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Investigating Seventh Grade Students’ Mathematical Communication Skills: Student Journals

Yıl 2018, Cilt: 9 Sayı: 3, 476 - 512, 17.12.2018
https://doi.org/10.16949/turkbilmat.367513

Öz

This study aims to investigate students’ mathematical
communication skills through investigating their defining, using mathematical
concepts and mathematical language skills. Additionally, this study aims to
investigate the relationship between students’ mathematical communication
skills with their academic achievements. A seventh grade classroom at a public
middle school in the Eastern Anatolia region and 34 students and their
mathematics teacher participated in the study. Students were asked to keep
journals during seven weeks for sixteen Geometry standards after each standard.
Student journals were analyzed in four hierarchical levels—Level 0 (Avoidance),
Level 1 (Incorrect Use), Level 2 (Incomplete Use) and Level 3(Correct and
Complete Use) — by two researchers individually. Later, the researchers
compared their categorizations and discussed till solving the disagreements.
According to the findings of the study, participating students did not
comprehend the concept definitions. It was seen that students attempted to use
mathematical language in their journals as a way of communication. However, it
should be noted that some incorrect use of mathematical language was apparent
in student journals. This study also showed that it was hard to conclude that
student mathematical communication skills differ based on their academic
achievement levels.

Kaynakça

  • Açıl, E. (2015). Ortaokul 3. sınıf öğrencilerin denklem kavramına yönelik soyutlama süreçlerinin incelenmesi: APOS Teorisi (Yayınlanmamış doktora tezi). Atatürk Üniversitesi, Eğitim Bilimleri Enstitüsü, Erzurum.
  • Adams, A. (2010). Rehearsal or reorganization two patterns of literacy strategy use in secondary mathematics class. The Montana Mathematics Enthusiast, 7, 371-390.
  • Adams, T., L. (2003). Reading mathematics: More than words can say. The Reading Teacher, 56, 786–795.
  • Akkoç, H. (2006). Fonksiyon kavramanın çoklu temsillerinin çağrıştırdığı kavram görüntüleri. Hacettepe Üniversitesi Eğitim Fakültesi Dergisi, 30(30), 1-10.
  • Ayyıldız, N., & Altun, S. (2013). Matematik dersine ilişkin kavram yanılgılarının giderilmesinde öğrenme günlüklerinin etkisinin incelenmesi. Hacettepe Üniversitesi Eğitim Fakültesi Dergisi, 28(2), 71-86.
  • Azzolino, A. (1990). Writing as a tool for teaching mathematics: The silent revolution. In T. J. Cooney & C. R. Hirsh (Eds.), Teaching and learning mathematics in the 1990s, 1990 yearbook of the National Council of Teachers of Mathematics (NCTM) (pp. 92-100). Reston, VA: NCTM.
  • Baber, R., L. (2011). The language of mathematics: Utilizing math in practice. New Jersey: John Wiley & Sons, Inc.
  • Barwell, R. (2005). Language in the mathematics classroom. Language and Education, 19(2), 97–102.
  • Bagley, T., & Gallenberger, C. (1992). Assessing students’ dispositions: Using journal to improve students’ performance. Mathematics Teacher, 85, 660-663.
  • Boulet, G. (2007). How does language impact the learning of mathematics? Let me count the ways. Journal of Teaching and Learning, 5(1), 1-12.
  • Brethouwer, J. (2008). Vocabulary instruction as a tool for helping students of diverse backgrounds and ability levels to understand mathematical concepts (Unpublised master’s thesis). University of Nebraska, Lincoln.
  • Chapman, K., P. (1996). Journals: Pathways to thinking in second-year algebra. Mathematics Teacher, 89, 588-90.
  • Chen, C., & Herbst, P. (2013). The interplay among gestures, discourses, and diagrams in students’ geometrical reasoning. Educational Studies in Mathematics, 83, 285-307.
  • Clements, D., H. (2003). Teaching and learning geometry. In J. Kilpatrick, G. Martin & D. Schifter (Eds.), Research companion to principles and standards for school mathematics (pp. 15–78). Reston, VA: National Council of Teachers of Mathematics.
