Research Article
An Investigation of Acquisitions of Length Measurement in The Primary and Secondary School’s Mathematics Curriculum Through Learning Trajectories
Abstract
The aim of this study was to investigate acquisitions in the Turkish primary and secondary schools’ current mathematics curriculum through learning trajectories in the context of length measurement. In this qualitative study, we used document analysis as a research method (Bowen, 2009). We analyzed primary and secondary school’s curriculum descriptively through learning trajectories levels. Document analysis of the curriculum highlighted that the general order of the acquisitions was suitable to the learning trajectory in terms of length measurement. Our analysis also showed that the most frequent level was the “length measurer” level, and all the acquisitions from the sixth, seventh and eighth grades fit in the “abstract length measurer” level. Findings also showed some missing levels which were not included in the curriculum. Some were the initial levels- presumably present in kindergarten, but others were more advanced levels. The probable outcomes of these gaps are discussed in the study. Based on the findings and the limitations of the study, some suggestions were made for future research.
References
- Asil-Güzel, A. (2018). Ortaokul öğrencilerinin uzunluk ölçme ve karşılaştırmaya dair kavrayışlarının incelenmesi. (Yayımlanmamış yüksek lisans tezi) Gaziantep Üniversitesi Eğitim Bilimleri Enstitüsü.
- Battista, M. T. (2006). Understanding the development of students' thinking about length. Teaching Children Mathematics, 13(3), 140-146. https://doi.org/10.5951/TCM.13.3.0140
- Battista, M. T. (2011) Conceptualizations and Issues related to Learning Progressions, Learning Trajectories, and Levels of Sophistication, The Mathematics Enthusiast, 8(3)https://doi.org/10.54870/1551-3440.1228
- Bowen, G.A. (2009), Document analysis as a qualitative research method, Qualitative Research Journal, 9(2), 27-40. https://doi.org/10.3316/QRJ0902027
- Bozkurt, A. , Özmantar, M. F. & Güzel, M. (2018). Uzunluk ölçme ve farklı uzunlukları karşılaştırmaya dair öğrenci düşünüşlerinin incelenmesi. International Journal of Educational Studies in Mathematics , 5 (2) , 39-55.
- Bozkurt, A., Şapul, Y., & Şimşekler-Dizman, T. H. (2020). Türkiye ve Singapur okul öncesi eğitim programlarının matematik içeriklerinin karşılaştırılması. Erken Çocukluk Çalışmaları Dergisi, 4(3), 444-468. https://doi.org/10.24130/eccd-jecs.1967202043235
- Bright, G. W. (1976). Estimation as part of learning to measure. In D. Nelson & R. E. Reys (Eds.), Measurement in school mathematics: 1976 yearbook (pp. 87–104).
- Clements, D. H., & Sarama, J. (2004 a). Building blocks for early childhood mathematics. Early Childhood Research Quarterly, 19, 181–189. https://doi.org/10.1016/j.ecresq.2004.01.014
- Clements, D. H., & Sarama, J. (2004). Learning trajectories in mathematics education. Mathematical thinking and learning, 6(2),81-89. https://doi.org/10.1207/s15327833mtl0602_1
- Clements, D. H., & Sarama, J. (2014). Learning trajectories. In Alan P. M, Jere C. Kenny H. N. (Eds) Learning over time Learning Trajectories in Mathematics Education, (pp 1-30.) Charlotte: Information Age Publishing.
- Clements, D. H., & Sarama, J. (2021). Learning and teaching early math: The learning trajectories approach (3 th edition). London: Routledge.
- Clements, D. H., Sarama, J., & Wilson, D. C. (2001). Composition of geometric figures. In M. Van den Heuvel- panhuizen (Ed.), Proceedings of the 25th conference of the international group for the psychology of mathematics education (Vol. 2, pp. 273–280). Freudenthal Institute.
