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Year 2020, Volume: 9 Issue: 2, 448 - 467, 24.06.2020

Pinar Yıldız , İffet Elif Yetkin Özdemir

Abstract

References

  • Akkan, Y., Baki, A. ve Çakıroğlu, Ü. (2012). 5-8. sınıf öğrencilerinin aritmetikten cebire geçiş süreçlerinin problem çözme bağlamında incelenmesi. Hacettepe Üniversitesi Eğitim Fakültesi Dergisi, 43, 1-13.
  • An, S., Kulm, G., and Wu, Z. (2004). The pedagogical content knowledge of middle school mathematics teachers in China and U.S.. Journal of Mathematics Teachers Education, 7, 145-172.
  • Asquith, P., Stephens, A. C., Knuth, E. J., and Alibali, M. W. (2007). Middle school mathematics teachers’ knowledge of students’ understanding of core algebraic concepts: Equal sign and variable. Mathematical Thinking and Learning, 9(3), 249-272.
  • Attorps, I. (2003). Teachers’ images of the ‘equation’concept. European Research in Mathematics Education, 3, 1-8.
  • Ball, D. L. (1990). The mathematical understandings that prospective teachers bring to teaeher education. Elementary School Journal, 90(4), 449-446.
  • Ball, D. L., Hill, H. C., ve Bass, H. (2005). Knowing mathematics for teaching: Who knows mathematics well enough to teach third grade, and how can we decide? American Educator, 29(1), 14-17.
  • Ball, D. B., Thames, M. H., and Phelps, G. (2008). Content knowledge for teaching: What makes it special?. Journal of Teacher Education, 59(5), 389-407.
  • Baroody, A.J., and Ginsburg, H. P. (1983). The effects of instruction on children’s understanding of the “equals” sign. The Elementary School Journal, 84(2), 198-212.
  • Behr, M., Erlwanger, S., and Nichols, E. (1980). How children view the equals sign. Mathematics Teaching, 92, 13-15.
  • Black, D. J. W. (2007). The relationship of teachers’ content knowledge and pedagogical content knowledge in algebra, and changes in both types of knowledge as a professional development (Unpublished Doctoral Dissertation). Auburn University, Auburn.
  • Booth, L. (1988). Children’s difficulties in beginning algebra. The ideas of algebra, K-12, 20-32.
  • Brizuela, B. M. (2016). Variables in elementary mathematics education. The Elementary School Journal, 117(1), 46-71.
  • Chalouh, L., and Herscovics, N. (1988). Teaching algebraic expressions in a meaningful way. In A.F. Coxford (Ed.). The ideas of Algebra, K-12. (pp. 33-42). Reston, VA: National Council of Teachers of Mathematics.
  • Charalambous, C. Y., Hill, H. C., Chin, M. J., & McGinn, D. (2018). Mathematical content knowledge and knowledge for teaching: exploring their distinguishability and contribution to student learning. Journal of Mathematics Teacher Education, 1-35.
  • Copur-Gencturk, Y. (2015). The effects of changes in mathematical knowledge on teaching: A longitudinal study of teachers' knowledge and instruction. Journal for Research in Mathematics Education, 46(3), 280-330.
  • Creswell, J. W. (2007). Qualitative inquiry and research design: Choosing among five approaches (2nd ed.). London: Sage.
  • Dede, Y. (2005). Değişken kavramı üzerine. Kastamonu Eğitim Dergisi, 13(1), 139-148.
  • Dede, Y. ve Argün, Z. (2003). Cebir, öğrencilere niçin zor gelmektedir?. Hacettepe Üniversitesi Eğitim Fakültesi Dergisi, 24, 180-185.
  • Dede, Y. ve Peker, M. (2004, Temmuz). Öğrencilerin cebire yönelik hata ve yanlış anlamaları: Matematik öğretmen adaylarının tahmin becerileri ve çözüm önerileri. XIII. Ulusal Eğitim Bilimleri Kurultayı. İnönü Üniversitesi Eğitim Fakültesi, Malatya.
  • Delaney, S., Ball, D. L., Hill, H.C., Schilling, S. G., and Zapf, D. (2008). “Mathematical knowledge for teaching”: Adapting U.S. measures for use in Ireland. Journal of Mathematics Teacher Education, 11(3), 171-197.