  • Common Core State Standards Initiative [CCSSI]. (2010). Common core state standards for mathematics. Retrieved July 12, 2017 from http://www.corestandards.org/Math/Practice/
  • Cresswell, J., W. (2005). Educational research: Planning, conducting, and evaluating quantitative and qualitative research (2nd ed.). Ohio: Pearson. Denzin, K., & Lincoln, S. (2000). The sage handbook of qualitative research (3rd ed.). London: Sage Publications.
  • Dickson, L., Brown, B., & Gibson, O. (1993). Children learning mathematics: A teacher’s guide to recent research. London: Cassell.
  • Dougherty, B., J. (1996). The write way: A look at journal writing in first-year algebra. Mathematics Teacher, 89, 556-60.
  • Dursun, Ş., & Dede, Y. (2004). Öğrencilerin matematikte başarısını etkileyen faktörler matematik öğretmenlerinin görüşleri bakımından. Gazi Üniversitesi Gazi Eğitim Fakültesi Dergisi, 24(2), 217-230.
  • Duval, R. (1995). Geometrical pictures: Kinds of representation and specific processings. In R. Sutherland & J. Mason (Eds.), Exploiting mental imagery with computers in mathematics education (pp. 142–157). Berlin: Springer.
  • Edwards, B. S., & Ward, M. B. (2008). The role of mathematical definitions in mathematics and in undergraduate mathematics courses. Retrieved November 22, 2017 from https://books.google.com.tr/
  • Edwards, B. S., & Ward, M. B. (2005). New practices in teaching mathematical definitions. In D. Smith & E. Swanson (Eds.), Preparing future science and mathematics teachers: Faculty write about cept innovations on campuses today (pp. 23-25). Bozeman, MT: Science Math Resource Center.
  • Edwards, B. S., & Ward, M. B. (2004). Surprises from mathematics education research: Student (mis)use ofmathematical definitions. The American Mathematical Monthly, 111(5), 411-424.
  • Eker, C. & Coşkun, I. (2012). Ders günlüğü yazmanın ilkokul 4. sınıf öğrencilerinin sosyal bilgiler dersi akademik başarılarına etkisi. Muğla Sıtkı Koçman Universitesi Sosyal Bilimler Enstitüsü Dergisi, 29, 111-122.
  • Ernest, P. (1999). Forms of knowledge in mathematics and mathematics education: Philosophical and rhetorical perspectives. Educational Studies in Mathematics, 38(1–3), 67–83.
  • Goldin-Meadow, S., & Singer, M. A. (2003). From children‘s hands to adults’ ear: Gesture’s role in the learning process. Development Psychology, 39(3), 509–520.
  • Gökbulut, Y. & Ubuz, B. (2013). Sınıf öğretmeni adaylarının prizma bilgileri: Tanım ve örnekler oluşturma. İlköğretim Online, 12(2), 401-412.
  • Harley, T., A. (1995). The psychology of language: From data to theory. England: Erlbaum (UK) Taylor & Francis.
  • Hershkowitz, R. (1990). Psychological aspects of learning geometry. In P. Nesher & J. Kilpatric (Eds.), Mathematics and cognition (pp. 70–95). Cambridge: Cambridge University Press.
  • Kotsopoulos, D. (2007). Mathematics discourse: “It’s like hearing a foreign language”. Mathematics Teacher, 101(4), 301-305.
  • Köroğlu, H., Yavuz, G., & Ertem, S. (2004, Ekim). 11. sınıf öğrencilerinin geometri dersinde karşılaştıkları bazı kavram yanılgıları ve çözüm önerileri. XII. Eğitim Bilimleri Kongresi’nde sunulan bildiri, Gazi Üniversitesi.
  • Kranda, J. (2008). Precise mathematical language: Exploring the relationship between student vocabulary understanding and student achievement (Unpublished master’s thesis). University of Nebraska, Lincoln.
  • Lim, L., & Pugalee, D. K. (2004). Using journal writing to explore they communicate to learn mathematics and they learn to communicate mathematically. Ontario Action Researcher, 7(2), 17-24.
  • Mason, J. (1980). When is a symbol symbolic? For the Learning of Mathematics, 1(2), 8-12.
  • Mili Eğitim Bakanlığı [MEB]. (2013). Ortaokul matematik dersi öğretim program (5, 6, 7, ve 8. sınıflar). Ankara: MEB.
  • Meel, D. (1999). Email dialogue journals in a college calculus classroom: A look at the implementation and benefits. Journal of Computers in Mathematics and Science Teaching, 18(4), 387-413.
  • Mercer, N., & Sams, C. (2006). Teaching children how to use language to solve maths problems. Language and Education, 20(6), 507-528.