- Clements,D.H.,Wilson,D.C.,& Sarama,J.(2004).Young children’s compositions of geometric figures: A learning trajectory. Mathematical Thinking and Learning, 6(2),163–184. https://doi.org/10.1207/s15327833mtl0602_5
- Cobb, P., Yackel, E., & Wood, T., (1992), Interaction and learning in mathematics classroom situations. Educational Studies in Mathematics, 23(1), 99-122. https://doi.org/10.1007/BF00302315
- Confrey, J, Maloney, A., & Corley, A. K. (2014). Learning trajectories: a framework for connecting standards with curriculum. ZDM—The International Journal on Mathematics Education, 46 (5. doi:10.1007/s11858-014-0598-7.
- Confrey, J., Maloney, A. (2015). A design research study of a curriculum and diagnostic assessment system for a learning trajectory on equipartitioning. ZDM Mathematics Education 47, 919–932. https://doi.org/10.1007/s11858-015-0699-y
- Creswell, J., & Plano Clark, V. (2011) Designing and Conducting Mixed Methods Research. SAGE Publications.
- Curry, M., Mitchelmore, M., & Outhred, L. (2006). Development of children’s understanding of length, area, and volume measurement principles. Paper presented at the Thirtieth Annual Meeting of the International Group for the Psychology of Mathematics Education. Prague, Czech Republic.
- Curry, M. & Outhred, L. (2005). Conceptual understanding of spatial measurement. In P. Clarkson, A. Downton, D. Gronn, M. Horne, A. McDonough, R. Pierce & A. Roche (Eds.), Building connections: Theory, research and practice: Proceedings of the 28th annual conference of the Mathematics Education Research Group of Australasia [MERGA] (pp. 265–272). Sydney, Australia: MERGA
- Daro, P., Mosher, F., & Corcoran, T. (2011). Learning trajectories in mathematics: A foundation for standards, curriculum, assessment, and instruction (Consortium for Policy Research in Education Report #RR-68). Philadelphia, PA: Consortium for Policy Research in Education.
- Deitz, K., Huttenlocher, J., Kwon, M. K., Levine, S. C., & Ratliff, K. (2009). Children's understanding of ruler measurement and units of measure: A training study. In Proceedings of the Annual Meeting of the Cognitive Science Society 31, (31). 2391-2395
- Drake, M. (2014). The problem with the school ruler. Australian Primary Mathematics Classroom, 19(3), 27–32. https:// files. eric. ed.gov/fulltext/EJ1093323.pdf
- Huttenlocher, J., Haight, W., Bryk, A., Seltzer, M., & Lyons, T. (1991). Early vocabulary growth: relation to language input and gender. Developmental Psychology, 27 (2), 236–248.
- Kıral. B., (2020). Nitel bir veri analiz yöntemi olarak doküman analizi. Siirt Üniversitesi Sosyal Bilimler Enstitüsü Dergisi, 8(15), 170-189.
- Lehrer, R., Jaslow, L., & Curtis, C. (2003). Developing an understanding of measurment in the elementary grades. In D. H. Clements & G. Bright (Eds.), Learning and teaching measurement: 2003 Yearbook (pp. 3–16). Reston, VA: National Council of Teachers of Mathematics.
- Liu, J., Liu, Q., Zhang, J. Shao, Y., & Zhang, Z (2022). The trajectory of Chinese mathematics textbook development for supporting students’ interest within the curriculum reform: a grade eight example. ZDM Mathematics Education 54, 625–637 https://doi.org/10.1007/s11858-022-01372-4
- Wijngaards-de Meij, L. & Merx, S. (2018). Improving curriculum alignment and achieving learning goals by making the curriculum visible, International Journal for Academic Development, 23:3, 219-231, https://doi.org/10.1080/1360144X.2018.1462187
- Miles,M.B.,&Huberman,A.M.(1994).Qualitative data analysis: An expanded source book(2nded.). Sage Publications.
