Download or read book The Effects of a Framework for Procedural Understanding on College Algebra Students Procedural Skill and Understanding written by John Fredrick Hasenbank and published by . This book was released on 2006 with total page 324 pages. Available in PDF, EPUB and Kindle. Book excerpt: This dissertation examined the effectiveness of an instructional treatment consisting of lecture content, homework tasks, and quiz assessments built around a common Framework for Procedural Understanding. The study addressed concerns about increasing numbers of students enrolling in remedial mathematics courses because they did not develop sufficient understanding in previous courses. The Framework-oriented instruction was designed to help students develop deep and well-connected knowledge of procedures, which has been shown to facilitate recall and promote future learning. Data collection spanned the Fall 2005 semester at a western land-grant university. In the quasi-experimental design, instructors from six intact sections of college algebra were matched into pairs based on prior teaching experience, and the treatment condition was assigned to one member of each pair. Equivalence of treatment and control groups was established by comparing ACT / SAT scores for the 85% of students for whom those scores were available. Data collection consisted of classroom observations, homework samples, common hour exams scores, procedural understanding assessments, supplemental course evaluations, and a final interview with treatment instructors. Analysis of covariance was the primary statistical tool used to compare treatment and control group performances while controlling for attendance rates and pre-requisite mathematical knowledge. Treatment group students scored significantly higher than control group students on the procedural understanding assessments. Moreover, although treatment students were assigned 18% fewer drill questions than controls and 8% fewer problems overall, the gains in procedural understanding were realized without declines in procedural skill. The relationship between understanding and skill was also examined, and students with greater procedural understanding tended to score higher on the skills-oriented final exam regardless of which treatment condition was assigned to them. Finally, the interview with the treatment instructors provided insight into the implementation issues surrounding the treatment. They expressed concerns about time constraints and reported initial discomfort with, but eventual appreciation for, using the Framework for Procedural Understanding to guide instruction. The Framework-oriented treatment was found to be effective at helping students develop deeper procedural understanding without declines in procedural skill. Additional implications and recommendations for future research are also discussed.
Download or read book Dissertation Abstracts International written by and published by . This book was released on 2009 with total page 640 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Abstracts of Papers Presented to the American Mathematical Society written by American Mathematical Society and published by . This book was released on 2008 with total page 784 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book The Use of Computer Algebra Systems in a Procedural Algebra Course to Facilitate a Framework for Procedural Understanding written by Jonathan Lee Harper and published by . This book was released on 2007 with total page 454 pages. Available in PDF, EPUB and Kindle. Book excerpt: Analyses of covariance and independent samples t-tests were used to compare treatment and control groups based on the quantitative measures. The treatment instructor and students were able to integrate CAS technology into the classroom without difficulty. The instructor implemented the curriculum with fidelity but the discourse in the classroom did not reach the desired level. No significant difference was found between treatment and control students on the skills-based final exam, indicating that the introduction of CAS did not diminish procedural skill levels. No difference in procedural understanding based on the Framework was observed. The data indicated that the students viewed mathematics as learning how to do procedures. This philosophy of mathematics and the limited classroom discourse impeded progress towards learning other aspects of the Framework. Recommendations include changing classroom norms to foster more discussion and placing more emphasis on Framework-based understanding in the assessment structure and course grade.
Download or read book The Effects of Writing to Learn Mathematics on Conceptual Understanding and Procedural Ability in Introductory College Calculus written by Mary Kathleen Porter and published by . This book was released on 1996 with total page 130 pages. Available in PDF, EPUB and Kindle. Book excerpt: Initially, the primary goal of this study was to investigate the effects of writing to learn mathematics on the conceptual and procedural understanding of students in an introductory college calculus course. As the study began, an additional goal emerged: to develop a system for classifying students' errors in calculus that could be used to analyze the data in this study and future ones. To achieve these goals, the examinations of students in two sections of introductory calculus were studied. The instruction of the two groups was very similar: Both groups had the same instructor and were taught with a focus on the concepts of the course. However, in one group, students used writing activities; in the other, students used related activities that did not involve writing. The writing and nonwriting activities were similar in their focus and both groups of students discussed the activities in class. The only major difference between the two groups was that one group used writing to learn mathematics in their activities and the other group did not. Using the errors made by both groups on their examinations, a classification system for errors in calculus was developed, which had not previously been done. This classification system consisted of two procedural error categories and four conceptual error categories. Using this system, the errors of the students in the writing and comparison groups were categorized and the data were statistically analyzed for information about the students' conceptual and procedural understanding. No significant differences were found between the two groups in terms of their conceptual errors, nor for their procedural errors, which suggested that the writing activities did not have a different effect than the related nonwriting activities on students' conceptual and procedural understanding. If students who engage in nonwriting activities that focus on concepts and involve discussion can achieve the same level of conceptual and procedural understanding as students who use writing activities, then mathematics instructors have a viable alternative to using writing activities. This study indicated a need for further research into this matter.