  • Denzin, N., and Lincoln, Y. (2000). Introduction: The discipline and practice of qualitative research. In N. Denzin, and Y. Lincoln (Eds.). Handbook of qualitative reseacrh (pp. 1-28). Thousand Oaks, CA: Sage Publications.
  • Even, R. (1993). Subject matter knowledge and pedagogical content knowledge: Prospective secondary teachers and the functions concepts. Journal for Reseacrh in Mathematics Education, 24, 94-116.
  • Falkner, K.P., Levi, L., and Carpenter, T. P. (1999). Childrens understanding of equality: A foundation for algebra. Teaching Children Mathematics, 6, 231-236.
  • Fennema, E., Sowder, J., and Carpenter, T. P. (1999). Creating classrooms that promote understanding. In E. Fennema, and T. A. Romberg (Eds.). Mathematics classrooms that promote understanding (pp. 185-199). Hilsdale, NJ: Lawrence Erlbaum Associates.
  • Gökkurt, B., Şahin, Ö., Soylu, Y., ve Soylu, C. (2013). Öğretmen Adaylarının Kesirlerle İlgili Pedagojik Alan Bilgilerinin Öğrenci Hataları Açısından İncelenmesi. International Online Journal of Educational Sciences, 5(3).
  • Hill, H. C., Ball, D. L., and Schilling, S. G. (2008). Unpacking pedagogical content knowledge: conceptualizing and measuring teachers’ topic-specific knowledge of students. Journal of Research in Mathematics Education, 39(4), 372-400.
  • Hill, H. C., Schilling, S. G., and Ball, D. L. (2004). Developing measures of teachers’ mathematics knowledge for teaching. The Elementary School Journal, 105(1), 11-30.
  • Herscovics, N., and Linchevski, L. (1994). A cognitive gap between arithmetic and algebra. Educational Studies in Mathematics, 27(1), 59-78.
  • Kaput, J. (1998, May). Transforming algebra from an engine of inequity to an engine of mathematical power by “algebrafying” the K-12 curriculum. Paper presented at the Algebra Symposium, Washington, DC.
  • Kieran, C. (1981). Concepts associated with the equality symbol. Educational Studies in Mathematics, 12, 317-326.
  • Kieran, C. (1992). The learning and teaching of school algebra. In D.A. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 390-419). New York, NY: Macmillan.
  • Kieran, C. (2007). What do students struggle with when first introduced to algebra symbols? National Council of Teachers of Mathematics Research Brief. Retrieved from http://www.nctm.org/news/content.aspx?id=12332
  • Knuth, E. J., Alibali, M. W., McNeil, N.M., Weinberg, A., and Stephens, A.C. (2005). Middle school students’ understanding of core algebraic concepts: Equivalence & Variable. Zentralblatt für Didaktik der Mathematik, 37(1), 68-76.
  • Kuchemann, D. (1978). Children’s understanding of numerical variables. Mathematics in School, 7(4), 23-26.
  • Kutluk, B. (2011). İlköğretim matematik öğretmenlerinin örüntü kavramına ilişkin öğrenci güçlükleri bilgilerinin incelenmesi (Yayınlanmamış Yüksek Lisans Tezi). Dokuz Eylül Üniversitesi Eğitim Bilimleri Enstitüsü, İzmir.
  • Lee, J. E. (2011). A study of pre-kindergarten teachers’ mathematical knowledge for teaching (Unpublished Doctoral Dissertation). The University of Texas, Austin, United States.
  • MacGregor, M., and Stacey, K. (1997). Students' understanding of algebraic notation: 11–16. Educational Studies in Mathematics. 33, 1–19.
  • Matz, M. (1980). Towards a computational theory of algebraic competence. Journal of Mathematical Behavior, 3(1), 93–166.
  • Merriam, S. B. (2009). Qualitative research: A guide to design and implementation. San Francisco, CA: Jossey- Bass.
  • Meyer, B. C. (2016). The equal sign: Teachers’ specialised content knowledge and learners’ misconceptions (Unpublished doctoral dissertation). Cape Peninsula University of Technology.
