TY  - JOUR
T1  - A diagnostic assessment to middle school students’ proportional reasoning
TT  - Ortaokul öğrencilerinin orantısal akıl yürütmeleri üzerine tanısal bir değerlendirme
AU  - Arıcan, Muhammet
PY  - 2019
DA  - October
Y2  - 2019
DO  - 10.19128/turje.522839
JF  - Turkish Journal of Education
JO  - TURJE
PB  - Mehmet TEKEREK
WT  - DergiPark
SN  - 2147-2858
SP  - 237
EP  - 257
VL  - 8
IS  - 4
LA  - en
AB  - This study investigated Turkish middle school students’ proportionalreasoning and provided a diagnostic assessment of their strengths andweaknesses on the ratio and proportion concepts. A proportional reasoning testwith 22 multiple-choice items was developed from the context of the log-linearcognitive diagnosis model. The test was developed around four core cognitiveskills (attributes) that required in solving middle school ratio and proportionproblems. These skills included understanding ratios, directly, inversely, andnonproportional relationships. The test was applied to 282 seventh gradestudents, and the collected data were analyzed using the Mplus software. Theanalysis showed that approximately 62% of the students were able to recognizedirectly proportional relationships. Whereas, roughly 48% of them were able torecognize inversely proportional relationships. Moreover, while 25% of thestudents did not master any of the four cognitive skills, 39.1% mastered allfour of these skills. In addition, many students had difficulty distinguishingproportional relationships from nonproportional relationships. Diagnosticfeedbacks on the students’ strengths and weaknesses were provided based on thefindings.
KW  - Diagnostic assessment
KW  - Diagnostic classification models
KW  - Middle school students
KW  - Ratios and proportions
KW  - Proportional reasoning
N2  - Bu çalışmada ortaokulöğrencilerinin orantısal akıl yürütmeleri araştırılmış ve oran ve orantıkonuları için güçlü ve zayıf yönlerinin bilişsel bir tanısal değerlendirmesisağlanmıştır. Yirmi iki çoktan seçmeli madde içeren bir orantısal akıl yürütmetesti log-linear bilişsel tanı modeli perspektifinden faydalanılarakgeliştirilmiştir. Test, ortaokul öğrencilerinin oran ve orantı problemleriniçözmeleri için gerekli olan dört temel bilişsel beceri etrafında tasarlanmıştır.Bu beceriler sırasıyla oran, doğru orantılı ilişki, ters orantılı ilişki veorantısal olmayan ilişki kavramlarını anlamayı içermektedir. Test 282 yedincisınıf öğrencisine uygulanmış ve toplanan veriler Mplus yazılımı kullanılarakanaliz edilmiştir. Yapılan analizler neticesinde öğrencilerin en çok (yaklaşık62%) doğru orantılı ilişkileri tanıma becerisine ve en az (yaklaşık 48%) tersorantılı ilişkileri tanıma becerisine sahip oldukları görülmüştür. Ayrıca,öğrencilerin 25%’inin dört temel becerinin hiçbirisine sahip olmadıkları,39,1%’inin ise bütün becerilere sahip oldukları görülmüştür. Bunlara ek olarak,pek çok öğrencinin orantısal ilişkileri orantısal olmayanlardan ayırt etmedezorlandıkları görülmüştür. Elde edilen bulgular yorumlanarak öğrencilerin güçlüve zayıf yönleri ile ilgili tanısal geri bildirimler verilmiştir.
CR  - Arican, M. (2018). Preservice middle and high school mathematics teachers’ strategies when solving proportion problems. International Journal of Science and Mathematics Education, 16(2), 315–335. DOI: 10.1007/s10763-016-9775-1
CR  - Arican, M. (2019). Preservice mathematics teachers’ understanding of and abilities to differentiate proportional relationships from nonproportional relationships. International Journal of Science and Mathematics Education, 17(7), 1423–1443. DOI: 10.1007/s10763-018-9931-x
CR  - Arican, M., & Kuzu, O. (2019). Diagnosing preservice teachers’ understanding of statistics and probability: Developing a test for cognitive assessment. International Journal of Science and Mathematics Education, 1–20. DOI: 10.1007/s10763-019-09985-0
CR  - Atabas, S., & Oner, D. (2017). An examination of Turkish middle school students’ proportional reasoning. Boğaziçi University Journal of Education, 33(1), 63–85.
