<p> Many students enter college inadequately prepared to take college-level math courses like College Algebra, and as a consequence must take one or more developmental math courses. It is becoming increasingly common for colleges to offer math courses online, including various developmental math courses including Intermediate Algebra. Many computer-assistive technologies exist, some coupled with mathematics textbooks, to purportedly help students learn mathematics better. These technologies are often used in online developmental math courses, and in developmental math course taught in the traditional face-to-face classroom. </p><p> The purpose of this study was to compare the effectiveness of the use of technology in Intermediate Algebra courses taught through regular and blended instruction, online, in the traditional classroom supplemented with technology, and in the traditional classroom. The independent variable was the type of instruction received but students were not randomly assigned to the three types of instruction, as they were free to take whichever instruction they chose. The dependent variables were the final course grades of those who completed the course, and a comparison of the rate of course completion, versus withdrawing or failing for all students enrolled in the course past the first week drop/add period. Dummy variables of 1 and 0 were assigned to completing and not completing the course, respectively. </p><p> An analysis of variance was used to analyze the data. There was no statistically significant difference in the course grades of those who took the courses in the three types of instruction; nor was there any statistically significant difference in the rate of course completion in the three types of instruction. </p>

This case study investigated the polyphonic discourse in a beginning secondary school mathematics classroom in Trinidad. It relates how classroom and research interview ‘talk’ contributed to students’, their teacher’s and the researcher’s developing conceptions of mathematics, themselves and each other. The study is approached from dialogical and socio-constructivist orientations. Students and their teacher professed a diverse set of prior conceptions of mathematics which included viewing mathematics as rule based with a problem solving orientation and emphasizing attention to the teacher. Several cases are reported that describe the authoritative elements which included a well defined structure to lessons mirroring the textbook, ‘cloze’ questions, and a reliance on rules and absent historical referents as justifications for mathematical activities and substitution for mathematical reasoning. Student and teacher questions and their desire to understand, however, served to interrupt the monological discourse. What was internally persuasive for students was the relational competency of their teacher as well as the communicative acts of their peers. Students’ responses to pedagogy were internally persuasive for the teacher and precipitated ideological assessment. Both discourse types contributed to the formation of individual as well as social identities. Student and teacher utterances were internally persuasive for the researcher. I recommend that research needs to attend more meaningfully to what is internally persuasive for students and teachers in mathematics teaching and learning. In addition I theorize on the need for a dialogical relationship between dialogue and pedagogy that is attentive to the ambiguities in communication.

<p>This study in an extension of a Master's study, entitled Realistic Mathematics Education and the strategies grade 8 learners develop for the solution of two simultaneous linear equations. the current study investigates how new content could be introduced into a school mathematical curriculum. The new topic under discussion for this study is the topis of Cryptology. Two research cycles were carried out. For the first design research cycle there were three teaching experiments with teachers, grade 10 learners and students as participants. Seven activities weere developed from the second design research cycle which was worked through with gade 10 learners. All sessions for the second design research cycle were video taped. Important to the development of instrutional materials was the development of a hypothetical learning trajetory about the learning and teaching of each activity. the results of the study indicated that the way learners understood the content and the different ways in which they presented solutions augers well for the introduction of a specific new content strand, cryptology, into a new school mathematical curriculum. It is also important for developers of instructional material to have a strong mathematical content knowledge for the design of instructional materials</p>

<p> Se analizaron los discursos docentes en tres clases de nivel universitario. La teor&iacute;a que se propone destaca la importancia de una identidad discursiva de negociaci&oacute;n para crear las condiciones que favorezcan la construcci&oacute;n de significados. Los discursos docentes flexibles y democr&aacute;ticos contribuyen a aumentar la motivaci&oacute;n de los estudiantes para crear discursos propios, negociar normas socio matem&aacute;ticas y crear una cultura de reflexi&oacute;n e investigaci&oacute;n. Estas caracter&iacute;sticas de los discursos promueven la discusi&oacute;n de argumentos intersubjetivos que contribuyen a una comprensi&oacute;n compartida de los temas bajo estudio. Los silencios reflexivos, el tono coloquial, la pregunta ret&oacute;rica y el lenguaje social inclusivo, entre otros aspectos, contribuyen a consolidar un proyecto de influencia mediante el cual se promueven las construcciones de conocimiento. En el caso espec&iacute;fico de la noci&oacute;n de variaci&oacute;n, las construcciones de los estudiantes se pueden apoyar con un discurso simple y directo que se ancle en procesos de tanteo y error, con atenci&oacute;n al registro semi&oacute;tico num&eacute;rico y a la negociaci&oacute;n de palabras claves para describir el cambio.</p>