  • Patton, M. Q. (2002). Qualitative research and evaluation methods. Thousand Oaks, CA: Sage Publications.
  • Perso, T. (1992). Overcoming misconceptions in algebra: using diagnostic (conflict) teaching. Subiaco, Western Australia: Mathematical Association of Western Australia.
  • Philipp, R. (1992). The many uses of algebraic variables. Mathematics Teacher, 85, 557-561.
  • Rizvi, N. F., and Lawson, M. J. (2007). Prospective teachers’ knowledge: Concept of division. International Education Journal, 8(2), 377-392.
  • Shulman, L. S. (1986). Those who understand: Knowledge growth in teaching. Educational Researcher, 15(2), 4-14.
  • Shulman, L. S. (1987). Knowledge and teaching: Foundations of the new reform. Harward Educational Review, 57(1), 1-21.
  • Slavit, D. (1999). The role of operation sense in transitions from arithmetic to algebraic thought. Educational Studies in Mathematics, 37, 251-274.
  • Stacey, K., and MacGregor, M. (1997).Ideas about symbolism that students bring to algebra. The Mathematics Teacher, 90(2), 110-113.
  • Stephens, A. C. (2005). Developing students understanding of variable. Mathematics Teaching in the Middle School, 11(2), 96-100.
  • Stephens, A. C. (2006.) Equivalence and relational thinking: Preservice elementary teachers’ awareness of opportunities and misconceptions. Journal of Mathematics Teacher Education, 9, 249-278.
  • Stephens, A. C. (2008). What “counts” as algebra in the eyes of preservice elementary teachers?.Journal of Mathematical Behavior, 27, 33-47.
  • Stump, S. L., and Bishop, J. (2002). Preservice elementary and middle school teachers’ conceptions of algebra revealed through the use of exemplary curriculum materials. In D. S. Mewborn, P. Sztajn, D.Y. White, H. G.Wiegel, R. L. Bryant, and K. Nooney (Eds.). Proceedings of the twenty-fourth annual meeting of the international group for the psychology of mathematics education (pp. 1903–1914). Columbus, OH: ERIC.
  • Tanışlı, D. (2013). İlköğretim matematik öğretmeni adaylarının pedagojik alan bilgisi bağlamında sorgulama becerileri ve öğrenci bilgileri. Eğitim ve Bilim, 38(169).
  • Tchoshanov, M., Cruz, M. D., Huereca, K., Shakirova, K., Shakirova, L., & Ibragimova, E. N. (2017). Examination of lower secondary mathematics teachers’ content knowledge and its connection to students’ performance. International Journal of Science and Mathematics Education, 15(4), 683-702.
  • Tirosh, D., Even, R., and Robinson, N. (1998). Simplifying algebraic expressions: Teacher awareness and teaching approaches. Educational Studies in Mathematics, 35(1), 51-64.
  • Usiskin, Z. (1999). Conceptions of school algebra and uses variables. In edited by B. Moses (Ed.). Allgebraic Thinking, Grades K-12: Readings from NCTM’s School-Based Journals and Other Publications (pp. 7-13). Reston, VA: Natinoal Council of Teachers Mathematics.
  • Vermeulen, C., & Meyer, B. (2017). The equal sign: teachers’ knowledge and students’ misconceptions. African Journal of Research in Mathematics, Science and Technology Education, 21(2), 136-147.
  • Wagner, S. (1983). What are these things called variables. Mathematics Teacher, 76(7), 474–479.
  • Weinberg, A., Dresen, J., & Slater, T. (2016). Students’ understanding of algebraic notation: A semiotic systems perspective. The Journal of Mathematical Behavior, 43, 70-88.
  • Yaman, H., Toluk, Z. ve Olkun, S. (2003). İlköğretim öğrencileri eşit işaretini nasıl algılamaktadırlar?. Hacettepe Üniversitesi Eğitim Fakültesi Dergisi, 24, 142-151.Yin, R. K. (2009). Case study reseacrh: Design and methods. Thousand Oaks, CA: Sage.