Download or read book Resources in Education written by and published by . This book was released on 2001 with total page 756 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Conceptual and Procedural Knowledge written by James Hiebert and published by Routledge. This book was released on 2013-08-21 with total page 357 pages. Available in PDF, EPUB and Kindle. Book excerpt: First Published in 1986. This book is intended for those people who are interested in how mathematics is learned. It is intended especially for those who are interested in the mental processes involved in becoming mathematically competent and the mental processes that inhibit such competency from developing. The volume opens with an overview of the issue and then traces the relationships between conceptual and procedural knowledge in mathematics from preschool days through the years of formal schooling. Mathematics educators and cognitive psychologists from a variety of perspectives contribute theoretical arguments and empirical data to illuminate the nature of the relationships and, in tum, the nature of mathematics learning.
Download or read book Helping Children Learn Mathematics written by National Research Council and published by National Academies Press. This book was released on 2002-07-31 with total page 53 pages. Available in PDF, EPUB and Kindle. Book excerpt: Results from national and international assessments indicate that school children in the United States are not learning mathematics well enough. Many students cannot correctly apply computational algorithms to solve problems. Their understanding and use of decimals and fractions are especially weak. Indeed, helping all children succeed in mathematics is an imperative national goal. However, for our youth to succeed, we need to change how we're teaching this discipline. Helping Children Learn Mathematics provides comprehensive and reliable information that will guide efforts to improve school mathematics from pre-kindergarten through eighth grade. The authors explain the five strands of mathematical proficiency and discuss the major changes that need to be made in mathematics instruction, instructional materials, assessments, teacher education, and the broader educational system and answers some of the frequently asked questions when it comes to mathematics instruction. The book concludes by providing recommended actions for parents and caregivers, teachers, administrators, and policy makers, stressing the importance that everyone work together to ensure a mathematically literate society.
Download or read book The Effect of Two Technologies on College Algebra Students Understanding of the Concept of Function written by Gregory Harrell and published by . This book was released on 2018-12-06 with total page 202 pages. Available in PDF, EPUB and Kindle. Book excerpt: Dissertation Discovery Company and University of Florida are dedicated to making scholarly works more discoverable and accessible throughout the world. This dissertation, "The Effect of Two Technologies on College Algebra Students' Understanding of the Concept of Function" by Gregory Kent Harrell, was obtained from University of Florida and is being sold with permission from the author. A digital copy of this work may also be found in the university's institutional repository, IR@UF. The content of this dissertation has not been altered in any way. We have altered the formatting in order to facilitate the ease of printing and reading of the dissertation.
Download or read book Effects of a Vocabulary enhanced College Algebra Curriculum on Student Understanding written by Olivia Rodriguez Garcia and published by . This book was released on 2002 with total page 252 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Vital Directions for Mathematics Education Research written by Keith R Leatham and published by Springer Science & Business Media. This book was released on 2014-07-08 with total page 212 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a collection of chapters from prominent mathematics educators in which they each discuss vital issues in mathematics education and what they see as viable directions research in mathematics education could take to address these issues. All of these issues are related to learning and teaching mathematics. The book consists of nine chapters, seven from each of seven scholars who participated in an invited lecture series (Scholars in Mathematics Education) at Brigham Young University, and two chapters from two other scholars who are writing reaction papers that look across the first seven chapters. The recommendations take the form of broad, overarching principles and ideas that cut across the field. In this sense, this book differs from classical “research agenda projects,” which seek to outline specific research questions that the field should address around a central topic.
