Document Type : Research
Authors
1 Ph.D. Student, Curriculum Planning, Shahid Rajaee Teacher Training University & Math Educator of Far-hangian University
2 Associate Professor, Department of Educational Sciences, Shahid Rajaee Teacher Training University, Tehran, Iran
Abstract
The aim of the present research was the designing and validating a Pattern of Curriculum for Developing the Student Teachers Specialized Content Knowledge in Division of Fractions. This research was the mixed Research with Exploratory Design and Taxonomy Devlopment Model. In the qualitative part, the Curriculum Pattern was designed with case study method , and in the quantitative part, the Pattern validation was done with Descriptive-survey method. Participants in the qualitative Part included 19 experts and 61 sources. The statistical population in quantitative part included the specialists in math education and primary school teachers. Through purposive sampling, 22 specialists and 85 teachers were selected. For collecting qualitative data, documentary study, semi-structured interviews and for collecting quantitative data, researcher-made questionnaire with 13 items were used. For analyzing the qualitative data, the content analysis was used and in the quantitative part, confirmatory factor analysis was used. Results of analysis of elements showed that the items of content and learning activities, skill goals, cognitive goals at the level of analysis and composition level and evaluation methods have the most explanatory power. Also other elements such as teaching-learning methods, attitudinal goals and Clarity and comprehensiveness were in next priorities.
Keywords
ایزدی، مهدی و ریحانی، ابراهیم (1399). استفاده از یک تکلیف غیرمعمول برای بررسی دانش تکلیف ریاضی و دانش محتوایی عمومی معلمان دورة ابتدایی استان تهران از مفهوم کسر. فصلنامه علمی پژوهش در یادگیری آموزشگاهی و مجازی. سال هفتم، شماره چهارم. دانشگاه پیام نور. صص: 7055
داناییفرد، حسن و اسلامی، آذر (1390). ساخت نظریة بیتفاوتی سازمانی (کاربرد استراتژی پژوهشی نظریة داده بنیاد در عمل). تهران: دانشگاه امام صادق. چاپ اول.
رحیمی، زهرا؛ طلایی، ابراهیم؛ ریحانی، ابراهیم و فردانش، هاشم (1396). تاکید بر راهحلهای چندگانه: کلیدی برای تقویت مهارت تعمیم در تفکر ریاضی‌وار. فصلنامه تعلیم و تربیت. شماره130. 40 9.
شورای عالی آموزش و پرورش (1391). برنامة درسی ملی جمهوری اسلامی ایران. وزارت آموزش و پرورش.
شورای عالی آموزش و پرورش (1390). سند تحول بنیادین آموزش و پرورش. وزارت آموزش و پرورش.
فراستخواه، مقصود (1395). روش تحقیق کیفی در علوم اجتماعی با تاکید بر نظریة بر پایه. تهران: آگاه. چاپ سوم.
کرسول، جان و کلارک، پلانو (2007). روشهای پژوهش ترکیبی. ترجمة علیرضا کیامنش و جاوید سرابی (1394). تهران: آییژ. چاپ دوم.
ملایینژاد، اعظم (1391). صلاحیت‌های حرفه‌ای مطلوب دانشجو معلمان دورة آموزش ابتدایی. فصلنامه نوآوریهای آموزشی، شماره 44.
مرکز ملی مطالعات بین‌المللی پرلز و تیمز (1395)، پژوهشگاه مطالعات آموزش و پرورش، سازمان پژوهش و برنامه‌ریزی آموزشی، وزارت آموزش و پرورش.
Alenazi. A. (2014). Understanding pre-service teachers' self-assessment : the case of fraction division. Submitted to the Graduate Faculty as partial fulfillment of the requirements for the Doctor of Philosophy Degree in Curriculum and Instruction. University of Toledo.
Alenazi. A. (2016). Development of an Instrument to Measure Fraction Division Paration Sense. Proceedings of Intcess. International Conference on Education and Social Sciences. 656-663.
Bair, S.G & Rich, B.S. (2011). Characterizing the Development of Specialized Mathematical Content Knowledge for Teaching in Algebraic Reasoning and Number Theory. Mathematical Thinking and Learning, Illinois State University. 13: 292–321.
