Research on mathematics education often includes some experimental manipulation of instruction in order to compare the effects of one type of instruction with that of one or more others. Tracking students' progress during treatments may be difficult in studies with special populations where numbers of participants are sometimes very small. In this study, we illustrate a method for scaling and reporting test results that helps to overcome this problem, particularly when number-correct scoring is used on measures to assess treatment effectiveness. Results are compared for an instructional experiment with remedial and nonremedial students using a number-correct scoring and a standardized score scale developed using item response theory (IRT).
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References
1.
BakerF. B. (1992). Item response theory: Parameter estimation techniques. New York: Marcel Dekker.*
2.
BottgeB.HeinrichsM.ChanS. Y.WatsonE. A. (2000). Integrating math knowledge of low-achieving students. Madison, WI: University of Wisconsin, Wisconsin Center for Education Research.*
3.
ChangH. H.MazzeoJ. (1994). The unique correspondence of the item response function and item category response functions in polytomously scored item response models. Psychometrika, 59 (3), 391.
4.
CookL.EignorD. (1989). Using item response theory in test score equating. International Journal of Educational Research, 13, 161.
5.
CookL. L.PetersonN. S. (1987). Problems related to the use of conventional and item response theory equating methods in less than optimal circumstances. Applied Psychological Measurement, 11, 225–244.
6.
GoldmanS. R.HasselbringT. S., & The Cognition and Technology Group at Vanderbilt. (1997). Achieving meaningful mathematics literacy for students with learning disabilities. Journal of Learning Disabilities, 30, 198–208.
7.
GulliksenH. (1950). Theory of mental tests. New York: Wiley.*
HattieJ. (1985). Methodology review: Assessing unidimensionality of tests and items. Applied Psychological Measurement, 9 (2), 139–164.
10.
JohnsonE.KimballK.BrownS. O.AndersonD. (2001). A statewide review of the use of accommodations in large-scale, high-stakes assessments. Exceptional Children, 67, 251–264.
11.
KimS. H.CohenA. S. (1998a). Detection of differential item functioning under the graded response model with the likelihood ratio test. Applied Psychological Measurement, 22 (4), 345–355.
12.
KimS. H.CohenA. S. (1998b). A comparison of linking and concurrent calibration under item response theory. Applied Psychological Measurement, 22 (2), 131–143.
13.
KolenM. J. (1988). An NCME instructional module on traditional equating methodology. Educational Measurement: Issues and Practice, 7, 29–36.
14.
LordF. M. (1980). Applications of item response theory to practical testing problems. Mahwah, NJ: Erlbaum.*
15.
LordF. M.NovickM. R. (1968). Statistical theories of mental test scores. Reading, MA: Addison-Wesley.*
16.
MayerR. E. (1993). Understanding individual differences in mathematical problem solving: Towards a research agenda. Learning Disabilities Quarterly, 16, 2–5.
17.
MillerS. P.MercerC. D. (1993). Using data to learn about concrete-semiconcrete-abstract instruction for students with math disabilities. Learning Disabilities Research and Practice, 8, 89–96.
18.
MortweetS. L.UtleyC. A.WalkerD.DawsonH. L.DelquadriJ. C.ReddyS. S.GreenwoodC. R.HamiltonS.LedfordD. (1999). Classwide peer tutoring: Teaching students with mild mental retardation in inclusive classrooms. Exceptional Children, 65, 524–536.
19.
PineS. M. (October 1976). Application of item characteristic curve theory to the problem of test bias. In WeissD. J. (Ed.), Application of computerized adaptive testing: Proceedings of a symposium presented at the 18th annual convention of the Military Testing Association (Research Rep. No. 77–1, pp. 37–43). Minneapolis: University of Minnesota, Department of Psychology, Psychometric Methods Program. (ERIC Document Reproduction Service No. ED 137 360).
20.
ReckaseM. (1979). Unifactor latent trait models applied to multifactor tests: Results and implications. Journal of Educational Statistics, 4 (3), 207.
21.
SamejimaF. (1969). Estimation of ability using a response pattern of graded scores. Psychometrika Monograph, No. 17.*
22.
SamejimaF. (1972). A general model for free-response data. Psychometrika Monograph, No. 18.
23.
SamejimaF. (1997). Graded response model. In van der LindenW. J.HambletonR. K. (Eds.), Handbook of modern item response theory (pp. 85–100). New York: Springer.*
24.
ThissenD. (1991). MULTILOG user's guide: Multiple categorical item analysis and test scoring using item response theory [computer program]Chicago: Scientific Software International.*
25.
XinY. P.JitendraA. K. (1999). The effects of instruction in solving mathematical word problems for students with learning problems: A meta-analysis. The Journal of Special Education, 32, 207–225.
