوهش می‌تواند در تغییر و تقویت راهبردها، فرایندهای آموزشی، برنامه‌ریزی درسی و ابزار‌های آموزشی مناسب برای بهبود تجسم فضایی دانش‌آموزان، کارآمد باشد.

کلیدواژه‌ها

موضوعات

عنوان مقاله [English]

Investigation of spatial ability of male and female students in 10th and 11th grade according to factors including spatial visualization, mental rotation, and spatial orientation

نویسندگان [English]

  • E. Reyhani 1
  • F. Ghasemi 1
  • Z. Rahimi 2

1 Department of Mathematics, Faculty of sciences, Shahid Rajaee Teacher Training University, Tehran, Iran

2 Department of Education, Faculty of Psychology and Educational sciences, Allameh Tabataba'i University (ATU), Tehran, Iran

چکیده [English]

Background and Objectives: Spatial ability is an important notion because of its application in everyday life and its place in science and engineering. In recent decades, there have been many studies on spatial ability in the field of mathematics education. Part of these studies have been conducted in the field of school mathematics, emphasizing the importance of the spatial ability in the process of teaching school mathematics. Of course, it should be noted that the number of research studies related to mathematics education in Iran is not very large and most of them have been conducted in the field of psychology. It is also stated in the educational documents such as the principles and standards of school Mathematics (NCTM) that students should use a variety of visual representations to analyze mathematical problems and issues. Numerous definitions of spatial ability have been proposed and various terms, such as visual thinking, intuitive thinking, and visual ability have been used to describe it and various factors and components have also been identified to explain its nature. The purpose of this study was to investigate the spatial ability of students with regard to their gender, grade, and field of study and also according to factors including spatial visualization, mental rotation, and spatial orientation.
Methods: The method of this study was the survey method and its participants were 901 students from secondary schools in Shahriyar studying in the 10th and 11th grade in the academic year of 2017-2018. The measurement instrument was a researcher-made test whose formal and content validity was confirmed by a number professors and teachers of mathematics and its reliability was also confirmed by the approximate amount of Cronbach's alpha which was 0.83. In addition, descriptive statistics (mean and standard deviation) and inferential statistics (independent t-test) were used to analyze the data.
Findings: The findings of the study showed a significant difference between male and female students in the field of spatial ability. In addition, the performance of math students was significantly better than the students in the field of experimental sciences. Also, the performance of the 11th grade students was significantly better than that of the 10th grade students. This difference can be justified by the implicit teaching that takes place in the 10th and 11th grades, as well as the courses which are taken by the 11th grade students in geometry until the exam. These findings show that the growth of spatial ability depends on education, and because of its place in everyday and professional life, needs more attention in school mathematics. The qualitative findings of this study showed that tasks related to spatial ability are a good platform for developing mathematical thinking and mathematical processes, such as problem solving, reasoning, and proof. Moreover, teaching and increasing the level of education seem to have an undeniable effect on the growth of spatial ability and the improvement of students' problem-solving performance.
Conclusion: Although the problem-solving approach has clearly established its presence in Iranian mathematics textbooks in recent decades, little research has been done on the place and role of spatial ability in teaching the process of solving mathematical problems. Moreover, the field of school mathematics needs more research on spatial ability in different areas, such as curricula, teacher training, and methods of math teaching and learning. The findings of this study can be useful in modifying and strengthening the strategies, educational processes, curricula and appropriate educational instruments to improve students' spatial visualization.

کلیدواژه‌ها [English]

  • Keywords: Spatial ability
  • Spatial visualization
  • 10th and 11th grade students
  • Gender
  • Experimental science and mathematics field of study

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