Exploring Evidence of Mathematical Tasks and Representations in the Drawings of Middle School Students

Vesife Hatisaru

doi:10.29333/iejme/8482

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Vesife Hatisaru ¹ ^*

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¹ University of Tasmania, AUSTRALIA^* Corresponding Author

Abstract

The drive to explore students’ experiences in mathematics classrooms remains imperative for mathematics education research in order to better understand how effective teaching and learning classroom practices lead to desirable learning outcomes. As part of a larger research project exploring a group of 120 Turkish middle school students’ (grades 6 to 8, aged 11 to 14) perceptions of their mathematics classroom experiences, this article presents an analysis of the nature of mathematical tasks and the forms of mathematical representations depicted in students’ drawings. An analysis of the data obtained from the students’ drawing task (Draw a Mathematics Classroom Test) revealed little to no variety in students’ classroom experiences in relation to the types of mathematical tasks and mathematical representations. The most common mathematical tasks were found to be tasks that focus on procedural skills, while the most common way students represented the mathematics was through symbolic representations. None of the student drawings involved physical or contextual representations. Findings raise concerns about whether Turkish students are well prepared for the demands of the 21^st century.

Keywords

classroom experiences
drawings
mathematical tasks
mathematical representations
middle school students

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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Article Type: Research Article

