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This study was an exploration into the effects of four categories of extra-student variables: high school performance, demographic characteristics, Myers-Briggs personality preferences and mathematics attitudes on three measures of college mathematics achievement (a Problem-Solving Test, an Algebra Skills Final Examination and course grade for all seven classes of 175 undergraduate students taking Pre-Calculus I Fall semester 1993). High school performance explained the most variation for all measures of mathematics achievement. Demographic characteristics and mathematics attitudes do not significantly influence any measure of mathematics achievement. The Myers-Briggs Type Indicator (MBTI) preference Extravert versus Intraverts (E versus 1) was a significant predictor for the Problem-Solving Test; the Judging versus Perception a versus P) preference was a significant predictor for the Algebra Skills Final Examination, and both E versus I and J versus P were predictors for the course grade. An experimental design was used to explore four classroom variables--3 class times, 2 instructional settings, MBTI E versus I and J versus P-- in six classes. Students taking 8:00 classes averaged 9 points lower than students taking 10:00 classes and 11 points lower than students taking 1:00 classes for all measures of mathematics achievement. There was no significant difference for the two instructional settings--cooperative learning or traditional lecture--for any measure of mathematics achievement. Students who were Introverted averaged 8 points higher on the Problem-Solving Test. Students who had the Judging preference averaged 11 points higher on the Algebra Skills Final Examination and 5 points higher for the course grade. There was a significant interaction (p<.01) for the Problem-Solving Test of class Time x instructional setting caused by the poor performance of the 8:00 Cooperative Learning class. The interaction of E versus I x J versus P or the EIJP learning styles was significant (p<.05) for the Algebra Skills Final Examination and course grade. The students with the IJ learning style averaged 13 to 20 points higher for scores on the Algebra Skills Final Examination and 11 points higher for scores on the course grade than students with the other three learning styles--EP, EJ and IP. / Ph. D.

Perspective and Purpose Recent investigations by Steffe, Richards, and von Glasersfeld (1979) have indicated that addition and subtraction problem-solving competencies are developmental in nature and that these competencies build upon counting abilities. They postulate that, in beginning addition and subtraction, a type of problem-solving strategy termed counting-all develops prior to another kind of strategy termed counting-on (for addition) and counting-back (for subtraction). If these tasks are developmental, one may assume that students approach the tasks in qualitatively different ways based upon their developmental levels. Neo-Piagetian researchers have postulated that a quantitative measure of development explains the qualitatively different ways in which children react to the same cognitive task at different stages of development. The measure, termed mental space or M-Space, describes the number of schemes which may be coordinated at one time. First graders, the majority of whom have an M-Space of a+2 or a+3, are capable of solving addition and subtraction word problems by utilizing the counting-all and/or the counting-on (back) strategies. Given this information, the purpose of this study was to determine what effect M-Space level has on the strategy a subject uses to solve problems when he is trained on a strategy which either matches or mismatches his M-Space level. Design To determine whether a match between M-Space and strategy demand is necessary or whether instruction will facilitate the chunking of schemes which allows the developmental task to be solved by a strategy which would otherwise be above the subject's M-Space level, the following steps occurred: one hundred thirty-nine first graders were pretested to identify those who could count to sixteen, perform numeral/number correspondence to sixteen, but could not solve addition and subtraction number fact problems to sixteen. One hundred fifteen subjects meeting these criteria were given the Cucumber Test and Backward Digit Span Test to assess their M-Space levels. After eliminating subjects before and during training, 50 subjects remained. Twenty-six subjects with an a+2 M-Space were divided into two training groups. Approximately half of the group was trained to use an a+2 strategy (the count-all strategy) to solve addition and subtraction word problems and the other half of the group was trained to use an a+3 strategy (the count-on (back) strategy). The same training procedure was used for the twenty-four subjects with an M-Space of a+3. Four to five weeks later, a delayed posttest consisting of four addition and four subtraction problems and one each of three types of transfer problems was presented. Results Mann-Whitney test results indicated that there were significantly fewer a+3 responses by the subjects with an a+2 M-Space who were trained to use an a+3 strategy than there were for subjects with an a+3 M-Space trained to use an a+3 strategy. However, there was no significant difference between those with an a+2 M-Space trained on an a+2 strategy and those with an a+2 M-Space trained on an a+3 strategy. Results of other research questions indicated that subjects gave similar responses to transfer problems which varied by material or additional variable; for subjects with an a+3 M-Space trained on an a+3 strategy, there were significantly more a+3 addition responses than subtraction responses; the implied comparison subtraction problem was answered incorrectly more often than straight take-away subtraction problems, and students tended to devise simple addition and subtraction problems and solve them by using memorized number facts. Discussion The findings indicate that more study is warranted for the application of the M-Space construct to a theory of how mathematical knowledge develops sequentially, the different ways in which addition and subtraction tasks can be conceptualized, and the instructional implications of applying a developmentally based theory of instruction to mathematics problem-solving. / Ph. D.