CR  - Ayan, R., & Isiksal-Bostan, M. (2018). 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, 1–17. DOI: 10.1080/0020739X.2018.1468042
CR  - Beckmann, S. (2011). Mathematics for elementary teachers (3rd. ed.). Boston, MA: Pearson.
CR  - Bradshaw, L., & Cohen, A. (2010). Accuracy of multidimensional item response model parameters estimated under small sample sizes. In A. Izsák (Chair), Using cognitive attributes to develop mathematics assessments, opportunities, and challenges. Symposium conducted at the annual American Educational Research Association conference in Denver, CO.
CR  - Bradshaw, L., Izsak, A., Templin, J., & Jacobson, E. (2014). Diagnosing teachers’ understandings of rational numbers: Building a multidimensional test within the diagnostic classification framework. Educational Measurement: Issues and Practice, 33(1), 2–14. DOI: 10.1111/emip.12020
CR  - Choi, K. M., Lee, Y. S., & Park, Y. S. (2015). What CDM can tell about what students have learned: An analysis of TIMSS eighth grade mathematics. Eurasia Journal of Mathematics, Science & Technology Education, 11(6), 1563–1577. DOI: 10.12973/eurasia.2015.1421a
CR  - Common Core State Standards Initiative. (2010). The common core state standards for mathematics. Washington, D.C.: Author.
CR  - Cramer, K., & Post, T. (1993). Making connections: A case for proportionality. Arithmetic Teacher, 60(6), 342–346.
CR  - Cramer, K., Post, T., & Currier, S. (1993). Learning and teaching ratio and proportion: Research implications. In D. Owens (Ed.), Research ideas for the classroom: Middle grades mathematics (pp. 159–178).	New York, NY: Macmillan.
CR  - De Bock, D., Verschaffel, L., & Janssens, D. (1998). The predominance of the linear model in secondary school students’ solutions of word problems involving length and area of similar plane figures. Educational Studies in Mathematics, 35(1), 65–83. DOI: 10.1023/A:1003151011999
CR  - Degrande, T., Van Hoof, J., Verschaffel, L., & Van Dooren, W. (2017). Open word problems: Taking the additive or the multiplicative road? ZDM, 50(1), 1–12. DOI: 10.1007/s11858-017-0900-6
CR  - de la Torre, J. (2008). An empirically based method of Q‐matrix validation for the DINA model: Development and applications. Journal of Educational Measurement, 45(4), 343–362. DOI: 10.1111/j.1745-3984.2008.00069.x
CR  - de la Torre, J. (2011). The generalized DINA model framework. Psychometrika, 76(2), 179–199. DOI: 10.1007/s11336-011-9207-7
CR  - DiBello, L. V., Stout, W. F., & Roussos, L. A. (1995). Unified cognitive/psychometric diagnostic assessment likelihood–based classification techniques. In P. Nichols, S. Chipman, & R. Brennan (Eds.), Cognitively diagnostic assessment (pp. 361–390). Hillsdale, NJ: Lawrence Erlbaum.
CR  - Dogan, E., & Tatsuoka, K. (2008). An international comparison using a diagnostic testing model: Turkish students’ profile of mathematical skills on TIMSS–R. Educational Studies in Mathematics, 68(3), 263–272. DOI: 10.1007/s10649-007-9099-8
CR  - Fisher, L. C. (1988). Strategies used by secondary mathematics teachers to solve proportion problems. Journal for Research in Mathematics Education, 19(2), 157–168.
CR  - Hartz, S. (2002). A Bayesian framework for the Unified Model for assessing cognitive abilities: Blending theory with practice (Unpublished doctoral dissertation). University of Illinois at Urbana–Champaign.