INT ELECT J MATH ED, 2020, Volume 15, Issue 3, Article No: em0609

https://doi.org/10.29333/iejme/8482

Publication date: 29 Aug 2020

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References

Aguilar, M. S., Rosas, A., Zavaleta, J., & Romo-Vázquez, A. (2016). Exploring high-achieving students’ images of mathematicians. International Journal of Science and Mathematics Education, 14(3), 527-548. https://doi.org/10.1007/s10763-014-9586-1
Altinyelken, H. K. (2011). Student-centred pedagogy in Turkey: Conceptualizations, interpretations and practices. Journal of Education Policy, 26(2), 137-160. https://doi.org/10.1080/02680939.2010.504886
Altinyelken, H. K., & Sozeri, S. (2017). Assumptions and implications of adopting educational ideas from the west: the case of student-centered pedagogy in Turkey. In M. Akiba & G. LeTendre (Eds.), International Handbook of Teacher Quality and Policy (pp. 254-270). Routledge: New York. https://doi.org/10.4324/9781315710068-17
Anthony, G., & Walshaw, M. (2009). Effective pedagogy in mathematics. Educational Series 19. Brussels: International Academy of Education; Geneva: International Bureau of Education.
Australian Curriculum, Assessment and Reporting Authority (ACARA). Australian Curriculum: Mathematics. Retrieved from https://www.australiancurriculum.edu.au/f-10-curriculum/mathematics/
Blazar, D. (2015). Effective teaching in elementary mathematics: Identifying classroom practices that support student achievement. Economics of Education Review, 48, 16-29. https://doi.org/10.1016/j.econedurev.2015.05.005
Boaler, Jo. (2015). What’s math got to do with it? How teachers and parents can transform mathematics learning and inspire success. New York, New York: Penguin Books.
Bobis, J., Anderson, J., Martin, A., & Way, J. (2011). A model for mathematics instruction to enhance student motivation and engagement. In D. J. Brahier & W. R. Speer (Eds.), Motivation and disposition: Pathways to learning, 73rd yearbook of the National Council of Teachers of Mathematics (pp. 1-12). Reston, VA: NCTM.
Bragg, L. (2007). Students’ conflicting attitudes towards games as a vehicle for learning mathematics: A methodological dilemma. Mathematics Education Research Journal, 19(1), 29-44. https://doi.org/10.1007/BF03217448
Brown, L. (1992). The influence of teachers on children’s image of mathematics. For the Learning of Mathematics, 12(2), 29-33.
Chambers, D. W. (1983). Stereotypic images of the scientist: The Draw-a-Scientist Test. Science Education, 67(2), 255-265. https://doi.org/10.1002/sce.3730670213
Cramer, K. (2003). Using a translation model for curriculum development and classroom instruction. In R. Lesh & H. Doerr (Eds.), Beyond constructivism. Models and modeling perspectives on mathematics problem solving, learning, and teaching. Mahwah, NJ: Lawrence Erlbaum.
Dreher, A., Kuntze, S., & Lerman, S. (2016). Why use multiple representations in the mathematics classroom? Views of English and German preservice teachers. International Journal of Science and Mathematics Education, 14(2), 363-381. https://doi.org/10.1007/s10763-015-9633-6
Echazarra, A., Salinas, D., Méndez, I., Denis, V., & Rech, G. (2016). How teachers teach and students learn: Successful strategies for school. OECD Education Working Papers, No. 130. OECD Publishing, Paris. https://doi.org/10.1787/5jm29kpt0xxx-en
Elo, S., & Kyngäs (2008). The qualitative content analysis process. Journal of Advanced Nursing, 62(1), 107-115. https://doi.org/10.1111/j.1365-2648.2007.04569.x
Erbilgin, E. (2017). A comparison of the mathematical processes embedded in the content standards of Turkey and Singapore. Research in Social Sciences and Technology, 2(1), 53-74. https://doi.org/10.46303/ressat.02.01.3
Ernest, P. (2010). Add it up. Why teach mathematics? Professional Educator, 9(2), 44-47.
European Schoolnet (October, 2018). Science, technology, engineering and mathematics education policies in Europe. Scientix observatory report. European Schoolnet, Brussels.
Eurydice (2019a). Initial Education for Teachers Working in Early Childhood and School Education. Retrieved from https://eacea.ec.europa.eu/national-policies/eurydice/content/turkey_en
Eurydice (2019b). Continuing Professional Development for Teachers Working in Early Childhood and School Education. Retrieved from https://eacea.ec.europa.eu/national-policies/eurydice/content/turkey_en
Fraser, B. (2014). Classroom learning environments: Historical and contemporary perspectives. In Lederman, N. & Abell, S. (Eds), Handbook of Research on Science Education Volume II (pp. 104-119). USA: Routledge.
Finson, K. D., Beaver, J. B., & Cramond, B. L. (1995). Development and field test of a checklist for the Draw-a-Scientist Test. School Science and Mathematics, 95(4), 195-205. https://doi.org/10.1111/j.1949-8594.1995.tb15762.x
Goldin, G. A. (2004). Problem solving heuristics, affect, and discrete mathematics. ZDM, 36(2), 56-60. https://doi.org/10.1007/BF02655759
Goldin, G. A. (2014). Mathematical Representations. In Lerman S. (Eds), Encyclopedia of Mathematics Education. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-4978-8_103
Goldin, G. A. (2018). Discrete mathematics and the affective dimension of mathematical learning and engagement. In E. W. Hart, & J. Sandefur (Eds), Teaching and learning discrete mathematics worldwide: Curriculum and research (pp. 53-65). Cham: Springer; 2017. p. 53-65 https://doi.org/10.1007/978-3-319-70308-4_4
Goodenough, F. L. (1926). Measurements of intelligence by drawings. World Book Co.
Gulek, C. (1999). Using multiple means of inquiry to gain insight into classrooms: A multi-trait multi-method approach (Unpublished doctoral dissertation). Boston College, Chestnut Hill, MA.
Haney, W., Russel, M., & Bebell, D. (2004). Drawing on education: Using drawings to document schooling and support change. Harvard Educational Review, 74(3), 241-271. https://doi.org/10.17763/haer.74.3.w0817u84w7452011
Harris, L. R., Harnett, J. A., & Brown, G. (2009). “Drawing” out student conceptions: Using pupils’ pictures to examine their conceptions of assessment. In D. M. McInerney, G. T. L. Brown, & G. A. D. Liem (Eds.), Students perspectives on assessment: What students can tell us about assessment for learning (pp. 53-83). Charlotte, NC: Information age publishing, Inc.
