Matching Items (13)

135776-Thumbnail Image.png

Problem-Solving with Algebra I Students: The Effects on Accuracy, Attitude, and Fluency

Description

Current research on problem based tasks in the mathematics classroom and the effects are examined. As well educators are provided with an analysis regarding the importance of teaching students to

Current research on problem based tasks in the mathematics classroom and the effects are examined. As well educators are provided with an analysis regarding the importance of teaching students to problem solve through the use of novel problems, as well as equip them with the know-how to implement a problem-based unit in their classrooms. A sample unit plan and fifteen novel problems and their solutions appropriate for Algebra I students are also provided. Keywords: problem-solving, attitude, algebra

Contributors

Agent

Created

Date Created
  • 2016-05

151688-Thumbnail Image.png

Does self-regulated learning-skills training improve high-school students' self-regulation, math achievement, and motivation while using an intelligent tutor?

Description

This study empirically evaluated the effectiveness of the instructional design, learning tools, and role of the teacher in three versions of a semester-long, high-school remedial Algebra I course to determine

This study empirically evaluated the effectiveness of the instructional design, learning tools, and role of the teacher in three versions of a semester-long, high-school remedial Algebra I course to determine what impact self-regulated learning skills and learning pattern training have on students' self-regulation, math achievement, and motivation. The 1st version was a business-as-usual traditional classroom teaching mathematics with direct instruction. The 2rd version of the course provided students with self-paced, individualized Algebra instruction with a web-based, intelligent tutor. The 3rd version of the course coupled self-paced, individualized instruction on the web-based, intelligent Algebra tutor coupled with a series of e-learning modules on self-regulated learning knowledge and skills that were distributed throughout the semester. A quasi-experimental, mixed methods evaluation design was used by assigning pre-registered, high-school remedial Algebra I class periods made up of an approximately equal number of students to one of the three study conditions or course versions: (a) the control course design, (b) web-based, intelligent tutor only course design, and (c) web-based, intelligent tutor + SRL e-learning modules course design. While no statistically significant differences on SRL skills, math achievement or motivation were found between the three conditions, effect-size estimates provide suggestive evidence that using the SRL e-learning modules based on ARCS motivation model (Keller, 2010) and Let Me Learn learning pattern instruction (Dawkins, Kottkamp, & Johnston, 2010) may help students regulate their learning and improve their study skills while using a web-based, intelligent Algebra tutor as evidenced by positive impacts on math achievement, motivation, and self-regulated learning skills. The study also explored predictive analyses using multiple regression and found that predictive models based on independent variables aligned to student demographics, learning mastery skills, and ARCS motivational factors are helpful in defining how to further refine course design and design learning evaluations that measure achievement, motivation, and self-regulated learning in web-based learning environments, including intelligent tutoring systems.

Contributors

Agent

Created

Date Created
  • 2013

155595-Thumbnail Image.png

Predicting student success in a self-paced mathematics MOOC

Description

While predicting completion in Massive Open Online Courses (MOOCs) has been an active area of research in recent years, predicting completion in self-paced MOOCS, the fastest growing segment of open

While predicting completion in Massive Open Online Courses (MOOCs) has been an active area of research in recent years, predicting completion in self-paced MOOCS, the fastest growing segment of open online courses, has largely been ignored. Using learning analytics and educational data mining techniques, this study examined data generated by over 4,600 individuals working in a self-paced, open enrollment college algebra MOOC over a period of eight months.

Although just 4% of these students completed the course, models were developed that could predict correctly nearly 80% of the time which students would complete the course and which would not, based on each student’s first day of work in the online course. Logistic regression was used as the primary tool to predict completion and focused on variables associated with self-regulated learning (SRL) and demographic variables available from survey information gathered as students begin edX courses (the MOOC platform employed).

The strongest SRL predictor was the amount of time students spent in the course on their first day. The number of math skills obtained the first day and the pace at which these skills were gained were also predictors, although pace was negatively correlated with completion. Prediction models using only SRL data obtained on the first day in the course correctly predicted course completion 70% of the time, whereas models based on first-day SRL and demographic data made correct predictions 79% of the time.

