تبیین مدلی برای تدریس مبحث ساده‌کردن عبارت‌های جبری در پایه هشتم

نوع مقاله: مقاله پژوهشی

نویسندگان

1 گروه آموزش ریاضی، دانشکده ریاضی و کامپیوتر، دانشگاه شهید باهنر کرمان

2 دانشیار بخش آموزش ریاضی، دانشکده ریاضی و کامپیوتر، دانشگاه شهید باهنر کرمان

چکیده

پژوهش حاضر با هدف طراحی مدلی مبتنی بر نظریه ساخت­وسازگرایی، برای تدریس مبحث ساده­کردن عبارت­های جبری و بررسی تأثیر آن بر یادگیری دانش­آموزان پایه هشتم انجام شد. روش این پژوهش ترکیبی بود؛ بدین ترتیب که برای تبیین مدل طراحی­شده، یک گروه کانونی در سه جلسه تشکیل شد و 15 معلم ریاضی داوطلب در یکی از شهرستان­های شرقی ایران، شرکت کردند. در بخش کمّی، 60 دانش­آموز پایه هشتم همان شهرستان به صورت نمونه­گیری تصادفی خوشه­ای انتخاب شدند و با توجه به طرح آزمایشی، به تصادف در دو گروه کنترل و آزمایش گمارده شدند. پس از گرفتن پیش­آزمون، به گروه آزمایش، مبتنی بر مدل آموزشیِ اعتباربخشی شده و به گروه کنترل، به روش سنتی تدریس شد و در پایان، داده­ها از طریق یک پس­آزمون جمع­آوری شدند. تجزیه و تحلیل داده­ها نشان داد که روش طراحی­شده مبتنی بر ساخت­وسازگرایی، مناسب­تر از روش­های سنتی بود و تأثیر مثبتی بر یادگیری دانش­آموزان پایه هشتم گذاشت.

کلیدواژه‌ها


عنوان مقاله [English]

Developing a Model based on Constructivism Approavh for Teaching Simplification of Algebraic Expressions in the 8th Grade

نویسندگان [English]

  • nooshin faramarzpoor 1
  • , Mohammad Reza Fadaee 2
2 Associate Professor of Department of Mathematics Education, Shahid Bahonar University of Kerman
چکیده [English]

The aim of the present study was developing a model based on constructivism approach, for teaching simplification of algebraic expressions in the 8th Grade. Mixed method proved to be suitable for the study. At the first phase, a primitive model was designed and a focus group was formed consisting of 15 volunteer mathematics teachers of the same grade and they met three times until the model was modified and validated for implementation. At the second phase, an experimental study was designed involving 60 Grade 8 students that randomely selected and assigned to two experimental and control groups. After taking the pre-test, the control group was taught as usual and the experimental group was taught using the developed model as treatment. At the end, a post- test was carried out for both groups. The results showed that the difference between two groups was statistically significant in the favor of the experimental group that indicates that posivie effectiveness of the developed model on the students’ performance in Grade 8.

کلیدواژه‌ها [English]

