The Role Of Graphing Calculators In Students Algebraic Thinking

Author : Sandy Margaret Spitzer
Publisher : ProQuest
ISBN 13 : 9780549811756
Total Pages : pages
Book Rating : 4.53/5 ( download)

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Download or read book The Role of Graphing Calculators in Students' Algebraic Thinking written by Sandy Margaret Spitzer and published by ProQuest. This book was released on 2008 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Chapter 1 provides a review of the literature on the effects of using graphing calculators on students' mathematics achievement. General findings suggest that calculators can have a positive effect on students' performance on assessments. In particular, students using graphing calculators seem to do better on some types of problems, such as those requiring translation between different representations of a function, and perform about the same as students without calculators on procedural symbolic-manipulation problems. In order to identify possible mechanisms for these changes, the chapter explores four possible reasons for students' improved performance: improved representational fluency, wider repertoire of solution strategies, increased reification of mathematical concepts, and changes in classroom processes. While the general trend of improved achievement appears robust, none of the four hypothesized reasons for improvement were substantiated by enough data to be confirmed. While it appears that the basic effects of graphing calculators are relatively well determined, mechanisms for those effects are poorly understood. Chapter 2 presents the result of a study whose goal was to investigate how the presence of graphing calculator technology influences the mathematical ideas that students encounter while solving algebra problems. Thirty-three Algebra II students, divided randomly into two conditions, participated in task-based interviews. In one condition, students were encouraged to solve algebra problems using their graphing calculator, and in the other condition, students solved the same problems with no access to technology. Results indicate that when students used graphing calculators, they were more likely to interpret letters as variables rather than fixed unknowns, used a wider range of strategies, were more likely to use more than one strategy to solve a problem, and expressed deeper levels of conceptual understanding. The differences in conceptual understanding and interpretation of letters were strongly related to the types of strategies that students used to solve problems, with graphing and tables encouraging more sophisticated interpretations and evidence of conceptual understanding.

Author : Ann Lawrence
Publisher : Math Solutions
ISBN 13 : 0941355497
Total Pages : 278 pages
Book Rating : 4.90/5 ( download)

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Download or read book Lessons for Algebraic Thinking written by Ann Lawrence and published by Math Solutions. This book was released on 2002 with total page 278 pages. Available in PDF, EPUB and Kindle. Book excerpt: These lessons show how to maximize instruction that prepares students for formal algebra. Through a series of investigations, students build their proficiency with key algebraic concepts. Connections between arithmetic and algebra are made through the use of drawings, tables, graphs, words, and symbols. Lessons include a technology component with suggestions for teaching with graphing calculators.

Author : Steve Rhine
Publisher : IAP
ISBN 13 : 1641134135
Total Pages : 351 pages
Book Rating : 4.32/5 ( download)

