آموزش جمع و تفریق: مطالعه مقایسه‌ای در باره اهداف برنامه و محتوای کتب درسی ریاضی پایه‌ی اول ابتدایی کشورهای ایران، ژاپن و آمریکا
محورهای موضوعی : پژوهش در برنامه ریزی درسیمهدی ایزدی 1 , ابراهیم ریحانی 2 , غلامعلی احمدی 3
1 - 1کارشناس ارشد آموزش ریاضی، واحد علوم و تحقیقات فارس، دانشگاه آزاد اسلامی، فارس، ایران
2 - 2دانشیار گروه ریاضی دانشگاه تربیت دبیر شهید رجایی، تهران، ایران
3 - 3دانشیار گروه برنامه ریزی درسی دانشگاه تربیت دبیر شهید رجایی، تهران، ایران
کلید واژه: برنامه درسی ریاضی, تفریق, اول ابتدایی و کتاب درسی, آموزش جمع,
چکیده مقاله :
پژوهش حاضر با هدف بررسی فرآیند آموزش اعمال جمع و تفریق در اهداف برنامه و محتوای کتب درسی ریاضی پایه اول ابتدایی سه کشور ایران، ژاپن و آمریکا، صورت گرفت. جامعه آماری این تحقیق، اهداف برنامه و محتوای کتب درسی ریاضی پایه اول ابتدایی سه کشور فوق بود. این تحقیق با روش توصیفی تحلیلی تطبیقی صورت گرفت که برای جمع‌آوری داده‌ها از روش مطالعه اسنادی و برای تحلیل داده‌ها، از روش تحلیل کیفی استفاده شد. نتایج این بررسی نشان داد که در برنامه‌ی درسی در آمریکا تمرکز بر روی افزایش توانایی حل مسأله است درحالی‌که برنامه درسی ایران، بیشتر بر روی مفهوم‌سازی مناسب این دو عمل و ایجاد درک درست" در دانش‌آموزان تمرکز دارد. برنامه درسی ژاپن هم بیشترین تأکید را بر کسب درک صحیح و کشف روش‌های جمع و تفریق توسط خود دانش‌آموزان دارد. در فرآیند آموزش این دو عمل کتاب درسی آمریکا، بیشترین تعداد روش آموزش را نسبت به کتاب‌های دیگر داراست. در شروع آموزش عمل جمع و تفریق، به جز کتاب جدید ایران (2011) در همه کتاب‌ها از جنبه ترکیبی جمع و جنبه کاهشی تفریق استفاده شده است.
Focusing on the math curriculum goals and content of the first-grade math textbooks in Iran, Japan and the USA, this research aimed to study about the process of teaching addition and subtraction. The math curriculum goals and content of the first-grade math textbooks of these three countries were considered as the statistical populations of the study. To collect the data documentary research was utilized and comparative method was used in order to analyze the data. The findings showed that the American curriculum focused on enhancing the ability of "problem solving " whereas, the Iranian program focused more on the "making sense and understanding the concept". On the other hand, Japan's curriculum emphasized on "understanding and exploring adding and subtracting ways" by the students themselves. During the process of teaching these two operations, American textbooks introduced the largest number of teaching methods. In the beginning of teaching addition and subtraction, except the new version of Iranian book (2011), all the books, initially teaching addition and subtraction, focused on the combination aspect of addition and reduction aspect of subtraction.
Abedi, M.R. (2004). Creativity. Tehran: Jami publication. Alamian, V. (2011). Guide to first-grade math reprogram. first-grade Mathematics. Retrieved april 3, 2012, from http://saheleriyaziyat.com California Department of Education. (2010). K-12 California’s Common Core Content Standards for Mathematics. Curriculum & Instruction. Retrieved July 7, 2012 from http://www.cde.ca.gov. Carpenter, T. P., & Moser, J. M. (1984). The acquisition of addition and subtraction concepts in grades one through three. Journal for Research in Mathematics Education, 15, 179–202. Davoodi, KH., Rastgar, A., & Alamian, V. (2011). Grade 1 Math- 2,volume1 .Iran: General Department printing and distribution of textbooks. Erdoĝan, E. Ö. (2010). A comparison of curricula related to the teaching of addition and subtraction concepts. Procedia social and behavioral sciences, 2(2011), 5247-5250. doi:10.1016/j.sbspro .2010.03.854 Fan, L., & Zhu, Y. (2007). Representation of problem-solving procedures: A Comparative Look at China, Singapore, and US mathematics textbooks. Educ Stud Math, 66, 61-75. doi: 10.1007/s10649-006-9069-6 Fujii, T., & Iitaka, S. (2012). Mathematics International Grade1. Tokyo: Tokyo shoseki. Gooya, Z. (2006). The process of change the content of the school mathematics curriculum. Roshd Mathematics Education Journal, 12(46), 8-12. Teaching-Aids Publications Office, Organization of Research& Educational Planning, Ministry of Education [Persian]. International Association for the Evaluation of Educational Achievement (IEA) (2011). TIMSS & PIRLS. Retrieved july 7, 2012, from http://timss.bc.edu Izadi, M. (2012). A Comparative Content Analysis of the First-Grade Math Curriculum Goals and Content of the Bookʼ Iran, Japan and America (State of California) (Unpublished masterʼs