A Meta-Synthesis Study on Algebraic Thinking Skill
Year 2017,
Volume: 2 Issue: 2, 25 - 39, 31.12.2017
Dilek Türkoğlu
Ahmet Cihangir
Abstract
Algebraic thinking skills and algebraic achievements seem to be inadequate in the most of the researches in recent years. This leds to the research into algebraic thinking skills. Purpose of research, examine algebraic thinking in terms of prerequisite skills and critical process. In this study, meta-synthesis method was used. In this context between 2005 and 2016 by using “algebra” and “algebraic thinking” keywords 23 research which suitable for inclusion criteria in study are examined and presented with support of researcher. In the large part of studies examined, it has been found that both pattern generalizations for prerequisite skills and critical period is between 4-12 years for algebraic thinking.
References
- Altun, M. (2005). İlköğretim ikinci kademe matematik öğretimi. Bursa: Aktüel.
- Amit, M., & Neria, D. (2008). Rising to the challenge: Using generalization in pattern problems to unearth the algebraic skills of talented pre- algebra students. Zentralblatt fuer Didaktik der Mathematic, 40, 111-129.
- Aspfors, J., & Fransson, G. (2015). Research on mentor education for mentors of newly qualified teachers: A qualitative meta-synthesis. Teaching and Teacher Education, 48, 75-86.
- Bal, A. P. (2016). The effect of the differentiated teaching approach in the algebraic learning field on students’ academic achievements. Eurasian Journal of Educaional Research, 63, 185-204.
- Balcı, A. (2011). Sosyal bilimlerde araştırma yöntem, teknik ve ilkeler. Ankara: Pegem Akademi.
- Blanton, M. L., & Kaput, J.J. (2004). Elementary grades students’ capacity for functional thinking. In M. J. Hoines & A. Fuglestad (Ed.), Proceeding of The 28th Conference of the international Group for the Psychology of Mathematics Education (pp. 135-142). Bergen, Norway.
- Blanton, M. L., Levi, L., Crites, T., Dougherty, B., & Zbiek, R. M. (2011). Developing essential understanding of algebraic thinking for teaching mathematics in grades 3-5. Series in essential understandings. National Council of Teachers of Mathematics.
- Blanton, M., & Kaput, J. J. (2011). Functional thinking as a route into algebra in the elemantary grades. In J. Cai & E. Knuth (Ed.), Early algebrazation: A dialogue from multiple perspectives (pp. 5-25). USA: Springer.
- Bobis J., Mulligan, J., & Lowrie T. (2009). Mathematics for children: Challenging children to think mathematically (3rd edition). French, Forest, NSW: Pearson.
- Bush, S. B., & Karp, K. S. (2013). Prerequisite algebra skills and associated misconceptions of middle grade students: A review. The Journal of Mathematical Behavior, 32, 613-632.
- Cai, J., & Moyer, J. C. (2007). Developing algebraic thinking in the earlier grades: Some insights from international comparative studies (pp. 1-20). National Science Foundation.
- Cai, J., Moyer, J. C., Lew, H. C., Morris, A., Ng, S. F., & Schmittau, J. (2005). The develepment of studies’ algebraic thinking in earlier grades. ZDM: International Journal on Mathematics Education, 37(1), 4-15.
- Carpenter, T. P., Franke, L. M., & Levi, L. (2003). Thinking mathematically: Integrating arithmetic and algebra in elementary school. Portsmouth, NH: Heinemann.
- CCSSM (Common Core State Standards for Mathematics). (2010). Council of chief state school officers and the national governors association center for best practices. http://www.corestandards.org adresinden ulaşılmıştır.
- Crino, P. T., Tolar, T., & Fuchs, L. S. (2013). Arithmetic and cognitive contributions to algebra. Society for Research on Educational Effectiveness.
- Curriculum Russian School of Mathematics (2015). Developing Russian programs and curriculum. http://www.sras.org/ adresinden ulaşılmıştır.
- Çelik, D. (2007). Öğretmen adaylarının cebirsel düşünme becerilerinin analitik incelenmesi (Yayımlanmamış doktora tezi). Karadeniz Teknik Üniversitesi, Trabzon, Türkiye.
- Desli, D., & Gaitaneri, D. (2016). Grade 3 and 4 students’ understanding of mathematical patterns and their strategies. Pre-school and Primary Education, 5, 63-83.