  • Moralı, S., Köroğlu, H., & Çelik, A. (2004). Buca Eğitim Fakültesi matematik öğretmen adaylarının soyut matematik dersine yönelik tutumları ve rastlanan kavram yanılgıları. Gazi Üniversitesi Gazi Eğitim Fakültesi Dergisi, 24(1), 161-175.
  • Monroe, E. E., & Orme, M. P. (2002). Developing mathematical vocabulary. Preventing School Failure: Alternative Education for Children and Youth, 46(3), 139-142.
  • Moon, J. (2010). Assessment: Learning journals and logs. Retrieved June 15, 2017 from: http://ar.cetl.hku.hk/pdf/ucdtla0035.pdf
  • Morgan, C. (1998). Writing mathematically: The discourse of investigation. London: Falmer Press.
  • National Council of Teachers of Mathematics [NCTM]. (2006). Principles and standards for school mathematics. Reston, VA: Author.
  • National Council of Teachers of Mathematics [NCTM]. (2000). Principles and standards for school mathematics. Reston, VA: Author.
  • National Council of Teachers of Mathematics [NCTM]. (1989). The curriculum and evaluation standards. Reston, VA: Author.
  • National Research Council [NRC]. (2001). Adding it up: Helping children learn mathematics. In J. Kilpatrick, J. Swafford & B. Findell (Eds.), Center for education, division of behavioral and social sciences and education (pp. 115-116). Washington, DC: National Academies Press.
  • Parzysz, B. (1988). Knowing vs seeing. Problems of the plane representation of space geometry figures. Educational Studies in Mathematics, 19, 79-92.
  • Pimm, D. (1991). Communicating mathematically. In K. Durkin & B. Shire (Eds.), Language in mathematical education: Research and practice (pp. 17-23). Philadelphia: Open University Press.
  • Pimm, D. (1987). Speaking mathematically: Communications in mathematics classrooms. London: Routledge & Keanen Paul.
  • Pugalee, D., K. (2001). Writing, mathematics, and metacognition: looking for connections through students’ work in mathematical problem solving. School Science and Mathematics, 101(5), 236–45.
  • Riccomini, P. J., Smith, G. W., Hughes, E. M., & Fries, K. M. (2015). The language of mathematics: The importance of teaching and learning mathematical vocabulary. Reading & Writing Quarterly, 31(3), 235-252.
  • Roth, W. M., & Lawless, D. (2002). Scientific investigations, metaphorical gestures, and the emergence of abstract scientific concepts. Learning and Instruction, 12, 285–304.
  • Roth, W. M., & Welzel, M. (2001). From activity to gestures and scientific language. Journal of Research in Science Teaching, 38(1), 103–136.
  • Rubenstein, R., & Thompson, D. (2002). Understanding and supporting children’s mathematical vocabulary development. Teaching Children Mathematics, 9, 107–112.
  • Rubenstein, R., N., & Thompson, D., R. (2001). Learning mathematical symbolism: Challenges and instructional strategies. The Mathematics Teacher, 94(4), 265-271.
  • Sloyer, C., W. (2003). Mathematical insight: Changing perspective. Mathematics Teacher, 96, 238–242.
  • Sáenz-Ludlow, A., & Presmeg, N. (2006). Semiotic perspectives on learning mathematics and communicating mathematically. Educational Studies in Mathematics, 61(1/2), 1-10.
  • Soylu, Y., & Aydın, S. (2006). Matematik derslerinde kavramsal ve işlemsel öğrenmenin dengelenmesinin önemi üzerine bir çalışma. Erzincan Üniversitesi Eğitim Fakültesi Dergisi, 8(2), 83-95.
  • Sucuoğlu, B., Büyüköztürk, Ş., & Ünsal, P. (2008). Türk çocuklarının temel-ilişkisel kavram bilgilerinin değerlendirilmesi. İlköğretim Online, 7(1), 203-217.
  • Tall, D., & Vinner, S. (1981). Concept image and concept definition in mathematics with particular reference to limits and continuity. Educational Studies in Mathematics, 12(2), 151-169.
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  • Türnüklü, E., Alaylı, F. G. & Akkaş, E. N. (2013). İlköğretim matematik öğretmen adaylarının dörtgenlere ilişkin algıları ve imgelerinin incelenmesi. Kuram ve Uygulamada Eğitim Bilimleri, 13(2), 1213-1232.
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Yedinci Sınıf Öğrencilerinin Matematiksel İfade Becerilerinin İncelenmesinde Yazma Aktiviteleri: Öğrenci Günlükleri

