An Investigation of the Geometric Thinking Levels of Middle School Mathematics Preservice Teachers According to SOLO Taxonomy: "Social Distance Problems"

Year 2021, Volume: 8 Issue: 3, 188 - 209, 01.08.2021

Mehmet İhsan Yurtyapan , Gül Kaleli Yılmaz

https://doi.org/10.17275/per.21.61.8.3

Cited By: 2

Abstract

The aim of this study is to examine the geometric thinking levels of middle school mathematics preservice teachers regarding the problem situations regarding the concept of social distance according to the SOLO taxonomy. The research was conducted using the special case method, one of the qualitative research methods. The working group, studying at a state university in Turkey in middle school mathematics teaching department consists of 80 preservice teachers. While determining the participants, purposeful sampling method was used because the preservice teachers who took "Basics of Mathematics II" and "Special Teaching Methods II" courses were selected. In the study, semi-structured interviews were conducted with 15 preservice teachers since it was aimed to examine remarkable situations from the answers given to open-ended questions. Descriptive analysis technique was used while analyzing the data. Most of the answers given in the study were found to be below the relational geometric thinking level. As a result, it was determined that most of the answers given reflected quantitative learning. In line with this result obtained in the study, it is suggested that open-ended questions about life should be included frequently in teaching in order to reach the relational and extended abstract level answers that reflect qualitative learning.

Keywords

Coronavirus, covid-19, geometric thinking, prospective teachers, social distance, solo taxonomy