Hatisaru, V. (2018). Teachers' beliefs about knowledge of teaching and their impact on teaching practices. In Rott, B., Torner, G., Peters-Dasdemir, J., Moller, A., & Safrudiannur (Eds), Views and Beliefs in Mathematics Education: The Role of Beliefs in the Classroom (pp. 149-159). Switzerland: Springer.
Hatisaru, V. (2019a). Lower secondary students’ views about mathematicians depicted as mathematics teachers. LUMAT: International Journal on Math, Science and Technology Education, 7(2), 27-49. https://doi.org/10.31129/LUMAT.7.2.355
Hatisaru, V. (2019b). Putting the spotlight on mathematics classrooms. In J. Novotná & H. Moraová (Eds.), Proceedings of the International Symposium Elementary Mathematics Teaching (pp. 182–192). ISBN 9788076030695.
Hatisaru, V. (2020). Perceived need for mathematics among lower secondary students. Australian Mathematics Education Journal, 2(1), 9-14.
Hatisaru, V. (submitted). School Students’ Depictions of Mathematics Teaching and Learning Practices. International Journal of Science and Mathematics Education.
Hatisaru, V., & Erbaş, A. K. (2017). Mathematical knowledge for teaching and student learning outcomes. International Journal of Science and Mathematics Education, 15(4), 703-722.
Hatisaru, V., & Murphy, C. (2019). ‘Creature' teachers 'monster' mathematicians: students' views about mathematicians and their stated attitudes to mathematics. International Journal of Education in Mathematics, Science and Technology, 7(3), 215-221.
Hiebert, J., & Grouws, D. A. (2007). The effects of classroom mathematics teaching on students’ learning. In F. K. Lester (Ed.), Second handbook of research on mathematics teaching and learning (pp. 371-404). Greenwich, CT: Information Age.
Huinker, D. (2015). Representational competence: a renewed focus for classroom practice in mathematics. Wisconsin Teacher of Mathematics, 67(2), 4-8
Johansson, D. A., & Sumpter, L. (2010). Childrens’ conceptions about mathematics and mathematics education. In K. Kislenko (Ed.), Proceedings of the MAVI-16 conference June 26-29, 2010 (pp. 77-88). Tallinn, Estonia: Tallinn University of Applied Sciences.
Johnson, E. L. (2018). A New Look at the Representations for Mathematical Concepts: Expanding on Lesh’s Model of Representations of Mathematical Concepts. Forum Public Policy Online 11.
Kearney, K. S., & Hyle, A. E. (2004). Drawing out emotions: The use of participant-produced drawings in qualitative inquiry. Qualitative Research, 4(3), 361-382. https://doi.org/10.1177/1468794104047234
Kilpatrick, J., Swafford, J., & Findell, B. (Eds.). (2001). Adding it up: Helping children learn mathematics. Washington, DC: National Academy Press.
Laine, A., Näveri, L., Ahtee, M., Hannula, M. S., & Pehkonen, E. (2013). Emotional atmosphere in third graders’ mathematics classroom - An analysis of pupils’ drawings. Nordic Studies in Mathematics Education, 17(3-4), 101-116.
Laine, A., Ahtee, M., & Näveri, L. (2020). Impact of teachers’ actions on emotional atmosphere in mathematics lessons in primary school. International Journal of Science and Mathematics Education, 18, 163-181. https://doi.org/10.1007/s10763-018-09948-x
Lane, C., Stynes, M., & O’Donoghue, J. (2014). The image of mathematics held by Irish post-primary students. International Journal of Mathematical Education in Science and Technology, 45(6), 879-891. https://doi.org/10.1080/0020739X.2014.884648
Latterell, C. M., & Wilson, J. L. (2012). Students’ perceptions of what mathematicians do. The Mathematics Educator, 13(2), 73-84.
Lesh R., Post, T., & Behr, M. (1987). Representations and translations among representations in mathematics learning and problem solving. In C. Janvier (Ed.), Problems of Representation in the Teaching and Learning of Mathematics (pp. 33-40) Hillsdale, NJ: Lawrence Erlbaum Associates.
Lesh, R., Cramer, K., Doerr, H., Post, T., & Zawojewski, J., (2003) Using a translation model for curriculum development and classroom instruction. In R. Lesh & H. Doerr (Eds.) Beyond Constructivism. Models and Modeling Perspectives on Mathematics Problem Solving, Learning, and Teaching. Lawrence Erlbaum Associates, Mahwah, New Jersey. https://doi.org/10.4324/9781410607713
Losh, S. C., Wilke, R., & Pop, M. (2008). Some methodological issues with “Draw a Scientist Tests” among young children. International Journal of Science Education, 30(6), 773-792. https://doi.org/10.1080/09500690701250452
Malkevitch, J. (1997). Discrete mathematics and public perceptions of mathematics. In J. G. Rosenstein, D. S. Franzblau, & F. S. Roberts (Eds.), Discrete Mathematics in the Schools (pp. 89-97). American Mathematical Society/NCTM, Providence, RI. https://doi.org/10.1090/dimacs/036/10
Mead, M., & Metraux, R. (1957). Image of the scientist among high school students: A pilot study. Science, 126, 384-390. https://doi.org/10.1126/science.126.3270.384
Ministry of National Education (2018). Matematik dersi öğretim programı (İlkokul ve Ortaokul 1, 2, 3, 4, 5, 6, 7 ve 8. Sınıflar) [Mathematics curriculum (Primary and Lower Secondary School Grades 1, 2, 3, 4, 5, 6, 7, and 8)]. Retrieved from: http://mufredat.meb.gov.tr/
Mullis, I. V. S., Martin, M. O., Foy, P., & Hooper, M. (2016). TIMSS 2015 international results in mathematics. Retrieved from Boston College, TIMSS & PIRLS International Study Center website: http://timssandpirls.bc.edu/timss2015/international-results/
Murphy, P. K., Delli, L. A. M., & Edwards, M. N. (2004). The good teacher and good teaching. Comparing the beliefs of second-grade students, preservice teachers, and inservice teachers. The Journal of Experimental Education, 72(2), 69-92. https://doi.org/10.3200/JEXE.72.2.69-92
Narayan, R., Park, S., Peker, D., & Suh, J. (2013). Students’ images of scientists and doing science: an international comparison study. Eurasia Journal of Mathematics, Science & Technology Education, 9(2), 115-129. https://doi.org/10.12973/eurasia.2013.923a
National Council of Teachers of Mathematics (2000). Principles and standards for school mathematics. Reston VA: Author.
National Council of Teachers of Mathematics (2014). Principles to actions: Ensuring mathematical success for all. Reston VA: Author.