Historically, scheduling has not been a major concern for elementary school principals but has been viewed by many as the task of the secondary principal (Canady, 1985). Recently, however, more attention has been given to the merits of scheduling for several reasons. The purpose of this study was to determine the impact of parallel scheduling upon classroom instructional time and the scores of elementary students in language arts and mathematics. Parallel scheduling was defined as the structuring Of the school day by the principal to ensure that specialist schedules (art, music and physical education) and the support schedules (special programs for selected students) enhance rather than fragment the instructional day. This scheduling design ensured that all children received direct teacher instruction without interruption to attend a pull-out program. It also reduced the number of students in the classroom during direct instruction in reading and mathematics allowing the teacher the opportunity to provide direct instruction to 12-15 students without the presence of the remainder of the students in the classroom. This encouraged efficient and effective use of instructional time during each school day. This study was designed to address the following questions: 1. What impact, if any, does the use of parallel scheduling as compared to a regular elementary schedule have upon elementary students? 2. Does the performance level of elementary students in parallel scheduling interact with student achievement? 3. Does parallel scheduling impact classroom instructional time? To accomplish this purpose, a quasi-experimental non-equivalent control group design was used as the researcher was unable to randomly assign the participants to the pilot and control groups. Data was collected from an assigned pilot school and a control school, that had been matched based on socio-economic level, size of school, and standardized test scores. All students in grades two, four, and five in the pilot and control schools served as subjects for the study. A pre and post-test, the Metropolitan Achievement Test, was utilized to measure growth and achievement of the elementary students. Analysis of covariance was the statistical method used to determine the relationship of parallel scheduled schools and regular scheduled schools with regard to reading, language and mathematics achievement. Secondly, the Classroom Check List, designed by Jane Stallings (1977), was used to collect data relative to the type of activities that were occurring in the classroom, the size of the group involved in their activity, and whether students were working directly with the teacher or independently. The Chi-Square test was used to determine the relationship between classroom activities, size of groups, and whether students worked directly with the teacher or independently. It was determined from this study that there were significant differences in the vocabulary, word recognition, total reading, math computation and post total battery achievement scores of children in parallel scheduling as compared to children in regular scheduled schools. No relationship could be established between classroom activities, the size of student groups, nor the direct interaction with teachers and parallel scheduling. Therefore, no relationship could be established between parallel scheduling and classroom instructional time. / Ed. D.

The primary purpose of this study was to examine the extent to which age-related bias exists when ACT Mathematics test scores are used as the sole predictor of future academic performance in entry-level college mathematics courses. A secondary purpose was to investigate the extent to which academic and attitudinal variables, in conjunction with ACT Math scores, a) lessen or eliminate the age-related bias, and b) enhance the prediction of course grades and posttest scores in freshman level mathematics courses. ACT Mathematics test scores were used to predict course grades and posttest scores of students enrolled in Developmental Math and General Math classes at Bluefield State College, WV, or one of its community college components. Course grades of Developmental Math students and posttest scores of General Math students were found to be under-predicted for nontraditional-age students and over-predicted for traditional-age students. No differences were found in predictions of posttest scores for Developmental Math students or in predictions of course grades for General Math students. When attitudinal and other academic variables were introduced to the regression equation, there was less evidence of prediction bias and a significant increase in the amount of variance explained in the criterion measures. / Ed. D.

The problem of this thesis is to evaluate the progress in general reading efficiency of a group of children taught by the socialized group plan, as compared to a group of children taught by the traditional reading plan and to determine whether the socialized group plan aids in the development of certain other general attributes, such as arithmetic reasoning, arithmetic computation, and social maturity growth.