References

• Akbaş-Ertem, A. (2016). Evaluation of the learning of the students of vocational high schools in computer assisted environment about the concept of 'limit and continuity' by SOLO taxonomy. (Unpublished doctoral dissertation). Black Sea University, Trabzon.
• Akkaş, E. N. (2009). Investigation of the middle school students' statistical thinking. (Unpublished master’s thesis). Abant İzzet Baysal University, Bolu.
• Aristoteles, (1993). Aristoteles, Metafizik Cilt II, (Trans. A. Arslan). İzmir: Ege Univercity Press, İzmir.
• Bağdat, O. (2013). Investigation of the 8th grade students' algebraic thinking skills with SOLO taxonomy. (Unpublished doctoral dissertation). Eskişehir Osmangazi University, Eskişehir.
• Biggs, J. & Collis, K. (1991). Multimodal learning and the quality of ıntelligent behaviour. H. Rowe, Intelligence (Ed.), New Jersey: Reconceptualization and Measurement, Laurence Erlbaum Assoc.
• Biggs, J. B., & Collis, K. F. (1982). Evaluating the quality of learning: The SOLO taxonomy (Structure of the observed learning outcome). New York: Academic Press.
• Brabrand, C., & Dahl, B. (2009). Using the SOLO taxonomy to analyze competence progression of university science curricula. Higher Education, 58(4), 531-549. https://doi.org/10.1007/s10734-009-9210-4
• Bulut, İ., Öner-Sünkür, M., Oral, B., & İlhan, M. (2012). Analysis of the relationship between geometrical thinking levels and intelligence domains of 8th grade students. Electronic Journal of Social Sciences, 11(41), 161-173. Retrieved from https://dergipark.org.tr/en/pub/esosder/issue/6155/82709
• Callingham, R. A. (1999). Developing performance assessment tasks in mathematics: A case study. Paper presented at the Making the Difference (Proceedings of the 22nd Annual Conference of the Mathematics Education Research Group of Australasia, pp. 135–142). MERGA: Adelaide, SA.
• Çelik, D. (2007). Analytical examination of the preservice teachers' algebraic thinking skills. (Unpublished doctoral dissertation). Black Sea University, Trabzon.
• Çetin, B., & İlhan, M. (2016). SOLO taksonomisi [SOLO Taxonomy]. In Bingölbali, E., Özarslan, S., & Zembat İ. Ö. (Ed.), Matematik eğitiminde teoriler [Theories in mathematics education] (861- 879). Ankara: Pegem Academy.
• Denzin, N. K., & Lincoln, Y. S. (Ed.). (1998). Collecting and interpreting qualitative materials. Thousand Oaks, Calif: Sage Publications.
• Duatepe, A. (2004). The effects of drama based instruction on seventh grade students’ geometry achievement, van Hiele geometric thinking levels, attitude toward mathematics and geometry. (Unpublished doctoral dissertation). Middle East Technical University, Ankara.
• Fennema, E., & Loef, F. M. (1992). Teachers’ knowledge and its impact. D. A. Grouws, (Ed.), Handbook of research on mathematics teaching and learning (147-164). NewYork: Macmillan.
• Fi̇dan, Y. & Türnüklü, E. (2010). Investigation of some types of variables in the depths of primary school 5th grade students. Pamukkale University Journal of Education, 27 (27), 185-197. Retrieved from https://dergipark.org.tr/tr/pub/pauefd/issue/11116/132940
• Gökbulut, Y., Sidekli, S., & Yangın, S. (2010). Researching prospective primary teacher’s van Hiele geometric thinking levels according to some variables (graduat ion type of high school, high school sphere, high school average, Öğrenci Seçme Sınavı [Student Selection Exam] points, university academic average and sex). Turkish Journal of Educational Sciences, 8(2), 375-396. Retrieved from https://dergipark.org.tr/en/pub/tebd/issue/26104/275039
• Göktepe, S. (2013). Examining the spatial abilities of pre-service mathematics teachers with a solo model. (Unpublished doctoral dissertation). Marmara University, İstanbul.
• Göktepe, S., & Özdemir, A. Ş. (2013). Examing elementary mathematics teacher candidates’ special visualization skills by SOLO model. KALEM International Journal of Educational and Human Sciences, 3(2), 91-146. https://doi.org/10.23863 / kalem.2017.26
• Groth, R. E., & Bergner, J. A. (2006). Preservice elementary teachers’ conceptual and procedural knowledge of mean, median, and mode. Mathematical Thinking and Learning, 8(1), 37-63. https://doi.org/10.1207/s15327833mtl0801_3
• Güven, B., Ardıç, E. Ö., Yılmaz, B., & Demir, E. (2012, June). Examination of the statistical literacy levels of primary school 8th grade students on central tendency and spread measures according to solo taxonomy. Paper presented at the meeting of X. National Science and Mathematics Education Congress, Niğde, Turkey. Abstract retrieved from https://www.pegem.net/Akademi/bildiri_detay.aspx?id=135891
• Halat, E. (2006). Sex-related differences in the acquisition of the van hiele levels and motivation in learning geometry. Asia Pacific Education Review, 7(2), 173-183. https://doi.org/10.1007/BF03031541
• Hvizdo, M. M. (1992). A study of the effect of spatial ability on geometry grades. (Unpublished master’s thesis). Southern Connecticut State University, Connecticut.
• İlhan, M. (2015). The identification of rater effects on open-ended math questions rated through standard rubrics and rubrics based on the SOLO taxonomy in reference to the many facet Rasch model. (Unpublished doctoral dissertation). Gaziantep University, Gaziantep.
• Jurdak, M. (1991). Van Hiele levels and the SOLO taxonomy†. International Journal of Mathematical Education in Science and Technology, 22(1), 57-60. https://doi.org/10.1080/0020739910220109
• Kahan, J. A., Cooper, D. A., & Bethea, K. A. (2003). The role of mathematics teachers’ content knowledge in their teaching: A framework for research applied to a study of student teachers. Journal of Mathematics Teacher Education, 6, 223-252. https://doi.org/10.1023/A:1025175812582
• Karlı, M.G. (2019). Investigation of the 7th grade students' proportional thinking skills with SOLO Taxonomy. (Unpublished master’s thesis). Tokat Gaziosmanpaşa University, Tokat.