- French, D. (2002). Teaching and learning algebra. London: Continuum.
- Girit, D., & Akyüz, D. (2015). Farklı sınıf seviyelerindeki ortaokul öğrencilerinde cebirsel düşünme: Örüntülerde genelleme hakkındaki algıları. Necatibey Eğitim Fakültesi Elektronik Fen ve Matematik Eğitimi Dergisi, 10(2), 243-272.
- Herbert, K, & Brown, R. (1997). Patterns as tools for algebraic reasoning. Teaching Children Mathematics, 3(6), 340-344.
- Kabael, T., & Tanışlı, D. (2010). Cebirsel düşünme sürecinde örüntüden fonksiyona öğretim. Elementary Education Online, 9(1), 213-228.
- Kaf, Y. (2007). Matematikteki model kullanımın 6. sınıf öğrencilerinin cebir erişilerine etkisi (Yayımlanmamış yüksek lisans tezi). Hacettepe Üniversitesi, Ankara, Türkiye.
- Kaya, D., & Keşan, C. (2014). İlköğretim seviyesindeki öğrencilerden cebirsel düşünme ve cebirsel muhakeme becerisinin önemi. International Journal of New Trends in Arts, Sports and Science Education, 3(2), 38-47.
- Kieran, C. (1992). The learning and teaching of schools algebra. In D. A. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 390-419). New York: Macmillan.
- Kieran, C. (2005). Algebraic thinking in the early grades: What is it. The Mathematics Educator, 1(8), 139-151.
- Kinach, B. M. (2014). Generalizing: The core of algebraic thinking. Mathematics Teacher, 107(6), 432-439.
- Knuth, E. J., Stephens, A., Blanton, M., & Gardiner, A. (2016). Build an early foundation for algebra success. Phi Delta Kappan, 97(6), 65-68.
- Kriegler, S. (2007). Introduction to algebra. Los Angeles, CA: Center for Mathematics and Teaching Press.
- Lee, J., Collins, D., & Melton, J. (2016). What does algebra look likes in early childhood. Childhood Education, 92(4), 305-310.
- Lee, L., & Freiman, V. (2006). Developing algebraic thinking through pattern exploration. Mathematics Teaching in the Middle School, 11(9), 428-433.
- MEB (Milli Eğitim Bakanlığı) (2013). İlköğretim Matematik Dersi 5,6,7,8. Sınıflar Öğretim Programı. Ankara: Talim ve Terbiye Kurulu Başkanlığı.
- Ministry of Education China (2007). National college entrance examination for science majors in China. https://www.zxsx.com/Soft/showsoft.asp?SoftID1315 adresinden ulaşılmıştır.
- Ministry of Education Singapore (2013). Mathematics syllbus primary one to five. https://www.moe.gov.sg/docs/default-source/document/education/syllabuses/sciences/files/primary_mathematics_syllabus_pri1_to_pri5.pdf adresinden ulaşılmıştır.
- Ministry of Education South Korea (2008). Proclamation of the ministry education, science and technology. http://gangwonepik.weebly.com/uploads/1/3/8/5/13851570/national_school_curriculum-english2008.pdf adresinden ulaşılmıştır.
- NCTM (2000). Principles and standards for school mathematics. Reston, VA: National Council of Teachers of Mathematics.
- OME (Ontario Ministry of Education) (2014). Paying attention to algebraic reasoning: K-12. http://www.edu.gov.on.ca/eng/literacynumeracy/Paying Attentionto Algebra.pdf adresinden ulaşılmıştır.
- Ormond, C. (2012). Developing algebraic thinking two key ways to establish some early algebraic ideas in primary classrooms. Australian Primary Mathematics Classroom, 17(4), 13-21.
- Pearn, C., & Stephens, M. (2016). Competence with fraactions in fifth or sixth grade as a unique predictor of algebraic thinking. In M. Chinnappan & S. Treholm (Ed.), Opening up Mathematics Education Reserch (pp. 519-526).
- Polat, S., & Ay, O. (2016). Meta-Sentez: Kavramsal bir çözümleme. Eğitimde Nitel Araştırmalar Dergisi, 4(2), 52-59.
- Radford, L. (2012). On the development of early algebraic thinking. PNA. Revista de Investigación en Didáctica de la Matemática, 6(4), 117-133.
