PEER PROBLEM SOLVING AS AN INSTRUCTIONAL STRATEGY TO ENHANCE MATHEMATICAL DISCOURSE IN 6TH GRADE MATHEMATICS
Öz
Recent studies on mathematics education focus on improving higher order thinking skills instead
of merely attaining and using knowledge. Deep understanding of mathematics requires to engage in the
processes of mathematical thinking. Defining and solving problems, discovering patterns, making conjectures,
inferences and justifying one's own thinking are among those mathematical processes. Using mathematical talk,
discussion and discourse to promote new goals of mathematics education have been widely researched in the last
decades. For these reasons, creating a classroom atmosphere which provides a fruitful communication is an
important area for research in mathematics education. The purpose of the study was to implement and investigate
an instructional strategy to enhance mathematical discourse among students. Students' approaches to
mathematical discourse as a learning tool is also examined. Qualitative methodology was used to investigate the
effectiveness of group problem solving as an instructional strategy in fostering mathematical discourse. A two
hour lesson plan was developed and implemented to 20 students attending 6th grade. Students filled open-ended
question forms before and after implementation. Researchers also made observations and took field notes during
the implementation. Content analysis was used to analyze data. Findings of the study indicated that group
problem solving is an effective way to foster mathematical discourse in the classroom. Students pointed out that
they enjoy and learned from mathematical talk they engaged in this group activity. Observation and field notes
also indicated if the instruction presents a problem to solve through groupwork students need to engage in
mathematical talk.
Anahtar Kelimeler
mathematical communication mathemtical discussion mathemtical discourse peer learning problem solving mathematics education
Kaynakça
- Bandura, A. (1969). Social learning theory of identificatory processes. In D.A. Goslin (Ed.), Handbook of Socialization Theory and Research (pp. 213-262). Chicago: Rand McNally.
- Brown, A. L., & Palincsar, A. S. (1989). Guided, cooperative learning and individual knowledge acquisition. Knowing, learning, and instruction: Essays in honor of Robert Glaser, 393-451.
- Chapin, S. H., O'Connor, C., & Anderson, N. C. (2009). Classroom Discussions: Using Math Talk to Help Students Learn, Grades K-6. Sausalito, CA: Math Solutions.
- Cobb, P., Boufi, A., McClain, K., & Whitenack, J. (1997). Reflective discourse and collective reflection. Journal for Research in Mathematics Education, 258-277.
- Creswell, J.W. (2012). Educational research:Planning, conducting, and evaluating quantitative and qualitative research (4th ed.). Boston: Pearson.
- Hiebert, J. (1992). Reflection and communication: Cognitive considerations in school mathematics reform. International Journal of Educational Research, 17(5), 439-456.
- Hiebert, J., Stigler, J. W., Jacobs, J. K., Givvin, K. B., Garnier, H., Smith, M., ... & Gallimore, R. (2005). Mathematics teaching in the United States today (and tomorrow): Results from the TIMSS 1999 video study. Educational Evaluation and Policy Analysis, 27(2), 111-132.
- Jansen, A. (2006). Seventh graders' motivations for participating in two discussion‐oriented mathematics classrooms. The Elementary School Journal, 106(5), 409-428.
- Kilpatrick, J., Swafford, J., & Findell, B. (Eds.). (2001). Adding+ it up: Helping children learn mathematics. National Academies Press.
- Kostos, K., & Shin, E. K. (2010). Using math journals to enhance second graders’ communication of mathematical thinking. Early Childhood Education Journal, 38(3), 223-231.
- Lampert, M. (1990). When the problem is not the question and the solution is not the answer: Mathematical knowing and teaching. American educational research journal, 27(1), 29-63.
- Lynch, S. D., & Bolyard, J. J. (2012). Putting Mathematical Discourse In Writing. Mathematics Teaching in the Middle School, 17(8), 486-492.
- McNair, R. E. (2000). Working in the mathematics frame: Maximizing the potential to learn from students' mathematics classroom discussions. Educational Studies in Mathematics, 42(2), 197-209.
- Moschkovich, J. N. (1996). Moving up and getting steeper: Negotiating shared descriptions of linear graphs. The Journal of the Learning Sciences, 5(3), 239-277.
- National Council of Teachers of Mathematics. (1989). Curriculum and evaluation standards for school mathematics. Reston, VA.
- Pape, S. J., Bell, C. V., & Yetkin, İ. E. (2003). Developing mathematical thinking and self-regulated learning: A teaching experiment in a seventh-grade mathematics classroom. Educational Studies in Mathematics, 53(3), 179-202.
- Resnick, L. (1990). Treating mathematics as an ill structured discipline. In R.Charles & A. Silver (Eds.), Research agenda for mathematics education: Vol.3. The teaching and assessing of mathematical problem solving (pp.32-60). Hillsdale, NJ: Lawrence Erlbaum Associates, Inc.