Yıl 2018, Cilt: 9 Sayı: 3, 476 - 512, 17.12.2018
https://doi.org/10.16949/turkbilmat.367513

Öz

Bu çalışmada
öğrencilerin geometri öğrenme alanında matematiksel iletişim becerilerinin
tanım yapabilme, kavram kullanımı ve matematiksel dil kullanımı alt başlıkları
halinde incelenmesi ve öğrencilerin matematiksel iletişim becerileri ile
akademik başarıları arasındaki olası ilişkinin araştırılması amaçlanmıştır. Bu
amaçla Doğu Anadolu bölgesinde bir ortaokulun 7. Sınıfına devam etmekte olan 34
öğrencinin geometri öğrenme alanında yer alan toplam 16 kazanım süresince
bireysel olarak tuttukları günlükleri incelenmiştir. Geometri öğrenme alanında
yapılan uygulama 7 hafta süresince devam etmiştir. Elde edilen veriler dört
seviyede —Seviye 0 (kaçınma), Seviye 1 (yanlış kullanım), Seviye 2 (eksik
kullanım) ve Seviye 3 (doğru ve tam kullanım)— iki araştırmacı tarafından
bireysel olarak sınıflandırılmıştır. Bireysel sınıflandırmalar karşılaştırılıp
sınıflamalar arasındaki uyuşmazlıklar tartışılarak giderilmiştir. Çalışmanın
bulgularına göre, çalışmaya katılan öğrencilerin çoğunun tanım yapabilme
becerilerinin sınırlı olduğu ve yaptıkları tanımların anlamlandırılmadan ezbere
dayalı olduğu görülmüştür. Öğrencilerin matematiksel kavramları ifade ederken
notasyon, sembol ve figür kullanımından genellikle kaçınmadıkları fark
edilmiştir. Her ne kadar öğrenciler matematiksel dil kullanımından kaçınmasa
da, bazı yanlış kullanımların olduğu görülmüştür. Öğrencilerin söz konusu
becerilerinin ise başarı düzeyine göre farklılaştığını net bir şekilde ifade
etmenin doğru olmayacağı yine bu çalışmanın bulgularınca ortaya koyulmuş bir
sonuçtur.

