Abstract
The purpose of this study is to assess preservice teachers’ mathematical knowledge for teaching statistics (MKT-S) and identify the relationship between the components of this knowledge. For this purpose, MKT-S instrument consisting of two dimensions, ‘content knowledge’ (CK) and ‘pedagogical content knowledge’ (PCK) was developed, and applied to 659 preservice middle school mathematics teachers (PTs). Confirmatory factor analysis showed that CK and PCK are two different dimensions of mathematical knowledge of teaching statistics. Third year and fourth year preservice teachers’ factor scores were significantly different and fourth year preservice teachers’ factor scores were slightly higher. It was found that CK factor scores were highly correlated with PCK factor scores. The reliability levels were 0.65 for CK factor scores and 0.76 for PCK factor scores. MKT-S instrument developed in this study has several implications for teacher education. MKT-S instrument can be used to evaluate efficiency of PTs’ mathematical knowledge for teaching statistics. Instrument can be adapted for in-service teachers.
Keywords
Teacher knowledge content knowledge pedagogical content knowledge teaching statistics Item Response Theory Confirmatory Factor Analysis.
References
- An, S., Kulm, G., & Wu, Z. (2004). The pedagogical content knowledge of middle school mathematics teachers in China and the U.S. Journal of Mathematics Teacher Education, 7(2), 145–172.
- Ball, D. L. (2002). Knowing mathematics for teaching: Relations between research and practice. Mathematics and Education Reform Newsletter, 14(3), 1-5.
- Barrett, P. (2007). Structural equation modelling: Adjudging model fit. Personality and Individual Differences, 42, 815-824.
- Blömeke, S., Houang, R. T., & Suhl, U. (2011). TEDS-M: Diagnosing teacher knowledge by applying multidimensional item response theory and multiple-group models. IERI Monograph Series: Issues and Methodologies in Large-Scale Assessments, 4, 109-129.
- Retrieved May 10, 2013, from http://www.ierinstitute.org/dissemination-area.html
- Borko, H., Eisenhart, M., Brown, C. A., Underhill, R. G., Jones, D., & Agard, P. C. (1992). Learning to teach hard mathematics: Do novice teachers and their instructors give up too easily?. Journal for Research in Mathematics Education, 194-222.
- Cartwright. F., (2013). IATA Manual. Retrieved June 25, 2013, from www.polymetrika.org
- Fan, L., & Cheong, N. P. (2002). Investigating the sources of Singaporean mathematics teachers' pedagogical knowledge. In D. Edge & B. H. Yeap (Eds.), Mathematics education for a knowledge-based era : Vol. 2 (pp. 224-23 1). Singapore: AME.
- Hill, H. C., Ball, D. L., & Schilling, S. G. (2008). Unpacking pedagogical content knowledge: Conceptualizing and measuring teachers’ topic-specific knowledge of students. Journal for Research in Mathematics Education, 39(4), 372–400.
- Hill, H.C., Rowan, B., & Ball, D.L. (2005) Effects of teachers' mathematical knowledge for teaching on student achievement. American Educational Research Journal, 42, 371-406.
- Hill, H.C., Schilling, S.G., & Ball, D. L. (2004). Developing measures of teachers’ mathematics knowledge for teaching. Elementary School Journal, 105, 11-30.
- İncikabı, L. (2013). TPAB-temelli “Teknolojiyle Öğretim” dersi: Matematik öğretimi için bilgisayar oyunu tasarlama. In T. Yanpar-Yelken, H. Sancar-Tokmak, S. Özgelen, & L. İncikabı, (Eds.), Fen ve matematik eğitiminde teknolojik, pedagojik alan bilgisi temelli öğretim tasarımları, (pp. 221-238). Ankara: Anı Yayıncılık.
- Incikabi, L., & Sancar-Tokmak, H. (2013). Integrating technology into mathematics teaching: A TPACK (Technological, Pedagogical, Content knowledge) - based course design for college students. In J. Keengewe (Ed.), Research Perspectives and Best Practices in Educational Technology Integration (pp. 288-303). Hersley, PA: IGI Global.
- Krauss, S., Brunner, M., Kunter, M., Baumert, J., Blum, W., Neubrand, M., & Jordan, A. (2008). Pedagogical content knowledge and content knowledge of secondary mathematics teachers. Journal of Educational Psychology, 100(3), 716-725.
