بدفهمی های ریاضی و عوامل بروز آن در دانش آموزان پایه چهارم ابتدایی مبتنی بر تجارب زیسته دانش آموختگان دانشگاه فرهنگیان: (مطالعه کیفی)

محورهای موضوعی : پژوهش در برنامه ریزی درسی

ساره حق خواه ¹ ( استادیار، گروه علوم پایه، دانشگاه فرهنگیان، تهران، ایران )
آذر داودی ² ( استادیار، گروه علوم تربیتی، دانشگاه فرهنگیان، تهران، ایران )
آمنه امیری ³ ( دانش‌آموخته کارشناسی ارشد رشته آموزش ابتدایی، دانشگاه فرهنگیان، تهران، ایران )

تاریخ دریافت : 1400/01/15 تاریخ پذیرش : 1400/08/15 تاریخ انتشار : 1400/09/01

کلید واژه: تجارب زیسته, بدفهمی ریاضی, پایه چهارم ابتدایی, دانش آموختگان دانشگاه فرهنگیان,

چکیده مقاله :

هدف پژوهش حاضر، واکای تجارب نومعلمان در زمینۀ شناخت و برخورد با بدفهمی های ریاضی دانش آموزان چهارم ابتدایی و عوامل بروز آن است. این پژوهش، کیفی با رویکرد پدیدارشناسی است. مشارکت کنندگان این پژوهش شامل 10 نفر از دانش آموختگان دانشگاه فرهنگیان استان فارس بودند که تجربۀ تدریس ریاضی پایۀ چهارم را داشتند و بر مبنای نمونه گیری هدفمند تا اشباع نظری داده ها برای انجام مصاحبه انتخاب شدند. روش گردآوری داده ها، مصاحبۀ نیمه ساختاریافتۀ عمیق بود. برای تجزیه و تحلیل اطلاعات حاصل از این پژوهش از روش تحلیل مضمون استفاده شد. بر اساس یافته های پژوهش 111 مضمون پایه، 19 مضمون سازمان دهنده و 2 مضمون فراگیر زیرِ عنوان بدفهمی های ریاضی و عوامل بروز آن شکل گرفت. با تحلیل مضامین استخراج شده می توان دریافت که مشارکت کنندگان شناخت نسبتاً مطلوبی از بدفهمی های ریاضی داشته و محتوای سنگین مطالب کتاب ریاضی پایۀ چهارم و عدم تناسب آن با رشد شناختی دانش آموزان این پایه و در نتیجه مواجه شدن با کمبود زمان برای ارائۀ مفاهیم را مهم ترین عوامل بروز بدفهمی ریاضی در این پایه می دانستند؛ بنابراین با بازنگری محتوای کتاب ریاضی پایۀ چهارم می توان انتظار داشت که بستر مناسب تری برای فرایند یادگیری- یاددهی ریاضی و جلوگیری از بروز بدفهمی ها فراهم گردد.

چکیده انگلیسی:

The purpose of this study was to explore the experiences of new teachers in the field of recognizing and dealing with the mathematical misunderstandings and their causes in the fourth grade elementary school students. This research was qualitative with a phenomenological approach. The participants were 10 teachers who were graduated from Fars Farhangian University and had experiences of teaching mathematics in the fourth grade of elementary, which were selected by a purposive sampling for interview until the data were saturated. The data collection method was in-depth semi-structured interview. The thematic analysis method was used to analyze the data. The findings showed that, 111 basic themes, 19 organizing themes and 2 comprehensive themes were formed under the title of mathematical misunderstandings and their causes. By analyzing the extracted themes, it can be realized that the participants had a relatively good knowledge of mathematical misunderstandings. They considered the heavy content of the fourth grade mathematics textbook and its incompatibility with the cognitive development of the students and the lack of time to present the concepts as the most important causes of mathematical misunderstandings in this grade. Therefore, by reviewing the content of the fourth- grade mathematics textbook, it can be expected that a more appropriate platform for the mathematic teaching _learning process and preventing misunderstandings should be provided.

منابع و مأخذ:

Abdullahi, H., Moradi Weis, A. (2016). The effect of students’ learning styles on solving geometry problems. Proceedings of the 14^th Iranian Mathematics Education Conference, Volume 6. (Persian)

Alamian, V., Seyyedi, M. & Habibi, M. (2018). Identifying the misconceptions of eighth grade students on geometry skills and the use of Van Hiele theory to improve their geometry skills. Quarterly Journal of Educational Innovations, 17(67), 123-148. (Persian)

Alamolhodaei, H. (2014). Principles of Mathematics Education. Third edition. Mashhad: Ferdowsi University Press. (Persian)

Alamolhodaei, H. (2000). Mathematical Anxiety. Journal of Psychology and Educational Sciences, 5(1), 99-119. (Persian)

Allen, G. D. (2007). Misconceptions in mathematics. Department of Mathematics, Texas A & M University, College Station.

Bakhshalizadeh, S., broojerdian, N. (2018). Identifying the primary school fourth grade students’ common misconceptions in content area of geometry and measurement: A comparison of their performance with the mean performance at international level. Quarterly Journal of Educational Innovations, 16(4), 101-126. (Persian)

Bakhshalizadeh, S., Gholamazad, S. (2014). Identifying common misunderstandings of fourth grade elementary students in the field of mathematical content. Educational Research and Planning Organization, Research Studies Institute. (Persian)

Basani Rose, M. (2011). Learners’ Errors and Misconceptions Associated with Common Fractions, Mini desertation submitted for degree of Masters in Mathematics Education. University of Johannesberg.