- Millî Eğitim Bakanlığı, [MEB]. (2018). Matematik Dersi Öğretim Programı (İlkokul ve ortaokul 1, 2, 3, 4, 5, 6, 7 ve 8. sınıflar). Ankara: Talim ve Terbiye Kurulu Başkanlığı
- Millî Eğitim Bakanlığı, [MEB]. (2014). Okul Öncesi Eğitim ve İlköğretim Kurumlar Yönetmeliği http://mevzuat.meb.gov.tr/dosyalar/1703.pdf sayfasından erişilmiştir . Özyurt, M., & Kuşdemir-Kayıran, B (2020). Program geliştirme süreci bağlamında ortaokul matematik öğretim programlarının temel bileşenleri. M.F. Özmantar, H. Akkoç ve B. Kuşdemir Kayıran ve M. Özyurt (Eds). Ortaokul Matematik Öğretim Programları Tarihsel Bir İnceleme. (s.1-27). Ankara: PegemA Yayıncılık.
- Rezat, S., Fan, L. & Pepin, B. (2021). Mathematics textbooks and curriculum resources as instruments for change. ZDM Mathematics Education 53, 1189–1206. https://doi.org/10.1007/s11858-021-01309-3
- Sarama, J., & Clements, D. H. (2009). Early childhood mathematics education research: Learning trajectories for young children. London: Routledge.
- Sarama, J., & Clements, D. H. (2022, 20 Jun). Learn about measurement: length. Learning and Teaching with Learning Trajectories,https://www.learningtrajectories.org/math/learning-trajectories/measurement-length
- Sarama, J., Clements, D. H., Barrett, J. E., Cullen, C. J., Hudyma, A., & Vanegas, Y. (2021). Length measurement in the early years: teaching and learning with learning trajectories. Mathematical Thinking and Learning, 1-24. https://doi.org/10.1080/ 10986065.2020.1858245
- Simon, M. A. (1995). Reconstructing mathematics pedagogy from a constructivist perspective. Journal for Research in Mathematics Education, 26(2), 114-145. https://doi.org/10.5951/jresematheduc.26.2.0114
- Simon, M. (2014). Hypothetical learning trajectories in mathematics education. In S. Lerman (Ed.), Encyclopedia of Mathematics Education (pp. 272-275): Springer.
- Stephan, M., & Clements, D. H. (2003). Linear and area measurement in prekindergarten to grade 2. Learning and teaching measurement, 5(1), 3-16.
- Tan-Sisman, G., & Aksu, M. (2012). The length measurement in the Turkish mathematics curriculum: Its potential to contribute to students’ learning. International Journal of Science and Mathematics Education, 10(2), 363–385. https://doi.org/10.1007/s10763-011-9304-1.
- Varış, F. (1996). Eğitimde program geliştirme "teori ve teknikler". Ankara: Alkım Kitapçılık Yayıncılık.
- Xie, H., & Song, J. (2022). Research on the guiding role of curriculum ideology and politics on students’ social character. Psychiatria Danubina, 34(suppl 4), 818-818.
- Zembat, İ. Ö. (2013). Matematiksel analizi ile ölçme kavramı ve uzunluk, alan ve hacim nitelikleri. İ. Ö. Zembat, M. F. Özmantar, E. Bingölbali, H. Şandır ve A. Delice (Eds.), Tanımları ve Tarihsel Gelişimleriyle Matematiksel Kavramlar (s.175-188). Ankara: PegemA Yayıncılık.
