تأثیر آموزش مسائل مدل‌سازی ریاضی بر تجربه‌های شوقِ دانش‌آموزان

نوع مقاله: مقاله پژوهشی

نویسندگان

1 دانش آموخته دکتری آموزش ریاضی دانشکده علوم ریاضی دانشگاه فردوسی مشهد

2 استادیار گروه آمار، دانشکده علوم ریاضی، دانشگاه فردوسی مشهد، ایران

3 استاد گروه ریاضی کاربردی، دانشکدة علوم ریاضی، دانشگاه فردوسی مشهد

چکیده

با توجه به این‌که «مدل‌سازی و کاربردها» و یادگیری آن در مدرسه و دانشگاه می‌تواند کاربرد ریاضیات را در علوم، فناوری و زندگی روزانه بهتر نمایان سازد، لذا ایجاد فرصت‌هایی که دانش‌آموزان را قادر کند مهارت‌های مدل‌سازی خود را ارتقا دهند، یکی از موضوعات برجسته در تحقیقات آموزش ریاضی است. از این رو، در این پژوهش به آموزش مسائل مدل‌سازی ریاضی به دو شیوة مستقیم (معلم محور) و استراتژی عملگر (دانش‌آموز محور) به 244 دانش‌آموز دختر پایة دهم پرداخته شده است. این مطالعه در نیم‌سال اول سال تحصیلی ۱۳۹۳- ۱۳۹۲ در سه دبیرستان غیردولتی شهر مشهد انجام شد. هدف از این تحقیق، بررسی تأثیر آموزش مسائل مدل‌سازی ریاضی به دو شیوة آموزشی متفاوت بر تجربه‌های شوق دانش‌آموزان در مسائل مختلف ریاضی (مدل‌سازی، کلامی و درون‌ـ‌ریاضی) است. روش پژوهش کمی و از نوع نیمه‌تجربی است. جمع‌آوری اطلاعات به‌وسیلة یک پرسش‌نامة درکِ شوق در مقیاس لیکرت انجام شد. تجزیه و تحلیل آماری داده‌ها با استفاده از آزمون آنالیز واریانس اندازه‌های مکرر نوع دوم نشان داد که آموزش مسائل مدل‌سازی ریاضی بر تجربه‌هایِ شوق دانش‌آموزان در مسائل دنیای واقعی تأثیر معناداری داشته است. علاوه بر این، محیط آموزشیِ دانش‌آموز محور بستر مناسبی برای بروز این تجربه‌های مثبت در دانش‌آموزان بود. بنابراین استفادة معلمان از فعالیت‌های مدل‌سازی برای علاقه‌مند‌کردن دانش‌آموزان به درس ریاضی ضرورت و اهمیت پیدا می‌کند.

کلیدواژه‌ها


عنوان مقاله [English]

The effect of teaching mathematical modeling problems on the students’ flow experiences

نویسندگان [English]

  • Zakie Parhizgār 1
  • Mehdi Jabbāri Nooghābi 2
  • Hassan Alamolhodāyi 3
1 Ph.D GRADUATED Faculty of Mathematical Sciences, Ferdowsi University of Mashhad
2 Department of Statistics, Faculty of Math Sciences, Ferdowsi University of Mashhad, Iran
3 (PhD), Ferdowsi University of Mashhad
چکیده [English]

 Abstract: Given the fact that “modeling and applications” and learning them at school and University can better illustrate the application of mathematics in science, technology, and daily life, creating opportunities for students in order to broaden their modeling skills is one of the prominent topics in the mathematics education studies. Hence, in this research, 244 grade 10 female students were taught mathematical modeling problems through two teaching methods: the direct teaching method which is teacher-centered, and the operative-strategic method which is student-centered. This study was conducted in 3 private high schools in Mashhad on the first semester of 2013-2014 academic year. The purpose of this study was to investigate the effect of teaching mathematicalmodeling problems through two different teaching methods on the students’ flow experiences in various mathematical problems (modeling problems,word problems andintra-mathematical problems).The research method was quantitative of quasi-experimental type. Data were gathered by a flow perception questionnaire in the Likert scale. The statistical analysis of the data using a repeated measures ANOVA Type II test indicated that teaching mathematical modeling problems had a beneficial effect on the students’ flow experiences in the real-world problems. In addition, the student-centered environments were good platforms for students to gain these positive experiences. Therefore, using modeling activities by teachers to make students interested in mathematics is important and necessary.

