published_or_final_version / Education / Master / Master of Education

This study compared the estimates of reliability made using one, two, three, four, five, and unlimited consecutive failures as ceiling rules in scoring a mathematics achievement test which is part of the Iowa Tests of Basic Skill (ITBS), Form 8. There were 700 students randomly selected from a population (N=2640) of students enrolled in the eight grades in a large urban school district in the southwestern United States. These 700 students were randomly divided into seven subgroups so that each subgroup had 100 students. The responses of all those students to three subtests of the mathematics achievement battery, which included mathematical concepts (44 items), problem solving (32 items), and computation (45 items), were analyzed to obtain the item difficulties and a total score for each student. The items in each subtest then were rearranged based on the item difficulties from the highest to the lowest value. In each subgroup, the method using one, two, three, four, five, and unlimited consecutive failures as the ceiling rules were applied to score the individual responses. The total score for each individual was the sum of the correct responses prior to the point described by the ceiling rule. The correct responses after the ceiling rule were not part of the total score. The estimate of reliability in each method was computed by alpha coefficient of the SPSS-X. The results of this study indicated that the estimate of reliability using two, three, four, and five consecutive failures as the ceiling rules were an improvement over the methods using one and unlimited consecutive failures.

Since the 1960s, the advocacy of teaching mathematics so as to be useful is not without hindrance in school curricula, partly due to the lack of appropriate assessment tools. Practical approaches have been accumulating quickly, but researchers showed that they are not satisfactory in testing students’ ability to apply mathematical knowledge, be they “word problems” in school textbooks, national tests, or large-scale international assessments. To understand the causes behind the dissatisfaction, there is a need to reveal (1) the theories that are used in the test designs, and (2) what the actual assessments are in various curricula. This motive leads to the purpose of the current study, which is to identify empirically consistent theories about students’ ability to apply; the results can be organized as a framework to analyze assessment tools such as PISA, as well as various curricular materials. Based on the current theories, a framework of assessment analysis is created in order to study the coverage of modeling steps of public assessment items. This study finds that, though many education systems have claims of introducing modeling and application into their curricula, high-stake assessments mostly involve a small fraction of the steps that are required in a full modeling cycle. It furthers an earlier result that certain textbooks, though claiming the importance of modeling, almost ignored the first and last steps of modeling. It is found in this study that public assessments are even more limited: most test items that are supposed to test students’ knowledge of application involve only one or two steps of modeling. Furthermore, the tool “modeling spectrum” that is used in the analysis does not only reveal how modeling steps are covered, but can also assists educators to improve or create problems with modeling and application.

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The Department of Mathematics of the Florida State University gives a mathematics placement test to each entering freshman. This study examines relationships between the scores attained on the mathematics placement test, other tests measuring ability and achievement, and academic success as reflected by grades earned in University classes. The sample for this study is composed of the students who took the placement test as first-time freshmen in the 1953 summer session, the 1953 fall semester, and the 1954 spring semester. This group was selected because its members have had time to complete a four-year program leading to the baccalaureate degree. / Typescript. / "August, 1958." / "Submitted to the Graduate Council of Florida State University in partial fulfillment of the requirements for the degree of Master of Science." / Advisor: Dwight B. Goodner, Professor Directing Paper. / Includes bibliographical references (leaves 55-56).

It was with an idea of establishing a tool to aid in vocabulary growth that E. L. Bellhorn, Ft. Lauderdale, Florida, and the writer, during the summer quarter of 1948 at Florida State University, built a test for ability to recognize and to apply algebraic language. Realizing their inexperience in such an important matter as developing a testing device which would meet the requirements of highly specialized experts in the field of testing, they took no credit in attempting to devise new techniques or devices, but followed rather slavishly the steps in procedure in good test construction. This study grew out of the desire to improve the test items to answer such questions as: 1. how much is student performance affected by the inability to recall an exact word at a specific instant? 2. Can the student choose the right word when it is coupled with a wrong one? 3. What would be the effect if the range of choice of response-words is increased? 4. What would happen if non-verbal items are introduced? / Typescript. / "August, 1950." / "Submitted to the Graduate Council of Florida State University in partial fulfillment of the requirements for the degree of Master of Science." / Includes bibliographical references (leaves 62-64).

This study is an investigation of the performance of a discrete latent state model devised by Paulson (1982) to account for signed-number arithmetic test data gathered by Birenbaum and Tatsuoka (1980). One hundred twenty nine students took a test which consists of sixteen item types with four parallel arithmetic items of each type. The present study utilizes the five addition item types of four items each; hence, there are four parallel subtests. Responses to the addition items can be analyzed in terms of two components: the siqn component (is the sign correct?), and the absolute value component (is the size of the answer correct?). Paulson's model describes how students perform on the two components separately and how the component responses are related. This study examines the parallelism of the four subtests, in terms of equality of means, standard deviations, and correlations between all pairs of subtests. Decision consistency between subtests is another useful indicator of measurement reliability, particularly for tests of concept mastery. The model implies that the consistency between any two pairs of subtests should be equal; this implication is tested. The specific numerical values predicted by the model for the means, standard deviations, correlations, and decision consistency indices are tested against the corresponding observed statistics. All the analyses described so far are done separately for both the sign and the absolute value components of the responses. A method to synthesize overall correct response from estimated parameter values of two components is derived and tested against observed values. The results are that "parallel" items within item types are not all parallel and finer characterization would be needed to describe the items completely. However, the deviations from strict parallelism are slight. Paulson's model demonstrates good predictive ability; on both components and on the overall responses. Most of the deviations from the prediction can be attributed to not strictly parallel subtests and estimated parameter values not being the best possible estimates.

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