Ball, D. (1990). The mathematical understandings that prospective teachers bring to teacher education. Elementary School Journal , 90 (4), 449-466.
Ball, D. L, Hill, H. C, & Bass, H. (2005). Knowing Mathematics for Teaching. the quarterly journal of the American Federationof Teachers, AFL-CIO. American Educator,14–22.
Ball, D. L, Thames, M. H, & Phelps, G. (2008). Content Knowledge for Teaching. What makes it special? Journal of Teacher Education. 389-407.
Ball, D. L. (1990). Prospective elementary and secondary teachers’understanding of division. Journal for Research in Mathematics Education. 132–144.
Ball, D. L., & Bass, H. (2000). Interweaving content and pedagogy in teaching and learning to teach: Knowing and using mathematics. In J. Boaler (Ed)., Multiple perspectives on the teaching and learning of mathematics. 83 – 104.
Ball, D. L. (2016). Content knowledge for Teaching: Examples from Elementary Mathematics. Client Conference.
Burke, M.K. (2013). Examining Mathematical Knowledge for Teaching In TheMathematics Teaching Cycle:A Multiple Case Study. A Dissertation Presented in Partial Fulfillment of the Requirements for the Degree Doctor of Philosophy.Rizona State University.
Carollo, L.R. (2013). Beyond Elementary: Examining Conceptual Demands of Division of Fractions in Current US Curricula. Oregon Undergraduate Research Journal. 4:35-53.
Carpenter, T. C., Lindquist, M. M., Brown, C. A., Kouba, V. L,Silver, E. A., & Swafford, J. O. (1988). Results of the fourth NAEP assessment of mathematics: Trends and conclusions. Arithmetic Teacher. 36 (4), 38–41.
Carreno. E, Rojas. N, Montes .M, Flores. P. (2013). Mathematics Teacher’s Specialized Knowledge. Reflections Based on Specific Descriptors of Knowledge. ‘Research Seminar. into Mathematics Education "University of Huelva, Spain. 2976-2984.
Chapin, S. (2014). Teachers Specialized Content Knowledge: Preparing Future Elementry School Teachers to Teach Mathematics. Boston University. 1-28.
Chen, X. (2010). A Study of Prospective Mathematics Teachers Knowledge Devlopment and Beliefs Changes for Teachings Fraction Division. Submitted to the Office of Graduate Studies of Texas A&M University in partial fulfillment of the requirements for the degree of Doctor of Philosophy.
Chinapan, S. (2014). Teachers Specialized Content Knowledge: Preparing Future Elementery School Teachers to Teach Mathematics. Elementry Pre-Service Teachers Mathematics Project (EMP) Bostone University.
Chinnappan, M & White, B. (2015). Specialised Content Knowledge: Evidence of Pre-service teachers’Appraisal of Student Errors in Proportional Reasoning. Mathematics education in the margins (Proceedings of the 38th annual conference of the Mathematics Education Research Group of Australasia), 157–164.
Chinnappan, M., Forrester. T, Hoare. E.T. (2012). Developments in Pre-service Teachers’ Mathematics for Teaching of Fractions. Mathematics education: Expanding horizons (Proceedings of the 35th annual conference of the Mathematics Education Research Group of Australasia). Singapore: MERGA.
Christou.C & et ai. (2005). An empirical taxonomy of problem posing processes. ZDM 2005 Vol. 37 (3)
Diaz.j.p , Felmer.P , Randolph.V , González.G. (2017). Problem Solving as a Professional Development Strategy for Teachers: A Case Study with Fractions. EURASIA Journal of Mathematics Science and technology Education. 13 (3):987-999.
Ding. M & Heffernan. K. (2018).Transferring specialized content knowledge to elementary classrooms: preservice teachers’ learning to teach the associative property. International Journal of Mathematical Education in Science and Technology. 1-23.
Ding, M. (2016). Developing preservice elementary teachers’specialized content knowledge: the case of associative property. International Journal of STEM Education. 3:9. 1-19.
English, L. D. (1998). Children’s problem posing within formal and informal contexts. – In: Journal for Research in Mathematics Education 29 (No.1: 83-106.