- Rittle-Johnson, B., Fyfe, E. R., McLean, L. E., & McEldoon, K. L. (2013). Emerging understanding of patterning in 4-year-olds. Journal of Cognition and Development, 14(3), 376-396.
- Staneva, A. A., Bogossian, F., & Wittkowski, A. (2015). The experience of psychological distress, depression, and anxiety during pregnancy: A meta-synthesis of qualitative research. Midwifery, 31, 563-573.
- Stephens, A., Blanton, M., Knuth E., İşler, I., & Gardiner A. M. (2015). Just say yes to early algebra. Teaching Children Mathematics, 22(2), 92-101.
- Tabach, M., & Friedlander, A. (2003). The role of context in learning beginnig algebra. Proceedings of the Third Conference of the European Society for Research in Mathematics Education, Bellaria, Italia.
- Tagle, J., Belecina, R., & Ocampo, J. M. (2016). Developing algebraic thinking skills among grade three pupils through pictoral models. International Journal Educational Studies, 8(2), 147-158.
- Tanışlı, D., & Özdaş, A. (2009). İlköğretim beşinci sınıf öğrencilerinin örüntüleri genellemede kullandıkları stratejiler. Educational Sciences: Theory and Practice, 9(3), 1453-1497.
- U.S. Investigations (2008). Investigations center for curriculum and Professional development. http://www.investigations.terc.edu/inv3/the-curriculum/ adresinden ulaşılmıştır.
- Warren, E., Mollinson, A., & Destrich, K. (2009). Equaivalence and equations in early years classroom. Australian Primary Mathematics Classroom, 14(1), 10-15.
- Zbiek, R. M., & Larson, M. R. (2015). Teaching strategies to improve algebra learning. Mathematics Teacher, 108(9), 696-699.
Cebirsel Düşünme Becerisi Üzerine Bir Meta-Sentez Çalışması
Year 2017,
Volume: 2 Issue: 2, 25 - 39, 31.12.2017
Dilek Türkoğlu
Ahmet Cihangir
Abstract
Cebirsel düşünme üzerine son yıllarda yapılan araştırmaların çoğunda cebirsel düşünme ve işlem becerilerinin yetersiz olduğu görülmüştür. Bu durum ise araştırmacıları cebirsel düşünme becerisi üzerine araştırma yapmaya yöneltmiştir. Araştırmanın amacı; cebirsel düşünme becerisi ile ilgili yapılan çalışmaları, meta-sentez yöntemi ile cebirsel düşünmede ön koşul beceriler ve kritik süreç açısından incelemektir. Bu bağlamda, “cebir” ve “cebirsel düşünme” anahtar kelimeleri kullanılarak yapılan tarama sonucu yayınlandığı 2005-2016 yılları arasında ulaşılan tezlerden dâhil edilme kriterlerine uygun olan 23 çalışma incelenmiş ve sonuçlar araştırmacı önerileriyle desteklenerek sunulmuştur. İncelenen çalışmaların büyük kısmında cebirsel düşünmede, ön koşul beceriler için örüntü genellemelerinin ve kritik süreç olarak da 4-12 yaş aralığının belirtildiği görülmüştür.
References
- Altun, M. (2005). İlköğretim ikinci kademe matematik öğretimi. Bursa: Aktüel.
- Amit, M., & Neria, D. (2008). Rising to the challenge: Using generalization in pattern problems to unearth the algebraic skills of talented pre- algebra students. Zentralblatt fuer Didaktik der Mathematic, 40, 111-129.
- Aspfors, J., & Fransson, G. (2015). Research on mentor education for mentors of newly qualified teachers: A qualitative meta-synthesis. Teaching and Teacher Education, 48, 75-86.
- Bal, A. P. (2016). The effect of the differentiated teaching approach in the algebraic learning field on students’ academic achievements. Eurasian Journal of Educaional Research, 63, 185-204.
- Balcı, A. (2011). Sosyal bilimlerde araştırma yöntem, teknik ve ilkeler. Ankara: Pegem Akademi.
- Blanton, M. L., & Kaput, J.J. (2004). Elementary grades students’ capacity for functional thinking. In M. J. Hoines & A. Fuglestad (Ed.), Proceeding of The 28th Conference of the international Group for the Psychology of Mathematics Education (pp. 135-142). Bergen, Norway.