Ortaokul Matematik Öğretmenlerinin Temel Cebir Kavramlarına İlişkin Öğrenci Bilgisi

Year 2020, Volume: 9 Issue: 2, 448 - 467, 24.06.2020

Pinar Yıldız , İffet Elif Yetkin Özdemir

Abstract

Bu araştırmanın amacı, ortaokul matematik
öğretmenlerinin değişken, cebirsel ifadeler, eşitlik ve denklem kavramlarına
ilişkin öğrenci bilgisini incelemektir. Araştırmada nitel araştırma
desenlerinden durum çalışması deseni kullanılmıştır. Araştırmaya bir devlet
okulunda görev yapan üç ortaokul matematik öğretmeni katılmıştır. Katılımcılar
amaçlı örneklem yöntemi ile belirlenmiştir. Araştırmanın katılımcılarından
Ayla, Hale ve Emre araştırma sırasında sırasıyla 2, 3 ve 8 yıllık mesleki
deneyime sahiptir. Veriler, sınıf içi gözlemler ve öğretmenlerle yapılan yarı
yapılandırılmış görüşmeler aracılığıyla toplanmıştır. Bu sürecin ilk aşamasında
veri toplama araçları (görüşme formları) geliştirilmiştir. Ayrıca katılımcılar
belirlenerek ön görüşmeler yapılmıştır. İkinci aşamada ise dersler gözlenmiş ve
ders gözlemleri sonrası görüşme formları düzenlenmiştir. Görüşme formlarında
yapılan düzenlemeler sonrası ise bir öğretmen ile görüşme formlarının pilot
uygulaması yapılmıştır. Sonrasında görüşme formları düzenlenerek son şekli
oluşturulmuş ve öğretmenlerle bireysel görüşmeler gerçekleştirilmiştir.
Araştırma kapsamında elde edilen veriler öğretmenlerin değişken, cebirsel
ifadeler, eşitlik ve denklem konularına ilişkin öğrenci bilgilerini
derinlemesine ortaya koymak için betimsel analiz yoluyla analiz edilmiştir. Araştırma
sonucunda öğretmenlerin değişken, cebirsel ifade, eşitlik ve denklem
kavramlarına ilişkin olası öğrenci düşünceleri, zorlukları ve hataları hakkında
bilgi sahibi oldukları; ancak bunların nedenine yönelik sınırlı bilgiye sahip
oldukları belirlenmiştir. Öğretmenler öğrencilerin bu düşüncelerine yönelik
derinlemesine bir analiz yapamamışlardır. Ayrıca,
öğretmenler olası öğrenci düşünceleri ve hataları hakkında bilgi sahibi
olmalarına rağmen derslerini yapılandırırken bu bilgilerini kullanmamışlardır.

Keywords

Ortaokul matematik öğretmenleri cebir temel cebir kavramları pedagojik alan bilgisi öğrenci bilgisi