Kaynakça

  • Açıl, E. (2015). Ortaokul 3. sınıf öğrencilerin denklem kavramına yönelik soyutlama süreçlerinin incelenmesi: APOS Teorisi (Yayınlanmamış doktora tezi). Atatürk Üniversitesi, Eğitim Bilimleri Enstitüsü, Erzurum.
  • Adams, A. (2010). Rehearsal or reorganization two patterns of literacy strategy use in secondary mathematics class. The Montana Mathematics Enthusiast, 7, 371-390.
  • Adams, T., L. (2003). Reading mathematics: More than words can say. The Reading Teacher, 56, 786–795.
  • Akkoç, H. (2006). Fonksiyon kavramanın çoklu temsillerinin çağrıştırdığı kavram görüntüleri. Hacettepe Üniversitesi Eğitim Fakültesi Dergisi, 30(30), 1-10.
  • Ayyıldız, N., & Altun, S. (2013). Matematik dersine ilişkin kavram yanılgılarının giderilmesinde öğrenme günlüklerinin etkisinin incelenmesi. Hacettepe Üniversitesi Eğitim Fakültesi Dergisi, 28(2), 71-86.
  • Azzolino, A. (1990). Writing as a tool for teaching mathematics: The silent revolution. In T. J. Cooney & C. R. Hirsh (Eds.), Teaching and learning mathematics in the 1990s, 1990 yearbook of the National Council of Teachers of Mathematics (NCTM) (pp. 92-100). Reston, VA: NCTM.
  • Baber, R., L. (2011). The language of mathematics: Utilizing math in practice. New Jersey: John Wiley & Sons, Inc.
  • Barwell, R. (2005). Language in the mathematics classroom. Language and Education, 19(2), 97–102.
  • Bagley, T., & Gallenberger, C. (1992). Assessing students’ dispositions: Using journal to improve students’ performance. Mathematics Teacher, 85, 660-663.
  • Boulet, G. (2007). How does language impact the learning of mathematics? Let me count the ways. Journal of Teaching and Learning, 5(1), 1-12.
  • Brethouwer, J. (2008). Vocabulary instruction as a tool for helping students of diverse backgrounds and ability levels to understand mathematical concepts (Unpublised master’s thesis). University of Nebraska, Lincoln.
  • Chapman, K., P. (1996). Journals: Pathways to thinking in second-year algebra. Mathematics Teacher, 89, 588-90.
  • Chen, C., & Herbst, P. (2013). The interplay among gestures, discourses, and diagrams in students’ geometrical reasoning. Educational Studies in Mathematics, 83, 285-307.
  • Clements, D., H. (2003). Teaching and learning geometry. In J. Kilpatrick, G. Martin & D. Schifter (Eds.), Research companion to principles and standards for school mathematics (pp. 15–78). Reston, VA: National Council of Teachers of Mathematics.
  • Common Core State Standards Initiative [CCSSI]. (2010). Common core state standards for mathematics. Retrieved July 12, 2017 from http://www.corestandards.org/Math/Practice/
  • Cresswell, J., W. (2005). Educational research: Planning, conducting, and evaluating quantitative and qualitative research (2nd ed.). Ohio: Pearson. Denzin, K., & Lincoln, S. (2000). The sage handbook of qualitative research (3rd ed.). London: Sage Publications.
  • Dickson, L., Brown, B., & Gibson, O. (1993). Children learning mathematics: A teacher’s guide to recent research. London: Cassell.
  • Dougherty, B., J. (1996). The write way: A look at journal writing in first-year algebra. Mathematics Teacher, 89, 556-60.
  • Dursun, Ş., & Dede, Y. (2004). Öğrencilerin matematikte başarısını etkileyen faktörler matematik öğretmenlerinin görüşleri bakımından. Gazi Üniversitesi Gazi Eğitim Fakültesi Dergisi, 24(2), 217-230.
  • Duval, R. (1995). Geometrical pictures: Kinds of representation and specific processings. In R. Sutherland & J. Mason (Eds.), Exploiting mental imagery with computers in mathematics education (pp. 142–157). Berlin: Springer.
  • Edwards, B. S., & Ward, M. B. (2008). The role of mathematical definitions in mathematics and in undergraduate mathematics courses. Retrieved November 22, 2017 from https://books.google.com.tr/
  • Edwards, B. S., & Ward, M. B. (2005). New practices in teaching mathematical definitions. In D. Smith & E. Swanson (Eds.), Preparing future science and mathematics teachers: Faculty write about cept innovations on campuses today (pp. 23-25). Bozeman, MT: Science Math Resource Center.
  • Edwards, B. S., & Ward, M. B. (2004). Surprises from mathematics education research: Student (mis)use ofmathematical definitions. The American Mathematical Monthly, 111(5), 411-424.