Bottle, G. (2010). Teaching mathematics in the primary school. Translator: Bakhshalizadeh, S., First Edition. Tehran: Samat Publications, original work publication, 2005. (Persian)

Daryabegy, S., Yaftian, N. (2020). The effect of teaching by making use of tracking and pursuing continuity of learning of the 9^th grade students on learning mathematics course. Research in Curriculum Planning, 17(65), 158-169. (Persian)

Dorri, M., Rafiepour. A. (2019). Evaluating of Rational Number Misconception Test (RNMT) with Rasch model. Quarterly Journal Educational Measurement, 8 (32), 103- 126. (Persian)

Doosti, M., Reyhani, E. (2015).  Identifying misconceptions, strategies and reasoning of sixth grade students in problems solving of fraction. Technical and Vocational Education, 4(4), 40-60. (Persian)

Elliot, A. J. (2006). The hierarchical model of approach-avoidance motivation. Motivation and emotion, 30(2), 111-116.‏

Fischbein, E., Muzicant, B. (2002). Richard Skemp and his conception of relational and instrumental understanding: Open sentences and open phrases. Intelligence, learning and understanding in mathematics: A tribute to Richard Skemp, 49-77.‏

Goya, Z., Hesam, A. (2007). Mental Schemas: Explaining Students’ Mathematical Misunderstandings. Quarterly Journal of Applied Psychology, 2(1), 77-1200. (Persian)

Hajizadeh, M. (2014). Teaching based on individual differences and examining its effect on increasing the level of learning of mathematics and science courses in middle school students. Modiriat-e Farda Journal, 12(37), 119-138. (Persian)

Hansen, A. (2011). Children's Errors in Mathematics: Understanding Common Misconceptions in Primary Schools. 2nd Edition. Learning Matters, Exeter.

Izadi, M., Reyhani, E. (2021). Investigating the understanding of Tehran’s second elementary school students of the fraction’s part- whole subconstruct, based on APOS and SOLO theories with using an unusual task. Research in Curriculum Planning, 18(68), 124-141. (Persian)

Kahki, A., reyhani E. & bahrami Saman E. (2019). Assessment of Understanding and Understanding of Eighth Grade Students of Probability. Andishe -ye Amari, 24 (1), 57-80. (Persian)

Kakavand, A. (2009). Cognition, education and treatment of autism disorders. Karaj: Sarafraz Publications. (Persian)

Karimzadeh, R., Abbaslo, M. (2017). The role of teachers in correcting students’ mathematical misunderstandings. Provincial Scientific Research Conference on Strategies and Solutions for Quality Improvement in Education. (Persian)

Keazer, A. (2004). Students’ misconceptions in middle school mathematics. B. S. Undergraduate mathematics exchange, 2(1), 2-4.

Mortazi Mehrabani, N., Gholamazad, S. (2016). Developing a model for required mathematics knowledge of elementary teachers. Journal of higher education curriculum studies, 6(12), 135-152. (Persian)

Norad Seddigh, M. (2016). Investigating some of the students’ misunderstandings in the ninth math textbook. Proceedings of the 14^th Iranian Mathematics Education Conference, Volume 6. (Persian)

Olivier, A. (1996). Handling pupils’ misconceptions. Pythagoras, 21(10–19).

Rafipour, A., Goya, Z. (2004). Why was the performance of Iranian students in Thames unique? Roshd Mathematics Education Journal, 21(75), 15-20. (Persian)

Rahimi, S., Arvin, B. (2017). Common misunderstandings of elementary students in mathematics. The First Educational Conference and the Use of Math. Scientific Association of Kermanshah Math Teachers. (Persian)

Rahimi Sherbaf, S. (2013). An algorithmic approach to developing a deep understanding of mathematics using classroom discussion. Journal of technology of education (journal of technology and education), 7(2), 129-138. (Persian)

Reyhani, E. (2014). Analysis of policies, approved documents, research and credible resources related to the field of mathematical learning. Educational Research and Planning Organization. Ministry of Education. (Persian)

Reyhani, E., Faridi, H. & Rashedi, F. (2016). A Study on negative numbers Conception of students and their misconceptions. Quarterly Publication of Education Technology (Technology and Education), 10(2), 115-131. (Persian)

Sadock, B. J., & Sadock, V. A. (2007). Synopsis of psychiatry: Behavioral sciences/ Clinical psychiatry. l0th Edition. NewYork: Lippincott Williams & Wilkins.

Sahlberg, P. (2006). Education reform for raising economic competitiveness. Journal of Educational Change, 7(2), 259-287.

Shahvarani, A., Behzadi, M. & Moradi, A. (2015). Misconceptions of students about comparing decimal numbers from 6th, 7th and 8th year of girl pishva town. Journal of Educational Psychology, Islamic Azad University, Tonekabon Branch, 5(4), 61-75. (Persian)

Smith, J. P., DiSessa, A. A., & Roschelle, J. (1994). Misconceptions reconceived: A constructivist analysis of knowledge in transition. The journal of the learning sciences, 3(2), 115-163.‏

Soygur, M. (2008). Misconceptions of Students in Algebra Lessons: An Investigation of Issues in the Middle Schools of the TRNC (Doctoral dissertation, Eastern Mediterranean University).‏

Stacey, K., MacGregor, M. (1997). Ideas about symbolism that students bring to algebra. The Mathematics Teacher, (90)2, 110-113.

Yarmohamadi Vasel, M., Rashid, K. & Bahrami, F. (2014). The effectiveness of instruction through the play in improving mathematics attitude of primary girl students. Journal of School Psychology, 3(3), 122-135. (Persian)

Zohrehvand, S., Mashhodi, S. & Heidari, M. (2016). Why and how do students make more mistakes in mathematics?! (Experiences from the misunderstandings of fraction education from the new fifth grade elementary book). Proceedings of the 14^th Iranian Mathematics Education Conference, Volume 6. (Persian)