İlkokul ve Ortaokul Matematik Öğretim Programı’nın Uzunluk Ölçme Kazanımlarının Öğrenme Rotalarına Göre İncelenmesi
Abstract
Bu çalışmanın amacı, güncel Matematik Dersi Öğretim Programında yer alan uzunluk ölçme kazanımlarını öğrenme rotalarına göre incelemektir. Nitel bir araştırma olan bu çalışmada doküman incelemesi yöntemi (Bowen, 2009) kullanılmıştır. Çalışmada güncel ilkokul ve ortaokul matematik öğretim programı doküman olarak incelenmiştir. Öğretim programında yer alan uzunluk ölçme kazanımları öğrenme rotaları çerçevesinde betimsel olarak analiz edilmiştir. Veri analizinden elde edilen bulgular, öğretim programında uzunluk ölçme ile ilgili kazanımların, öğrenme rotalarında varsayılan gelişime genel olarak uygun şekilde sıralandığını göstermiştir. Analizler ayrıca öğretim programında sayıca en fazla “uzunluk ölçme” seviyesinden kazanımların bulunduğunu; altı, yedi ve sekizinci sınıf kazanımlarının ise tamamının “soyut uzunluk ölçme” seviyesinde olduğunu göstermiştir. Ancak öğretim programında bazı seviyelere dönük kazanımlara yer verilmediği görülmüştür. Programda yer verilmeyen kazanımların muhtemelen ana sınıfında geçilen, öğrenme rotalarındaki ilk seviyeler olduğu; ancak diğerlerinin ise daha ileri seviyelerde olduğu görülmüştür. Eksik olan bu seviyelerin öğrenme üzerindeki muhtemel sonuçları tartışılmıştır.
References
- Asil-Güzel, A. (2018). Ortaokul öğrencilerinin uzunluk ölçme ve karşılaştırmaya dair kavrayışlarının incelenmesi. (Yayımlanmamış yüksek lisans tezi) Gaziantep Üniversitesi Eğitim Bilimleri Enstitüsü.
- Battista, M. T. (2006). Understanding the development of students' thinking about length. Teaching Children Mathematics, 13(3), 140-146. https://doi.org/10.5951/TCM.13.3.0140
- Battista, M. T. (2011) Conceptualizations and Issues related to Learning Progressions, Learning Trajectories, and Levels of Sophistication, The Mathematics Enthusiast, 8(3)https://doi.org/10.54870/1551-3440.1228
- Bowen, G.A. (2009), Document analysis as a qualitative research method, Qualitative Research Journal, 9(2), 27-40. https://doi.org/10.3316/QRJ0902027
- Bozkurt, A. , Özmantar, M. F. & Güzel, M. (2018). Uzunluk ölçme ve farklı uzunlukları karşılaştırmaya dair öğrenci düşünüşlerinin incelenmesi. International Journal of Educational Studies in Mathematics , 5 (2) , 39-55.
- Bozkurt, A., Şapul, Y., & Şimşekler-Dizman, T. H. (2020). Türkiye ve Singapur okul öncesi eğitim programlarının matematik içeriklerinin karşılaştırılması. Erken Çocukluk Çalışmaları Dergisi, 4(3), 444-468. https://doi.org/10.24130/eccd-jecs.1967202043235
- Bright, G. W. (1976). Estimation as part of learning to measure. In D. Nelson & R. E. Reys (Eds.), Measurement in school mathematics: 1976 yearbook (pp. 87–104).
- Clements, D. H., & Sarama, J. (2004 a). Building blocks for early childhood mathematics. Early Childhood Research Quarterly, 19, 181–189. https://doi.org/10.1016/j.ecresq.2004.01.014
- Clements, D. H., & Sarama, J. (2004). Learning trajectories in mathematics education. Mathematical thinking and learning, 6(2),81-89. https://doi.org/10.1207/s15327833mtl0602_1
- Clements, D. H., & Sarama, J. (2014). Learning trajectories. In Alan P. M, Jere C. Kenny H. N. (Eds) Learning over time Learning Trajectories in Mathematics Education, (pp 1-30.) Charlotte: Information Age Publishing.
- Clements, D. H., & Sarama, J. (2021). Learning and teaching early math: The learning trajectories approach (3 th edition). London: Routledge.
- Clements, D. H., Sarama, J., & Wilson, D. C. (2001). Composition of geometric figures. In M. Van den Heuvel- panhuizen (Ed.), Proceedings of the 25th conference of the international group for the psychology of mathematics education (Vol. 2, pp. 273–280). Freudenthal Institute.