Flores. E, Escudero .D.I, Carillo. G. (2013). A Theoritical Review of Specialised Content Knowledge. University of Huelva, Spain. 3055-3064.
Gregg, J., & Gregg, D. (2007). Measurement and fair-sharing models for dividing fractions. Mathematics Teaching in the Middle Grades, 12 (9), 490–496.
Hiebert, J., & Lefevre, P. (1986). Conceptual and procedural knowledge in mathematics:An introductory analysis. In J. Hiebert (Ed.), "Conceptual and procedural knowledge: The case of mathematics". 1-27.
Hill, Heather .C & Ball, Deborah. L & Schilling, Stephan, G. (2008). UnpackingPedagogical Content Knowledge: Conceptualizing and Measuring Teachers’Topic-Specific Knowledge of Students. Journal for Research in Mathematics Education, Vol. 39, No. 4,372-400.
Hurrell, D. P. (2013). What Teachers Need to Know to Teach Mathematics: An argument for a econceptualised model. Australian Journal of Teacher Education, Vol 38.54-64.
International Journal of Scientific and Research Publications (2016). Pre-service teachers’ procedural and conceptual knowledge of fractions. Vol. 6.324-328.
Jacinto & Jakobsen. (2020). Mathematical Knowledge for Teaching: How do Primary Pre-service Teachers in Malawi Understand it? African Journal of Research in Mathematics, Science and Technology Education. 1-10.
Jackson. B, Dimmel. J , Muller, M. (2016). Developing mathematical knowledge for teaching in content courses for preservice elementary teachers. University of Maine. 1-6.
Jane Lo, J.J & Luo. F. (2012). Prospective elementary teachers’ knowledge of fraction division. J Math Teacher Educ. Springer Science+Business Media B.V.
Jóhannsdóttir, B. (2013). The Mathematical Content Knowledge of Prospective Teachers in Iceland .Submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy under the Executive Committee of the Graduate School of Arts and Sciences. Columbia University.
Lai, M.Y & Clark, J. (2018). Extending the notion of Specialized Content Knowledge: Proposing constructs for SCK. Mathematics Teacher Education and Development. Vol 20.2, 75-95
Lai, M.Y & Ho, S.Y. (2012). Preservice Teachers Specialized Content Knowledge on Multiplication of Decimals. 12th International Congress on Mathematical Education Program Name XX-YY-zz (pp. abcde-fghij) .8 July – 15 July, 2012, Coex, Seoul, Korea.
Leung, I.K, Carbone. R.E. (2013). Pre-service Teachers’ Knowledge about Fraction Division Reflected through Problem Posing. The Mathematics Educator. Vol. 14, No. 1&2, 80-92.
Li, Y. (2008). What do students need to learn about division of fractions? Mathematics Teaching in the Middle School, 13, 546–552.
Li.Y , Kulm.G (2008). Knowledge and confidence of pre-service athematics teachers:the case of fraction division. ZDM Mathematics Education. 40:833–843.
Lin, Y. C., Chin, C. & Chiu, H.Y. (2011). Developing an instrument to capture high school mathematics teachers’ specialized content knowledge: An exploratory study. In Ubuz, B. (Ed.). Proceedings of the 35th Conference of the International Group for the Psychology of Mathematics Education, Vol. 1, pp. 353. Ankara, Turkey: PME.
Lo. J.J, Luo. F. (2012). Prospective elementary teachers’ knowledge of fraction division. J Math Teacher Educ. DOI 10.1007/s10857-012-9221-4.
Lueke, H.M. (2009). Pre-Service Teachers Mathematical Knowledge for Teaching: A Comparison of Two University Mathematics Courses. Dissertation submitted to the Faculty of the Graduate School of the University of Maryland, College Park, in partial fulfillment of the requirements for the degree of Doctor of Philosophy.
Ma, L. (1999). Knowing and teaching elementary mathematics:Teachers’ understanding of fundamental mathematics in China and the United States. Mahwah, N.J: Lawrence Erlbaum Associates.
Maniraho, j.f. (2017). The pedagogical content knowledge (PCK) of Rwandan grade six mathematics teachers and its relationship to student learning. School of Education, College of Humanities University of KwaZulu-Natal Pietermaritzburg, South Africa.
