Email this article Assessing Pre-service Mathematics Education Teachers Deductive Reasoning via Proof Writing in Basic Geometry: The Power of SOLO Taxonomy
) (1) Cebu Normal University, Philippines
Corresponding AuthorCopyright (c) 2025 Ray Ferdinand Gagani
| Article Metrics→ |
| Indexing Database→ |  |
 |
Abstract
Assessing Pre-service Mathematics Education Teachers Deductive Reasoning via Proof Writing in Basic Geometry: The Power of SOLO Taxonomy. Objectives: This study characterizes the developmental patterns of deductive reasoning via proof-writing of pre-service mathematics education teachers using the Structure of the Observed Learning Outcome (SOLO) taxonomy. Methods: One hundred three pre-service teachers were given twelve items involving basic concepts of plane geometry to assess. An in-depth analysis of their proof was done and they were grouped through a two-step clustering technique. Findings: Four compatible levels of developmental pattern to the SOLO level were detected. At level 0, students do not know how to establish proof. At level 1, students provided a single or few valid idea/s. Students demonstrating level 2 thinking provided many true ideas. However, the proofs are unclear and illogical. Level 3 students' proof is precisely logical. Conclusion: A trend of difficulty and success characterizes their deductive reasoning and indicates that those who were not successful in a task have superficial conceptual geometry knowledge. The research concluded that the SOLO taxonomy is a precise framework for conceptual knowledge assessment and that knowledge indeed has structure. The use of the SOLO taxonomy for assessment activity is recommended.
Keywords: assessment, deductive reasoning, proof writing, solo taxonomy.
DOI: http://dx.doi.org/10.23960/jpp.v13.i3.202307
References
Afriyani, D., & Sa'dijah, C. (2018). Characteristics of students' mathematical understanding in solving multiple representation task based on solo taxonomy. International Electronic Journal of Mathematics Education, 13(3), 281-287. https://doi.org/10.12973/iejme/3920
Aiken, L. R. (1979). Relationships between the item difficulty and discrimination indexes. Educational and Psychological Measurement, 39(4), 821–824. doi:10.1177/001316447903900415
Ashcraft, M. H. (1994). Human Memory and Cognition (2nd ed.). New York: Harper Collins College.
Baturo, A. R., & Cooper, T. (2008). Developing mathematics understanding through cognitive diagnostic assessment tasks. Department of Education, Employment and Workplace Relations. retrieved from https://eprints.qut.edu.au/18714/1/CDAT_complete_document.pdf
Benkhalti, A. (2017). An analysis of transition-to-proof course students' proof construction attempts. (Order No. 10633405). Available from ProQuest Dissertations & Theses Global.(1927640549). Retrieved April 16, 2023, https://search.proquest.com/docview/1927640549?accountid=173015
Biggs, J.B., & Collis, K.F. (1982). Evaluating the quality of learning: The SOLO taxonomy (Structure of the Observed Learning Outcome) [Google Book version]. Retrieved from https://books.google.com.ph/books?id=xUO0BQAAQBAJ&printsec=frontcover#v=onepage&q&f=false
Biggs, J., & Collis, K.(1989).Towards a model of school-based curriculum development and assessment using the SOLO Taxonomy. Australian Journal of Education, 33(2), 151–163. https://doi:10.1177/168781408903300205
Biggs, J. & Tang, C. (2011). Teaching for Quality Learning at University. (4th ed.), [dig.ver.]. England: McGraw Hill.