- Clements,D.H.,Wilson,D.C.,& Sarama,J.(2004).Young children’s compositions of geometric figures: A learning trajectory. Mathematical Thinking and Learning, 6(2),163–184. https://doi.org/10.1207/s15327833mtl0602_5
- Cobb, P., Yackel, E., & Wood, T., (1992), Interaction and learning in mathematics classroom situations. Educational Studies in Mathematics, 23(1), 99-122. https://doi.org/10.1007/BF00302315
- Confrey, J, Maloney, A., & Corley, A. K. (2014). Learning trajectories: a framework for connecting standards with curriculum. ZDM—The International Journal on Mathematics Education, 46 (5. doi:10.1007/s11858-014-0598-7.
- Confrey, J., Maloney, A. (2015). A design research study of a curriculum and diagnostic assessment system for a learning trajectory on equipartitioning. ZDM Mathematics Education 47, 919–932. https://doi.org/10.1007/s11858-015-0699-y
- Creswell, J., & Plano Clark, V. (2011) Designing and Conducting Mixed Methods Research. SAGE Publications.
- Curry, M., Mitchelmore, M., & Outhred, L. (2006). Development of children’s understanding of length, area, and volume measurement principles. Paper presented at the Thirtieth Annual Meeting of the International Group for the Psychology of Mathematics Education. Prague, Czech Republic.
- Curry, M. & Outhred, L. (2005). Conceptual understanding of spatial measurement. In P. Clarkson, A. Downton, D. Gronn, M. Horne, A. McDonough, R. Pierce & A. Roche (Eds.), Building connections: Theory, research and practice: Proceedings of the 28th annual conference of the Mathematics Education Research Group of Australasia [MERGA] (pp. 265–272). Sydney, Australia: MERGA
- Daro, P., Mosher, F., & Corcoran, T. (2011). Learning trajectories in mathematics: A foundation for standards, curriculum, assessment, and instruction (Consortium for Policy Research in Education Report #RR-68). Philadelphia, PA: Consortium for Policy Research in Education.
- Deitz, K., Huttenlocher, J., Kwon, M. K., Levine, S. C., & Ratliff, K. (2009). Children's understanding of ruler measurement and units of measure: A training study. In Proceedings of the Annual Meeting of the Cognitive Science Society 31, (31). 2391-2395
- Drake, M. (2014). The problem with the school ruler. Australian Primary Mathematics Classroom, 19(3), 27–32. https:// files. eric. ed.gov/fulltext/EJ1093323.pdf
- Huttenlocher, J., Haight, W., Bryk, A., Seltzer, M., & Lyons, T. (1991). Early vocabulary growth: relation to language input and gender. Developmental Psychology, 27 (2), 236–248.
- Kıral. B., (2020). Nitel bir veri analiz yöntemi olarak doküman analizi. Siirt Üniversitesi Sosyal Bilimler Enstitüsü Dergisi, 8(15), 170-189.
- Lehrer, R., Jaslow, L., & Curtis, C. (2003). Developing an understanding of measurment in the elementary grades. In D. H. Clements & G. Bright (Eds.), Learning and teaching measurement: 2003 Yearbook (pp. 3–16). Reston, VA: National Council of Teachers of Mathematics.
- Liu, J., Liu, Q., Zhang, J. Shao, Y., & Zhang, Z (2022). The trajectory of Chinese mathematics textbook development for supporting students’ interest within the curriculum reform: a grade eight example. ZDM Mathematics Education 54, 625–637 https://doi.org/10.1007/s11858-022-01372-4
- Wijngaards-de Meij, L. & Merx, S. (2018). Improving curriculum alignment and achieving learning goals by making the curriculum visible, International Journal for Academic Development, 23:3, 219-231, https://doi.org/10.1080/1360144X.2018.1462187
- Miles,M.B.,&Huberman,A.M.(1994).Qualitative data analysis: An expanded source book(2nded.). Sage Publications.
- Millî Eğitim Bakanlığı, [MEB]. (2018). Matematik Dersi Öğretim Programı (İlkokul ve ortaokul 1, 2, 3, 4, 5, 6, 7 ve 8. sınıflar). Ankara: Talim ve Terbiye Kurulu Başkanlığı
- Millî Eğitim Bakanlığı, [MEB]. (2014). Okul Öncesi Eğitim ve İlköğretim Kurumlar Yönetmeliği http://mevzuat.meb.gov.tr/dosyalar/1703.pdf sayfasından erişilmiştir . Özyurt, M., & Kuşdemir-Kayıran, B (2020). Program geliştirme süreci bağlamında ortaokul matematik öğretim programlarının temel bileşenleri. M.F. Özmantar, H. Akkoç ve B. Kuşdemir Kayıran ve M. Özyurt (Eds). Ortaokul Matematik Öğretim Programları Tarihsel Bir İnceleme. (s.1-27). Ankara: PegemA Yayıncılık.
- Rezat, S., Fan, L. & Pepin, B. (2021). Mathematics textbooks and curriculum resources as instruments for change. ZDM Mathematics Education 53, 1189–1206. https://doi.org/10.1007/s11858-021-01309-3
- Sarama, J., & Clements, D. H. (2009). Early childhood mathematics education research: Learning trajectories for young children. London: Routledge.
- Sarama, J., & Clements, D. H. (2022, 20 Jun). Learn about measurement: length. Learning and Teaching with Learning Trajectories,https://www.learningtrajectories.org/math/learning-trajectories/measurement-length
- Sarama, J., Clements, D. H., Barrett, J. E., Cullen, C. J., Hudyma, A., & Vanegas, Y. (2021). Length measurement in the early years: teaching and learning with learning trajectories. Mathematical Thinking and Learning, 1-24. https://doi.org/10.1080/ 10986065.2020.1858245
- Simon, M. A. (1995). Reconstructing mathematics pedagogy from a constructivist perspective. Journal for Research in Mathematics Education, 26(2), 114-145. https://doi.org/10.5951/jresematheduc.26.2.0114
- Simon, M. (2014). Hypothetical learning trajectories in mathematics education. In S. Lerman (Ed.), Encyclopedia of Mathematics Education (pp. 272-275): Springer.
- Stephan, M., & Clements, D. H. (2003). Linear and area measurement in prekindergarten to grade 2. Learning and teaching measurement, 5(1), 3-16.
- Tan-Sisman, G., & Aksu, M. (2012). The length measurement in the Turkish mathematics curriculum: Its potential to contribute to students’ learning. International Journal of Science and Mathematics Education, 10(2), 363–385. https://doi.org/10.1007/s10763-011-9304-1.
- Varış, F. (1996). Eğitimde program geliştirme "teori ve teknikler". Ankara: Alkım Kitapçılık Yayıncılık.
- Xie, H., & Song, J. (2022). Research on the guiding role of curriculum ideology and politics on students’ social character. Psychiatria Danubina, 34(suppl 4), 818-818.
- Zembat, İ. Ö. (2013). Matematiksel analizi ile ölçme kavramı ve uzunluk, alan ve hacim nitelikleri. İ. Ö. Zembat, M. F. Özmantar, E. Bingölbali, H. Şandır ve A. Delice (Eds.), Tanımları ve Tarihsel Gelişimleriyle Matematiksel Kavramlar (s.175-188). Ankara: PegemA Yayıncılık.
There are 41 citations in total.
Details
| Primary Language | Turkish |
|---|---|
| Subjects | Mathematics Education |
| Journal Section | Research Article |
| Authors | |
| Publication Date | September 28, 2023 |
| Published in Issue | Year 2023Volume: 12 Issue: 3 |