Markworth, K., Goodwin, T., & Glisson, K. (2009). The Development of Mathematical Knowledge for Teaching in the Student Teaching Practicum. In D. S. Mewborn&H. S. Lee (Eds.).AMTE Monograph, 6. Scholarly Practices and Inquiry in thePreparation of Mathematics Teachers. San Diego, California: Association of Mathematics Teacher Educators.
Mccoy, A. C. (2011). SpecializedMathematical Content Knowledge of Preservice Elementery Teachers: The Effect of Mathematics Teachers Efficacy.A Dissertation in Curriculum and Instruction and Urban Leadership and Policy Studies in Education.
Morris, A., Hiebert, J., and Spitzer, S. (2009). Mathematical knowledge for teaching in planning and evaluating instruction: What can preservice teachers learn? Journal for Research in Mathematics Education. Vol. 40, No. 5, 491-529
Nillas, L. (2003). Division of Fractions: Preservice Teachers’ Understanding and Use of Problem Solving Strategies. The Mathematics Educator. Vol.7, No. 2, 96 - 113.
Olanoff. D, Lo. J, Tobias J.M. (2014). Mathematical Content knowledge for Teaching Elementary Mathematics: A Focus on Fractions. The Mathematics Enthusiast, Vol. 11, no. 2, pp. 267–310 .
Olanoff, D.E. (2011). Mathematical Knowledge for Teaching Teachers:The Case of Multiplication and Division of Fractions. Submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy in Mathematics Education in the Graduate School of Syracuse University .
Pettry, D. N. (2016). The Devlopment of Specialized Content Knowledge in Beginning Algebra Among Secondary Mathematics Pre-Service Teachers. A dissertation submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy in Mathematics.
Rayner, V. (2007). An Examination of the Type of Instruction that Facilitates Preservice Teachers Devlopment of Specialized Content Knowledge of Division with Fractions. A Thesis in the Department of Education. Concordia University. Montreal, Quebec,Canada.
Rayner. V, Osana, P.H & Pesco, D. (2013). A Comparison of Instruction That Devlops Preservice Teachers Specialized Content Knowledge of Division of Fractions. Concordia University. 3-5.
Redmond, A. (2009). Prospective Elementary Teachers Division of Fractions Understanding: A Mixed Methods Study.. Submitted to the Faculty of the Graduate College of the Oklahoma State University in partial fulfillment of the requirements for the Degree of Doctor of Philosophy.
Rosli. R, Goldsby. D, Capraro, M.M. (2015). Using Manipulatives in Solving and Posing Mathematical Problems. Creative Education. 6, 1718-1725
Sabri İpek, A. (2018). Pre-Service Elementary Mathematics Teachers’ Specialized Content Knowledge: The Case of Integer Addition and Subtraction. International Journal of Progressive Education, Vol. 14 Number 4.70-84.
Skilbeck, M. (1984). School – based curriculum development. London: Harper and Row Publisher.
Steenbrugge, H.V. (2012). Teaching fractions in elementary school. Proefschrift ingediend tot het behalen van de academische grad van Doctor in de Pedagogische Wetenschappen.
Stewart, V. (2005). Making Sense of Students' Understanding of Fractions: An Exploratory Study of Sixth Graders' Construction of Fraction Tirosh, D. (2000). Enhancing prospective teachers’ knowledge of children’s conceptions: The case of division of fractions. Journalfor Research in Mathematics Education, 31, 5–25.
Tirosh, D. (2000). Enhancing prospective teachers’ knowledge of children’s conceptions: The case of division of fractions. Journal for Research in Mathematics Education, 31, 5–25.
Whitehead, A.N, & Walkowiak, T. A (2017). Preservice Elementary Teachers’ Understanding of Operations for Fraction Multiplication and Division. International Journal for Mathematics Teaching and Learning. Vol. 18.3, 293 – 317.
Zembat & Bayram. (2019). An Articulation of Specialized Content Knowledge of Mathematics Teachers in the Context of Measurement Concept. The European Conference on Educational Research at Universität Hamburg, Germany.
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