thesis). Islamic Azad University Fars Science and Research Branch, Shiraz, Iran. Karimi, A. (2009). The main findings of the TIMSS and PIRLS studies Persian date Farvardin 1388 .Tehran: Research Institute for Education. Kiamanesh, A. (2005). The Role of Students’ Characteristics and Family Background in Iranian Students’ Mathematics Achievement. Prospects, 35(2), 161-174. Maleki, JH. (2012). Describe the processes of learning numbers by students with focusing on new book 0f first grade math (Unpublished masterʼs thesis). Shahid Beheshti University, Tehran, Iran. Nazari, k. (2011). Checking impact of visualization activities- centered on nurturing spatial abilities and understanding the concept of limit of third year of secondary of the female students (Unpublished masterʼs thesis). Shahid Rajaee University, Tehran, Iran. Peters, G., De Smedt, B., Torbeyns, J., Ghesquière, P., & Verschaffel, L. (2012). Children’s use of subtraction by addition on large single-digit subtractions. Educ Stud Math, 79(3), 335-349. doi: 10.1007/s10649-011-9308-3 Rafia poor gatabi, A. (2010). Designing framework for creating balance in Secondary mathematics curriculum of Iran (Unpublished doctoral dissertation). Shahid Beheshti University, Tehran, Iran. Reyhani, E., Ahmadi, GH., & Karami Zarandi, Z. (2011). Comparative study of the problem solving process taught in high school mathematics curriculum America, Australia, Japan, Singapore and Iran. Quarterly Journal of Education, 27(1), 115-142 [Persian]. Rostami, M.H., Karimpoor, R., & Lellahi, K. (2010). Grade 1 Math- 2 .Iran: General Department printing and distribution of textbooks. Salimi, M., Sadi Pour, E., Delavar, A., & Maleki, H. (2014). Comparison of training effects in imagery strategies of mental imagery of think-aloud of written representation and motor representation on the performance of elementary students in solving verbal math problems. Research in Curriculum Planning, 11(14), 12-22 [Persian]. Scribner, S. (1984). ‘Studying working intelligence’, in B. Rogoff and J. Lave (Eds.), Everyday Cognition: Its Development in Social Context (pp. 9–40). Harvard University Press, Cambridge, MA. Selter, C. (2001). Addition and Subtraction of Three-Digit Numbers: German Elementary Children’s Success, Methods and Strategies. Edue Stud Math, 47, 145-173. Selter, C., Prediger, S., Nührenbörger, M., & Hußmann, S. (2012). Taking away and determining the difference-a longitudinal perspective on two models of subtraction and the inverse relation to addition. Educ Stud Math, 79(3), 389-408. Takahashi, A., Watanabe, T., & Yoshida, M. (2008). English Translation of the Japanese Mathematics Curricula in the Course of Study (Grades 1-9). Globaledresources. Retrieved from http://www.globaledresources.com The McGraw-Hill. (2009). California mathematics,volume1 .USA: The McGraw-Hill companies. Torbeyns, J., De Smedt, B., Ghesquière, P., & Verschaffel, L. (2009). Solving subtractions adaptively by means of indirect addition: Influence of task, subject, and instructional factors. Mediterranean Journal for Research in Mathematics Education, 8(2), 1–30. Torbeyns, J., Verschaffel, L., & Ghesquière, P. (2005). Simple addition strategies in a first-grade class with multiple strategy instruction. Cognition and Instruction, 23, 1–21. Torner, G., Schoenfeld, A.H., & Reiss, K.M. (2007). Problem solving around the world: Summing up the state of the art. ZDM Mathematics Education. Springer: Berlin /Heidelberg. Treffers, A. (1987). Three dimensions: A model of goal and theory description in mathematics education. The Wiskobas project. Dordrecht: Reidel. Verschaffel, L., & De Corte, E. (1996). Number and arithmetic. In A. Bishop, K. Clements, C. Keitel, & C. Laborde (Eds.), International handbook of mathematics education (1st ed., pp. 99–138). Dordrecht: Kluwer. Verschaffel, L., Greer, B., & De Corte, E. (2007). Whole number concepts and operations. In F. K. Lester (Eds.), Second handbook of research on mathematics teaching and learning (pp. 557–628). Charlotte, NC: Information Age Publishing. Verzosa, D.B., & Mulligan, J. (2012). Learning to solve addition and subtraction word problems in English as an imported language. Edue Stud Math. doi: 10.1007/s10649-012-9420-z Watanabe, T. (2011). Shiki: A Critical Foundation for School Algebra in Japanese Elementary School Mathematics. In J. Cai & E. Knuth (Eds.), Early Algebraization (pp.109-124). USA, New York: Springer.
_||_