CR  - Henson, R., & Douglas, J. (2005). Test construction for cognitive diagnostics. Applied Psychological Measurement, 29(4), 262–277. DOI: 10.1177/0146621604272623
CR  - Henson, R., Roussos, L., Douglas, J., & He, X. (2008). Cognitive diagnostic attribute–level discrimination indices. Applied Psychological Measurement, 32(4), 275–288. DOI: 10.1177/0146621607302478
CR  - Henson, R., Templin, J., & Willse, J. (2009). Defining a family of cognitive diagnosis models using log–linear models with latent variables. Psychometrika, 74(2), 191–210. DOI: 10.1007/s11336-008-9089-5
CR  - Huebner, A. (2010). An overview of recent developments in cognitive diagnostic computer adaptive assessments. Practical Assessment, Research & Evaluation, 15(3), 1–7.
CR  - Im, S., & Park, H. J. (2010). A comparison of US and Korean students’ mathematics skills using a cognitive diagnostic testing method: Linkage to instruction. Educational Research and Evaluation, 16(3), 287–301. DOI: 10.1080/13803611.2010.523294
CR  - Izsák, A., & Jacobson, E. (2017). Preservice teachers’ reasoning about relationships that are and are not proportional: A knowledge-in-pieces account. Journal for Research in Mathematics Education, 48(3), 300–339. DOI: 10.5951/jresematheduc.48.3.0300
CR  - Junker, B. W., & Sijtsma, K. (2001). Cognitive assessment models with few assumptions, and connections with nonparametric item response theory. Applied Psychological Measurement, 25(3), 258–272. DOI: 10.1177/01466210122032064
CR  - Jurich, D. P., & Bradshaw, L. P. (2014). An illustration of diagnostic classification modeling in student learning outcomes assessment. International Journal of Testing, 14(1), 49–72. DOI: 10.1080/15305058.2013.835728
CR  - Kilpatrick, J., Swafford, J., & Findell, B. (2001). Adding it up: Helping children learn mathematics. Washington, DC: National Academy Press.
CR  - Kuzu, O. (2017). Matematik ve fen bilgisi öğretmen adaylarının integral konusundaki kazanımlarının incelenmesi. Ahi Evran Üniversitesi Kırşehir Eğitim Fakültesi Dergisi, 18(3), 948–970. DOI: 10.29299/kefad.2017.18.3.049
CR  - Lamon, S. (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 (Vol 1, pp. 629–667). Charlotte, NC: Information Age Publishing.
CR  - Lee, Y. S., Park, Y. S., & Taylan, D. (2011). A cognitive diagnostic modeling of attribute mastery in Massachusetts, Minnesota, and the US national sample using the TIMSS 2007. International Journal of Testing, 11(2), 144–177. DOI: 10.1080/15305058.2010.534571
CR  - Lei, P. W., & Li, H. (2016). Fit indices’ performance in choosing cognitive diagnostic models and Q-matrices. Paper presented at the annual meeting of the National Council on Measurement in Education (NCME), Philadelphia, PA.
CR  - 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). Reston, VA: National Council of Teachers of Mathematics.
CR  - 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.
CR  - Milli Eğitim Bakanlığı (2018). Matematik dersi öğretim programı (1, 2, 3, 4, 5, 6, 7 ve 8. Sınıflar) [Mathematics curriculum (1, 2, 3, 4, 5, 6, 7, and 8. Grades]. Ankara: Talim ve Terbiye Kurulu Başkanlığı.
CR  - Misailadou, C., & Williams, J. (2003). Measuring children’s proportional reasoning, the “tendency” for an additive strategy and the effect of models. In N. A. Pateman, B. J. Dougherty, & J. T. Zilliox (Eds.), Proceedings of the 27th Conference of the International Group for the Psychology of Mathematics Education (Vol. 3, pp. 293–300). Honolulu, HI: University of Hawaii.
CR  - Modestou, M., & Gagatsis, A. (2007). Students’ improper proportional reasoning: A result of the epistemological obstacle of “linearity”. Educational Psychology, 27(1), 75–92. DOI: 10.1080/01443410601061462
CR  - Muthen, L. K., & Muthen, B. O. (2011). Mplus user’s guide (6th ed.). Los Angeles, CA: Muthen & Muthen.
CR  - National Council of Teachers of Mathematics (2000). Principles and standards for school mathematics. Reston, VA: Author.