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Download or read book How Students Think When Doing Algebra written by Steve Rhine and published by IAP. This book was released on 2018-11-01 with total page 351 pages. Available in PDF, EPUB and Kindle. Book excerpt: Algebra is the gateway to college and careers, yet it functions as the eye of the needle because of low pass rates for the middle school/high school course and students’ struggles to understand. We have forty years of research that discusses the ways students think and their cognitive challenges as they engage with algebra. This book is a response to the National Council of Teachers of Mathematics’ (NCTM) call to better link research and practice by capturing what we have learned about students’ algebraic thinking in a way that is usable by teachers as they prepare lessons or reflect on their experiences in the classroom. Through a Fund for the Improvement of Post-Secondary Education (FIPSE) grant, 17 teachers and mathematics educators read through the past 40 years of research on students’ algebraic thinking to capture what might be useful information for teachers to know—over 1000 articles altogether. The resulting five domains addressed in the book (Variables & Expressions, Algebraic Relations, Analysis of Change, Patterns & Functions, and Modeling & Word Problems) are closely tied to CCSS topics. Over time, veteran math teachers develop extensive knowledge of how students engage with algebraic concepts—their misconceptions, ways of thinking, and when and how they are challenged to understand—and use that knowledge to anticipate students’ struggles with particular lessons and plan accordingly. Veteran teachers learn to evaluate whether an incorrect response is a simple error or the symptom of a faulty or naïve understanding of a concept. Novice teachers, on the other hand, lack the experience to anticipate important moments in the learning of their students. They often struggle to make sense of what students say in the classroom and determine whether the response is useful or can further discussion (Leatham, Stockero, Peterson, & Van Zoest 2011; Peterson & Leatham, 2009). The purpose of this book is to accelerate early career teachers’ “experience” with how students think when doing algebra in middle or high school as well as to supplement veteran teachers’ knowledge of content and students. The research that this book is based upon can provide teachers with insight into the nature of a student’s struggles with particular algebraic ideas—to help teachers identify patterns that imply underlying thinking. Our book, How Students Think When Doing Algebra, is not intended to be a “how to” book for teachers. Instead, it is intended to orient new teachers to the ways students think and be a book that teachers at all points in their career continually pull of the shelf when they wonder, “how might my students struggle with this algebraic concept I am about to teach?” The primary audience for this book is early career mathematics teachers who don’t have extensive experience working with students engaged in mathematics. However, the book can also be useful to veteran teachers to supplement their knowledge and is an ideal resource for mathematics educators who are preparing preservice teachers.

Author : Pamela H. Dase
Publisher : Shell Education
ISBN 13 : 1425800246
Total Pages : 241 pages
Book Rating : 4.46/5 ( download)

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Download or read book Graphing Calculator Strategies: Algebra written by Pamela H. Dase and published by Shell Education. This book was released on 2006-12-01 with total page 241 pages. Available in PDF, EPUB and Kindle. Book excerpt: Integrate TI Graphing Calculator technology into your mathematics instruction with these resource books. Lesson plans are easy to follow and each lesson explains the concepts, demonstrates how to use the calculator, and applies the concept. Differentiate instruction with "Extension Ideas" and strategies that simplify the lessons for students needing extra support. Teacher Resource CD includes a "Using the Calculator" section to help students visualize the concepts-great for English language learners. Practice pages help prepare students for testing situations that include the use of graphing calculators.

Author : Phil DeMarois
Publisher : Kendall Hunt
ISBN 13 : 9780757503887
Total Pages : 674 pages
Book Rating : 4.88/5 ( download)

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Download or read book Applying Algebraic Thinking to Data written by Phil DeMarois and published by Kendall Hunt. This book was released on 2005-12-30 with total page 674 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : Sonja L. Goerdt
Publisher :
ISBN 13 :
Total Pages : 334 pages
Book Rating : 4.33/5 ( download)

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Download or read book Fostering Algebraic Thinking with Casio Technology written by Sonja L. Goerdt and published by . This book was released on 2010 with total page 334 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : Pamela H. Dase
Publisher : Teacher Created Materials
ISBN 13 : 1425890652
Total Pages : 241 pages
Book Rating : 4.50/5 ( download)

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Download or read book Graphing Calculator Strategies: Algebra written by Pamela H. Dase and published by Teacher Created Materials. This book was released on 2006-12-04 with total page 241 pages. Available in PDF, EPUB and Kindle. Book excerpt: Integrate TI Graphing Calculator technology into your algebra instruction with this award-winning resource book. Perfect for grades 6-12, this resource includes lessons, problem-solving practice, and step-by-step instructions for using graphing calculator technology. 238pp plus Teacher Resource CD with PDF files of the tables, templates, activity sheets, and student guides for TI-83/84 Plus Family and TI-73 Explorer™. This resource is correlated to the Common Core State Standards, is aligned to the interdisciplinary themes from the Partnership for 21st Century Skills, and supports core concepts of STEM instruction.