- Mercimek, O. (2013). Assessment of Preservice Mathematics Teachers’ Knowledge For Teaching Statistics (Unpublished doctoral thesis). Middle East Technical University, Turkey
- Mullis, I. V. S., Martin, M. O., Ruddock, G. J., O’Sullivan C. Y., Arora, A. & Erberber, E.. (2005). TIMSS 2007 assessment frameworks. Chestnut Hill, MA: TIMSS & PIRLS International Study Center, Lynch School of Education, Boston College
- Muthen, L. K., & Muthen, B. O. (2006). IRT in Mplus. Retrieved March 25, 2013, from http://www.statmodel.com/download/MplusIRT1.pdf
- Muthén, L.K. and Muthén, B.O. (1998-2012). Mplus user’s guide (7th ed.). Los Angeles, CA: Muthén & Muthén
- OSYM (2008). Table 4: University Student Capacities for Bachelor Degree Level. Retrieved September 23, 2010, from http://dokuman.osym.gov.tr/pdfdokuman/arsiv/ 2008/ 2008_OSYS_TERCIH_KILAVUZU/6_tablo4.pdf Cumhuriyet International Journal of Education-CIJE e–ISSN: 2147-1606 Vol 6 (1), 2017, 173 – 184 - 184 -
- OSYM (2009). Table 4: University Student Capacities for Bachelor Degree Level. Retrieved September 23, 2010, from http://dokuman.osym.gov.tr/pdfdokuman/arsiv/2009/ 2009_OSYS_TERCIH_KILAVUZU/tablo4.pdf
- Schmidt, W., Tatto, M.T., Bankov, K., Blomeke, S., Cedillo, T., Cogan, L., Han, S. I., Houang, R., Hsieh, F. J., Paine, L., Santillan, M., & Schwille, J. (2007). The preparation gap: Teacher education for middle school mathematics in six countries (MT21 report). East Lansing, MI: Michigan State University. Retrieved February 25, 2010, from http://usteds.msu.edu/ MT21Report.pdf
- 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. Harvard educational review, 57(1), 1-23.
- Tatto, M. T., Schwille, J., Senk, S., Ingvarson, L., Peck, R., & Rowley, G. (2008). Teacher Education and Development Study in Mathematics (TEDS-M): Conceptual framework. East Lansing, MI: Teacher Education and Development International Study Center, College of Education, Michigan State University.
Abstract
Bu çalışmanın amacı matematik öğretmen adaylarının istatistik öğretimine yönelik
matematiksel bilgilerinin (MKT-S) ölçülmesi ve bu bilginin yapıtaşları arasındaki ilişkinin
belirlenmesidir. Bu amaçla, ‘alan bilgisi’ (CK) ve ‘pedagojik alan bilgisi’ (PCK) olmak üzere
iki bölümden oluşan MKT-S ölçeği geliştirilmiş ve 659 ilköğretim matematik öğretmeni adayı
(ÖA) üzerinde uygulanmıştır. Doğrulayıcı faktör analizi, CK ve PCK faktörlerinin, istatistik
öğretimine yönelik matematiksel bilginin iki ayrı boyutu olduğunu göstermiştir. Üçüncü ve
dördüncü sınıf öğretmen adaylarının faktör puanları arasında istatistiksel olarak anlamlı fark
bulunmuştur ve dördüncü sınıf öğretmen adaylarının faktör puanlarının az da olsa daha
yüksek olduğu görülmüştür. CK puanlarının PCK puanlarıyla yüksek derecede ilişkisinin
olduğu saptanmıştır. Ayrıca CK faktör puanlarının güvenirliği 0,65 düzeyinde iken PCK
faktör puanlarının güvenirliği 0,76 düzeyindedir. Bu çalışmada geliştirilen MKT-S ölçeğinin
sonuçlarının öğretmen eğitimi için çeşitli çıkarımları bulunmaktadır. Geliştirilen ölçek
ÖA’larının istatistik öğretimine yönelik matematiksel bilgilerinin etkinliğini
değerlendirmede kullanılabilir ya da çalışan öğretmenlere yönelik adapte edilebilir.
Keywords
Öğretmen Bilgisi Pedagojik Alan Bilgisi Alan Bilgisi istatistik öğretimi Madde Tepki Kuramı Doğrulayıcı faktör analiz
References
- An, S., Kulm, G., & Wu, Z. (2004). The pedagogical content knowledge of middle school mathematics teachers in China and the U.S. Journal of Mathematics Teacher Education, 7(2), 145–172.
- Ball, D. L. (2002). Knowing mathematics for teaching: Relations between research and practice. Mathematics and Education Reform Newsletter, 14(3), 1-5.
- Barrett, P. (2007). Structural equation modelling: Adjudging model fit. Personality and Individual Differences, 42, 815-824.
- Blömeke, S., Houang, R. T., & Suhl, U. (2011). TEDS-M: Diagnosing teacher knowledge by applying multidimensional item response theory and multiple-group models. IERI Monograph Series: Issues and Methodologies in Large-Scale Assessments, 4, 109-129.
- Retrieved May 10, 2013, from http://www.ierinstitute.org/dissemination-area.html
- Borko, H., Eisenhart, M., Brown, C. A., Underhill, R. G., Jones, D., & Agard, P. C. (1992). Learning to teach hard mathematics: Do novice teachers and their instructors give up too easily?. Journal for Research in Mathematics Education, 194-222.