  • Eker, C. & Coşkun, I. (2012). Ders günlüğü yazmanın ilkokul 4. sınıf öğrencilerinin sosyal bilgiler dersi akademik başarılarına etkisi. Muğla Sıtkı Koçman Universitesi Sosyal Bilimler Enstitüsü Dergisi, 29, 111-122.
  • Ernest, P. (1999). Forms of knowledge in mathematics and mathematics education: Philosophical and rhetorical perspectives. Educational Studies in Mathematics, 38(1–3), 67–83.
  • Goldin-Meadow, S., & Singer, M. A. (2003). From children‘s hands to adults’ ear: Gesture’s role in the learning process. Development Psychology, 39(3), 509–520.
  • Gökbulut, Y. & Ubuz, B. (2013). Sınıf öğretmeni adaylarının prizma bilgileri: Tanım ve örnekler oluşturma. İlköğretim Online, 12(2), 401-412.
  • Harley, T., A. (1995). The psychology of language: From data to theory. England: Erlbaum (UK) Taylor & Francis.
  • Hershkowitz, R. (1990). Psychological aspects of learning geometry. In P. Nesher & J. Kilpatric (Eds.), Mathematics and cognition (pp. 70–95). Cambridge: Cambridge University Press.
  • Kotsopoulos, D. (2007). Mathematics discourse: “It’s like hearing a foreign language”. Mathematics Teacher, 101(4), 301-305.
  • Köroğlu, H., Yavuz, G., & Ertem, S. (2004, Ekim). 11. sınıf öğrencilerinin geometri dersinde karşılaştıkları bazı kavram yanılgıları ve çözüm önerileri. XII. Eğitim Bilimleri Kongresi’nde sunulan bildiri, Gazi Üniversitesi.
  • Kranda, J. (2008). Precise mathematical language: Exploring the relationship between student vocabulary understanding and student achievement (Unpublished master’s thesis). University of Nebraska, Lincoln.
  • Lim, L., & Pugalee, D. K. (2004). Using journal writing to explore they communicate to learn mathematics and they learn to communicate mathematically. Ontario Action Researcher, 7(2), 17-24.
  • Mason, J. (1980). When is a symbol symbolic? For the Learning of Mathematics, 1(2), 8-12.
  • Mili Eğitim Bakanlığı [MEB]. (2013). Ortaokul matematik dersi öğretim program (5, 6, 7, ve 8. sınıflar). Ankara: MEB.
  • Meel, D. (1999). Email dialogue journals in a college calculus classroom: A look at the implementation and benefits. Journal of Computers in Mathematics and Science Teaching, 18(4), 387-413.
  • Mercer, N., & Sams, C. (2006). Teaching children how to use language to solve maths problems. Language and Education, 20(6), 507-528.
  • Moralı, S., Köroğlu, H., & Çelik, A. (2004). Buca Eğitim Fakültesi matematik öğretmen adaylarının soyut matematik dersine yönelik tutumları ve rastlanan kavram yanılgıları. Gazi Üniversitesi Gazi Eğitim Fakültesi Dergisi, 24(1), 161-175.
  • Monroe, E. E., & Orme, M. P. (2002). Developing mathematical vocabulary. Preventing School Failure: Alternative Education for Children and Youth, 46(3), 139-142.
  • Moon, J. (2010). Assessment: Learning journals and logs. Retrieved June 15, 2017 from: http://ar.cetl.hku.hk/pdf/ucdtla0035.pdf
  • Morgan, C. (1998). Writing mathematically: The discourse of investigation. London: Falmer Press.
  • National Council of Teachers of Mathematics [NCTM]. (2006). Principles and standards for school mathematics. Reston, VA: Author.
  • National Council of Teachers of Mathematics [NCTM]. (2000). Principles and standards for school mathematics. Reston, VA: Author.
  • National Council of Teachers of Mathematics [NCTM]. (1989). The curriculum and evaluation standards. Reston, VA: Author.
  • National Research Council [NRC]. (2001). Adding it up: Helping children learn mathematics. In J. Kilpatrick, J. Swafford & B. Findell (Eds.), Center for education, division of behavioral and social sciences and education (pp. 115-116). Washington, DC: National Academies Press.
  • Parzysz, B. (1988). Knowing vs seeing. Problems of the plane representation of space geometry figures. Educational Studies in Mathematics, 19, 79-92.
  • Pimm, D. (1991). Communicating mathematically. In K. Durkin & B. Shire (Eds.), Language in mathematical education: Research and practice (pp. 17-23). Philadelphia: Open University Press.
  • Pimm, D. (1987). Speaking mathematically: Communications in mathematics classrooms. London: Routledge & Keanen Paul.
  • Pugalee, D., K. (2001). Writing, mathematics, and metacognition: looking for connections through students’ work in mathematical problem solving. School Science and Mathematics, 101(5), 236–45.