- Romberg, T. A., & Kaput, J. J. (1999). Mathematics worth teaching, mathematics worth understanding. In Fennema, E., & Romberg, T. A. (Eds.), Mathematics classrooms that promote understanding (pp. 3-17). Mahwah, NJ: Lawrence Erlbaum Associates.
- Schoenfeld, A. H. (1992). Learning to think mathematically: Problem solving, metacognition, and sense making in mathematics. Handbook of research on mathematics teaching and learning, 334-370.
- Sfard, A. (2001). There is more to discourse than meets the ears: Looking at thinking as communicating to learn more about mathematical learning. Educational Studies in Mathematics, 46(1-3), 13-57.
- Stein, M. K., Grover, B. W., & Henningsen, M. (1996). Building student capacity for mathematical thinking and reasoning: An analysis of mathematical tasks used in reform classrooms. American Educational Research Journal, 33(2), 455-488.
- Trafton, P.R., & Claus, S.C. (1994). A changing curriculum for a changing age. In C.E. Thornton & N.S. Bley (eds.), Windows of opportunity mathematics for students with special needs (pp. 19-39). Reston, VA: National Council of Teachers of Mathematics.
- Vygotsky, L.S. (1978). Mind in society: The development of higher psychological processes. Cambridge, MA: Harvard University Press.
- Walshaw, M., & Anthony, G. (2008). The teacher’s role in classroom discourse: A review of recent research into mathematics classrooms. Review of Educational Research, 78(3), 516-551.
- Wood, T. (1999). Creating a context for argument in mathematics class. Journal for research in mathematics education, 30 (2), 171-191.
- Yackel, E., Cobb, P., & Wood, T. (1991). Small-group interactions as a source of learning opportunities in second-grade mathematics. Journal for research in mathematics education, 390-408.
AKRAN GRUPLARINDA PROBLEM ÇÖZMENİN 6. SINIF MATEMATİK DERSİNDE MATEMATİKSEL TARTIŞMAYI GELİŞTİRME AMAÇLI BİR ÖĞRETİM YÖNTEMİ OLARAK KULLANILMASI
Öz
Matematik eğitimi üzerine yapılan son çalışmalarda bilginin edinilmesi ve kullanılmasından çok
öğrencilerde düşünme becerilerinin geliştirilmesine odaklanılmaktadır. Anlamlı matematik öğrenimi
matematiksel düşünme süreçleri içerisine girmeyi gerektirmektedir. Problemi tanımlama ve çözme, örüntüleri
keşfetme, tahminlerde ve çıkarımlarda bulunma ile kendi fikir ve düşünme süreçlerini savunma matematiksel
düşünme süreçleri kapsamına girmektedir. Matematik eğitiminin söz konusu amaçlarına ulaşmak için
matematiksel konuşma ve tartışma kavramları üzerinde yapılmış bir çok araştırma bulunmaktadır. Buradan
hareketle sınıf ortamında verimli bir matematiksel tartışma deneyiminin oluşturulması matematik eğitimi
alanında önemli bir çalışma konusu olarak ön plana çıkmaktadır. Çalışmanın amacı sınıf ortamında matematiksel
tartışmayı geliştirmek için bir öğretim yöntemi uygulamak ve etkilerini incelemektir. Öğrencilerin bir matematik
öğrenme yöntemi olarak matematiksel tartışma hakkında neler düşündükleri de çalışma kapsamında ele
alınmıştır. Akran gruplarında problem çözmenin matematiksel tartışma ortamını geliştirme üzerindeki etkisini
incelemek üzere nitel araştırma deseni kullanılmıştır. Bunun için iki saatlik bir ders planı geliştirilmiş ve 6.sınıfa
devam eden 20 öğrenciye uygulanmıştır. Öğrenciler uygulama öncesi ve sonrasında açık uçlu sorulardan oluşan
anketleri doldurmuşlardır. Araştırmacılar uygulamayı gözlemleyerek saha notları tutmuşlardır. Verilerin çözümlenmesi için içerik analizi kullanılmıştır. Bulgular akran gruplarında problem çözmenin matematiksel
tartışma ortamı oluşturmada etkili olduğunu işaret etmektedir. Öğrenciler grup çalışması sırasında
gerçekleştirdikleri matematiksel tartışmadan öğrendiklerini ve keyif aldıklarını dile getirmişlerdir. Yapılan
gözlemler ile de öğrenciler için tasarlanan grup çalışmalarının onları matematiksel konuşmaya teşvik ettiği
görülmüştür.
Anahtar Kelimeler
matematiksel iletişim matematiksel tartışma matematiksel konuşma akran öğrenimi problem çözme
Kaynakça
- Bandura, A. (1969). Social learning theory of identificatory processes. In D.A. Goslin (Ed.), Handbook of Socialization Theory and Research (pp. 213-262). Chicago: Rand McNally.
- Brown, A. L., & Palincsar, A. S. (1989). Guided, cooperative learning and individual knowledge acquisition. Knowing, learning, and instruction: Essays in honor of Robert Glaser, 393-451.