National Governors Association Center for Best Practices & Council of Chief State School Officers. (2010). Common core state standards for mathematics. Washington, DC: Author. http://www.corestandards.org
Nesin, A. (2014, August). 2023 icin cok gec, belki 2073! [Too late for 2023, perhaps 2073!]. Gorus, 85, 24-26.
Nistor, A., Gras-Velazquez, A., Billon, N., & Mihai, G. (December 2018). Science, technology, engineering and mathematics education practices in Europe. Scientix Observatory Report. European Schoolnet, Brussels.
O’Dwyer, L., Wang, Y., & Shields, K. (2015). Teaching for conceptual understanding: A cross-national comparison of the relationship between teachers’ instructional practices and student achievement in mathematics. Large-scale Assessments in Education, 3(1), 1-30. https://doi.org/10.1186/s40536-014-0011-6
Organisation for Economic Co-operation and Development (OECD) (2016). Ten questions for mathematics teachers ... and how PISA can help answer them. PISA, OECD Publishing, Paris.
Ozdemir, E., Gonen, E., Polat, M., & Ari, S. A. (2015). Turkey: Overview of education system. TIMSS 2015 Encyclopedia: Education Policy and Curriculum in Mathematics and Science. Retrieved from Boston College, TIMSS & PIRLS International Study Center website: http://timssandpirls.bc.edu/timss2015/encyclopedia/
Ozpolat, V. (2013). The place of student-centered approach in teachers’ occupational priorities. National Education Journal, 43(200), 5-27.
Pape, S. J., & Tchoshanov, M. A. (2001). The Role of Representation(s) in Developing Mathematical Understanding. Theory into practice, 40(2), 118-127. https://doi.org/10.1207/s15430421tip4002_6
Pehkonen, E., Ahtee, M., & Laine, A. (2016). Pupils’ drawings as a research tool in mathematical problem-solving lessons. In P. Felmer, E. Pehkonen, & J. Kilpatrick (Eds.), Posing and solving mathematical problems: Advances and new perspectives (Research in mathematics education) (pp. 167-188). Cham, Switzerland: Springer. https://doi.org/10.1007/978-3-319-28023-3_11
Picker, S., & Berry, J., (2000). Investigating pupils’ images of mathematicians. Educational Studies in Mathematics, 43, 65-94. https://doi.org/10.1023/A:1017523230758
Picker, S., & Berry, J. (2001). Your students’ images of mathematicians and mathematics. Mathematics Teaching in the Middle School, 7(4), 202-208.
Remesal, A. (2009). Accessing primary pupils’ conceptions of daily classroom assessment practices. In D. M. McInerney, G. T. L. Brown, & G. A. D. Liem (Eds.), Students perspectives on assessment: What students can tell us about assessment for learning (pp. 25-51). Charlotte, NC: Information age publishing, Inc.
Rock, D., & Shaw, J. M. (2000). Exploring children’s thinking about mathematicians and their work. Teaching Children Mathematics, 6(9), 550-555.
Sam, L. C., & Ernest, P. (2000). A survey of public images of mathematics. Research in Mathematics Education, 2(1), 193-206. https://doi.org/10.1080/14794800008520076
Saunders, B., Sim, J., Kingstone, T., Baker, S., Waterfield, J., Bartlam, B., … Jinks, C. (2017). Saturation in qualitative research: Exploring its conceptualization and operationalization. Quality and Quantity, 52, 1893-1907. https://doi.org/10.1007/s11135-017-0574-8
Smith, M. S., & Stein, M. K. (1998). Selecting and creating mathematical tasks: From research to practice. Mathematics Teaching in the Middle School, 3(5), 344-50.
Stein, M. K., & Smith, M. S. (2011). Mathematical tasks as a framework for reflection: From research to practice. National Council of Teachers of Mathematics (NCTM). Reston, Va.: NCTM.
Stiles, D. A., Adkisson, J. L., Sebben, D., & Tamashiro, R. (2008). Pictures of hearts and daggers: Emotions are expressed in young adolescents’ drawings of their attitudes towards mathematics. World Cultures eJournal, 16(2).
Sullivan, P. (2011). Teaching mathematics: Using research-informed strategies. Camberwell, VIC: Australian Council for Educational Research.
Swan, M. (2005). Improving learning in mathematics: Challenges and strategies. Sheffield, England: Department of Education and Skills Standards Unity.
Thomas, J. A., Pedersen, J. E., & Finson, K. (2001). Validating the Draw-A-Science-Teacher-Test Checklist: Exploring mental models and teacher beliefs. Journal of Science Teacher Education, 12(4), 295-310. https://doi.org/10.1023/A:1014216328867
Tripathi, P. (2008). Developing mathematical understanding through multiple representations. Mathematics Teaching in the Middle School, 13(8), pp. 438-445.
Turkish Directorate of Teacher Education and Development (2017). Teacher 2017-2023 Strategy Document. Retrieved from http://oygm.meb.gov.tr/www/ogretmen-strateji-belgesi/icerik/406
Ucar, Z., Piskin, M., Akkas, E., & Tascı, D. (2010). Elementary students’ beliefs about mathematics, mathematics teachers and mathematicians. Education and Science, 35(155), 131-144.
Vieluf S., Kaplan, D., Klieme, E., & Bayer, S. (2012). Teaching practices and pedagogical innovation: Evidence from TALIS. OECD Publishing. https://doi.org/10.1787/9789264123540-en
Watson, A., & De Geest, E. (2005). Principled teaching for deep progress: Improving mathematical learning beyond methods and materials. Educational Studies in Mathematics, 58(2), 209-234. https://doi.org/10.1007/s10649-005-2756-x
Wilson, P. (2011). Disposition towards engagement in mathematics. In Smith, C. (Ed), Proceedings of the British Society for Research into Learning Mathematics, 31(2), 67-72.
Vincent-Lancrin, S., Urgel, J., Kar, S., & Jacotin, G. (2019). Measuring innovation in education 2019: What has changed in the classroom? Educational Research and Innovation, OECD Publishing, Paris. https://doi.org/10.1787/9789264311671-en
Wong, N. Y., Marton, F., Wong, K. M., & Lam, C. C. (2002). The lived space of mathematics learning. Journal of Mathematical Behavior, 21, 25-47. https://doi.org/10.1016/S0732-3123(02)00101-3
Yıldırım, S., & Yıldırım, H. H. (2019) Conceptions of Turkish mathematics teachers about the effectiveness of classroom teaching. International Journal of Mathematical Education in Science and Technology, 50(8), 1152-1165. https://doi.org/10.1080/0020739X.2019.1579929