  • Riccomini, P. J., Smith, G. W., Hughes, E. M., & Fries, K. M. (2015). The language of mathematics: The importance of teaching and learning mathematical vocabulary. Reading & Writing Quarterly, 31(3), 235-252.
  • Roth, W. M., & Lawless, D. (2002). Scientific investigations, metaphorical gestures, and the emergence of abstract scientific concepts. Learning and Instruction, 12, 285–304.
  • Roth, W. M., & Welzel, M. (2001). From activity to gestures and scientific language. Journal of Research in Science Teaching, 38(1), 103–136.
  • Rubenstein, R., & Thompson, D. (2002). Understanding and supporting children’s mathematical vocabulary development. Teaching Children Mathematics, 9, 107–112.
  • Rubenstein, R., N., & Thompson, D., R. (2001). Learning mathematical symbolism: Challenges and instructional strategies. The Mathematics Teacher, 94(4), 265-271.
  • Sloyer, C., W. (2003). Mathematical insight: Changing perspective. Mathematics Teacher, 96, 238–242.
  • Sáenz-Ludlow, A., & Presmeg, N. (2006). Semiotic perspectives on learning mathematics and communicating mathematically. Educational Studies in Mathematics, 61(1/2), 1-10.
  • Soylu, Y., & Aydın, S. (2006). Matematik derslerinde kavramsal ve işlemsel öğrenmenin dengelenmesinin önemi üzerine bir çalışma. Erzincan Üniversitesi Eğitim Fakültesi Dergisi, 8(2), 83-95.
  • Sucuoğlu, B., Büyüköztürk, Ş., & Ünsal, P. (2008). Türk çocuklarının temel-ilişkisel kavram bilgilerinin değerlendirilmesi. İlköğretim Online, 7(1), 203-217.
  • Tall, D., & Vinner, S. (1981). Concept image and concept definition in mathematics with particular reference to limits and continuity. Educational Studies in Mathematics, 12(2), 151-169.
  • Thompson, D. R., & Rubenstein, R. N. (2000). Learning mathematics vocabulary: Potential pitfalls and instructional strategies. The Mathematics Teacher, 93(7), 568-574.
  • Türnüklü, E., Alaylı, F. G. & Akkaş, E. N. (2013). İlköğretim matematik öğretmen adaylarının dörtgenlere ilişkin algıları ve imgelerinin incelenmesi. Kuram ve Uygulamada Eğitim Bilimleri, 13(2), 1213-1232.
  • Toluk-Uçar, Z. (2011). Öğretmen adaylarının pedagojik içerik bilgisi: Öğretimsel açıklamalar. Turkish Journal of Computer and Mathematics Education (TURCOMAT), 2(2), 87-102.
  • Uğurel, I., Tekin, Ç., & Moralı, S. (2009). Matematik eğitimi literatüründen “yazma aktiviteleri” üzerine genel bir bakış. E-journal of new World sciences Academy Education Science, 1C0038, 4(2), 494-507
  • Usiskin, Z. (1996). Mathematics as a language. In P. C. Elliot & M. J. Kenney (Eds.), Communication in mathematics, K-12 and beyond (pp. 231-243). Reston, VA: NCTM.
  • Van de Walle, J. A., Karp, K. S., & Williams, J. M. B. (2007). Elementary and middle school mathematics. Boston: Pearson.
  • Van der Walt, M., Maree, K., & Ellis, S. (2008). A mathematics vocabulary questionnaire for immediate use in the intermediate phase. South African Journal of Education, 28, 489–504.
  • Vinner, S. (1983). Conceptdefinition, concept image and the notion of function. International Journal of Mathematical Education in Science and Technology, 14, 293–305.
  • Vinner, S., & Dreyfus, T. (1989). Images and definitions for the concept of function. Journal forResearch in Mathematics Education, 20(4), 356-366.
  • Vinner, S., & Hershkowitz, R. (1980). Concept images and common cognitive paths in the development of some simple geometrical concepts. In R. Karplus (Ed.), Proceedings of the Fourth International Conference for the Psychology of Mathematics Education (pp. 177-184). Berkeley: University of California, Lawrence Hall of Science.
  • Wakefield, D. V. (2000). Math as a second language. The Educational Forum, 64(3), 272-279.
  • Warren, E. (2006). Comparative mathematical language in the elementary school: A longitudinal study. Educational Studies in Mathematics, 62, 169–189.
  • Yin, R., K. (2011). Oualitative research from start to finish. New York: A Division of Guilford Publications.
  • Zazkis, R., & Leikin, R. (2008). Exemplifying definitions: a case of a square. Educational Studies in Mathematics, 69(2), 131-148.
  • Zaslavsky, O., & Shir, K. (2005). Students’ conceptions of a mathematical definition. Journal for Research in Mathematics Education, 36(4), 317–346.
Toplam 74 adet kaynakça vardır.