References

  • Akkan, Y., Baki, A. ve Çakıroğlu, Ü. (2012). 5-8. sınıf öğrencilerinin aritmetikten cebire geçiş süreçlerinin problem çözme bağlamında incelenmesi. Hacettepe Üniversitesi Eğitim Fakültesi Dergisi, 43, 1-13.
  • An, S., Kulm, G., and Wu, Z. (2004). The pedagogical content knowledge of middle school mathematics teachers in China and U.S.. Journal of Mathematics Teachers Education, 7, 145-172.
  • Asquith, P., Stephens, A. C., Knuth, E. J., and Alibali, M. W. (2007). Middle school mathematics teachers’ knowledge of students’ understanding of core algebraic concepts: Equal sign and variable. Mathematical Thinking and Learning, 9(3), 249-272.
  • Attorps, I. (2003). Teachers’ images of the ‘equation’concept. European Research in Mathematics Education, 3, 1-8.
  • Ball, D. L. (1990). The mathematical understandings that prospective teachers bring to teaeher education. Elementary School Journal, 90(4), 449-446.
  • Ball, D. L., Hill, H. C., ve Bass, H. (2005). Knowing mathematics for teaching: Who knows mathematics well enough to teach third grade, and how can we decide? American Educator, 29(1), 14-17.
  • Ball, D. B., Thames, M. H., and Phelps, G. (2008). Content knowledge for teaching: What makes it special?. Journal of Teacher Education, 59(5), 389-407.
  • Baroody, A.J., and Ginsburg, H. P. (1983). The effects of instruction on children’s understanding of the “equals” sign. The Elementary School Journal, 84(2), 198-212.
  • Behr, M., Erlwanger, S., and Nichols, E. (1980). How children view the equals sign. Mathematics Teaching, 92, 13-15.
  • Black, D. J. W. (2007). The relationship of teachers’ content knowledge and pedagogical content knowledge in algebra, and changes in both types of knowledge as a professional development (Unpublished Doctoral Dissertation). Auburn University, Auburn.
  • Booth, L. (1988). Children’s difficulties in beginning algebra. The ideas of algebra, K-12, 20-32.
  • Brizuela, B. M. (2016). Variables in elementary mathematics education. The Elementary School Journal, 117(1), 46-71.
  • Chalouh, L., and Herscovics, N. (1988). Teaching algebraic expressions in a meaningful way. In A.F. Coxford (Ed.). The ideas of Algebra, K-12. (pp. 33-42). Reston, VA: National Council of Teachers of Mathematics.
  • Charalambous, C. Y., Hill, H. C., Chin, M. J., & McGinn, D. (2018). Mathematical content knowledge and knowledge for teaching: exploring their distinguishability and contribution to student learning. Journal of Mathematics Teacher Education, 1-35.
  • Copur-Gencturk, Y. (2015). The effects of changes in mathematical knowledge on teaching: A longitudinal study of teachers' knowledge and instruction. Journal for Research in Mathematics Education, 46(3), 280-330.
  • Creswell, J. W. (2007). Qualitative inquiry and research design: Choosing among five approaches (2nd ed.). London: Sage.
  • Dede, Y. (2005). Değişken kavramı üzerine. Kastamonu Eğitim Dergisi, 13(1), 139-148.
  • Dede, Y. ve Argün, Z. (2003). Cebir, öğrencilere niçin zor gelmektedir?. Hacettepe Üniversitesi Eğitim Fakültesi Dergisi, 24, 180-185.
  • Dede, Y. ve Peker, M. (2004, Temmuz). Öğrencilerin cebire yönelik hata ve yanlış anlamaları: Matematik öğretmen adaylarının tahmin becerileri ve çözüm önerileri. XIII. Ulusal Eğitim Bilimleri Kurultayı. İnönü Üniversitesi Eğitim Fakültesi, Malatya.
  • Delaney, S., Ball, D. L., Hill, H.C., Schilling, S. G., and Zapf, D. (2008). “Mathematical knowledge for teaching”: Adapting U.S. measures for use in Ireland. Journal of Mathematics Teacher Education, 11(3), 171-197.
  • Denzin, N., and Lincoln, Y. (2000). Introduction: The discipline and practice of qualitative research. In N. Denzin, and Y. Lincoln (Eds.). Handbook of qualitative reseacrh (pp. 1-28). Thousand Oaks, CA: Sage Publications.