- Cartwright. F., (2013). IATA Manual. Retrieved June 25, 2013, from www.polymetrika.org
- Fan, L., & Cheong, N. P. (2002). Investigating the sources of Singaporean mathematics teachers' pedagogical knowledge. In D. Edge & B. H. Yeap (Eds.), Mathematics education for a knowledge-based era : Vol. 2 (pp. 224-23 1). Singapore: AME.
- Hill, H. C., Ball, D. L., & Schilling, S. G. (2008). Unpacking pedagogical content knowledge: Conceptualizing and measuring teachers’ topic-specific knowledge of students. Journal for Research in Mathematics Education, 39(4), 372–400.
- Hill, H.C., Rowan, B., & Ball, D.L. (2005) Effects of teachers' mathematical knowledge for teaching on student achievement. American Educational Research Journal, 42, 371-406.
- Hill, H.C., Schilling, S.G., & Ball, D. L. (2004). Developing measures of teachers’ mathematics knowledge for teaching. Elementary School Journal, 105, 11-30.
- İncikabı, L. (2013). TPAB-temelli “Teknolojiyle Öğretim” dersi: Matematik öğretimi için bilgisayar oyunu tasarlama. In T. Yanpar-Yelken, H. Sancar-Tokmak, S. Özgelen, & L. İncikabı, (Eds.), Fen ve matematik eğitiminde teknolojik, pedagojik alan bilgisi temelli öğretim tasarımları, (pp. 221-238). Ankara: Anı Yayıncılık.
- Incikabi, L., & Sancar-Tokmak, H. (2013). Integrating technology into mathematics teaching: A TPACK (Technological, Pedagogical, Content knowledge) - based course design for college students. In J. Keengewe (Ed.), Research Perspectives and Best Practices in Educational Technology Integration (pp. 288-303). Hersley, PA: IGI Global.
- Krauss, S., Brunner, M., Kunter, M., Baumert, J., Blum, W., Neubrand, M., & Jordan, A. (2008). Pedagogical content knowledge and content knowledge of secondary mathematics teachers. Journal of Educational Psychology, 100(3), 716-725.
- Mercimek, O. (2013). Assessment of Preservice Mathematics Teachers’ Knowledge For Teaching Statistics (Unpublished doctoral thesis). Middle East Technical University, Turkey
- Mullis, I. V. S., Martin, M. O., Ruddock, G. J., O’Sullivan C. Y., Arora, A. & Erberber, E.. (2005). TIMSS 2007 assessment frameworks. Chestnut Hill, MA: TIMSS & PIRLS International Study Center, Lynch School of Education, Boston College
- Muthen, L. K., & Muthen, B. O. (2006). IRT in Mplus. Retrieved March 25, 2013, from http://www.statmodel.com/download/MplusIRT1.pdf
- Muthén, L.K. and Muthén, B.O. (1998-2012). Mplus user’s guide (7th ed.). Los Angeles, CA: Muthén & Muthén
- OSYM (2008). Table 4: University Student Capacities for Bachelor Degree Level. Retrieved September 23, 2010, from http://dokuman.osym.gov.tr/pdfdokuman/arsiv/ 2008/ 2008_OSYS_TERCIH_KILAVUZU/6_tablo4.pdf Cumhuriyet International Journal of Education-CIJE e–ISSN: 2147-1606 Vol 6 (1), 2017, 173 – 184 - 184 -
- OSYM (2009). Table 4: University Student Capacities for Bachelor Degree Level. Retrieved September 23, 2010, from http://dokuman.osym.gov.tr/pdfdokuman/arsiv/2009/ 2009_OSYS_TERCIH_KILAVUZU/tablo4.pdf
- Schmidt, W., Tatto, M.T., Bankov, K., Blomeke, S., Cedillo, T., Cogan, L., Han, S. I., Houang, R., Hsieh, F. J., Paine, L., Santillan, M., & Schwille, J. (2007). The preparation gap: Teacher education for middle school mathematics in six countries (MT21 report). East Lansing, MI: Michigan State University. Retrieved February 25, 2010, from http://usteds.msu.edu/ MT21Report.pdf
- 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. Harvard educational review, 57(1), 1-23.
- Tatto, M. T., Schwille, J., Senk, S., Ingvarson, L., Peck, R., & Rowley, G. (2008). Teacher Education and Development Study in Mathematics (TEDS-M): Conceptual framework. East Lansing, MI: Teacher Education and Development International Study Center, College of Education, Michigan State University.
Details
| Primary Language | Turkish |
|---|---|
| Other ID | JA37NE62GB |
| Journal Section | Research Article |
| Authors | |
| Publication Date | March 1, 2017 |
| Published in Issue | Year 2017Volume: 6 Issue: 1 |