Contributors

Agent

Created

Date Created
  • 2017

154345-Thumbnail Image.png

Cuntz-Pimsner algebras of twisted tensor products of correspondences

Description

This dissertation contains three main results. First, a generalization of Ionescu's theorem is proven. Ionescu's theorem describes an unexpected connection between

This dissertation contains three main results. First, a generalization of Ionescu's theorem is proven. Ionescu's theorem describes an unexpected connection between graph C*-algebras and fractal geometry. In this work, this theorem is extended from ordinary directed graphs to higher-rank graphs. Second, a characterization is given of the Cuntz-Pimsner algebra associated to a tensor product of C*-correspondences. This is a generalization of a result by Kumjian about graphs algebras. This second result is applied to several important special cases of Cuntz-Pimsner algebras including topological graph algebras, crossed products by the integers and crossed products by completely positive maps. The result has meaningful interpretations in each context. The third result is an extension of the second result from an ordinary tensor product to a special case of Woronowicz's twisted tensor product. This result simultaneously characterizes Cuntz-Pimsner algebras of ordinary and graded tensor products and Cuntz-Pimsner algebras of crossed products by actions and coactions of discrete groups, the latter partially recovering earlier results of Hao and Ng and of Kaliszewski, Quigg and Robertson.

Contributors

Agent

Created

Date Created
  • 2016

156227-Thumbnail Image.png

Using instructional design and cognitive load management theories to improve the efficiency of a video-based college algebra learning environment through a note-taking guide and learner control

Description

The problem under investigation was to determine if a specific outline-style learning guide, called a Learning Agenda (LA), can improve a college algebra learning environment and if learner control can

The problem under investigation was to determine if a specific outline-style learning guide, called a Learning Agenda (LA), can improve a college algebra learning environment and if learner control can reduce the cognitive effort associated with note-taking in this instance. The 192 participants were volunteers from 47 different college algebra and pre-calculus classes at a community college in the southwestern United States. The approximate demographics of this college as of the academic year 2016 – 2017 are as follows: 53% women, 47% men; 61% ages 24 and under, 39% 25 and over; 43% Hispanic/Latino, 40% White, 7% other. Participants listened to an approximately 9-minute video lecture on solving a logarithmic equation. There were four dependent variables: encoding as measured by a posttest – pretest difference, perceived cognitive effort, attitude, and notes-quality/quantity. The perceived cognitive effort was measured by a self-reported questionnaire. The attitude was measured by an attitude survey. The note-quality/quantity measure included three sub-measures: expected mathematical expressions, expected phrases, and a total word count. There were two independent factors: note-taking method and learner control. The note-taking method had three levels: the Learning Agenda (LA), unguided note-taking (Usual), and no notes taken. The learner control factor had two levels: pausing allowed and pausing not allowed. The LA resulted in significantly improved notes on all three sub-measures (adjusted R2 = .298). There was a significant main effect of learner control on perceived cognitive effort with higher perceived cognitive effort occurring when pausing was not allowed and notes were taken. There was a significant interaction effect of the two factors on the attitude survey measure. The trend toward an improved attitude in both of the note-taking levels of the note-taking factor when pause was allowed was reversed in the no notes level when pausing was allowed. While significant encoding did occur as measured by the posttest – pretest difference (Cohen’s d = 1.81), this measure did not reliably vary across the levels of either the note-taking method factor or the learner control factor in this study. Interpretations were in terms of cognitive load management, split-attention, instructional design, and note-taking as a sense-making opportunity.