  • constructivism
  • simplification of algebraic experessions
  • Mixed Method
  • Grade 8 Students
بیرامی­پور، علی و لیاقت­دار، محمدجواد. (1388). بررسی کیفیت تدریس درس ریاضی پایه چهارم دبستان شهر اصفهان به منظور ارائه راهکارهایی برای بهبود عملکرد دانش آموزان در آزمون بین المللی تیمز. فصلنامه تعلیم و تربیت. شماره 100. صص. 49 تا 68. سازمان پژوهش و برنامه­ریزی آموزشی، وزارت آموزش­وپرورش.  
Baker, W., Czarnocha, B., & Prabhu, V. (2004). Procedural and conceptual knowledge in mathematics. Proceedings of the North American Chapter of the International Group for the Psychology of Mathematics Education. Toronto, Ontario, Canada.
Beyrami poor, A., & Liaqat dar, M. J. (2009). Quality of teaching of mathematics of fourth grade in Isfahan in order to provide strategies for improving student performance in international tests Thames. Journal of Education, 25 (4), 49-68. (In Farsi.)
Booker, G. (1987). Conceptual obstacles to the development of algebraic thinking. In J. Bergeron, N. Herscovics & C. Kieran (Eds.). Proceedings of the eleventh international conference Psychology of Mathematics Education (Vol. 1, pp. 275-281). Montreal: PME.
Bush, S. B. (2011). Analyzing common algebra-related misconceptions and errors of middle school students (Doctoral dissertation). Retrieved from https://doi.org/10.18297/etd/187.
Capraro, M. M. & Joffrion, H. (2006). Algebraic equations: Can middle-school students meaningfully translate from words to mathematical symbols? Journal of Reading Psychology, 27 (1), 147-164. Doi: 10.1080/027027106006442467.
Cavallo, A.M.L., & Laubach, T.A. (2001). Students’ science Perceptions and Enrollment Decisions in Differing Learning Cycle Classrooms. Journal of Research in science Teaching, 38(9):1029- 1062.
Dekock, A., Sleepers, P., & Voeten, JM. (2004). New Learning and the Classification of Learning Environments in Secondary Education. Review of Educational Research. 74 (2). 141-170.
Doerr, H. (2004). Teacher’s knowledge and the teaching of algebra. In K. Stacey, H. Chick & Kendal (Eds.), The Future of Teaching and Learning of algebra. The 12th ICMI Study (pp. 267-290). Boston: Kluwer.
Dogru, A. P. and Tekkaya, C. (2008). Promoting Students Learning in Genetics with the Lesrning Cycle. Journal of Experimental Education, 76 (3).
Driscoll, M. (2000). Psychology of Learning for instruction. Needham Heights, MA, Allyn & Bacon.
Fleisch, B. (2008). Primary education in crisis: Why South African Schoolchildren underachieve in reading and mathematics. Juta Academic: Cape Town, South Africa. Retrieved from http://www.amazon.co.uk.
Floger, E. (2005). Efficacy of mastery learning as a method of instruction: implications for instructional leaders (Doctoral desertation). Ashland, Ashland University.
Frid, S. (2000). Using learning cycle in mathematics: more than the sum of parts. Australian Mathematics teacher, 56 (4): 32-37.
Guler, M. & Celic, D. (2016). A research on future mathematics teacher’s instructional explanations: the case of algebra. Journal of Educational Research and Reviews. 11(16), 1500-1508. 10.5897/ERR2016.2823.
Hakkarainen, A., Holopainen, L., & Savolainen, H. (2013). Mathematical and reading difficulties as predictors of school achievement and transition to secondary education. Scandinavian Journal of educational research, 57(5): 488-506.
Jacobse, A. E., & Harskamp, E. G. (2012). Toward efficient measurement of metacognition in mathematical problem solving. Metacognition and Learning, 7 (2): 133-149.
Jia, Q. (2010). A /brief Study on the Implication of Constructivism Teaching Theory on Classroom Teaching Reform in Basic Education. International Education Studies, 3 (2): 197-199.
Jordan, N. C., & Levine, S. C. (2009). Socioeconomic variation, number competence, and mathematics learning difficulties in young children. Developmental Disabilities Research Reviews, 15 (1): 60-68.
Kaput, J. (2008). What is algebra? What is algebraic reasoning? In J.J. kaput, D. W. Carraher & M. L. Blanton (Eds.), Algebra in the early grades (pp. 5-18). New York: Taylor & Francis Group & National Council of Teachers of Mathematics.
Lacroix, L.N. (1991). Mathematics Teaching Practice: A Constructivist Perseptive (Unpuplished manuscript), the University of British Columbia, Canada.
Lebow, D. (1993). Constructivist Values of Instructional System Design: Five Principles toward a new Mindset. Educational Technology Research & Development (ETR&D), 41 (3). 4-16.
MacGregor, M. (2004). Goals and Content of an algebra curriculum for the compulsory years of schooling. In K. Stacey, H. Chick & Kendal (Eds.), The Future of Teaching and Learning of algebra: The 12th ICMI Study (pp. 313-328). Boston: Kluwer.
Mamba, A. (2012). Learner’s errors when solving algebraic tasks: A case study of grade 12 mathematics examination papers in South Africa (Unpublished doctoral dissertation). Johannesburg University, South Africa.
Mest, O. (2006). The effect of (7E) learning cycle model on Improvement of fifth grade students’ critical thinking skills. A thesis submitted to the graduate school of natural land applied sciences of Middle East Technical University.
Norton, S. & Irwin, J. (2007). A concrete approach to teaching algebra. In J. M. Watson& K. Beswick (Eds.), Proceedings of the 30th annual conference of the Mathematics Education Research Group of Australasia. (pp. 561-570). Hobart, Sydney: MERGA.
Novello, A. C., Degraw, C., & Kleinman, D. (2007). Healthy children ready to learn: An essential collaboration between health and education. Public Healthy Reports, 107: 3-15.
Odom, A.L., & Kelly, P.V. (2001). Integrating Concept Mapping and the Learning Cycle to Teach Diffusion and Osmosis Concepts to High School Biology Students. Science Education, 85, 615-635.
Olsen, DG. (2000). Constructivist principles of Learning and Teaching Methods. Education. 120 (2). 347-355.
Olusegun, B.S. (2015). Constructivism Learning Theory: A Paradigm for Teaching and Learning. IOSR Journal of Research & Method in Education, 5(6): 66-70.Doi: 10.9790/7388-05616670
Owusu, J. (2015). The Impact of Constructivist- Based Training method on Secondary School Learners Errors in Algebra (Master dissertation). Retrieved from http://hdl.handle.net/10500/19207.
Polya, G. (1945). How to solve it. Princeton University Press. Princeton science library.
Reyna, V. F., & Brainerd. C. J. (2007). The importance of mathematics in health and human judgment: Numeracy, risk communication, and medical decision making. Learning and Individual Differences, 17(2):147-159.
Richard, J. C. (1996). Turning to the artistic: developing an enlightened eye by greating teaching self-portraits. Paper presented at the international conference, Herstmonceux castle, East Sussex, England, August 5-8.
Seng, L. K. (2010). An error analysis of Form 2 (Grade 7) students in simplifying algebraic expressions: A descriptive study. Electronic Journal of Research in Education Psychology, 8(1): 139-162.
Shoenfeld, A.H. (1995). Cognitive Science and Mathematics Education Overview.
Shulman, L.S. (1986). Those who understand: knowledge growth in teaching. Journal of Educational researcher, 15 (2), 4-14. doi: 10. 3102/0013189X015002004.
Thompson, S. A., & Tilden, V. P. (2009). Embracing quality and safety education for the 21st century: building inter ptofessional education. Journal of Nursing Education, 48: 698-701.
Usiskin, Z. (1995). Why is algebra important to learn? American Educator, 30-37.
Woolley, N. N., Jarvis, Y. (2007). Situated cognition and cognitive apprenticeship: A model for teaching and learning clinical skills in a technologically rich and authentic learning environment. Nurse Educ Today, 27(1): 73-9.