Construction Versus Choice in Cognitive Measurement: Issues in Constructed Response, Performance Testing, and Portfolio Assessment

By Randy Elliot Bennett; William C. Ward | Go to book overview

A theory of item construction was introduced in conjunction with K. Tatsuoka's ( 1991) work in Boolean algebra. If a subset of attributes has a connected, directed relation and forms a chain, then the number of combinations of "can/cannot" attributes will be reduced dramatically. Thus, it will become easier for us to construct a pool of items by which a particular group of misconceptions of concern can be diagnosed with a minimum of classification errors.

One of the advantages of the rule space model ( K. Tatsuoka, 1983, 1990) is that the model relates a scaled ability parameter 8 to misconception states. For a given misconception state, one can always identify the particular types of errors that relate to ability level θ. If the centroid of the state is located in the upper part of the rule space, then one can conclude that this type of error is rare. If the centroid lies on the θ axis, then this error type is observed very frequently.

Although rule space was developed in the context of binary IRT models, the concept and mathematics are general enough to be extended for use in more complicated IRT models. Further work to extend the rule space concept to accommodate complicated response models will be left for future research.


ACKNOWLEDGMENTS

The author gratefully acknowledges and thanks several people for their help: Randy Bennett, Robert Mislevy, Kathy Sheehan, Maurice Tatsuoka, and Bill Ward for valuable comments and suggestions, John Cordery for editorial help, and Donna Lembeck for various help.


REFERENCES

Bennett R. E., Rock D. A., Braun H. I., Frye D., Spohrer J. C., & Soloway E. ( 1990). The relationship of constrained free-response to multiple-choice and open-ended items. Applied Psychological Measurement, 14, 151-162.

Bennett R. E., Sebrechts M. M., & Yamamoto K. (in press). Fitting new measurement models to GRE General Test constructed-response item data. Princeton, NJ: Educational Testing Service.

Bennett R. E., Ward W. C., Rock D. A., & LaHart C. ( 1990). Toward a framework for constructed- response items (RR-90-7). Princeton, NJ: Educational Testing Service.

Birenbaum M., & Shaw D. J. ( 1985). "Task Specification Chart: A key to better understanding of test results". Journal of Educational Measurement, 22, 219-230.

Birenbaum M., & Tatsuoka K. K. ( 1987). Open-ended versus multiple-choice response formats--It does make a difference for diagnostic purposes. Applied Psychological Measurement, 11, 329-341.

Bock R. D. ( 1972). Estimating item parameters and latent ability when the responses are scored in two or more nominal categories. Psychometrika, 37, 29-51.

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