Contributors

Agent

Created

Date Created
  • 2018

149575-Thumbnail Image.png

Learning college algebra by creating student experts

Description

In any instructional situation, the instructor's goal is to maximize the learning attained by students. Drawing on the adage, 'we learn best what we have taught,' this action research project

In any instructional situation, the instructor's goal is to maximize the learning attained by students. Drawing on the adage, 'we learn best what we have taught,' this action research project was conducted to examine whether students, in fact, learned college algebra material better if they taught it to their peers. The teaching-to-learn process was conducted in the following way. The instructor-researcher met with individual students and taught a college algebra topic to a student who served as the leader of a group of four students. At the next step, the student who originally learned the material from the instructor met with three other students in a small group session and taught the material to them to prepare an in-class presentation. Students in these small group sessions discussed how best to present the material, anticipated questions, and prepared a presentation to be shared with their classmates. The small group then taught the material to classmates during an in-class review session prior to unit examinations. Quantitative and qualitative data were gathered. Quantitative data consisted of pre- and post-test scores on four college algebra unit examinations. In addition, scores from Likert-scale items on an end-of-semester questionnaire that assessed the effectiveness of the teaching-to-learn process and attitudes toward the process were obtained. Qualitative data consisted of field notes from observations of selected small group sessions and in-class presentations. Additional qualitative data included responses to open-ended questions on the end-of-semester questionnaire and responses to interview items posed to groups of students. Results showed the quantitative data did not support the hypothesis that material, which was taught, was better learned than other material. Nevertheless, qualitative data indicated students were engaged in the material, had a deeper understanding of the material, and were more confident about it as a result of their participation in the teaching-to-learn process. Students also viewed the teaching-to-learn process as being effective and they had positive attitudes toward the teaching-to-learn process. Discussion focused on how engagement, deeper understanding and confidence interacted with one another to increase student learning. Lessons learned, implications for practice, and implications for further action research were also discussed.

Contributors

Agent

Created

Date Created
  • 2011

156684-Thumbnail Image.png

A formative evaluation research study to guide the design of the Categorization Step Practice Utility (MS-CPU) as an integral part of preparation for the GED mathematics test using the Ms. Stephens Algebra Story Problem-solving Tutor (MSASPT)

Description

The mathematics test is the most difficult test in the GED (General Education Development) Test battery, largely due to the presence of story problems. Raising performance levels of story problem-solving

The mathematics test is the most difficult test in the GED (General Education Development) Test battery, largely due to the presence of story problems. Raising performance levels of story problem-solving would have a significant effect on GED Test passage rates. The subject of this formative research study is Ms. Stephens’ Categorization Practice Utility (MS-CPU), an example-tracing intelligent tutoring system that serves as practice for the first step (problem categorization) in a larger comprehensive story problem-solving pedagogy that purports to raise the level of story problem-solving performance. During the analysis phase of this project, knowledge components and particular competencies that enable learning (schema building) were identified. During the development phase, a tutoring system was designed and implemented that algorithmically teaches these competencies to the student with graphical, interactive, and animated utilities. Because the tutoring system provides a much more concrete rather than conceptual, learning environment, it should foster a much greater apprehension of a story problem-solving process. With this experience, the student should begin to recognize the generalizability of concrete operations that accomplish particular story problem-solving goals and begin to build conceptual knowledge and a more conceptual approach to the task. During the formative evaluation phase, qualitative methods were used to identify obstacles in the MS-CPU user interface and disconnections in the pedagogy that impede learning story problem categorization and solution preparation. The study was conducted over two iterations where identification of obstacles and change plans (mitigations) produced a qualitative data table used to modify the first version systems (MS-CPU 1.1). Mitigation corrections produced the second version of the MS-CPU 1.2, and the next iteration of the study was conducted producing a second set of obstacle/mitigation tables. Pre-posttests were conducted in each iteration to provide corroboration for the effectiveness of the mitigations that were performed. The study resulted in the identification of a number of learning obstacles in the first version of the MS-CPU 1.1. Their mitigation produced a second version of the MS-CPU 1.2 whose identified obstacles were much less than the first version. It was determined that an additional iteration is needed before more quantitative research is conducted.