Caniglia, J. C., & Meadows, M. (2018). An application of the Solo Taxonomy to classify strategies used by pre-service teachers to solve “one question problems. Australian Journal of Teacher Education, 43(9), 75-89. http://dx.doi.org/10.14221/ajte.2018v43n9.5
Carrascal, B. (2015). Proofs, mathematical practice and argumentation. Argumentation, 29(3), 305-324. http://dx.doi.org/10.1007/s10503-014-9344-0
Chan, C. C., Tsui, M. S., Chan, M. Y. C., & Hong, J. H. (2002). Applying the structure of the observed learning outcomes (SOLO) Taxonomy on student’s learning outcomes: An empirical study. Assessment & Evaluation in Higher Education, 27(6), 511–527. https://doi:10.1080/0260293022000020282
Chaphalkar, R., & Wu, K. (2020). Students’ reasoning about variability in graphs during an introductory statistics course. International Electronic Journal of Mathematics Education, 15(2), em0580. https://doi.org/10.29333/iejme/7602
Chick, H. (1998). Cognition in the formal modes: Research mathematics and the SOLO taxonomy. Mathematics Education Research Journal, 10(2), 4–26. https://doi.org/10.1007/BF03217340
Conner, A. (2013). Authentic argumentation with prospective secondary teachers: The case of 0.999… Mathematics Teacher Educator, 1(2), 172-180. https://doi.org/10.5951/mathteaceduc.1.2.0172
Cox, R. (2004). Using conjectures to teach students the role of proof. The Mathematics Teacher, 97(1), 48-52. Retrieved December 2, 2020, from http://www.jstor.org/stable/20871499
Crompton, H., Grant, M., & Shraim, K. (2018). Technologies to enhance and extend children’s under standing of geometry: A configurative thematic synthesis of the literature. Journal of Educational Technology & Society, 21(1), 59-69. Retrieved December 2, 2020, from http://www.jstor.org/stable/26273868
De Jong, T., & Ferguson-Hessler, M. G. (1996). Types and qualities of knowledge. Educational psychologist, 31(2), 105-113. Retrieved from https://ris.utwente.nl/ws/files/6401593/types.pdf
Dudley, D., & Baxter, D. (2009) Assessing levels of student understanding in pre-service teachers using a two-cycle SOLO model. Asia-Pacific Journal of Teacher Education, 37(3), 283-293. https://doi.org/10.1080/13598660903052282
Gagani, R. F. M., & Misa, R. O. (2017). Solo based-cognition levels of inductive reasoning in Geometry. Alberta Journal of Educational Research, 63(4), 344-356. https://doi.org/10.11575/ajer.v63i4.56331
Goodboy, A. K., & Martin, M. M. (2020). Omega over alpha for reliability estimation of unidimensional communication measures. Annals of the International Communication Association, 44(4), 422-439. https://doi.org/10.1080/23808985.2020.1846135
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.10.1207/s15327833mtl0801_3
Günhan, B. C. (2014). An investigation of pre-service elementary school teachers' knowledge concerning quadrilaterals. Çukurova University. Faculty of Education Journal, 43(2), 137-154. Retrieved April 16, 2023, https://search.proquest.com/docview/1640676328?accountid=173015
Harel, G., Weber, K. (2020). Deductive Reasoning in Mathematics Education. In: Lerman, S. (eds) Encyclopedia of Mathematics Education. Springer, Cham. https://doi.org/10.1007/978-3-030-15789-0_43
Hingorjo, M. R., & Jaleel, F. (2012). Analysis of one-best MCQs: the difficulty index, discrimination index and distractor efficiency. JPMA-Journal of the Pakistan Medical Association, 62(2), 142-147. Retrieved April 16, 2023, https://jpma.org.pk/article-details/3255?article_id=3255
Huey, M. E. (2011). Characterizing middle and secondary preservice teachers' change in inferential reasoning (Order No. 3533846). Available from ProQuest Dissertations & Theses Global. (1262397961). Retrieved April 16, 2023, https://www.proquest.com/dissertations-theses/characterizing-middle-secondary-preservice/docview/1262397961/se-2
Imrie, B.W. (1995). Assessment for learning: quality and taxonomies. Assessment & Evaluation in Higher Education, 20(2), 175-189. https://doi.org/10.1080/02602939508565719
Johnson-Laird, P. N. (1999). Deductive reasoning. Annual Review of Psychology, 50(1), 109-135. https://doi.org/10.1146/annurev.psych.50.1.109
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:10.1080/0020739910220109
Lawshe, C. H. (1975). A quantitative approach to content validity. Personnel Psychology, 28(4), 563-575. Retrieved March 4, 2023, https://parsmodir.com/wp-content/uploads/2015/03/lawshe.pdf
Luo, X., Wei, B., Shi, M., & Xiao, X. (2020). Exploring the impact of the reasoning flow scaffold (RFS) on students’ scientific argumentation: based on the structure of observed learning outcomes (SOLO) taxonomy. Chemistry Education Research and Practice, 21(4), 1083-1094. https://doi.org/10.1039/C9RP00269C
Maarif, S., Perbowo, K. S., Noto, M. S., & Harisman, Y. (2019). Obstacles in constructing geometrical proofs of mathematics-teacher-students based on boero’s proving model. In Journal of Physics: Conference Series, 13151, p. 012043. IOP Publishing. doi:10.1088/1742-6596/1315/1/012043
Moseley, D., Baumeld, V., Elliott, J., Gregson, M., Higgins, S., Miller, J., & Newton, D. P. (2005). Frameworks for thinking: A handbook for teaching and learning [dig. Ver.]. Cambridge, UK: Cambridge University Press.