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APA

Hatisaru, V. (2020). Exploring Evidence of Mathematical Tasks and Representations in the Drawings of Middle School Students. International Electronic Journal of Mathematics Education, 15(3), em0609. https://doi.org/10.29333/iejme/8482

Vancouver

Hatisaru V. Exploring Evidence of Mathematical Tasks and Representations in the Drawings of Middle School Students. INT ELECT J MATH ED. 2020;15(3):em0609. https://doi.org/10.29333/iejme/8482

AMA

Hatisaru V. Exploring Evidence of Mathematical Tasks and Representations in the Drawings of Middle School Students. INT ELECT J MATH ED. 2020;15(3), em0609. https://doi.org/10.29333/iejme/8482

Chicago

Hatisaru, Vesife. "Exploring Evidence of Mathematical Tasks and Representations in the Drawings of Middle School Students". International Electronic Journal of Mathematics Education 2020 15 no. 3 (2020): em0609. https://doi.org/10.29333/iejme/8482

Harvard

Hatisaru, V. (2020). Exploring Evidence of Mathematical Tasks and Representations in the Drawings of Middle School Students. International Electronic Journal of Mathematics Education, 15(3), em0609. https://doi.org/10.29333/iejme/8482

MLA

Hatisaru, Vesife "Exploring Evidence of Mathematical Tasks and Representations in the Drawings of Middle School Students". International Electronic Journal of Mathematics Education, vol. 15, no. 3, 2020, em0609. https://doi.org/10.29333/iejme/8482