تحليل ارتباط بارشناختی، شیوة توضیح و فعالیت های کتاب ریاضی پایة ششم ابتدایی با پيشرفت تحصيلي دانشآموزان
محورهای موضوعی : پژوهش در برنامه ریزی درسیاحسان خسروانی 1 , احمد مدنی 2 * , رسول کاظمی 3
1 - دانشآموختة کارشناسي ارشد برنامهريزي درسي، گروه علوم تربیتی، دانشکده علوم انسانی، دانشگاه کاشان، کاشان، ايران
2 - استاديار گروه علوم تربيتي، دانشکده علوم انسانی، دانشگاه کاشان، کاشان، ايران
3 - دانشیار گروه ریاضی محض، دانشکدة علوم ریاضی، دانشگاه کاشان، کاشان، ايران
کلید واژه: برنامة درسي, محتوا, آموزش ریاضی, ویژگیهای کتاب درسی, ریاضی پایة ششم. ,
چکیده مقاله :
کتاب درسی را میتوان مهمترین و اساسیترین ابزار فناورانة آموزش در نظام متمرکز آموزش و پرورش ایران محسوب کرد که ویژگیهای آن فرایندهای یاددهی-یادگیری را تحت تأثیر قرار میدهند. هدف اين پژوهش بررسي ارتباط بين ويژگيهاي کتاب ریاضی پاية ششم ابتدايي با پيشرفت تحصيلي دانشآموزان بود. پژوهش از نوع توصيفي و روش آن از نوع همبستگي بود. جامعة آماری پژوهش را 1260 دانشآموز پایة ششم ابتدایی تشکیل دادند که در سال تحصیلی 1401-1400 در شهرستان آران و بیدگل مشغول به تحصیل بودهاند. حجم نمونة آماری برابر با 850 دانشآموز بود که به روش خوشهای چندمرحلهای انتخاب شدند. ابزار گردآوری دادهها «امتحان پایانی سراسری» در درس ریاضی در پایة ششم بود. برای انجام این تحقیق، برگههای امتحانی دانشآموزان به تفکیک هر فصل (موضوع درسی) در مقياس فاصلهاي تصحیح و نمرهگذاري شد. برای آزمون فرضیة پژوهش، ابتدا مباحث کتاب ریاضی بر اساس ویژگیهای بار شناختی، شیوة توضیح، فعالیتهای ریاضیاتی (بازنماییها و الگوسازیها، محاسبات و عملیات، تفسیرها و استدلالها)، ماهیت تمرینها و نوع تصویرها کدگذاری گردید و فراوانی آنها به تفکیک فصول کتاب ثبت شد. اجرای رگرسیون از نوع «مدلهای آمیختة چندسطحی» ارتباطات مختلفی را بین ویژگیهای کتاب درسی ریاضی پایة ششم و پیشرفت تحصیلی دانشآموزان آشکار کرد. ضریب رگرسیونی «بارشناختی بالا» نشان داد که با افزایش مطالبِ دارای بار شناختی بالا، تعداد تصاویر گرافیکی، توضیحهای همگرا و تعداد «کار در کلاس»ها پیشرفت تحصیلی دانشآموزان افزایش مییابد. در مقابل، با افزایش تعداد توضیحهای واگرا، تعداد مطالب طولانی و نیز با افزایش تعداد مطالب حاوی بازنماییها و استدلالها، افت معناداری در نمرات دانشآموزان مشاهده میشود. با توجه به یافتهها میتوان گفت که مطالب دارای بارشناختی بالا هم معلمان و هم دانشآموزان را مجبور به تمرکز بیشتر روی محتوای کتاب درسی میکنند. همچنین افزایش تعداد تصاویر گرافیکی اثر مثبتی بر پیشرفت ریاضی دانشآموزان دارد. سرانجام میتوان از تحلیلها نتیجه گرفت که وقتی مطلب به صورت همگرا تشریح شود تمرکز و توجه فراگیران معطوف یک روش مشخص میشود و سردرگمی و ابهام آنها کاهش مییابد. در مقابل، مطالبی که به صورت واگرا تشریح شدهاند نوعی ناپیوستگی را در ارائة مطلب ایجاد کردهاند که میتواند مانعی برای یادگیری عمیق دانشآموزان باشد.
