The effect of an interdisciplinary algebra/science course on students' critical thinking skills was examined. A traditional college algebra course was used as a comparison group. The students in the sample enrolled in college algebra and then half were randomly placed into the interdisciplinary course. A quasi-experimental pretest-posttest comparison group design was used. The Watson-Glaser Critical Thinking Appraisal was used to measure the students' critical thinking skills. This instrument consists of an overall critical thinking score as well as five subscores in the areas of Inference, Recognition of Assumptions, Deduction, Interpretation and Evaluation of Arguments. It was found that the students in the interdisciplinary course made greater gains in the overall critical thinking score as well as in four of the five subscores. However, the differences in the gains made in the two courses were not statistically significant. Disregarding course, other factors that were found to be closely related to critical thinking were Composite ACT, grade received in the course, Math ACT and grade point average. It was also found that students whose majors were in the Schools of Arts and Letters or Science and Technology scored higher on critical thinking than students whose majors were in the Schools of Business or Education. Factors found to have no relationship to critical thinking were ethnicity, gender and classification.

This dissertation consists of three related papers. The first paper, Rethinking mathematics bridge courses--An inquiry model for community colleges, introduces the activities of conventionalizing and axiomatizing from a practitioner perspective. In the paper, I offer a curricular model that includes both inquiry and traditional instruction for two-year college students interested in mathematics. In particular, I provide both examples and rationales of tasks from the research-based Teaching Abstract Algebra for Understanding (TAAFU) curriculum, which anchors the inquiry-oriented version of the mathematics bridge course. The second paper, the role of past experience in creating a shared representation system for a mathematical operation: A case of conventionalizing, adds to the existing literature on mathematizing (Freudenthal, 1973) by "zooming in" on the early stages of the classroom enactment of an inquiry-oriented curriculum for reinventing the concept of group (Larsen, 2013). In three case study episodes, I shed light onto "How might conventionalizing unfold in a mathematics classroom?" and offer an initial framework that relates students' establishment of conventions in light of their past mathematical experiences. The third paper, Collective axiomatizing as a classroom activity, is a detailed case study (Yin, 2009) that examines how students collectively engage in axiomatizing. In the paper, I offer a revision to De Villiers's (1986) model of descriptive axiomatizing. The results of this study emphasize the additions of pre-axiomatic activity and axiomatic creation to the model and elaborate the processes of axiomatic formulation and analysis within the classroom community.

The problems with which this study was concerned were threefold: (a) to design a computer-based graphics presentation on the topics of functions and graphing, (b) to develop the presentation, and (c) to determine the instructional effectiveness of this computer-based graphics instruction. The computerized presentation was written in Authorware for the Macintosh computer. The population of this study consisted of three intermediate algebra classes at Collin County Community College (n = 51). A standardized examination, the Descriptive Tests of Mathematics Skills for Functions and Graphs, was used for pretest and posttest purposes. Means were calculated on these scores and compared using a t-test for correlated means. The level of significance was set at .01. The results of the data analysis indicated: 1. There was a significant difference between the pretest and posttest performance after exposure to the computer-based graphics presentation. 2. There was no significant gender difference between the pretest and posttest performance after exposure to the computer-based graphics presentation. 3. There was no significant difference between the pretest and posttest performance of the traditional and nontraditional age students after exposure to the computer-based graphics presentation. Females had a lower posttest score than the mean male posttest score, but an analysis of the differences showed no significance. Traditional age students had a higher posttest performance score than the mean traditional age student posttest score, but their pretest performance scores were higher as well. An analysis of the differences showed no significance. In summary, this computer-based graphics presentation was an effective teaching technique for increasing mathematics performance.

A report issued in 2012 by the United States Government Accountability Office (US Government Accountability Office, 2012) concluded that the United States is not producing enough graduates in Science, Technology, Engineering, and Mathematics (STEM) to meet the demands of its economy. According to the National Center for Educational Statistics (2001), fewer than fifty percent of students nationally possess a solid command of mathematical content. This study tested whether the insertion of Academic Service Learning (ASL) into intermediate algebra courses improved students’ performance, their motivation to learn the subject, and attitudes towards mathematics learning. ASL is an educational strategy that integrates meaningful community service with instruction and reflection to enrich the learning experience, teach civic responsibility, and strengthen communities (Duffy, Barrington, West, Heredia, & Barry, 2011). The subjects in this study were thirty-four students enrolled in intermediate algebra at a large public university in southeast Florida. The participant group consisted of fifteen students who completed the requirements of the ASL program and the comparison group consisted of nineteen students who initially showed interest in the program but dropped out of the study early in the semester. Through a mixed method analysis, the study found that the proportion of students who passed the course in the ASL group was greater than the proportion of students in the non-ASL group. Similarly, the mean final course grade in the ASL group was higher than the mean final course grade in the non-ASL group. The results of the qualitative analyses showed that all the participants enjoyed the ASL experience. In addition, some participants felt that the ASL project raised their motivation to learn mathematics and increased their competence in mathematics. However, both quantitative and qualitative analyses revealed that the students’ participation in the ASL project did not affect their attitudes towards mathematics learning. The study concluded that Academic Service Learning has the potential to help improve students’ success rates in developmental mathematics courses as well as increase their motivation to learn the subject. / Includes bibliography. / Dissertation (Ph.D.)--Florida Atlantic University, 2016. / FAU Electronic Theses and Dissertations Collection