• Kılıç, Ç. (2003). The Effect of teaching geometry based on Van Hiele Levels on the acedemic success, attitudes and recall levels of the 5 th grade primary school students in mathematics course. (Unpublished master’s thesis). Anadolu University, Eskişehir.
• Konyalıhatipoğlu, M. E. (2016). A SOLO taxonomy research on holistic and analytic thinking styles of seventh grade secondary school students. (Unpublished master’s thesis). Recep Tayyip Erdogan University, Rize.
• Köse, O. (2018). Determination of SOLO taxonomy levels of mathematics teacher candidates with high level saptial ability accordingto thinking structures. (Unpublished master’s thesis). Selçuk University, Konya.
• Lian, L. H. & Idris, N. (2006). Assessing algebraic solving ability of form four students. International Electronic Journal of Mathematics Education (IEJME), 1(1), 55-76.
• Lian, L.H., & Yew, W. T. (2012). Assessing algebraic solving ability: A theoretical framework. International Education Studies, 5(6), p177. https://doi.org/10.5539/ies.v5n6p177
• Lloyd, G. M., & Wilson, M. (1998). Supporting innovation: The impact of a teacher's conceptions of functions on his implementation of a reform curriculum. Journal for Research in Mathematics Education, 29(3), 248-274. https://doi.org/10.2307/749790
• Lucander, H., Bondemark, L., Brown, G., & Knutsson, K. (2010). The structure of observed learning outcome (Solo) taxonomy: A model to promote dental students’ learning: The SOLO taxonomy: a model to promote learning. European Journal of Dental Education, 14(3), 145-150. https://doi.org/10.1111/j.1600-0579.2009.00607.x
• Miles, M. B., & Huberman, A. M. (1994). Qualitative data analysis: An expanded sourcebook. London: Sage.
• MoNE, (2009a). Mathematics lesson (grades 1-5)curriculum, Ankara.
• MoNE, (2009b). Mathematics lesson (grades 6-8) curriculum, Ankara.
• MoNE, (2012). Mathematics applications lesson (5th, 6th, 7th and 8th grades) curriculum, Ankara.
• NCTM, (2000). Principles and standards for school mathematics. Reston, VA: National Council of Teachers of Mathematics. Olkun, S. (2003). Making connections: Improving spatial abilities with engineering drawing activities. International journal of mathematics teaching and learning, 3(1), 1-10.
• Olkun, S., & Toluk, Z. (2007). İlköğretimde etkinlik temelli matematik öğretimi [Activity-based mathematics teaching in primary education]. Ankara, Turkey: Maya Academy Publication Distribution.
• Özdemir, A. Ş., & Yildiz, S. G. (2015). The examination of elementary mathematics pre-service teachers’ spatial abilities. Procedia - Social and Behavioral Sciences, 174, 594-601. https://doi.org/10.1016/j.sbspro.2015.01.588
• Padiotis, I., & Mikropoulos, T.A. (2010). Using SOLO to evaluate an educational virtual environment in a technology education setting. Educational Technology & Society, 13(3), 233-245.
• Pegg, J. ve Tall, D. (2001). Fundamental cycles in learning algebra: An analysis. 10 October 2020, http://www.warwick.ac.uk/staff/David.Tall/drafts/dot2001z-pegg-icmi-algebra.pdf
• Pegg, J., & Davey, G. (1998). Interpreting Student Understanding in Geometry: A Synthesis of two Models (s.109-135). Ed: Richard Lehrer ve Daniel Chazen, In Designing Learning Environments for Developing Understanding of Geometry and Space., NJ: Lawrence Erlbaum Associates, Mahwah.
• Pittalis, M., Christou, C., & Papageorgiou, E. (2003). Students’ ability in solving proportional problems. Proceedings of the 3rd European Research Conference in Mathematics Education: Bellaria: Italy, 3.
• Shulman, L. S. (1986). Those who understand: Knowledge growth in teaching. Educational Researcher, 15(2), 4-14. https://doi.org/10.3102/0013189X015002004
• Strauss, A. L., & Corbin, J. M. (1998). Basics of qualitative research: Techniques and procedures for developing grounded theory (2nd ed). Sage Publications.
• Tekin, A. T. (2007). Comparative investigation of nineth and eleventh grade students mental rotation and spatial visualization abilities. (Unpublished master’s thesis). Ankara University, Ankara.
• Tomperi, P. (2016). SOLO taxonomy supporting practical chemistry instruction. LUMAT-B: International Journal on Math, Science and Technology Education, 1(3). Retrieved from https://journals.helsinki.fi/lumatb/article/view/1202
• Türnüklü, A. (2000). Qualitative research technique that can be used effectively in pedagogical research: Interview. Educational Administration: Theory and Practice, 6(4), 543-559.
• Usiskin, Z. (1982). Van Hiele levels and achievement in secondary school geometry. Final report of the Cognitive Development and achievement in secondary school geometry project, University of Chicago, Department of Education.
• Van Dooren, W., Verschaffel, L., & Onghena, P. (2002). The impact of preservice teachers’ content knowledge on their evaluation of students’ strategies for solving arithmetic and algebra word problems. Journal for Research in Mathematics Education, 33(5), 319-351. JSTOR. https://doi.org/10.2307/4149957
• Van Hiele, P. (1986). Structure and insight: A theory of mathematics education. London: Academic Press.
• Weyers, M. (2006). Teaching the FE Curriculum: Encouraging active learning in the classroom. London: Continuum.
• Yıldırım, A., & Şimşek, H. (2016). Sosyal bilimlerde nitel araştırma yöntemleri.[ Qualitative research methods in the social sciences]. Ankara: Seçkin Publications.
• Yılmaz, G. K., & Koparan, T. (2015). The effect of designed geometry teaching lesson to the candidate teachers’ van hiele geometric thinking level. Journal of Education and Training Studies, 4(1), 129-141. https://doi.org/10.11114/jets.v4i1.1067
• Yi, M., Flores, R., & Wang, J. (2020). Examining the influence of van Hiele theory-based instructional activities on elementary preservice teachers’ geometry knowledge for teaching 2-D shapes. Teaching and Teacher Education, 91, 103038. https://doi.org/10.1016/j.tate.2020.103038
• Yin, R. K. (1984). Case study research: Design and methods. Beverly Hills, Calif: Sage Publications.