کلیدواژه‌ها [English]

  • Word Problems
  • intra-mathematical problems
  • Student-centered Teaching Method
 پرهیزگار، زکیه، علم‌الهدایی، حسن، و جباری نوقابی، مهدی. (1396). ظرفیت آموزش مسائل مدل‌سازی برای تغییر نگرش دانش‌آموزان نسبت به ریاضی. دو فصلنامة نظریه و عمل در برنامة درسی، 9(5)، 167-162.
 پرهیزگار، زکیه. (1397). تأثیر آموزش مسائل مدل‌سازی ریاضی بر روی تجربه‌های جریان دانش‌آموزان در مسائل مختلف ریاضی. مقاله ارائه شده در شانزدهمین کنفرانس آموزش ریاضی، بابلسر.
 رحیم‌پور، شکوفه، عارفی، مژگان و منشئی، غلامرضا (1398). اثربخشی ذهن‌آگاهی بر غرقگی و ثبات قدم دانش‌آموزان دختر دورة دوم متوسطه. مجلة مطالعات آموزش و یادگیری، 11(1)، 70-91.
 عبدالله‌پور، کاظم، رفیع‌پور, ابوالفضل (1396). پدیدارشناسی چرخة مدل‌سازی دانش‌آموزان پایة نهم در حل یک مسئلة اصیل. فناوری آموزش، 11(3)، 237-248.
 Abbott, J. A. (2000). “Blinking out” and “having the touch”: Two fifth-grade boys talk about flow experiences in writing. Written Communication, 17(1), 53–92.
 Armstrong, A. C. (2008). The fragility of group flow: The experiences of two small groups in a middle school mathematics classroom. The Journal of Mathematical Behavior, 27, 101-115.
 Asakawa, K. (2004). Fow experience and autotelic personality in japanese college students: how do they experience challenges in daily life? Journal of Happiness Studies, 5, 123–154.
 Azizi, Z., & Ghonsooly , B. (2015). Exploring flow theory in toefl texts: Expository and argumentative genre. Journal of Language Teaching and Research, 6(1), 210-215.
 Blum, W. (2011). Can modelling be taught and learnt? Some answers from empirical research. In G. Kaiser,W. Blum, R. Borromeo Ferri, & G. Stillman (Eds.), Trends in teaching and learning mathematical modelling (pp. 15 -30). New York: Springer.
 Blum, W., & Niss, M. (1991). Applied mathematical problem solving, modelling, application, and links to other subjects-state, trends, and issues in mathematics instruction. Educational Studies in Mathematics, 22(1), 37-68.
 Csikszentmihalyi, M. (1975). Beyond boredom and anxiety. San Francisco: Jossey-Bass.
 Csikszentmihalyi, M. (1990). Flow: The psychology of optimal experience. New York: Harper and Row.
 Csíkszentmihályi, M. (1996). Creativity: Flow and the Psychology of Discovery and Invention. New York, NY: Harper Perennial.
 Csikszentmihalyi, M. (1997). Flow and Education. The NAMTA Journal, 22(2), 3-35.
 Csíkszentmihályi, M. (1998). Finding flow: the psychology of flow experiences with everyday life (REP edition). New York: Basic Books
 Custodero, L. A. (2002). Seeking challenge, finding skill: Flow experience and music education. Arts Education Policy Review, 103(3), 3–9.
 Drakes, C. I. (2012). Mathematical Modelling: from Novice to Expert (Unpublished doctoral dissertation), Simon Fraser University, Burnaby.
 Egbert, J. (2003). A study of flow theory in the foreign language classroom. The Modern Language Journal, 87k(IV), 499–518.
 English, L. D., & Sriraman, B. (2010). Problem solving for the 21st century. In B. Sriraman & L. D. English (Eds.), Theories of mathematics education: Seeking new frontiers (pp. 263-285). Advances in Mathematics Education, Series: Springer.
 Galbraith P., & Clatworthy, N. (1990). Beyond standard models-meeting the challenge of modeling. Educational Studies in Mathematics, 21, 137-163.
 Greer, B., Verschaffel, L., & Mukhopadhyay, S. (2007). Modelling for life: Mathematics and children’s experience. In W. Blum, W. Henne, & M. Niss (Eds.), Applications and Modelling in Mathematics Education (ICMI Study 14, pp. 89–98). Dordrecht: Kluwer.
 Hattie, J., Biggs, J. B., & Purdie, N. (1996). Effects of learning skills interventions on student learning: A meta analysis. Review of Educational Research, 66 ,99–136.
