This study investigated the effects of teaching middle school students with mathematics disabilities equivalent fraction concepts and procedures using the concrete-representational-abstract (CRA) instructional sequence or the representational-abstract (RA) instructional sequence. Twenty-six students formed the CRA group, and 24 students formed the RA group. The two treatment groups received carefully sequenced instruction over 10 lessons. The only difference between the two treatment groups was that the CRA group used concrete manipulative devices for the first three lessons while the RA group used representational drawings. Analyses of the data indicated that students in both treatment groups improved overall in their understanding of fraction equivalency from pretest to posttest. On all achievement measures, students in the CRA group had overall higher mean scores than did students in the RA group. Implications for classroom instruction and suggestions for further research are discussed.

This study examined the validity of two item-writing rules in the design of test items: (a) the desirable number of options for a multiple-choice test item and (b) use of the inclusive none of these option. An experimental repeated measures design found that items with three options were more difficult than those with four options and items employing the none of these option were more difficult than those not using this inclusive option format. Neither format manipulation affected item discrimination. Therefore, evidence allows no recommendation for the none of these option but suggests an advantage for multiple-choice items with fewer than the traditional four or five options.

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Various item selection techniques are compared on resultant criterionreferenced reliability and validity. Techniques compared include three nominal criterion-referenced methods, a traditional point biserial selection, teacher selection, and random selection.Eighteen volunteer junior and senior high school teachers supplied behavioral objectives and item pools ranging from 26 to 40 items. Each teacher obtained reponses from four classes. Pairs of tests of various length were developed by each item selection method. Estimates of test reliability and validity were obtained using responses independent of the test construction sample. Resultant reliability and validity estimates were compared across item selection techniques. Two of the criterion-referenced item selection methods resulted in consistently higher observed validity. However, the small magnitude of improvement over teacher or random selection raises a question as to whether the benefit warrants the necessary extra effort on the part of the classroom teacher.Glaser and Nitko (1971) define a criterion-referenced measure (CRM) as "'one that is deliberately constructed so as to yield measurements that are directly interpretable in terms of specified performance standards." A CRM differs from the more familiar norm-referenced measure (NRM) in that interpretation of the latter depends on performance relative to other individuals rather than on an a priori criterion.Popham and Husek (1969) point out the limitations of norm-referenced measurement techniques for the development and evaluation of CRMs. Their major criticism is the dependence of norm-referenced measurement on score variability; e.g., most normreferenced techniques of estimating test reliability and validity are directly related to score variability. However, a "good" CRM administered after adequate instruction may result in very low score variation. Since this test would fail to satisfy usual normreferenced standards of reliability and validity, new criterion-referenced concepts of reliability and validity are necessary.Popham and Husek also question the interpretation of traditional norm-referenced item discrimination indices for use in criterion-referenced item selection. Typical norm-referenced item discrimination indices relate item score to total test score. An item with a low discrimination index on a NRM is suspect. However, in criterionreferenced measurement, if an item accurately measures an essential behavior and all examinees respond correctly (or incorrectly), the item cannot be faulted.A mastery test is a CRM used in formative evaluation. The mastery test is designed to measure the essential behaviors associated with each unit of instruction. Given following instruction, the mastery test allows for a dichotomous decision regarding the student's mastery status and identifies the deficiencies of the student below criterion. The student demonstrating mastery would go on to the next unit of instruction while tThis paper is based on the author's Ph.D. dissertation submitted to the faculty of...

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