It is well documented that students are struggling in developmental and introductory mathematics courses at community colleges across the nation. However, the reasons that these students struggle are not as well known. While numerous researchers have investigated the effects of inquiry-based learning on K-12 students, the research on this topic at the community college level is lacking. For my dissertation work, I have collected attitudinal surveys, observational data, and final exams from eight sections of a developmental mathematics course and nine sections of College Algebra at a large Texas community college. Approximately half of the instructors involved in the study incorporated some level of inquiry-based teaching strategies in their classrooms (referred to in this dissertation as “student-led” sections) while the remaining instructors employed a more direct strategy (referred to as “lecture” sections). Using this data, I investigated the relationships between teaching methods and attitudes, teaching methods and content knowledge, and attitudes and content knowledge. The evidence showed that IBL teaching strategies have a greater effect on students’ attitudes for students enrolled in a developmental mathematics course than those enrolled in College Algebra. IBL teaching strategies had no positive effects on developmental students’ performance on a skills-based final exam, but student-led sections performed just as well as lecture sections. In College Algebra, participants in student-led sections scored significantly higher than lecture sections on two out of five objectives: write the equation of a line in slope-intercept form (p<0.001) and use properties of logarithms to write an expression as a single logarithm (p<0.01). Lecture sections scored significantly higher than student-led sections on one objective: write the equation of an exponential function given two data points (p<0.05). However, the wording of the problems for this objective differed between lecture and student-led sections. Finally, when comparing the eight Basic Math Skills objectives with the 17 attitudinal variables, 1.4% of pairs were significantly correlated on the pre-survey and 15.4% of pairs were significantly correlated on the post-survey. Of the five College Algebra objectives and 17 attitudinal variables, 16.5% of pairs were significantly correlated on the pre-survey and 7.1% of pairs were significantly correlated on the post-survey. / text

The problem with which this investigation is concerned is that of determining whether utilizing self-help groups for remedial mathematics students would improve their course completion rates, achievement, and attitudes toward learning mathematics. The methods of determining the success/failure of self-help groups in this study were the Z-test from inferences concerning two proportions, the t-test from inferences concerning the difference between two independent means, and the t-test from inferences concerning the difference between two dependent means. The participants of the study were chosen from the students enrolled in "daytime" mathematics classes at Tarrant County Junior College - Northeast Campus, Hurst, Texas. The experiment was conducted over two semesters and the data combined for statistical analysis. There were one hundred four students involved in the study. Fifty-two students comprised each of the experimental and control classes. The term self-help group was utilized to describe a small group of two-to-fifteen people who engaged in discussion of responsibility, standards, confession, lay leadership, and action. The students did not study mathematics in self-help group sessions. The group meetings dealt with anxieties, attitudes, and commitment that may be associated with mathematics in general. To investigate the hypotheses of this study, data was collected to calculate the percentage completion rates, the means of the final exams taken by students, and the differences of the Semantic Differential scores given to students in the experimental class at the beginning and the end of the semester. This data was utilized for statistical analysis to determine if the experiment was successful. The report concludes that self-help groups did not significantly improve course completion rates, achievement, or attitudes of students toward learning mathematics. Forty-four per cent of the students that completed the experimental class participated in self-help groups.

Problem This study was concerned with the effectiveness of two different programs for teaching remedial mathematics to community college students. An individualized instruction program, making use of independent study and the small group setting, was compared with the traditional lecture-textbook instruction program to determine if there existed significant differences in (a) the rate of attrition, and (b) mathematics performance. A secondary objective was to determine if significant differences existed between students enrolled in remedial mathematics classes at 9 AM and those enrolled at 12 Noon. Method The target population consisted of all students in fourteen community colleges in the Los Angeles area. The sample consisted of all students enrolled in the 9 AM and 12 Noon elementary algebra classes at Rio Hondo College during the fall semester, 1972. One experimental group and one control group were randomly formed from all the students enrolled at 9 AM. The same procedure was used at 12 Noon. The posttest-only control group design was utilized in the study. A chisquare test was used to determine if frequency of dropout is associated with being in the control or experimental groups. Mean scores on a mathematics posttest of achievement were analyzed by two -way analysis of covariance to determine if mathematics performance is associated with being in the control or experimental groups, and if mathematics performance is associated with being in the 9 AM or 12 Noon classes. Results According to the study, there appeared to be no significant differences, at the .05 level, in either the rate of attrition or mathematics performance of community college students taught remedial mathematics under an individualized instruction program as compared with those students taught under the traditional lecture-textbook instruction program. Also, there appeared to be no significant difference, at the .05 level, in the mathematics performance of community college students enrolled in 9 AM remedial mathematics classes compared to students enrolled in 12 Noon remedial mathematics classes. Conclusions As a result of the findings of this study, the following conclusions were drawn. Community college remedial mathematics classes using an individualized instruction program as described in this study did not have significantly fewer dropouts than those classes using the traditional lecture-textbook approach. Community college students enrolled in remedial mathematics courses taught under an individualized instruction program as described in this study did not receive significantly higher scores on a mathematics posttest of achievement than those students taught under the traditional lecture-textbook instruction program. There was no significant difference in mathematics performance of community college students enrolled in remedial mathematics courses taught at 9 AM and those taught at 12 Noon. The study, even though the results did not show significant differences at the .05 level, proved to be very helpful in planning for further mathematics classes at the community college.