 Kahn, D. (2003). Montessori and optimal experience research: toward building a comprehensive education reform. The NAMTA Journal, 28(3), 1-10.
 Kim, H. K., & Kim, S. (2010). The effects of mathematical modeling on creative production ability and self-directed learning attitude. Asia Pacific Educ. Rev, 11, 09–120.
 Liljedahl, P. (2016). Flow: A Framework for Discussing Teaching. In Proceedings of the 40th Conference of the International Group for the Psychology of Mathematics Education (Vol. 3, pp. 203-210). Szeged, Hungary.
 Liljedahl, P. (2018). On the edges of flow: Student problem solving behavior. In S. Carreira, N.Amado, & K. Jones (Eds.), Broadening the scope of research on mathematical problem solving: A focus on technology, creativity and affect (pp. 505–524). New York: Springer.
 Liu, M., & Liljedahl, P. (2019). Flow and modelling. In Chamberlin, S. A. & Sriraman, B. (Eds.), Affect in Mathematical Modeling (pp. 273-295). Switzerland: Springer.
 Ma, X., & Kishor, N. (1997). Assessing the relationship between attitude toward mathematics and achievement in mathematics: A meta-analysis. Journal For Research In Mathematics Education, 28(1), 26-47.
 Mandigo, J. L., & Thompson, L. P. (1998). Go with their flow: How flow theory can help practitioners to intrinsically motivate children to be physically active. Physical Educator, 55(3), 145–160.
 Mirlohi, M., Egbert, J., & Ghonsooly, B. (2011). Flow in translation Exploring optimal experience for translation trainees. Target, 23(2), 251–271.
 National Council of Teachers of Mathematics Education (NCTM) (2000). Principles and standards for school mathematics. Reston, VA: The National Council of Teachers of Mathematics, Inc.
 Niss, M., Blum, W., & Galbraith, P. L. (2007). Introduction. In W. Blum, P. L. Galbraith, H.-W. Henn, & M. Niss (Eds.), Modelling and applications in mathematics education: The 14th ICMI study (pp. 1 – 32). New York: Springer.
 Prince, M. (2004). Does Active Learning Work? A Review of the Research. Journal of Engineering Education, 93(3), 223-231.
 Parhizgar, Z., & Liljedahl, P. (2019). Teaching Modelling Problems and its Effects on Students' Engagement and Attitude toward Mathematics. In Chamberlin, S. A. & Sriraman, B. (Eds.), Affect in Mathematical Modeling (pp. 235-25). Switzerland: Springer.
 Schukajlow, S., Leiss, D., Pekrun, R., Blum, W., Müller, M., & Messner, R. (2012). Teaching methods for modelling problems and students’ task-specific enjoyment, value, interest and self-efficacy expectations. Educational Studies in Mathematics, 79(2), 215–237.
 Schukajlow, S., & Krug, A. (2013). Planning, monitoring and multiple solutions while solving modelling problems. In A. M. Lindmeier & A. Heinze (Eds.), Proc. 37th Conf. of the Int. Group for the Psychology of Mathematics Education (Vol. 4, pp. 177-184). Kiel,Germany: PME.
 Sedig, K. (2007). Toward operationalization of 'flow' in mathematics learnware. Computers in Human Behavior, 23, 2064-2092.
 Shernoff, D. J., Csikszentimihalyi, M., Schneider, B., & Shernoff, E. S. (2003). Student engagement in high school classrooms from the perspective of flow theory. School Psychology Quarterly, 18(2), 158–176.
 Skemp, R. R. (1986). The psychology of learning mathematics (2nd ed.). Middlesex, UK: Penguin Books.
 Whitson, C. & Consoli, J. (2009). Flow Theory and Student Engagement. Journal of Cross-Disciplinary Perspectives in Education, 2(1), 40 – 49.
 Winberg, T. M., & Hedman, l. (2008). Student attitudes toward learning, level of pre-knowledge and instruction type in a computer-simulation: effects on flow experiences and perceived learning outcomes. Instructional science, 36, 269–287.