The effect of problem posing on learning geometric concepts of students based on APOS theory
Subject Areas : Statisticsvahid alamian 1 , esmaeil andayeshgar 2
1 - department of mathematics farhangian university, tehran ,iran
2 - department of mathematics farhangian university, tehran ,iran
Keywords: Problem posing , Actions , Processes , Objects , Shemas,
Abstract :
Problem posing is one of the new teaching-learning methods in which students are given the opportunity to construct their own problems or reformulate existing problems. The purpose of this study is the effect of problem posing on ninth-grade students’ understanding of mathematics in concept of volume and area of geometric solids based on APOS theory. Its statistical population is the ninth-grade high school male students of Salmas County of West Azerbaijan province who studied in1400-1399. The sample was available to40 people for both experimental and control groups. This study is quasi-experimental in terms of practical purpose and implementation. The measurement tool of this research was two researcher-made written tests whose questions were selected based on APOS theory. Cronbach's alpha coefficient of pre-test and post-test were 0.794 and 0.809, respectively. The results of this study showed that the problem posing improved the average level of understanding of students in the experimental group compared to the control group based on APOS theory. Also, the problem posing created a significant difference between the performance of students in the experimental group and the control group in favor of the experimental group at the level of 0.05. Therefore, problem posing has an effect on students' mathematical understanding and improves their level of understanding based on APOS theory.
[1] National Research Council.(2001). Adding it up: Helping children learn mathematics. J. Kilpatrick, J. Swafford, and B. Findell (Eds.). Mathematics Learning Study Committee, Center for Education, Division of Behavioral and Social Sciences and Education. Washington, DC: National Academy Press.
[2] سازمان پژوهش و برنامه¬ریزی آموزشی (1396). هندسه1، پایة دهم دوره دوم متوسطه، شرکت چاپ و نشر کتابهای درسی ایران.
[3] Silver, E. A.(1994): On mathematical problem posing . For the Learning of Mathematics, 14(1), 19–28.
[4] Erdik, C.(2019). Investigation of Mathematics Teachers’ Opinions about Problem Posing. Journal on Mathematics Education, 10(1), 1-20
[5] Arnon et al.(2014), APOS Theory: A Framework for Research and Curriculum Development in Mathematics Education, Springer Science+Business Media New York2014
[6] Cai et al.(2015), Mathematical Problem Posing : From Research to Effective Practice, Springer Science+Business Media New York 2015
[7] Cildir, s & sezen, n(2011). A study on the evaluation of problem posing skills in terms of academic success. Procedia Social and Behavioral Sciences15, 2494–2499.
[8] Kontorovich,I. et al(2012): An exploratory framework for handling the complexity of mathematical problem posing in small groups. Journal of Mathematical Behavior 31(1), 149– 161.
[9] ریحانی، ابراهیم و اسکندری، مجتبی.(1393). بررسی فرآیند طرح¬مسئله در آموزش ریاضی. دو فصل نامه نظریه و عمل در برنامه درسی، سال دوم، شماره3، بهار و تابستان1393،117-140
[10] NCTM.(2000): Principles and Standards for School Mathematics. Reston, VA: The National Council of Teachers of Mathematics, Inc.
[11] Stoyanova, E. & Ellerton, N. F.(1996). A framework for research into students’ problem posing. P. Clarkson(Ed.), Technology in Mathematics Education,(pp.518–525). Melbourne: Mathematics Education Research Group of Australasia.
[12] English, Lyn D.(1997). The Development of Fifth-Grade Children's Problem-Posing Abilities. Educational Studies in Mathematics, 34(3): 183-217.
[13] Christou, C et al. (2005). An Empirical Taxonomy of Problem Posing Processes. International Reviews on Mathematical Education, 37(3), 1-10.
[14] Brown, S. I. & Walter, M. I.(2005). The art of problem posing. London, Lawrence Erlbaum Associates, Ink
[15] Lavy, I. & Bershadsky, I.(2003). Problem Posing via "What if not?" strategy in Solid Geometry - A Case Study. The Journal of Mathematical Behavior, 22(4), 369-387.
[16] Contreras, José(2007). Unraveling the Mystery of the Origin of Mathematical Problems: Using a Problem-Posing Framework With Prospective Mathematics Teachers. The Mathematics Educator, 17(2), 15–23.
[17] Song, S. H. et al(2007). Posing problems with use the ‘what if not?’ strategy in nim game. In Woo, J. H. Lew, H. C. Park, K. S. & Seo, D. Y. (Eds). Proceedings of the 31st Conference of the International Group for the Psychology of Mathematics Education(pp. 193-200). Seoul: PME.
[18] Vistro-Yu, C.(2009). Using Innovation Techniques to Generate New Problems. In: In B. Kaur, Y. B. Har, M. Kapur (Eds.), Mathematical Problem Solving (pp.185-207). Singapore: World Scientific Publishing Co. Pte. Ltd.
[19] Asiala, M. et al(1996).A framework for research and curriculum development in undergraduate mathematics education.In Research in Collegiate mathematics education II. CBMS issues in mathematics education(Vol. 6, pp. 1–32). Providence, RI: American Mathematical Society.
[20] Tall, D. (1999). What is the object of the encapsulation of process? Proc. Of MERGA (pp.132-139). New Zealand: Rotarua.
[21] Weyer, S.(2010). APOS Theory as a Conceptualization for Understanding Mathematical Learning. Summation: Mathematics and Computer Science Scholarship at Ripon, 3, 9-15.
[22] نظری،کامل(1390). بررسی تاثیر تدریس بر میزان درک دانش¬آموزان دختر سال سوم ریاضی از مفهوم حد و رشد توانایی فضایی آن¬ها با تاکید بر فعالیت¬های مبتنی بر تجسم، پایان¬نامه کارشناسی ارشد، تهران، دانشگاه تربیت دبیر شهید رجایی.
[23] خوشنود خناچاه، محمد(1397)، تأثیر کنترل از دیدگاه شونفیلد بر میزان افزایش سطح درک دانش¬آموزان از موضوع حد براساس نظریةAPOS، پایان¬نامه کارشناسی ارشد، تهران، پردیس شهید چمران، مرکز آموزش عالی شهید بهشتی.
[24]Matenga Bernard (2016). Exploring Students’ Understanding Of Ordinary Differential Equations At A High School In Bikita District: A Case Of An Apos Theory , requirements For A Degree Of Master Of Science Education In Mathematics, Zimbabwe , Bindura , University Of Science Education.
[25] Kemal Ozgen et al ,(2019), An Investigation of Eighth Grade Students’ Skills in Problem-Posing , International Journal For Mathematics Teaching And Learning 2019, Vol. 20.1, 106-130
[26] María C. Cañadas et al ,( 2018 ), Meanings given to algebraic symbolism in problem-posing , Springer Science+Business Media B.V., part of Springer Nature2018
[27] برجی، وحید(1397)، بررسی تأثیر کاربرد نظریةAPOS-ACE در رشد درک نموداری دانشجویان از مفهوم مشتق، پایان¬نامه دکتری، مشهد، دانشگاه فردوسی، دانشکده علوم ریاضی.