  • Even, R. (1993). Subject matter knowledge and pedagogical content knowledge: Prospective secondary teachers and the functions concepts. Journal for Reseacrh in Mathematics Education, 24, 94-116.
  • Falkner, K.P., Levi, L., and Carpenter, T. P. (1999). Childrens understanding of equality: A foundation for algebra. Teaching Children Mathematics, 6, 231-236.
  • Fennema, E., Sowder, J., and Carpenter, T. P. (1999). Creating classrooms that promote understanding. In E. Fennema, and T. A. Romberg (Eds.). Mathematics classrooms that promote understanding (pp. 185-199). Hilsdale, NJ: Lawrence Erlbaum Associates.
  • Gökkurt, B., Şahin, Ö., Soylu, Y., ve Soylu, C. (2013). Öğretmen Adaylarının Kesirlerle İlgili Pedagojik Alan Bilgilerinin Öğrenci Hataları Açısından İncelenmesi. International Online Journal of Educational Sciences, 5(3).
  • Hill, H. C., Ball, D. L., and Schilling, S. G. (2008). Unpacking pedagogical content knowledge: conceptualizing and measuring teachers’ topic-specific knowledge of students. Journal of Research in Mathematics Education, 39(4), 372-400.
  • Hill, H. C., Schilling, S. G., and Ball, D. L. (2004). Developing measures of teachers’ mathematics knowledge for teaching. The Elementary School Journal, 105(1), 11-30.
  • Herscovics, N., and Linchevski, L. (1994). A cognitive gap between arithmetic and algebra. Educational Studies in Mathematics, 27(1), 59-78.
  • Kaput, J. (1998, May). Transforming algebra from an engine of inequity to an engine of mathematical power by “algebrafying” the K-12 curriculum. Paper presented at the Algebra Symposium, Washington, DC.
  • Kieran, C. (1981). Concepts associated with the equality symbol. Educational Studies in Mathematics, 12, 317-326.
  • Kieran, C. (1992). The learning and teaching of school algebra. In D.A. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 390-419). New York, NY: Macmillan.
  • Kieran, C. (2007). What do students struggle with when first introduced to algebra symbols? National Council of Teachers of Mathematics Research Brief. Retrieved from http://www.nctm.org/news/content.aspx?id=12332
  • Knuth, E. J., Alibali, M. W., McNeil, N.M., Weinberg, A., and Stephens, A.C. (2005). Middle school students’ understanding of core algebraic concepts: Equivalence & Variable. Zentralblatt für Didaktik der Mathematik, 37(1), 68-76.
  • Kuchemann, D. (1978). Children’s understanding of numerical variables. Mathematics in School, 7(4), 23-26.
  • Kutluk, B. (2011). İlköğretim matematik öğretmenlerinin örüntü kavramına ilişkin öğrenci güçlükleri bilgilerinin incelenmesi (Yayınlanmamış Yüksek Lisans Tezi). Dokuz Eylül Üniversitesi Eğitim Bilimleri Enstitüsü, İzmir.
  • Lee, J. E. (2011). A study of pre-kindergarten teachers’ mathematical knowledge for teaching (Unpublished Doctoral Dissertation). The University of Texas, Austin, United States.
  • MacGregor, M., and Stacey, K. (1997). Students' understanding of algebraic notation: 11–16. Educational Studies in Mathematics. 33, 1–19.
  • Matz, M. (1980). Towards a computational theory of algebraic competence. Journal of Mathematical Behavior, 3(1), 93–166.
  • Merriam, S. B. (2009). Qualitative research: A guide to design and implementation. San Francisco, CA: Jossey- Bass.
  • Meyer, B. C. (2016). The equal sign: Teachers’ specialised content knowledge and learners’ misconceptions (Unpublished doctoral dissertation). Cape Peninsula University of Technology.
  • Patton, M. Q. (2002). Qualitative research and evaluation methods. Thousand Oaks, CA: Sage Publications.
  • Perso, T. (1992). Overcoming misconceptions in algebra: using diagnostic (conflict) teaching. Subiaco, Western Australia: Mathematical Association of Western Australia.
  • Philipp, R. (1992). The many uses of algebraic variables. Mathematics Teacher, 85, 557-561.
