Developing a Two-Tier Proportional Reasoning Skill Test: Validity and Reliability Studies

KÜBRA AÇIKGÜL

Authors

KÜBRA AÇIKGÜL İnonu University

Keywords:

Proportional reasoning, Two-tier test, Middle school

Abstract

The main aim of this study is to develop a useful, valid, and reliable two-tier proportional reasoning skill test for middle school 7th and 8th-grade students. The research was carried out using the sequential explanatory mixed method. The study group of this research comprised of 391 (n_7th-grade= 223, n_8th-grade= 168) students. With validity and reliability studies, the content, face, construct, discriminant validity, and reliability coefficient of the test were examined. As a result, the two-tier proportional reasoning skill test with 12 items under 3 factors (qualitative prediction and comparison, missing value, numerical comparison) valid and reliable for adequate values specified in the literature.

References

Afnia, P.N., & Istiyono, E. (2020, February). The development of two-tier multiple choice instruments to measure higher order thinking skills bloomian. In 3rd International Conference on Learning Innovation and Quality Education (ICLIQE 2019) (pp. 1038-1045). Atlantis Press. https://doi.org/10.2991/assehr.k.200129.128

Akkus, O., & Duatepe-Paksu, A. (2006). Construction of a proportional reasoning test and its rubrics. Eurasian Journal of Educational Research, 25, 1-10.

Alfieri, L., Higashi, R., Shoop, R., & Schunn, C. D. (2015). Case studies of a robot-based game to shape interests and hone proportional reasoning skills. International Journal of STEM Education, 2(4), 1-13. https://doi.org/10.1186/s40594-015-0017-9

Allain, A. (2000). Development of an instrument to measure proportional reasoning among fast-track middle school students. [Master’s thesis]. University of North Carolina State.

Arıcan, M. (2019). A diagnostic assessment to middle school students’ proportional reasoning. Turkish Journal of Education, 8(4), 237 257. https://doi.org/10.19128/turje.522839

Ayan, R., & Isiksal-Bostan, M. (2019). Middle school students’ proportional reasoning in real life contexts in the domain of geometry and measurement. International Journal of Mathematical Education in Science and Technology, 50(1), 65 81. https://doi.org/10.1080/0020739X.2018.1468042

Behr, M., Lesh, R., & Post, T. (1988). Proportional reasoning, In M. Behr and J. Hiebert (Eds.), Number concepts and operations in the middle grades. Lawrence Erlbaum Associates.

Behr, M., Harel, G., Post, T., & Lesh, R. (1992). Rational number, ratio and proportion. In D. Grouws (Eds.), Handbook on research of teaching and learning (pp. 296-333). McMillan.

Brown, T. A. (2006). Confirmatory factor analysis for applied research. In David A. Kenny (Eds.), Methodology in the Social Sciences. The Guilford Press.

Bright, G. W., Joyner, J. M., & Wallis, C. (2003). Assessing proportional thinking. Mathematics Teaching in the Middle School, 9(3), 166-172. https://www.jstor.org/stable/41181882

Burton, S. J., Sudweeks, R. E., Merrill, P. F., & Wood, B. (1991). How to prepare better multiple-choice test items: Guidelines for university faculty. Brigham Young University Testing Services and The Department of Instructional Science. https://testing.byu.edu/handbooks/betteritems.pdf

Büyüköztürk, S. (2010). Sosyal bilimler için veri analizi el kitabı [Data analysis handbook for social sciences]. Pegem Akademi.

Cameron, A. (2004). Kurtosis. In M. Lewis-Beck, A. Bryman and T. Liao (Eds.). Encyclopedia of social science research methods. (pp. 544-545). SAGE Publications, Inc.

Common Core State Standards Initiative (US). Common core state standards for mathematics. http://www.corestandards.org/Math/

Cramer, K., & Post, T. (1993). Proportional reasoning. The Mathematics Teacher, 86(5), 404-407. https://www.jstor.org/stable/27968390

Cramer, K., Post, T., & Currier, S. (1993). Learning and teaching ratio and proportion: research implications. In D. Owens (Eds.), Research ideas for the classroom (pp. 159-178). Macmillan Publishing Company.

Crocker, L., & Algina, J. (2008). Introduction to classical and modern test theory. Cengage Learning.

Cohen, J. (1988). Statistical power analysis for the behavioral sciences. Erlbaum.

Cohen, L., Manion, L., & Morrison, K. (2013). Research methods in education. Routledge.

Creswell, J .W., & Plano Clark, V. L. (2011). Designing and conducting mixed methods research. Sage Publications.