Textbooks can be considered the most important and fundamental educational technological tool in the centralized education system of Iran; whose characteristics affect the teaching-learning processes. The aim of this study was to investigate the relationship between the characteristics of the sixth-grade mathematics textbook and students’ academic progress. The research was descriptive and its method was correlational. The statistical population of the study consisted of 1260 sixth-grade students who were studying in Aran and Bidgol in the academic year 1400-1401. The statistical sample size was 850 students who were selected using a multi-stage cluster method. The data collection tool was the “provincial final exam” in the sixth-grade mathematics course. To conduct this study, the students’ exam papers were corrected and scored separately for each chapter (subject) on an interval scale. To test the research hypothesis, first, the topics of the math textbook were coded based on the characteristics of cognitive load, explanation method, mathematical activities (representations and modeling, calculations and operations, interpretations and arguments), the nature of the exercises, and the type of images, and their frequency was recorded by book chapters. Running a regression of the type "multilevel mixed models" revealed various relationships between the characteristics of the sixth-grade math textbook and students’ academic achievement. The regression coefficient of “high cognitive load” showed that with an increase in materials with high cognitive load, the number of graphic images, convergent explanations, and the number of “classwork”, students’ academic achievement increases. In contrast, with an increase in the number of divergent explanations, the number of long materials, and the number of materials containing representations and arguments, a significant drop in students' scores is observed. According to the findings, it can be said that materials with high cognitive load force both teachers and students to focus more on the content of the textbook. Also, increasing the number of graphic images has a positive effect on students' mathematical progress. Finally, it can be concluded from the analyses that when the material is explained in a convergent manner, the focus and attention of the learners are directed to a specific method and their confusion and ambiguity are reduced. In contrast, materials that are explained in a divergent manner have created a kind of discontinuity in the presentation of the material, which can be an obstacle to students’ deep learning.
Abdi, Ali., & Rostami, Maryam. (2018). The Effect of Instruction Based on Cognitive Load theory on Academic Achievement, Perceived Cognitive Load and Motivation to Learning in Science Courses, Journal of Instruction and Evaluation, 40 (1): 43-67. [In Persian]
Ahmadpour, F., Fadae, M. and Rafepour, A. (2017). The Necessity of Rethinking in the Content of 7th and 8th Grades Mathematics Textbooks from the Aspect of Reasoning and Proof. Journal of Curriculum Studies, 12(46), 59-84. [In Persian]
Annisah, S., Zulela. Z., & Boeriswati, E. (2020). Analysis of student needs for mathematics teaching materials. Journal of Physics: Conf. Series, 1469 (2020): 1-8. doi:10.1088/1742-6596/1469/1/012156
Bahrambeiguy, M. (2016). The Role of Image and Color in Textbooks and Academic Books and Its Impacts on Foreign Language Teaching. Popularization of Science, 7(1), 37-53. [In Persian]
Bellens, Kim., Noortgate, Wim. Van den., & Damme, Jan. Van. (2019). The informed choice: mathematics textbook assessment in light of educational freedom, effectiveness, and improvement in primary education. School Effectiveness and School Improvement, 31 (2): 1-20. DOI: 10.1080/09243453.2019.1642215.
Butuner, Suphi. Onder. (2019). A comparison of the instructional content on division of fractions in Turkish and Singaporean textbooks. International Journal of Mathematical Education in Science and Technology, 51 (2): 265-293. DOI: 10.1080/0020739X.2019.1644681
Dockx, Jonas., Bellens, Kim., & De Fraine, Bieke. (2020). Do Textbooks Matter for Reading Comprehension? A Study in Flemish Primary Education. Frontiers in Psychology, 10 (-): doi: 10.3389/fpsyg.2019.02959
Dorri, M., Rafiepour, A. and Dorri, F. (2019). The Capacity of Junior Secondary Math Textbooks to Enhance Deep Learning. Journal of Curriculum Studies, 14(52), 1-30. [In Persian]
Fujita, Taro., & Jones, Keith. (2014). Reasoning-and-proving in geometry in school mathematics textbooks in Japan. International Journal of Educational Research, 64 (-) 81-91. Doi: 10.1016/j.ijer.2013.09.014
Gracin, Glasnovic, D. (2018). Requirements in mathematics texbooks: A five-dimensional analysis of textbook exercises and examples. International Journal of Mathematical Education in Science and Technology, 49 (7): 1003-1024.
Ham, Ann-Katrin., & Heinze, Aiso. (2018). Does the textbook matter? Longitudinal effects of textbook choice on primary school students’ achievement in mathematics. Studies in Educational Evaluation, 59 (-): 133–140.