Mak, Hok Kiu Edward. / Thesis (Ed.D.)--Chinese University of Hong Kong, 2011. / Includes bibliographical references (leaves 262-276). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web.

The study reported here examined the move towards online assessments and addressed the question of whether or not different assessment tools affect student scores and student learning. The research activities covered a three-week period, from June 5, 2006 to June 23, 2006. During this time, seventeen third grade students served as their own control group by taking several math tests online and several math tests with paper and pencil. Results were compared to see if performance on computer-based tests would be more successful than pencil-and-paper tests. A follow-up survey to evaluate and interpret the quantitative results was also used. Findings revealed that 59% of the students did better on the paper tests. Further analysis revealed that the overall average of the computer tests was 71.9%, while paper tests revealed an average of 69.9%. In summary, these findings report that there is no significant difference in scores when taking a test on the computer or a test on paper. Suggestions for further research and recommendations are included.

The purposes of this study were (1) to determine the scores on the quantitative portion of the SAT for 110 students and these students' math teachers' ratings on the TTAS, (2) to determine the nature of the relationship of the students' SAT scores to their teachers' TTAS ratings, and (3) to determine the nature of the relationship of the students' SAT scores to their sex. It was hypothesized that (1) there would be no significant relationship between a student's math score as measured by the quantitative portion of the SAT and the effectiveness of the student's math teacher as measured by the TTAS, and (2) there would be no significant relationship between a student's math score as measured by the quantitative portion of the SAT and the student's sex. The 110 subjects (60 males and 50 females) In this study took the quantitative portion of the SAT during the 1986-87 school year. This sample was drawn from a large suburban high school in the North Texas area. The effectiveness of the math teachers who taught the 110 students was measured by the Texas Teachers Appraisal System (TTAS). The statistical analyses indicated that (1) there was no significant relationship between a higher SAT score and a math teacher's higher TTAS rating and (2) there was no significant relationship between male and female SAT scores. Recommendations for future research include: (1) does the TTAS actually measure teacher effectiveness, (2) do appraisers in Texas follow state mandated training procedures, (3) does the quantitative portion of the SAT contain sexually biased items, (4) does the SAT actually predict student ability, (5) do teachers respond in like manner to male and female students, (6) does the high school curriculum tend to favor one sex more than the other.

A thesis submitted in fulfilment of the requirements for the degree of DOCTOR OF PIIILOSOPHY in the SCHOOL OF SCiENCE EDUCATION (MATHEMATICS) UNIVERSITY OF THE WITWATERSRAND / Cognitive gender differences in mathematics, which were noted in past research have latterly been found to be declining. but are still observed at secondary school level in the field of spatial skills and geometry. However, due to divergent geometry curricula and the multidimensional nature of spatial skills, results from gender studies have led to broad conclusions being drawn from investigations which were affected by random elements. Research results have been influenced by imbalanced representation of the two gender groups in samples and also by differential gender exposure to previous mathematical experience. Both these limitations in research have produced outcomes reflecting negatively On females. Internationally divergent geometry curricula are a result of the traditional synthetic approach to the teaching of Euclidean geometry falling Into disfavour in western countries. Thus, Euclidean geometry has been largely overlooked in current educational research and the cognitive processes such as deductive reasoning, proof writing and hypothesis testing, have received scant attention within geometry teaching over the past decade. The standardized system in most South African secondary schools coupled with a uniform core curriculum for mathematics lends itself to an advantageous environment for empirical studies in mathematics performance. The present gender investigation involved almost an equal number of males and females from 5' selected secondary schools near Johannesburg in South Africa. Performance in Euclidean geometry was evaluated for possible gender differences by means of multiple choice and open ended questions. In keeping with most existing research, mean differences were compared. No statistically significant gender difference in mean performance on Euclidean geometry was found. Further analysis at item level was undertaken for the multiple choice component of the test instrument by means of the one dimensional three parameter logistic model in Item Response Theory, This model, is considered to be very sensitive in identifying differences at different ability levels -a shortcoming in existing research. Four out of a total of twenty Euclidean geometry items, were identified as producing differential gender performance. Similar gender tendencies were observed for all four items. The performance was in favour of most males for each of these items. Females of lower ability (as measured by the item) did not perform as well as males of similar ability level. In all four Cases females of higher ability surpassed males of a corresponding ability level. Perceptual difficulties in females were more pronounced than in males for some of the items. / AC 2018