Download or read book Using Cognitive Conflict to Promote a Structural Understanding of Grade 11 Algebra written by Duncan Fraser and published by . This book was released on 2007 with total page 348 pages. Available in PDF, EPUB and Kindle. Book excerpt: This study examines the effect of cognitive conflict interventions on high school students' understanding of algebra. The concepts of algebra can be conceived of as both processes to carry out, and objects that can be used in higher processes. I examine this double nature with reference to several epistemological frameworks and describe a conceptual divide between procedural and structural understanding. I formulated a system to analyze student understanding and developed cognitive conflict instruments intended to promote structural understanding. Both the system and instrument involve questions that contain 'procedural traps'. I carried out interventions and tested the students for any change in understanding. The majority of the students had a procedural understanding before the interventions, and a structural understanding afterwards. I concluded that cognitive conflict interventions could effect a significant advance to structural understanding on the part of a majority of the students, but were not effective with the weakest students.
Download or read book The Impact of a Quantitative Reasoning Instructional Approach to Linear Equations in Two Variables on Student Achievement and Student Thinking about Linearity written by Paul Thomas Belue and published by . This book was released on 2015 with total page 99 pages. Available in PDF, EPUB and Kindle. Book excerpt: "A control group and an experimental group of college students at a community college in the Pacific Northwest were taught a unit on linear equations in two variables. The control group was taught using a traditional instructional approach that focused on learning procedures and the experimental group was taught using a quantitative reasoning instructional approach that focused on learning proportional and functional reasoning. Both groups were then given the same unit assessment that had 10 procedural understanding items and 10 conceptual understanding items related to linear equations in two variables. The assessment was given to determine the impact of the quantitative reasoning instructional approach on performance of linear equations in two variables tasks. A quantitative and qualitative analysis of items on the unit assessment found that in relation to the control group, the experimental students demonstrated better performance in proportional reasoning ability, and had no difference in either functional reasoning ability or performance on procedural tasks. The experimental students received more instruction focused on conceptual understanding compared to the control group without sacrificing their procedural understanding. Analysis also revealed that community college students enrolled in beginning algebra can have misconceptions about what constitutes a linear relationship and the meaning of a variable quantity."--Boise State University ScholarWorks.
Download or read book Procedural Versus Conceptual Algebra Refresher Interventions and Effects of Cognitive Abilities in Adults written by John T. Elias and published by . This book was released on 2012 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: The success rate of high school and college students in algebra is low (Tyson et al., 2007; Croft, 2006). As such, the present study compared the effectiveness of conceptual and procedural algebra “refresher” interventions for 63 college students and investigated the relationship of cognitive variables to math outcome. Results revealed that participants in both interventions improved significantly from pretest to posttest, but that there was no significant difference between the two interventions. However, a follow-up analysis in which participants who scored at ceiling or at floor on pretest were excluded revealed an advantage for the conceptual treatment group relative to the procedural group in terms of educationally meaningful effect size (d = +0.53). There were no relationships between cognitive variables and math outcomes; however, in the follow-up analysis, long-term memory was positively correlated with posttest performance, but working memory and executive functioning were still unrelated to math outcomes. There was no interaction between cognitive variables and posttest performance of the two groups, which likely reflects the lack of differential treatment effects or robust zero-order correlations. The present study addresses the shortage of research on algebra, particularly the shortage of experiments that compare the effectiveness of different algebraic interventions. It also provides insight into intervention methods that educators may potentially use.
Download or read book The Effect of Two Technologies on College Algebra Students Understanding of the Concept of Function written by Gregory Kent Harrell and published by . This book was released on 2001 with total page 372 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Talent Development as a Framework for Gifted Education written by Paula Olszewski-Kubillus and published by Routledge. This book was released on 2021-09-23 with total page 232 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Talent development” is a phrase often used in reference to the education of gifted children. Recently, it has been presented by researchers to refer to a specific approach to the delivery of gifted education services.
Download or read book The Effects of a Graphing Approach College Algebra Curriculum on Students Understanding of the Function Concept written by Jeannie Conrad Hollar and published by . This book was released on 1996 with total page 292 pages. Available in PDF, EPUB and Kindle. Book excerpt:
