Conceptual understanding of 8th grade students based on big ideas: The case of measurement
Özlem Kalaycı Eyeoğlu 1, Burçin Gökkurt Özdemir 2 * , Ulvi Eyeoğlu 3
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1 Ministry of National Education, Bartın, Turkey
2 Bartın University, Faculty of Education, Turkey
3 Ministry of National Education, Bartın, Turkey
* Corresponding Author


This study aims to examine the conceptual understanding of middle-school 8th graders on measurement based on big ideas. To this aim, a case study was carried out with six students from a state middle school. The data were collected through semi-structured interviews with the instrument developed by the researchers and consisting of seven open-ended questions. Both descriptive and content analysis were performed to analyze the data. Descriptive analyses were conducted considering the framework of two big ideas in the area of measurement identified by the NCTM (2000). Content analysis using NVivo was employed in analysing the audio-recorded interviews and written responses. The results revealed students had a limited understanding of measurement. It was also determined that the majority of the students made dimensional estimations, showed a rote-based approach in calculating the perimeter, area and volume, and had difficulties in making sense of these concepts. In addition, the understanding of students regarding the volume was found to be limited to interior volume. Finally, some recommendations were made to develop understanding of measurement of students.



  • Baroody, A. J., & Gatzke, M. R. (1991). The estimation of set size by potentially gifted kindergarten-age children. Journal for Research in Mathematics Education, 22, 59-68.
  • Barrett, J. E., Cullen, C. J., Miller, A. L., Eames, C. L., Kara, M., & Klanderman, D. (2017). Area in the middle and later elementary grades. In J. E. Barrett, D. H. Clements, & J. Sarama (Ed.), Children’s Measurement: A longitudinal study of children’s knowledge and learning of length, area, and volume (pp. 105–127). National Council of Teachers of Mathematics.
  • Battista, M. T. (2007). The development of geometric and spatial thinking. In F. K. Lester (Ed.), Second handbook of research on mathematics teaching and learning (pp. 843-908). Information Age Publishing.
  • Budak, M., & Okur, M. (2012). Teacher views about curriculum of 2005 elementary level mathematic course 6-8. classes. International Journal of New Trends in Arts, Sports & Science Education, 1(4), 8-22.
  • Charles, R. (2005). Big ideas and understandings as the foundation for elementary and middle school mathematics. Journal of Education Leadership, 7(3), 9‐24.
  • Charles, R.I., & Carmel, C.A. (2005). Big ideas and understanding as the foundation for elementary and middle school mathematics. Journal of Mathematics Education Leadership, 7(3), 9-24.
  • Common Core State Standards Initiative [CCSSI] (2010). Common Core State Standards Initiative: Preparing America's students for college and career. Retrieved from
  • Creswell, J.W. (2013). Qualitative research method (3rd Edition). Sage.
  • Çetin, Ö., Aksakal, U., Ertürk, Ü., Şay, G., & Tığlı, İ. (2019). Ortaokul ve imam hatip ortaokulu matematik 8 ders kitabı [Middle school mathematics 8th grade textbook] (1st Edition). MoNE Publishing.
  • D’Amore, B., & Fandiño Pinilla, M. I. (2006). Relationships between area and perimeter: Beliefs of teachers and students. Mediterranean journal for research in mathematics education. Mediterranean Journal for Research in Mathematics Education, 5(2), 1-29.
  • Dowker, A. (1992). Computational estimation strategies of professional mathematicians. Journal for Research in Mathematics Education, 23(1), 45-55.
  • Frade, C. (2005). The tacit-explicit nature of students’ knowledge: A case study on area measurement. In Chick, H. L. & Vincent, J. L. (Eds.). Proceedings of the 29 th Conference of the International Group for the Psychology of Mathematics Education (Vol. 2), pp. 321-328. PME.
  • Fujita, T. (2012). Learners’ level of understanding of the inclusion relations of quadrilaterals and prototype phenomenon. The Journal of Mathematical Behavior, 31, 60-72.
  • Gough, J. (2008). Fixing misconceptions: Length, area and volume. Australian Mathematics Teacher, 64(2), 34-35.
  • Gökkurt, B. (2014). An examination of secondary school mathematics teachers' pedagogical content knowledge on geometric shapes. [Unpublished doctoral dissertation]. Atatürk University.
  • Hanson, S. A. & Hogan, T. P. (2000). Computational estimation skills of college students. Journal for Research in Mathematics Education, 31(4), 483-499.
  • Hershkowitz, R. (1990). Psychological Aspects of Learning Geometry. In P. Nesher, & J. Kilpatrick (Eds.), Mathematics and cognition: a research synthesis by the international group for the psychology of mathematics education (pp. 70-95). Cambridge University Press.
  • Hiebert, J., & Carpenter, T. P. (1992). Learning and teaching with understanding. In D. A. Grouws (Eds.), Handbook of Research on Mathematics Teaching and Learning (pp. 65-98). Macmillan.
  • Huang, H. M. E., & Witz, K. G. (2013). Children’s conceptions of area measurement and their strategies for solving area measurement problems. Journal of Curriculum and Teaching, 2(1), 10-26. https://doi.org10.5430/jct.v2n1p10
  • Kayhan, H., C., & Argün., C. (2011). The relationship between primary school students’ knowledge about the length measurement tools and their usage. Journal of Gazi Education Faculty, 31(2), 479-496.
  • Kenney, P. A. & Kouba, V. L. (1997). What do students know about measurement? In P. A. Kenney & E. A. Silver (Eds.), Results from the Sixth Mathematics Assessment of the National Assessment of Educational Progress (pp. 141–163). Reston, VA: National Council of Teachers of Mathematics.
  • Kidman, G., & Cooper, T. J. (1997). Area integration rules for grades 4, 6 and 8 students. In E. Pehkonen (Ed.), Proceedings of the 21st International Conference for the Psychology of Mathematics Education (pp. 136–143). Lahti.
  • Kim, E. M., Haberstroh, J., Peters, S., Howell, H., & Oláh, L. N. (2019). Elementary students’ understanding of geometrical measurement in three dimensions (Research Report No. RR-19-14). Educational Testing Service.
  • Lee, H. J. (2012). Learning measurement with Interactive Stations. Ohio Journal of School Mathematics, 65, 30-36.
  • Markman, E. M., & Wachtel, G.F. (1988). Children’s use of mutual exclusivity to constrain the meaning of words. Cognitive Psychology, 20, 121–157.
  • Marks, R. (1990). Pedagogical content knowledge: From a mathematical case to a modified conception. Journal of Teacher Education, 41(3), 3-11.
  • Mcmillan, H. J. & Schumacher, S. (2010). Research in education. Boston, USA: Pearson.
  • Merriam, S. B. (2018). Qualitative research. A guide to design and implementation. Jossey-Bass.
  • Micklo, S. J. (1999). Estimation It's more than a guess. Childhood Education, 75(3), 142-145.
  • Miles, M, B. & Huberman, A. M. (1994). Qualitative data analysis: An expanded sourcebook. (2nd Edition). Sage.
  • Ministry of National Education [MONE] (2018). Matematik dersi öğretim programı [Mathematics lesson curriculum] (1, 2, 3, 4, 5, 6, 7 and 8. Class]. MoNE Publishing.
  • Moreira, C. Q. & Contente, M. do R. (1997). The role of writing to foster pupil’s learning about area. In Pehkonen, E. (Eds.), Proceedings of the Conference of the International Group for the Psychology of Mathematics Education (21st PME, Lahti, Finland), 3, 256-263.
  • National Council of Teachers of Mathematics [NCTM]. (2000). Principles and standards for school mathematics. Reston, VA: NCTM.
  • National Council of Teachers of Mathematics [NCTM]. (2005). Principles and standards for school mathematics. Reston, VA: NCTM.
  • Outhred, L. N., & Mitchelmore, M. C. (2000). Young children’s intuitive understanding of rectangular area measurement. Journal for Research in Mathematics Education, 31, 144–167.
  • Sarama, J. & Clements, D. H. (2009). Early childhood mathematics education research: Learning trajectories for young children. Routledge.
  • Schifter, D., & Fosnot, C. T. (1993). Reconstructing mathematics education: Stories of teachers meeting the challenges of reform. Teachers College Press.
  • Segovia, I., & Castro, E. (2009). Computational and measurement estimation; curriculum foundations and research carried out at the university of Granada. Electronic Journal of Research in and Educational Psychology, 17(7), 499-536.
  • Siemon, D., Bleckly, J., & Neal, D. (2012). Working with the big ideas in number and the australian curriculum: mathematics. In B. Atweh, M. Goos, R. Jorgensen & D. Siemon, (Eds.), Engaging the Australian National Curriculum: Mathematics – Perspectives From the Field (pp. 19-45). Online Publication of Mathematics Education Research Group of Australasia.
  • Sowder, J. (1992). Estimation and number sense. In D. A. Grouws (Ed.), Handbook of Research on Mathematics Teaching and Learning (pp. 371-389). Macmillan.
  • Yin, R. K. (2013). Case study research: Design and methods. SAGE.
  • Thompson, T. D. & Preston, R. V. (2004). Measurement in the middle grades: Insights from NAEP and TIMSS. Mathematics Teaching in the Middle School, 9(9), 514-519.
  • Tout, D., & Spithill, J. (2015). The challenges and complexities of writing items to test mathematical literacy. In K. Stacey & R. Turner (Eds.), Assessing mathematical literacy: The PISA experience (pp. 145–171). Springer International Publishing.
  • Tsamir, P., Tirosh, D., & Levenson, E. (2008). Intuitive nonexamples: the case of triangles. Educational Studies in Mathematics, 69(2), 81–95.
  • Van de Walle, J. A., Karp, K.S. & Bay-Williams, J. M. (2014). Elementary and middle school mathematics: Teaching develop – mentally. Pearson.
  • Van Hiele, P. (1986). Structure and insight: a theory of mathematics education. Academi Press.
  • Zaslavsky, O., & Zodik, I. (2014). Example-generation as indicator and catalyst of mathematical and pedagogical understandings. Y. Li, E. A. Silver., & S. Li (Eds.), Transforming mathematics instruction: Multiple approaches and practices (pp. 525-546). Springer International Publishing.


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