Ayrıntılar

Birincil Dil Türkçe
Bölüm Araştırma Makaleleri
Yazarlar

Zülfiye Zeybek

Elif Açıl Bu kişi benim

Yayımlanma Tarihi 17 Aralık 2018
Yayımlandığı Sayı Yıl 2018 Cilt: 9 Sayı: 3

Kaynak Göster

APA Zeybek, Z., & Açıl, E. (2018). Yedinci Sınıf Öğrencilerinin Matematiksel İfade Becerilerinin İncelenmesinde Yazma Aktiviteleri: Öğrenci Günlükleri. Turkish Journal of Computer and Mathematics Education (TURCOMAT), 9(3), 476-512. https://doi.org/10.16949/turkbilmat.367513
AMA Zeybek Z, Açıl E. Yedinci Sınıf Öğrencilerinin Matematiksel İfade Becerilerinin İncelenmesinde Yazma Aktiviteleri: Öğrenci Günlükleri. Turkish Journal of Computer and Mathematics Education (TURCOMAT). Aralık 2018;9(3):476-512. doi:10.16949/turkbilmat.367513
Chicago Zeybek, Zülfiye, ve Elif Açıl. “Yedinci Sınıf Öğrencilerinin Matematiksel İfade Becerilerinin İncelenmesinde Yazma Aktiviteleri: Öğrenci Günlükleri”. Turkish Journal of Computer and Mathematics Education (TURCOMAT) 9, sy. 3 (Aralık 2018): 476-512. https://doi.org/10.16949/turkbilmat.367513.
EndNote Zeybek Z, Açıl E (01 Aralık 2018) Yedinci Sınıf Öğrencilerinin Matematiksel İfade Becerilerinin İncelenmesinde Yazma Aktiviteleri: Öğrenci Günlükleri. Turkish Journal of Computer and Mathematics Education (TURCOMAT) 9 3 476–512.
IEEE Z. Zeybek ve E. Açıl, “Yedinci Sınıf Öğrencilerinin Matematiksel İfade Becerilerinin İncelenmesinde Yazma Aktiviteleri: Öğrenci Günlükleri”, Turkish Journal of Computer and Mathematics Education (TURCOMAT), c. 9, sy. 3, ss. 476–512, 2018, doi: 10.16949/turkbilmat.367513.
ISNAD Zeybek, Zülfiye - Açıl, Elif. “Yedinci Sınıf Öğrencilerinin Matematiksel İfade Becerilerinin İncelenmesinde Yazma Aktiviteleri: Öğrenci Günlükleri”. Turkish Journal of Computer and Mathematics Education (TURCOMAT) 9/3 (Aralık 2018), 476-512. https://doi.org/10.16949/turkbilmat.367513.
JAMA Zeybek Z, Açıl E. Yedinci Sınıf Öğrencilerinin Matematiksel İfade Becerilerinin İncelenmesinde Yazma Aktiviteleri: Öğrenci Günlükleri. Turkish Journal of Computer and Mathematics Education (TURCOMAT). 2018;9:476–512.
MLA Zeybek, Zülfiye ve Elif Açıl. “Yedinci Sınıf Öğrencilerinin Matematiksel İfade Becerilerinin İncelenmesinde Yazma Aktiviteleri: Öğrenci Günlükleri”. Turkish Journal of Computer and Mathematics Education (TURCOMAT), c. 9, sy. 3, 2018, ss. 476-12, doi:10.16949/turkbilmat.367513.
Vancouver Zeybek Z, Açıl E. Yedinci Sınıf Öğrencilerinin Matematiksel İfade Becerilerinin İncelenmesinde Yazma Aktiviteleri: Öğrenci Günlükleri. Turkish Journal of Computer and Mathematics Education (TURCOMAT). 2018;9(3):476-512.