With the introduction in 2006 of the school subject Mathematical Literacy (ML) in the further Education and Training band, there have been expectations that such a subject might develop responsible citizens, contributing workers and self-managing people. The extent to which the subject can meet these aims is dependent on the ways in which the subject is taught and assessed, which influences the focus of ML in the classrooms. One of the differences between the respective subjects of Mathematics and Mathematical Literacy is that when it comes to the latter, there has been less emphasis on carrying out algebraic procedures, and a greater focus on working with contexts. However, algebraic skills can be advantageous even when solving problems set within contexts. One area, which surfaces the distinction between arithmetic and algebraic skills, is in the substitution and computation of a formula, as compared to the solution of equations. In this study, I focus on this distinction by examining Grade 11 ML learner skills in solving both result-unknown problems and start-unknown problems, where the former involves substituting and computing the result of a formula or equation for which the input is given. The latter involves re-arranging the equation or formula in order to solve for the input when the output is given. With this in mind, this study sets out to explore the strategies used by Grade 11 learners to solve result-unknown and start-unknown problems set in real life contexts. This is a qualitative study, carried out with three hundred and forty Grade 11 Mathematical Literacy learners from rural and urban school in North Durban. Data was gathered from a document analysis of 340 learners’ written responses to the research instrument, along with interviews with ten of these learners. There were four tasks in the research instrument, each of which had a result-unknown, a start-unknown and a reflection question. In the four tasks with the exception of Question 1.2.1 and 1.2.2 in tasks one, were set around a linear equation, while Question 1.2.1 and 1.2.2 involved a hyperbolic equation. Semi-structured interviews were conducted individually with ten learners and the audio recorded. The purpose of the interviews was to explore some of the factors that influenced their written responses. The findings revealed the solving of start-unknown questions to be a serious problem for learners. On average, the success rate at result-unknown questions was 75%, while it was 26% for start-unknown questions. For start-unknown questions based on linear equations only, the success rate was a mere 19 percent. Some strategies used by learners in responding to start-unknown questions included number grabbing, systematic guess and test, conjoining, symbol manipulation and working backwards. On average, over the four tasks based on linear equations, only nine percent of learners successfully used strategies based on algebraic skill. Most learners who obtained correct answers in the start-unknown questions used the guess and test strategy. Strategies identified in result-unknown questions included direct arithmetic strategy. The study recommends that for ML learners, teachers need to impress upon learners that the location of the formula in the question is not an indication that certain questions would be answered using the formula, because the formula is placed next to them. It also recommends that teachers create opportunities for learners to continue to practice the algebraic skills they learned in the GET band, particularly in the area of transforming and solving simple linear equations. / M. Ed. University of KwaZulu-Natal, Durban 2013.

There is a need to understand the relationship between, the traditional 16-week versus an 8-week, and college-level mathematics success rates. This study applied chi-square (χ2) and analysis of variance to compare and contrast which course length of time, 8-weeks or 16-weeks, for college algebra resulted in a higher proportion of students successfully completing the course. In addition, success rates among ethnicities, gender, and age groups were also examined. The population sample for this study was 231 students enrolled in college algebra from fall 2004 through fall 2007. Data was analyzed on four sections of the traditional 16-week courses and four sections of 8-week courses. Success was defined as earning a grade of A, B, or C in the course. The study found that overall there was no significant difference in success rates for the 8-week and 16-week college algebra courses. However, significant differences were found in success rates among Asian, Pacific Islander students enrolled in the 8-week and 16-week courses. No significant differences in success rates were found for White, Non-Hispanic; African-American, and Hispanic, Mexican American students. There was a significant difference in the number of A's, B's, C's, D's and F's among White, Non-Hispanic students, but there was no difference in A's, B's, C's, D's or F's for African-American; Hispanic, Mexican American and Asian, Pacific Islander. When considering success rates among genders, no difference was found in success rates for males or females who were enrolled in the 8-week and 16-week college algebra courses. There were a significant greater number of students in the age group (23-30) who were successful in the 16-week college algebra course than in the 8-week college algebra course. However, no differences in success rates were found in the age groups (18-22) and (31-40).