Davis, L. L. (1992). Instrument review: getting the most from a panel of experts. Applied Nursing Research, 5, 194-197. https://doi.org/10.1016/S0897-1897(05)80008-4

Dinç-Artut, P., & Pelen, M. S. (2015). 6th grade students’ solution strategies on proportional reasoning problems. Procedia-Social and Behavioral Sciences, 197, 113-119. https://doi.org/10.1016/j.sbspro.2015.07.066

Duatepe, A., Akkus-Cıkla, O., & Kayhan, M. (2005). An investigation on students’ solution strategies for different proportional reasoning items. Hacettepe Journal of Education Faculty, 28, 73-81. https://dergipark.org.tr/en/pub/hunefd/issue/7808/102422

Ebel, R. L. (1965). Measuring educational achievement. Prentice Hall.

Ebel, R. L., & Frisbie, D. A. (1991). Essentials of educational measurement. Prentice Hall.

Field, A. (2009). Discovering statistics using SPSS. Sage Publication.

Fornell, C., & Larcker, D. F. (1981). Structural equation models with unobservable variables and measurement error: Algebra and statistics. Journal of Marketing Research, 18(3), 328–388. https://doi.org/10.1177/002224378101800313

Gable, R. K. (1986). Instrument development in the affective domain. Kluwer-Nijhoff Publishing.

Hair, J. F., Jr., Black, W. C., Babin, B. J., Anderson, R. E., & Tatham, R. L. (2014). Multivariate data analysis. Pearson New International Edition.

Haja, S., & Clarke, D. (2011). Middle school students’ responses to two-tier tasks. Mathematics Education Research Journal, 23(1), 67-76. https://doi.org/10.1007/s13394-011-0004-5

Haslam, F., & Treagust, D. F. (1987). Diagnosing secondary students' misconceptions of photosynthesis and respiration in plants using a two-tier multiple choice instrument. Journal of Biological Education, 21(3), 203 211. https://doi.org/10.1080/00219266.1987.9654897

Hatcher, L. (1994). A step-by-step approach to using the SAS® system for Factor Analysis and Structural Equation Modeling. SAS Institutte, Inc.

Hilton, A., Hilton, G., Dole, S., & Goos, M. (2013). Development and application of a two-tier diagnostic instrument to assess middle - years students’ proportional reasoning. Mathematics Education Research Journal, 25(4), 523 545. https://doi.org/10.1007/s13394-013-0083-6

Hu, L., & Bentler, P. M. (1999). Cutoff criteria for fit indexes in covariance structure analysis: Conventional criteria versus new alternatives. Structural Equation Modeling: A Multidisciplinary Journal, 6(1), 1-55. https://doi.org/10.1080/10705519909540118

Hyman, M. R., & Sierra, J. J. (2016). Open-versus close-ended survey problems. Business Outlook, 14(2), 1-5.

Kline, R. B. (2011). Principles and practice of structural equation modeling. Guilford Press.

Lamon, S. J. (2007). Rational numbers and proportional reasoning: Toward a theoretical framework for research. In F. K. Lester, Jr. (Ed.), Second handbook of research on mathematics teaching and learning (pp. 629–668). Information Age Publishing.

Lawton, C. A. (1993). Contextual factors affecting errors in proportional reasoning. Journal for Research in Mathematics Education, 24(5), 460-466. https://doi.org/10.2307/749154

Lesh, R., Post, T., & Behr, M. (1988). Proportional reasoning. In J. Hiebert & M. Behr (Eds.), Number concepts and operations in the middle grades (pp. 93-118). Lawrence Erlbaum & National Council of Teachers of Mathematics.

Lim, K. (2009). Burning the candle at just one end: Using nonproportional examples helps students determine when proportional strategies apply. Mathematics Teaching in the Middle School, 14(8), 492–500. https://doi.org/10.5951/MTMS.14.8.0492

Mersin, N. (2018). An evaluation of proportional reasoning of middle school 5th, 6th and 7th grade students according to a two-tier diagnostic test. Cumhuriyet International Journal of Education, 7(4), 319–348. https://doi.org/10.30703/cije.4266271

Ministry of National Education [MoNE], (2018). Matematik dersi öğretim programı. (İlkokul ve Ortaokul 1, 2, 3, 4, 5, 6, 7 ve 8. Sınıflar) [Mathematics curriculum. (Primary and Middle Schools 1, 2, 3, 4, 5, 6, 7 and 8th Grades) [Middle school mathematics curricula for grades 5, 6, 7, and 8)]. https://mufredat.meb.gov.tr/ProgramDetay.aspx?PID=329

Mueller, R. O., & Hancock, G. R. (2001). Factor analysis and latent structure: Confirmatory factor analysis. In N. J. Smelser & P. B. Baltes (Eds.), International Encyclopedia of the Social and Behavioral Sciences (pp. 5239-5244). Pergamon.