  • Rizvi, N. F., and Lawson, M. J. (2007). Prospective teachers’ knowledge: Concept of division. International Education Journal, 8(2), 377-392.
  • Shulman, L. S. (1986). Those who understand: Knowledge growth in teaching. Educational Researcher, 15(2), 4-14.
  • Shulman, L. S. (1987). Knowledge and teaching: Foundations of the new reform. Harward Educational Review, 57(1), 1-21.
  • Slavit, D. (1999). The role of operation sense in transitions from arithmetic to algebraic thought. Educational Studies in Mathematics, 37, 251-274.
  • Stacey, K., and MacGregor, M. (1997).Ideas about symbolism that students bring to algebra. The Mathematics Teacher, 90(2), 110-113.
  • Stephens, A. C. (2005). Developing students understanding of variable. Mathematics Teaching in the Middle School, 11(2), 96-100.
  • Stephens, A. C. (2006.) Equivalence and relational thinking: Preservice elementary teachers’ awareness of opportunities and misconceptions. Journal of Mathematics Teacher Education, 9, 249-278.
  • Stephens, A. C. (2008). What “counts” as algebra in the eyes of preservice elementary teachers?.Journal of Mathematical Behavior, 27, 33-47.
  • Stump, S. L., and Bishop, J. (2002). Preservice elementary and middle school teachers’ conceptions of algebra revealed through the use of exemplary curriculum materials. In D. S. Mewborn, P. Sztajn, D.Y. White, H. G.Wiegel, R. L. Bryant, and K. Nooney (Eds.). Proceedings of the twenty-fourth annual meeting of the international group for the psychology of mathematics education (pp. 1903–1914). Columbus, OH: ERIC.
  • Tanışlı, D. (2013). İlköğretim matematik öğretmeni adaylarının pedagojik alan bilgisi bağlamında sorgulama becerileri ve öğrenci bilgileri. Eğitim ve Bilim, 38(169).
  • Tchoshanov, M., Cruz, M. D., Huereca, K., Shakirova, K., Shakirova, L., & Ibragimova, E. N. (2017). Examination of lower secondary mathematics teachers’ content knowledge and its connection to students’ performance. International Journal of Science and Mathematics Education, 15(4), 683-702.
  • Tirosh, D., Even, R., and Robinson, N. (1998). Simplifying algebraic expressions: Teacher awareness and teaching approaches. Educational Studies in Mathematics, 35(1), 51-64.
  • Usiskin, Z. (1999). Conceptions of school algebra and uses variables. In edited by B. Moses (Ed.). Allgebraic Thinking, Grades K-12: Readings from NCTM’s School-Based Journals and Other Publications (pp. 7-13). Reston, VA: Natinoal Council of Teachers Mathematics.
  • Vermeulen, C., & Meyer, B. (2017). The equal sign: teachers’ knowledge and students’ misconceptions. African Journal of Research in Mathematics, Science and Technology Education, 21(2), 136-147.
  • Wagner, S. (1983). What are these things called variables. Mathematics Teacher, 76(7), 474–479.
  • Weinberg, A., Dresen, J., & Slater, T. (2016). Students’ understanding of algebraic notation: A semiotic systems perspective. The Journal of Mathematical Behavior, 43, 70-88.
  • Yaman, H., Toluk, Z. ve Olkun, S. (2003). İlköğretim öğrencileri eşit işaretini nasıl algılamaktadırlar?. Hacettepe Üniversitesi Eğitim Fakültesi Dergisi, 24, 142-151.Yin, R. K. (2009). Case study reseacrh: Design and methods. Thousand Oaks, CA: Sage.
There are 60 citations in total.

Details

Primary Language Turkish
Journal Section Research Article
Authors

Pinar Yıldız 0000-0002-6729-7721

İffet Elif Yetkin Özdemir 0000-0001-8784-0317

Publication Date June 24, 2020
Published in Issue Year 2020 Volume: 9 Issue: 2

Cite

APA Yıldız, P., & Yetkin Özdemir, İ. E. (2020). Ortaokul Matematik Öğretmenlerinin Temel Cebir Kavramlarına İlişkin Öğrenci Bilgisi. Cumhuriyet Uluslararası Eğitim Dergisi, 9(2), 448-467.
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