Haroldson, Rachelle., & Ballard, Dave. (2020). Alignment and representation in computer science: an analysis of picture books and graphic novels for K-8 students. Computer Science Education, 31 (4): 1-17. DOI: 10.1080/08993408.2020.1779520
Hwang, Sunghwan., Yeo, Sheunghyun., & Sonc, Taekwon. (2021). Comparative Analysis of Fraction Addition and Subtraction Contents in the Mathematics Textbooks in the U.S. and South Korea. International Electronic Journal of Elementary Education, 13 (4): 511-521.
Jader, Jonas., Lithner, Johan., & Sidenvall, Johan. (2019). Mathematical problem solving in textbooks from twelve countries. International Journal of Mathematical Education in Science and Technology, 51 (7): 1-17. DOI: 10.1080/0020739X.2019.1656826
Kazemi, Elham., Hintz, Allison. (2014). Intentional Talk: How to Structure and Lead Productive Mathematical Discussions. Portland, Maine: Stenhouse Publishers.
Kenny, David A., Kaniskan, Burcu., & McCoach, D. Betsy. (2014). The Performance of RMSEA in Models with Small Degrees of Freedom. Sociological Methods & Research, 44 (1): 1-22.
Khazaee, A., Khazaee, Thoraya., & Zamanian, Eesa. (2020). The Effect used multimedia with worked examples on learning and Retention in a mathematic course. Teaching and Learning Research, 15(2), 27-36. doi: 10.22070/tlr.2020.2526 [In Persian]
Kheneyfar, K., Shahhosseini, S. & Bagheri, M. (2021). Comparison of the effect of flipped learning through video images and multimedia methods on learning in the mathematical sciense course of sixth grad. Journal of Educational Sciences, 28(2), 79-96. [In Persian]
Khezri A. Peer Tutoring, The Strategy Teaching to Students with special need in the Inclusive system. Journal of Exceptional Education, 2012; 4 (112) :55-60. [In Persian]
Koedel, Cory., Li, Diyi., Polikoff, Morgan. S., Hardaway, Tenice., & Wrabel, Stephani. L. (2017). Mathematics curriculum effects on student achievement in california. AERA Open, 3 (1): 1-22. DOI: 10.1177/2332858417690511
Koparan, Timur. (2017). Analysis of Teaching Materials Developed by Prospective Mathematics Teachers and Their Views on Material Development. Malaysian Online Journal of Educational Technology, 5 (4): 8-28.
Lepik, Madis., Grevholm, Barbro., & Viholainen, Antti. (2015). Using textbooks in the Mathematics Classroom – the Teachers’ View. Nordic Studies in Mathematics Education, 20 (3-4): 129–156.
Li, Y., Chen, X., & An, S. (2009). Conceptualizing and organizing content for teaching and learning in selected Chinese, Japanese and US mathematics textbooks: The case of fraction division. ZDM Mathematics Education, 41 (-): 809–826.
Marple, Stacy., Bugler, Dan., Chen-Gaddini, Min., Burr, Elizabeth., & Finkelstein, Neal. (2017). Why and how teachers choose to supplement adopted materials: Selecting instructional materials. Brief 2-Supplementation. WestEd. Avalable at: http://wested.org/bookstore.
Mayer, R. E.; R. Moreno (1998). A Cognitive Theory of Multimedia Learning: Implications for Design Principles. DOI: 10.1177/1463499606066892.
Miao, Zhenzhen., & Reynolds, David. (2018). The Effectiveness of Mathematics Teaching in Primary Schools: Lessons from England and China. New York: Routledge.
Mikk, Jaan. (2000). Textbook: Research and Writing. Germany, Berlin: Peter Lang.
Mikk, Jaan., & Kukemelk, Hasso. (2009). The relationship of text features to the level of Interest in Science Texts. Trames Journal of the Humanities and Social Sciences, 1464 (1): 54-70.
Morrison, Gary., Ross, Steven. M., & Kalman, Howard. (2011). Designing Effective Instruction. New York: John Wiley & Sons, Inc.
Mortazi Mehrabani, Narges., & Gholamazad, Soheila. (2016). Developing A Model for Required Mathematics Knowledge of Elementary Teachers. Journal of higher education curriculum studies, 6 (12), 135-152. [In Persian]
Nazari Monazzam, Haadi., & Mousavi, Seyed Reza. (2017). Criticism and study of the educational role of images in books teaching Arabic to non-Arabic speakers (Case study: The book History of Arabic Literature, by Hanna Al-Fakhoury). University Textbooks; Research and Writting, 20 (39), 26-44. [In Persian]
Nejati Barzaki, N. , Madani, S. A. and Amini, M. (2020). Investigating Mastery of Female Senior Elementary Students over Science and Mathematics: A Contemplation on the Selection of Curriculum Content in terms of Learnability Criteria. Theory and Practice in the Curriculum, 8(15), 71-106. [In Persian]
Nicol, Cynthia. C.; Crespo, Sandra. M. (2006). Learning to teach with mathematics textbooks: How preservice teachers interpret and use curriculum materials. Educational Studies in Mathematics, 62 (3): 331–355.