National Council of Teachers of Mathematics (NCTM) (2000). Principles and Standards for School Mathematics. National Council of Teachers of Mathematics.

Ozuru, Y., Briner, S., Kurby, C. A., & McNamara, D. S. (2013). Comparing comprehension measured by multiple-choice and open-ended problems. Canadian Journal of Experimental Psychology, 67(3), 215-227. https://doi.org/10.1037/a0032918

Özgün-Koca, S. A., & Altay, M. K. (2009). An investigation of proportional reasoning skills of middle school students. Investigations in Mathematics Learning, 2(1), 26-48. https://doi.org/10.1080/24727466.2009.11790289

Pelen, M. S., & Dinç-Artut, P. (2015). 7th grade students’problem solving success rates on proportional reasoning problems. The Eurasia Proceedings of Educational and Social Sciences, 2, 96-100. https://doi.org/10.21890/ijres.71245

Peterson, R. F., Treagust, D. F., & Garnett, P. (1986). Identification of secondary students' misconceptions of covalent bonding and structure concepts using a diagnostic test instrument. Research in Science Education, 16, 40 48. https://doi.org/10.1007/BF02356816

Post, T. R., Behr, M. J., & Lesh, R. (1988). Proportionality and the development of pre-algebra understandings. In A. Coxford & A. Shulte (Eds.), The ideas of algebra, K-12 (pp. 78-90). National Council of Teachers of Mathematics.

Reja, U., Manfreda, K. L., Hlebec, V., & Vehovar, V. (2003). Open-ended vs. close-ended questions in web questionnaires. In A. Ferligoj & A. Mrvar (Eds.), Developments in applied statistics (pp. 159–177). FDV.

Rudner, L. M., & Shafer, W. D. (2002). What teachers need to know about assessment. National Education Association.

Singh, P. (2000). Understanding the concepts of proportion and ratio constructed by two grade six students. Educational Studies in Mathematics, 43, 271 292. https://doi.org/10.1023/A:1011976904850

Soyak, O., & Isiksal, M. (2017, February). Middle school students’ difficulties in proportional reasoning. Paper Presented at the CERME 10, Dublin, Ireland.

Suhr, D. (2006). Exploratory or confirmatory factor analysis. SAS Users Group International Conference (pp. 1- 17). SAS Institute, Inc.

Tabachnick, B. G., & Fidell, L. S. (2013). Using multivariate statistics. Pearson.

Tamir, P. (1989). Some issues related to the use of justifications to multiple-choice answers. Journal of Biological Education, 23(4), 285 292. https://doi.org/10.1080/00219266.1989.9655083

Tamir, P. (1990). Justifying the selection of answers in multiple choice items. International Journal of Science Education, 12(5), 563 573. https://doi.org/0.1080/0950069900120508

Tourniaire, F., & Pulos, S. (1985). Proportional reasoning: A review of the literature. Educational Studies in Mathematics, 16(2), 181 204. https://doi.org/10.1007/BF02400937

Tsui, C. Y., & Treagust, D. (2010). Evaluating secondary students’ scientific reasoning in genetics using a two‐tier diagnostic instrument. International Journal of Science Education, 32(8), 1073-1098. https://doi.org/10.1080/09500690902951429

Van De Walle, J. A., Karp, K. S., & Bay-Williams, J. M. (2013). Elementary and middle school mathematics: teaching developmentally. Pearson Education, Inc.

Van Dooren, W., De Bock, D., Hessels, A., Janssens, D., & Verschaffel, L. (2005). Not everything is proportional: Effects of age and problem type on propensities for over generalization. Cognition and Instruction, 23(1), 57 86. https://doi.org/10.1207/s1532690xci2301_3

Van Dooren, W., De Bock, D., & Verschaffel, L. (2010). From addition to multiplication and back: The development of students’ additive and multiplicative reasoning skills. Cognition and Instruction, 28, 360–381. https://doi.org/10.1080/07370008.2010.488306

Weinberg, S. L. (2002). Proportional reasoning: One problem, many solutions! In B. Litwiller (Eds.), Making sense of fractions, ratios, and proportions: 2002 year book (pp. 138-144). National Council of Teachers of Mathematics.

Wells, C. S., & Wollack, J. A. (2003). An instructor’s guide to understanding test reliability. Testing & Evaluation Services. University of Wisconsin. http://testing.wisc.edu/Reliability.pdf.

Developing a Two-Tier Proportional Reasoning Skill Test: Validity and Reliability Studies

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