- Chapin, S. H., O'Connor, C., & Anderson, N. C. (2009). Classroom Discussions: Using Math Talk to Help Students Learn, Grades K-6. Sausalito, CA: Math Solutions.
- Cobb, P., Boufi, A., McClain, K., & Whitenack, J. (1997). Reflective discourse and collective reflection. Journal for Research in Mathematics Education, 258-277.
- Creswell, J.W. (2012). Educational research:Planning, conducting, and evaluating quantitative and qualitative research (4th ed.). Boston: Pearson.
- Hiebert, J. (1992). Reflection and communication: Cognitive considerations in school mathematics reform. International Journal of Educational Research, 17(5), 439-456.
- Hiebert, J., Stigler, J. W., Jacobs, J. K., Givvin, K. B., Garnier, H., Smith, M., ... & Gallimore, R. (2005). Mathematics teaching in the United States today (and tomorrow): Results from the TIMSS 1999 video study. Educational Evaluation and Policy Analysis, 27(2), 111-132.
- Jansen, A. (2006). Seventh graders' motivations for participating in two discussion‐oriented mathematics classrooms. The Elementary School Journal, 106(5), 409-428.
- Kilpatrick, J., Swafford, J., & Findell, B. (Eds.). (2001). Adding+ it up: Helping children learn mathematics. National Academies Press.
- Kostos, K., & Shin, E. K. (2010). Using math journals to enhance second graders’ communication of mathematical thinking. Early Childhood Education Journal, 38(3), 223-231.
- Lampert, M. (1990). When the problem is not the question and the solution is not the answer: Mathematical knowing and teaching. American educational research journal, 27(1), 29-63.
- Lynch, S. D., & Bolyard, J. J. (2012). Putting Mathematical Discourse In Writing. Mathematics Teaching in the Middle School, 17(8), 486-492.
- McNair, R. E. (2000). Working in the mathematics frame: Maximizing the potential to learn from students' mathematics classroom discussions. Educational Studies in Mathematics, 42(2), 197-209.
- Moschkovich, J. N. (1996). Moving up and getting steeper: Negotiating shared descriptions of linear graphs. The Journal of the Learning Sciences, 5(3), 239-277.
- National Council of Teachers of Mathematics. (1989). Curriculum and evaluation standards for school mathematics. Reston, VA.
- Pape, S. J., Bell, C. V., & Yetkin, İ. E. (2003). Developing mathematical thinking and self-regulated learning: A teaching experiment in a seventh-grade mathematics classroom. Educational Studies in Mathematics, 53(3), 179-202.
- Resnick, L. (1990). Treating mathematics as an ill structured discipline. In R.Charles & A. Silver (Eds.), Research agenda for mathematics education: Vol.3. The teaching and assessing of mathematical problem solving (pp.32-60). Hillsdale, NJ: Lawrence Erlbaum Associates, Inc.
- Romberg, T. A., & Kaput, J. J. (1999). Mathematics worth teaching, mathematics worth understanding. In Fennema, E., & Romberg, T. A. (Eds.), Mathematics classrooms that promote understanding (pp. 3-17). Mahwah, NJ: Lawrence Erlbaum Associates.
- Schoenfeld, A. H. (1992). Learning to think mathematically: Problem solving, metacognition, and sense making in mathematics. Handbook of research on mathematics teaching and learning, 334-370.
- Sfard, A. (2001). There is more to discourse than meets the ears: Looking at thinking as communicating to learn more about mathematical learning. Educational Studies in Mathematics, 46(1-3), 13-57.
- Stein, M. K., Grover, B. W., & Henningsen, M. (1996). Building student capacity for mathematical thinking and reasoning: An analysis of mathematical tasks used in reform classrooms. American Educational Research Journal, 33(2), 455-488.
- Trafton, P.R., & Claus, S.C. (1994). A changing curriculum for a changing age. In C.E. Thornton & N.S. Bley (eds.), Windows of opportunity mathematics for students with special needs (pp. 19-39). Reston, VA: National Council of Teachers of Mathematics.
- Vygotsky, L.S. (1978). Mind in society: The development of higher psychological processes. Cambridge, MA: Harvard University Press.
- Walshaw, M., & Anthony, G. (2008). The teacher’s role in classroom discourse: A review of recent research into mathematics classrooms. Review of Educational Research, 78(3), 516-551.
- Wood, T. (1999). Creating a context for argument in mathematics class. Journal for research in mathematics education, 30 (2), 171-191.
- Yackel, E., Cobb, P., & Wood, T. (1991). Small-group interactions as a source of learning opportunities in second-grade mathematics. Journal for research in mathematics education, 390-408.
Ayrıntılar
| Birincil Dil | İngilizce |
|---|---|
| Konular | Eğitim Üzerine Çalışmalar |
| Bölüm | Makaleler |
| Yazarlar | |
| Yayımlanma Tarihi | 23 Eylül 2014 |
| Yayımlandığı Sayı | Yıl 2014 Cilt: 2 Sayı: 1(ÖZEL) |
ASYA ÖĞRETİM DERGİSİ (E-AJI)
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