- Blanton, M. L., Levi, L., Crites, T., Dougherty, B., & Zbiek, R. M. (2011). Developing essential understanding of algebraic thinking for teaching mathematics in grades 3-5. Series in essential understandings. National Council of Teachers of Mathematics.
- Blanton, M., & Kaput, J. J. (2011). Functional thinking as a route into algebra in the elemantary grades. In J. Cai & E. Knuth (Ed.), Early algebrazation: A dialogue from multiple perspectives (pp. 5-25). USA: Springer.
- Bobis J., Mulligan, J., & Lowrie T. (2009). Mathematics for children: Challenging children to think mathematically (3rd edition). French, Forest, NSW: Pearson.
- Bush, S. B., & Karp, K. S. (2013). Prerequisite algebra skills and associated misconceptions of middle grade students: A review. The Journal of Mathematical Behavior, 32, 613-632.
- Cai, J., & Moyer, J. C. (2007). Developing algebraic thinking in the earlier grades: Some insights from international comparative studies (pp. 1-20). National Science Foundation.
- Cai, J., Moyer, J. C., Lew, H. C., Morris, A., Ng, S. F., & Schmittau, J. (2005). The develepment of studies’ algebraic thinking in earlier grades. ZDM: International Journal on Mathematics Education, 37(1), 4-15.
- Carpenter, T. P., Franke, L. M., & Levi, L. (2003). Thinking mathematically: Integrating arithmetic and algebra in elementary school. Portsmouth, NH: Heinemann.
- CCSSM (Common Core State Standards for Mathematics). (2010). Council of chief state school officers and the national governors association center for best practices. http://www.corestandards.org adresinden ulaşılmıştır.
- Crino, P. T., Tolar, T., & Fuchs, L. S. (2013). Arithmetic and cognitive contributions to algebra. Society for Research on Educational Effectiveness.
- Curriculum Russian School of Mathematics (2015). Developing Russian programs and curriculum. http://www.sras.org/ adresinden ulaşılmıştır.
- Çelik, D. (2007). Öğretmen adaylarının cebirsel düşünme becerilerinin analitik incelenmesi (Yayımlanmamış doktora tezi). Karadeniz Teknik Üniversitesi, Trabzon, Türkiye.
- Desli, D., & Gaitaneri, D. (2016). Grade 3 and 4 students’ understanding of mathematical patterns and their strategies. Pre-school and Primary Education, 5, 63-83.
- French, D. (2002). Teaching and learning algebra. London: Continuum.
- Girit, D., & Akyüz, D. (2015). Farklı sınıf seviyelerindeki ortaokul öğrencilerinde cebirsel düşünme: Örüntülerde genelleme hakkındaki algıları. Necatibey Eğitim Fakültesi Elektronik Fen ve Matematik Eğitimi Dergisi, 10(2), 243-272.
- Herbert, K, & Brown, R. (1997). Patterns as tools for algebraic reasoning. Teaching Children Mathematics, 3(6), 340-344.
- Kabael, T., & Tanışlı, D. (2010). Cebirsel düşünme sürecinde örüntüden fonksiyona öğretim. Elementary Education Online, 9(1), 213-228.
- Kaf, Y. (2007). Matematikteki model kullanımın 6. sınıf öğrencilerinin cebir erişilerine etkisi (Yayımlanmamış yüksek lisans tezi). Hacettepe Üniversitesi, Ankara, Türkiye.
- Kaya, D., & Keşan, C. (2014). İlköğretim seviyesindeki öğrencilerden cebirsel düşünme ve cebirsel muhakeme becerisinin önemi. International Journal of New Trends in Arts, Sports and Science Education, 3(2), 38-47.
- Kieran, C. (1992). The learning and teaching of schools algebra. In D. A. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 390-419). New York: Macmillan.
- Kieran, C. (2005). Algebraic thinking in the early grades: What is it. The Mathematics Educator, 1(8), 139-151.
- Kinach, B. M. (2014). Generalizing: The core of algebraic thinking. Mathematics Teacher, 107(6), 432-439.
- Knuth, E. J., Stephens, A., Blanton, M., & Gardiner, A. (2016). Build an early foundation for algebra success. Phi Delta Kappan, 97(6), 65-68.