Mulbar, U., Rahman, A., & Ahmar, A. (2017). Analysis of the ability in mathematical problem-solving based on SOLO taxonomy and cognitive style. World Transactions on Engineering and Technology Education, 15(1). Available at SSRN: https://ssrn.com/abstract=2940939
Nardi, E., Biza, I., González-Martín, A.S., Gueudet, G., Winsløw, C. (2014). Institutional, sociocultural and discursive approaches to research in university mathematics education. Research in Mathematics Education, 16(2), 91–94. https://doi.org/10.1080/14794802.2014.918344
Niemela, P., Mikkolainen, V., & Vuorinen, J. (2018). Compute Mindlessly. Not! Map Consciously. Universal Journal of Educational Research, 6(11), 2669-2678. https://doi:10.13189/ujer.2018.061133
Nor, N. M., & Idris, N. (2010). Assessing students’ informal inferential reasoning using SOLO taxonomy based framework. Procedia-social and behavioral sciences, 2(2), 4805-4809. https://doi.org/10.1016/j.sbspro.2010.03.774
Ozdemir, A. S., & Goktepe Yildiz, S. (2015). The analysis of elementary mathematics preservice teach ers’spatial orientation skills with SOLO model. Eurasian Journal of Educational Research, 61,217-236. http://dx.doi.org/10.14689/ejer.2015.61.12
Padilla, M. A., & Divers, J. (2016). A comparison of composite reliability estimators: coefficient omega confidence intervals in the current literature. Educational and psychological measurement, 76(3), 436-453. doi: 10.1177/0013164415593776Putnam, R. T., Lampert, M., & Peterson, P. L. (1990). Chapter 2: Alternative Perspectives on Knowing Mathematics in Elementary Schools. Review of research in education, 16(1), 57-150. https://doi.org/10.3102/0091732X016001057
Radmehr, F. & Drake, M. (2019) Revised Bloom’s taxonomy and major theories and frameworks that influence the teaching, learning, and assessment of mathematics: a comparison. International Journal of Mathematical Education in Science and Technology, 50(6), 895-920. https://doi: 10.1080/0020739X.2018.1549336
Savalei, V., & Reise, S. P. (2019). Don’t forget the model in your model-based reliability coefficients: A reply to McNeish (2018). Collabra: Psychology, 5(1): 36. https://doi.org/10.1525/collabra.247
Sekaryanti, R., Cholily, Y. M., Darmayanti, R., Rahma, K., & Maryanto, B. P. A. (2022). Analysis of written mathematics communication skills in solving SOLO taxonomy assisted problems. JEMS:Jurnal Edukasi Matematika dan Sains, 10(2), 395-403. http://doi.org/10.25273/jems.v10i2.13707
Senk, S. (1985). How well do students write geometry proofs? The mathematics teacher, 78(6), 448-456. Retrieved December 1, 2020, http://www.jstor.org/stable/27964580
Senk, S.L. (1989). Van Hiele levels and achievement in writing geometry proofs. Journal for Research in Mathematics Education, 20(3), 309–321. https://doi.org/10.2307/749519
Simon, M. A. (1996). Beyond Inductive and Deductive Reasoning: The Search for a Sense of Knowing. Educational Studies in Mathematics, 30(2), 197–209. http://www.jstor.org/stable/3482744
Sinclair, N., & Robutti. O. (2012) Technology and the role of proof: The case of dynamic geometry. In: Clements M., Bishop A., Keitel C., Kilpatrick J., Leung F. (eds) Third International Handbook of Mathematics Education. Springer International Handbooks of Education, vol 27. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-4684-2_19
Sonnabend, T. (1997). Mathematics for elementary teachers: An integrative approach (2nd ed.). Orlando, FL: Saunders College Publishing.
Stålne, K., Kjellström, S., & Utriainen, J. (2015): Assessing complexity in learning outcomes – a comparison between the SOLO taxonomy and the model of hierarchical complexity. Assessment & Evaluation in Higher Education, 41(7), 1033-1048. https://doi.org/10.1080/02602938.2015.1047319
Wang, Y. (2008). On concept algebra: A denotational mathematical structure for knowledge and software modeling. International Journal of Cognitive Informatics and Natural Intelligence, 2(2), 1-8,10-19.RetrievedApril 16, 2023, https://search.proquest.com/docview/275149494?accountid=173015
Wong, B., & Bukalov, L. (2013). Improving student reasoning in geometry. The Mathematics Teacher, 107(1), 54-60. https://doi.org/10.5951/mathteacher.107.1.0054
Refbacks
- There are currently no refbacks.
This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.
View My Stats