Paas, F. & van Merrienboer, J. J. (2020). Cognitive-load theory: methods to manage working memory load in the learning of complex tasks. Current Directions in Psychological Science, 29, 394-398.
Paas, F., Renkl, A. & Sweller, J. (2003). Cognitive load theory and instructional design: recent developments. Educ. Psychol. 38, 1-4.
Parveen, N. (2025). Evidence-Based Practices of Cognitive Load Management to Enhance Learning. Psychol Stud 70, 374-386.
Polikoff, Morgan. S. (2015). How Well Aligned are Textbooks to The Common Core Standards in Mathematics? American Educational Research Journal. X (XX): 1–27. DOI: 10.3102/0002831215584435
Polikoff, Morgan. S., Campbell, Shauna. E., Rabovsky, Sarah., Koedel, Cory., Le, Quynh Tien., Hardaway, Tenice., & Gasparian, Hovanes. (2020): The formalized processes districts use to evaluate mathematics textbooks, Journal of Curriculum Studies, DOI: 10.1080/00220272.2020.1747116
Rahimi, Z., Etedal, A., & Yadegharzade, G. (2021). Assessing the compliance of multiplication and division in elementary school textbooks with mathematics curriculum. Teaching and Learning Research, 17(2), 151-163. [In Persian]
Samavi, S. A., Ebrahimi, K. & Javdan, M. (2017). Relationship between Academic Engagements, Self-efficacy and Academic Motivation with Academic Achievement among High School Students in Bandar Abbas. Journal of Cognitive Strategies in Learning, 4(7), 71-92. [In Persian]
Santrock, John. (2023). Educational Psychology. New York: McGraw Hill.
Sievert, Henning., van den Ham, Ann-Katrin., Niedermeyer, Inga., & Heinze, Aiso. (2019). Effects of mathematics textbooks on the development of primary school children's adaptive expertise in arithmetic. Learning and Individual Differences, 74 (-): 2019.
Silveira, Everaldo. (2021). A Study on the indications to the use of Base Ten Blocks and Green Chips in Mathematics textbooks in Brazil. The Mathematics Enthusiast, 18 (3): 369-501.
Slavin, Robert. E. (2017). Educational Psychology: Theory and Practice (Twelfth Edition). New York: Pearson.
Stylianides, Gabriel. J. (2009). Reasoning-and-proving in School Mathematics Textbooks. Mathematical Thinking and Learning, 11 (4): 258-288. doi:10.1080/10986060903253954
Sweller, J. (2010). Element interactivity and intrinsic, extraneous, and germane cognitive load. Educ. Psychol. Rev. 22, 123-138.
Tan, Kai. J., Ismail, Zaleha., & Abidin, Mardhiyana. (2018). A comparative analysis on cognitive domain for the Malaysian primary four textbook series. EURASIA Journal of Mathematics, Science and Technology Education, 14 (4): 1273–1286. doi.org/10.29333/ejmste/82625
Van de Walle, John A., Karp, Karen. S., & Bay-Williams, Jennifer M. (2018). Elementary and Middle School Mathematics: Teaching Developmentally (9th edition). Boston: Pearson.
Van Den Ham, Ann-Katrin. & Heinze, Aiso. (2018). Does the textbook matter? Longitudinal effects of textbook choice on primary school students’ achievement in mathematics. Studies in Educational Evaluation, 59 (1): 133-140.
Zhang, D., & Qi, C. (2019). Reasoning and proof in eighth-grade mathematics textbooks in China. International Journal of Educational Research, 98, 77–90.
Zhang, E., Ye, Y. & Ni, S. (2025). Effects of Principle- and Procedure-based Feedback on Students' Learning from Self-Made Errors: Roles of Cognitive Load and Learning Speed. Asia-Pacific Edu Res 34, 1689–1699 (2025).
Zou, L., Zhang, Z., Mavilidi, M. et al. (2025). The synergy of embodied cognition and cognitive load theory for optimized learning. Nat Hum Behav 9, 877-885.