- Kriegler, S. (2007). Introduction to algebra. Los Angeles, CA: Center for Mathematics and Teaching Press.
- Lee, J., Collins, D., & Melton, J. (2016). What does algebra look likes in early childhood. Childhood Education, 92(4), 305-310.
- Lee, L., & Freiman, V. (2006). Developing algebraic thinking through pattern exploration. Mathematics Teaching in the Middle School, 11(9), 428-433.
- MEB (Milli Eğitim Bakanlığı) (2013). İlköğretim Matematik Dersi 5,6,7,8. Sınıflar Öğretim Programı. Ankara: Talim ve Terbiye Kurulu Başkanlığı.
- Ministry of Education China (2007). National college entrance examination for science majors in China. https://www.zxsx.com/Soft/showsoft.asp?SoftID1315 adresinden ulaşılmıştır.
- Ministry of Education Singapore (2013). Mathematics syllbus primary one to five. https://www.moe.gov.sg/docs/default-source/document/education/syllabuses/sciences/files/primary_mathematics_syllabus_pri1_to_pri5.pdf adresinden ulaşılmıştır.
- Ministry of Education South Korea (2008). Proclamation of the ministry education, science and technology. http://gangwonepik.weebly.com/uploads/1/3/8/5/13851570/national_school_curriculum-english2008.pdf adresinden ulaşılmıştır.
- NCTM (2000). Principles and standards for school mathematics. Reston, VA: National Council of Teachers of Mathematics.
- OME (Ontario Ministry of Education) (2014). Paying attention to algebraic reasoning: K-12. http://www.edu.gov.on.ca/eng/literacynumeracy/Paying Attentionto Algebra.pdf adresinden ulaşılmıştır.
- Ormond, C. (2012). Developing algebraic thinking two key ways to establish some early algebraic ideas in primary classrooms. Australian Primary Mathematics Classroom, 17(4), 13-21.
- Pearn, C., & Stephens, M. (2016). Competence with fraactions in fifth or sixth grade as a unique predictor of algebraic thinking. In M. Chinnappan & S. Treholm (Ed.), Opening up Mathematics Education Reserch (pp. 519-526).
- Polat, S., & Ay, O. (2016). Meta-Sentez: Kavramsal bir çözümleme. Eğitimde Nitel Araştırmalar Dergisi, 4(2), 52-59.
- Radford, L. (2012). On the development of early algebraic thinking. PNA. Revista de Investigación en Didáctica de la Matemática, 6(4), 117-133.
- Rittle-Johnson, B., Fyfe, E. R., McLean, L. E., & McEldoon, K. L. (2013). Emerging understanding of patterning in 4-year-olds. Journal of Cognition and Development, 14(3), 376-396.
- Staneva, A. A., Bogossian, F., & Wittkowski, A. (2015). The experience of psychological distress, depression, and anxiety during pregnancy: A meta-synthesis of qualitative research. Midwifery, 31, 563-573.
- Stephens, A., Blanton, M., Knuth E., İşler, I., & Gardiner A. M. (2015). Just say yes to early algebra. Teaching Children Mathematics, 22(2), 92-101.
- Tabach, M., & Friedlander, A. (2003). The role of context in learning beginnig algebra. Proceedings of the Third Conference of the European Society for Research in Mathematics Education, Bellaria, Italia.
- Tagle, J., Belecina, R., & Ocampo, J. M. (2016). Developing algebraic thinking skills among grade three pupils through pictoral models. International Journal Educational Studies, 8(2), 147-158.
- Tanışlı, D., & Özdaş, A. (2009). İlköğretim beşinci sınıf öğrencilerinin örüntüleri genellemede kullandıkları stratejiler. Educational Sciences: Theory and Practice, 9(3), 1453-1497.
- U.S. Investigations (2008). Investigations center for curriculum and Professional development. http://www.investigations.terc.edu/inv3/the-curriculum/ adresinden ulaşılmıştır.
- Warren, E., Mollinson, A., & Destrich, K. (2009). Equaivalence and equations in early years classroom. Australian Primary Mathematics Classroom, 14(1), 10-15.
- Zbiek, R. M., & Larson, M. R. (2015). Teaching strategies to improve algebra learning. Mathematics Teacher, 108(9), 696-699.