CR  - Ranjbaran, F., & Alavi, S. M. (2017). Developing a reading comprehension test for cognitive diagnostic assessment: A RUM analysis. Studies in Educational Evaluation, 55, 167–179. DOI: 10.1016/j.stueduc.2017.10.007
CR  - Ravand, H., & Robitzsch, A. (2015). Cognitive diagnostic modeling using R. Practical Assessment, Research & Evaluation, 20(11), 1–12.
CR  - Ravand, H., & Robitzsch, A. (2018). Cognitive diagnostic model of best choice: A study of reading comprehension. Educational Psychology, 38(10), 1255–1277. DOI: 10.1080/01443410.2018.1489524
CR  - R Core Team. (2017). R: A language and environment for statistical computing. Vienna, Austria: R Foundation for Statistical Computing. Retrieved from http://www.R–project.org/
CR  - Rupp, A., & Templin, J. (2008). Effects of Q–matrix misspecification on parameter estimates and misclassification rates in the DINA model. Educational and Psychological Measurement, 68(1), 78–98. DOI: 10.1177/0013164407301545
CR  - Rupp, A., Templin, J., & Henson, R. A. (2010). Diagnostic measurement: Theory, methods, and applications. Guilford Press.
CR  - Satorra, A., & Bentler, P. M. (2010). Ensuring positiveness of the scaled difference chi–square test statistic. Psychometrika, 75(2), 243–248. DOI: 10.1007/s11336-009-9135-y
CR  - Sen, S., & Arican, M. (2015). A diagnostic comparison of Turkish and Korean students’ mathematics performances on the TIMSS 2011 assessment. Journal of Measurement and Evaluation in Education and Psychology, 6(2), 238–253. DOI: 10.21031/epod.65266
CR  - Stemn, B. S. (2008). Building middle school students’ understanding of proportional reasoning through mathematical investigation. Education 3–13, 36(4), 383–392. DOI: 10.1080/03004270801959734
CR  - Tatsuoka, K. (1985). A probabilistic model for diagnosing misconceptions by the pattern classification approach. Journal of Educational Statistics, 10(1), 55–73. DOI: 10.3102/10769986010001055
CR  - Templin, J. (2008). Test construction item discrimination. Lecture presented at the Diagnostic Modelling Seminar at the University of Georgia, Athens. Retrieved from https://jonathantemplin.com/files/dcm/ersh9800f08/ersh9800f08_lecture11.pdf
CR  - Templin, J., & Bradshaw, L. (2013). Measuring the reliability of diagnostic classification model examinee estimates. Journal of Classification, 30(2), 251–275. DOI: 10.1007/s00357-013-9129-4
CR  - Templin, J., & Henson, R. (2006). Measurement of psychological disorders using cognitive diagnosis models. Psychological Methods, 11(3), 287–305. DOI: 10.1037/1082-989X.11.3.287
CR  - Terzi, R., & Sen, S. (2019). A nondiagnostic assessment for diagnostic purposes: Q-matrix validation and item-based model fit evaluation for the TIMSS 2011 assessment. SAGE Open, 1–11. DOI: 10.1177/2158244019832684
CR  - Toker, T., & Green, K. (2012). An application of cognitive diagnostic assessment on TIMMS–2007 8th grade mathematics items. Paper presented at the annual meeting of the American Educational Research Association, Vancouver, British Columbia, Canada.
CR  - 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 overgeneralization. Cognition and Instruction, 23(1), 57–86. DOI: 10.1207/s1532690xci2301_3
CR  - Van Dooren, W., De Bock, D., Janssens, D., & Verschaffel, L. (2007). Pupils’ overreliance on linearity: A scholastic effect? British Journal of Educational Psychology, 77(2), 307–321. DOI: 10.1348/000709906X115967
CR  - von Davier, M. (2005). A general diagnostic model applied to language testing data. ETS Research Report. Princeton, NJ: Educational Testing Service.
CR  - Werner, C., & Schermelleh-Engel, K. (2010). Deciding between competing models: Chi–square difference tests. In Introduction to Structural Equation Modeling with LISREL (pp. 1–3). Frankfurt, Germany: Goethe University.
UR  - https://doi.org/10.19128/turje.522839
L1  - https://dergipark.org.tr/en/download/article-file/832383
ER  -