Contributors

Agent

Created

Date Created
  • 2018

153103-Thumbnail Image.png

Test algebra for concurrent combinatorial testing

Description

A new algebraic system, Test Algebra (TA), is proposed for identifying faults in combinatorial testing for SaaS (Software-as-a-Service) applications. In the context of cloud computing, SaaS is a new software

A new algebraic system, Test Algebra (TA), is proposed for identifying faults in combinatorial testing for SaaS (Software-as-a-Service) applications. In the context of cloud computing, SaaS is a new software delivery model, in which mission-critical applications are composed, deployed, and executed on cloud platforms. Testing SaaS applications is challenging because new applications need to be tested once they are composed, and prior to their deployment. A composition of components providing services yields a configuration providing a SaaS application. While individual components

in the configuration may have been thoroughly tested, faults still arise due to interactions among the components composed, making the configuration faulty. When there are k components, combinatorial testing algorithms can be used to identify faulty interactions for t or fewer components, for some threshold 2 <= t <= k on the size of interactions considered. In general these methods do not identify specific faults, but rather indicate the presence or absence of some fault. To identify specific faults, an adaptive testing regime repeatedly constructs and tests configurations in order to determine, for each interaction of interest, whether it is faulty or not. In order to perform such testing in a loosely coupled distributed environment such as

the cloud, it is imperative that testing results can be combined from many different servers. The TA defines rules to permit results to be combined, and to identify the faulty interactions. Using the TA, configurations can be tested concurrently on different servers and in any order. The results, using the TA, remain the same.

Contributors

Agent

Created

Date Created
  • 2014

151579-Thumbnail Image.png

Examining the effects of blended learning for ninth grade students who struggle with math

Description

Many students in the United States are graduating from high school without the math skills they need to be considered college ready. For many of these graduates, who find themselves

Many students in the United States are graduating from high school without the math skills they need to be considered college ready. For many of these graduates, who find themselves starting their higher education at a community college, remedial math can become an insurmountable barrier that ends their aspirations for a degree or certificate. Some students must take as many as four remedial courses before they are considered college ready. Studies report that between 60% and 70% of students placed into remedial math classes either do not successfully complete the sequence of required courses or avoid taking math altogether and therefore never graduate (Bailey, Jeong, & Cho, 2010). This study compared three low-level freshman math classes in one Arizona high school. The purpose of this study was to implement an innovative learning intervention to find out if there was a causal relationship between the addition of technology with instruction in a blended learning environment and performance in math. The intervention measured growth (pre- and posttest) and grade-level achievement (district-provided benchmark test) in three Foundations of Algebra classes. The three classes ranged on a continuum with the use of technology and personalized instruction. Additionally, focus groups were conducted to better understand the challenges this population of students face when learning math. The changes in classroom practices showed no statistical significance on the student outcomes achieved. Students in a blended online environment learned the Foundations of Algebra concepts similarly to their counterparts in a traditional, face-to-face learning environment.

Contributors

Agent

Created

Date Created
  • 2013

151625-Thumbnail Image.png

Cooperative learning in a community college setting: developmental coursework in mathematics

Description

This action research study, set in a community college in the southwestern United States, was designed to investigate the effects of implementing cooperative learning strategies in a developmental mathematics course.

This action research study, set in a community college in the southwestern United States, was designed to investigate the effects of implementing cooperative learning strategies in a developmental mathematics course. Introductory algebra was formerly taught in a lecture based format, and as such regularly had a low course completion rate. To create a more engaging learning environment, formal and informal cooperative learning activities were integrated into the curriculum. Bandura's self-efficacy theory, Vygotsky's constructivist theory, and Deutsch's social interdependence theory guided this study. Qualitative and quantitative data were collected through pre and post self-efficacy surveys, semi-structured student interviews, student journal entries, class observations, focus groups, and pre and post mathematics assessments. Data were analyzed using a mixed methods approach. As a result of implementing cooperative learning practices as a part of my teaching, there was an increase in student attendance as well as a decrease in student withdrawal rates. Students were also more motivated to work with each other on mathematics homework outside of class sessions. There was a strong sense of community that I had not witnessed in previous courses that I have taught. Use of cooperative learning practices served as a vehicle to motivate students to work on their mathematics coursework with their peers. Keywords: cooperative learning, developmental mathematics, constructivism, social interdependence theory, self-efficacy, community college

Contributors

Agent

Created

Date Created
  • 2013