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The problem of this study was performance on selected mathematics and reading assessment tests as predictors of achievement in remedial mathematics. The purpose of the study was twofold. The first was to determine the internal consistency of a locally developed remedial mathematics placement test and the mathematics section of the Pre-TASP Test. The second was to determine the predictive validity of performance on (a) the local remedial mathematics placement test, (b) the mathematics section of the Pre-TASP Test, and (c) the Descriptive Tests of Language Skills, Reading Comprehension Test in combination with demographic variables for mid-semester achievement, end-of-semester achievement, and course success in three levels of remedial mathematics at Richland College, Dallas, Texas.

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The research documented in this report had a twofold purpose. Firstly, it was to design and implement an intervention based on the theory of Realistic Mathematics Education (RME) aimed at improving the mathematical understanding of learners in two Grade 8 remedial mathematics classes, by revisiting the key number concepts of place value, fractions and decimals. In doing so, a second purpose was to investigate the viability and emerging characteristics of an intervention based on the theory of RME in such a setting (i.e. with low attainers to revisit key number concepts). Pending the realisation of these immediate outcomes, more distant outcomes in subsequent research would be: that learners' understanding and academic performance in mathematics improves and to develop a local instruction theory in using the RME theory to revisit the concepts of place value, fractions and decimals with low attaining learners in order to improve their understanding in this regard. Grade 8 low attainers were selected as the target group for this research as a result of the pending implementation of Mathematical Literacy as a compulsory subject for all learners, possibly from 2006. Currently in South Africa, learners who are not meeting the required standard by the end of their Grade 9 year are able to elect not to take mathematics through Grades 10, 11 and 12. When the new Further Education and Training (FET) policy is implemented, this will no longer be the case. All learners, who do not elect to take mathematics as a subject, will have to take Mathematical Literacy as a compulsory subject throughout Grades 10, 11 and 12. Although less detailed and abstract than the subject mathematics, the Mathematical Literacy curriculum still requires learners to have an understanding of key number concepts and also contains a substantial amount of algebra. As Grade 8 is when learners start working with algebra more formally, and is also their first year at secondary school, it was decided that this would be an appropriate year to try and diagnose and remediate problems in learners' understanding of the key number concepts, if and where possible. The intention was that this would then equip learners with a more appropriate structure of conceptualised knowledge of the above-mentioned concepts on which they could further construct their understanding of algebra. The study was carried out at a local urban high school in South Africa and the research design of this study was informed by two development research approaches (van den Akker&Plomp, 1993; Gravemeijer, 1994). Also, the study was only implemented with a small number of participants, within a bounded setting and without the intention to generalise the results. It was therefore regarded as a development case study. The results appear to indicate that it is viable to apply the theory of RME with low attaining Grade 8 learners in order to revisit the key number concepts of place value, fractions and decimals. Copyright 2004, University of Pretoria. All rights reserved. The copyright in this work vests in the University of Pretoria. No part of this work may be reproduced or transmitted in any form or by any means, without the prior written permission of the University of Pretoria. Please cite as follows: Barnes, HE 2004, A developmental case study : implementing the theory of realistic mathematics education with low attainers, MEd dissertation, University of Pretoria, Pretoria, viewed yymmdd < http://upetd.up.ac.za/thesis/available/etd-12032004-103122 / > / Dissertation (MEd (Curriculum design))--University of Pretoria, 2005. / Curriculum Studies / unrestricted

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