<p> This study investigates the development of flexibility and reversibility in a calculus environment that attends to linking multiple representations. Reversibility was studied through Krutetskii&rsquo;s framework of reversibility of two-way processes and reversibility of the mental process in reasoning. The study was conducted over approximately four months in a high school calculus classroom in an urban school district in a mid-Atlantic state. Instruction attended to linking multiple representations whenever possible. Four types of data were collected: 1) a pre-test, 2) a post-test, 3) daily assessments, and 4) clinical interviews. Twenty-one students completed a pretest and post-test that together assessed development of flexibility over the course of the study. They also completed daily assessments that were collected to provide evidence of the development of reversibility during the course of the study. Six students participated in four clinical interviews each, spread throughout the study. Inferential statistics were used to compare the results of the pre-test and post-test for significant differences and to determine significant differences in the presence of reversibility on the daily assessments over the course of the study. The clinical interviews were analyzed for evidence of students&rsquo; thought processes while solving reversible questions. Analysis revealed that over the course of the study, students demonstrated significant increases in both flexibility and reversibility. Two-way reversibility seemed to develop with relative ease for most students and often developed simultaneously with learning a forward process. Developing reversibility of the mental process in reasoning was difficult and tended to develop simultaneously with learning in a forward direction for students with high levels of flexibility. For students who did not develop reversibility simultaneously with forward learning, both two-way reversibility and reversibility of the mental process in reasoning were able to develop through multiple opportunities to solve reversible tasks of similar content. Analysis of the clinical interviews indicated that students typically followed a 4-step thought process when using reversibility to solve problems. Implications and limitations of the study and areas of further research were discussed.</p>

<p> The flipped classroom is an emerging teaching practice in which teachers employ a variety of methods to offload direct instruction prior to class and use class time to engage students in active learning. Despite its rapid rise in popularity over the past five years, there are relatively few studies on the efficacy of the flipped classroom teaching model. Of these studies, few use control groups to measure changes is student learning and even fewer use iterative analysis to determine the impact that successive implementation has on the efficacy of the flipped classroom model. This study addresses this gap by measuring the efficacy of a flipped classroom against a traditionally-taught class in two successive semesters. Results showed that the flipped classroom teaching method increased student learning during the second semester of the study. It also found that successive implementation of the flipped classroom was more effective at producing gains in measures of student learning outcomes than a class taught traditionally. Finally, the findings from this study were used to develop recommendations for educators interested in implementing the flipped classroom teaching model.</p>

<p> The purpose of this study was to determine the correlation between participation of low achieving math students in a before-school computer math lab and how their participation affected the fourth grade California Standardized Test (CST) math scale scores at San Joaquin Elementary School. Students participated in the lab based their below proficient performance on multiplication facts tests. The lab was available from January through April in both 2010 and 2011. Students used interactive computer software called IXL. The focus in the lab was for students to master their multiplication tables (0 through 12). To evaluate if there was a statistically significant change in the CST scores because of the treatment, an Abbreviate Interrupted Time Series analysis was applied. The two years before the lab was implemented, the two years with the lab in place and the year after the lab was discontinued were compared. A t-test evaluation of the mean scores in a year-by-year comparison was run. The Levene Test using Homogeneity of Variances test was run which showed similar variances. For this reason, the ANOVA was then used along with the Tukey HSD post-hoc test to identify which groups showed a significant difference from each other. There was a significant improvement in the CST mean scores for fourth grade at San Joaquin Elementary School during the years the treatment was in place. By extending the school day and using interactive computer software together they showed a positive impact on student's CST scores.</p>

No description available.

<p> Developmental math education continues to be a rising challenge for many post-secondary two-year institutions. In response to this challenge, many colleges are adapting their developmental math education programs by implementing best institutional and instructional practices as defined by recent literature. This descriptive and correlational study used data from the Developmental Education Program Survey (DEPS) and the selected state's Department of Education to explore how community colleges within the state have implemented these research-based, promising instructional and institutional practices in the area of developmental mathematics education. The quantitative study through multiple linear regression analysis determined if the implementation of certain practices predicted the success of the students. Findings indicated that developmental math education programs were implementing most of the research-based best practices for developmental math education. In addition, the results of this study indicated that changes in the instructional aspect of the program increased student success in developmental math more than changes in institutional policy. This study found that implementation of best institutional practices as defined in the literature had no relationship to student success while implementation of best research-based instructional practices had a significant relationship to student success. The researcher recommends that institutions utilize cooperative, collaborative and mastery learning in their developmental math courses and that they consider offering developmental math instruction as math refresher workshops, bridge programs, and co-requisite courses to college-level math. </p>

<p> According to statistics provided by the California State University Public Affairs Office, approximately 1/3 of incoming freshman need remediation in mathematics. However, there is little information available on which specific mathematical skills they lack. The CSU Entry Level Mathematics Test does not allow for disaggregation of scores by topic, so it is of limited use in studying students&rsquo; pre-existing skills. However, the Mathematics Diagnostic Testing Project Second Year Algebra Readiness Test is well correlated with the ELM, and can provide information regarding student deficiencies. </p><p> This study administered a student survey on prior preparation in mathematics and the MDTP to students enrolled in a required remedial mathematics course. The results were analyzed for patterns among the incorrect answers, and the correlation between students&rsquo; preparation and test results was studied. Results indicate that students can access only a small subset of the mathematical skills required for success in postsecondary courses.</p>