Author : National Research Council
Publisher : National Academies Press
ISBN 13 : 030917368X
Total Pages : 206 pages
Book Rating : 4.81/5 ( download)

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Download or read book The Nature and Role of Algebra in the K-14 Curriculum written by National Research Council and published by National Academies Press. This book was released on 1998-09-23 with total page 206 pages. Available in PDF, EPUB and Kindle. Book excerpt: With the 1989 release of Everybody Counts by the Mathematical Sciences Education Board (MSEB) of the National Research Council and the Curriculum and Evaluation Standards for School Mathematics by the National Council of Teachers of Mathematics (NCTM), the "standards movement" in K-12 education was launched. Since that time, the MSEB and the NCTM have remained committed to deepening the public debate, discourse, and understanding of the principles and implications of standards-based reform. One of the main tenets in the NCTM Standards is commitment to providing high-quality mathematical experiences to all students. Another feature of the Standards is emphasis on development of specific mathematical topics across the grades. In particular, the Standards emphasize the importance of algebraic thinking as an essential strand in the elementary school curriculum. Issues related to school algebra are pivotal in many ways. Traditionally, algebra in high school or earlier has been considered a gatekeeper, critical to participation in postsecondary education, especially for minority students. Yet, as traditionally taught, first-year algebra courses have been characterized as an unmitigated disaster for most students. There have been many shifts in the algebra curriculum in schools within recent years. Some of these have been successful first steps in increasing enrollment in algebra and in broadening the scope of the algebra curriculum. Others have compounded existing problems. Algebra is not yet conceived of as a K-14 subject. Issues of opportunity and equity persist. Because there is no one answer to the dilemma of how to deal with algebra, making progress requires sustained dialogue, experimentation, reflection, and communication of ideas and practices at both the local and national levels. As an initial step in moving from national-level dialogue and speculations to concerted local and state level work on the role of algebra in the curriculum, the MSEB and the NCTM co-sponsored a national symposium, "The Nature and Role of Algebra in the K-14 Curriculum," on May 27 and 28, 1997, at the National Academy of Sciences in Washington, D.C.

Author : National Research Council
Publisher : National Academies Press
ISBN 13 : 0309061474
Total Pages : 206 pages
Book Rating : 4.76/5 ( download)

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Download or read book The Nature and Role of Algebra in the K-14 Curriculum written by National Research Council and published by National Academies Press. This book was released on 1998-10-23 with total page 206 pages. Available in PDF, EPUB and Kindle. Book excerpt: With the 1989 release of Everybody Counts by the Mathematical Sciences Education Board (MSEB) of the National Research Council and the Curriculum and Evaluation Standards for School Mathematics by the National Council of Teachers of Mathematics (NCTM), the "standards movement" in K-12 education was launched. Since that time, the MSEB and the NCTM have remained committed to deepening the public debate, discourse, and understanding of the principles and implications of standards-based reform. One of the main tenets in the NCTM Standards is commitment to providing high-quality mathematical experiences to all students. Another feature of the Standards is emphasis on development of specific mathematical topics across the grades. In particular, the Standards emphasize the importance of algebraic thinking as an essential strand in the elementary school curriculum. Issues related to school algebra are pivotal in many ways. Traditionally, algebra in high school or earlier has been considered a gatekeeper, critical to participation in postsecondary education, especially for minority students. Yet, as traditionally taught, first-year algebra courses have been characterized as an unmitigated disaster for most students. There have been many shifts in the algebra curriculum in schools within recent years. Some of these have been successful first steps in increasing enrollment in algebra and in broadening the scope of the algebra curriculum. Others have compounded existing problems. Algebra is not yet conceived of as a K-14 subject. Issues of opportunity and equity persist. Because there is no one answer to the dilemma of how to deal with algebra, making progress requires sustained dialogue, experimentation, reflection, and communication of ideas and practices at both the local and national levels. As an initial step in moving from national-level dialogue and speculations to concerted local and state level work on the role of algebra in the curriculum, the MSEB and the NCTM co-sponsored a national symposium, "The Nature and Role of Algebra in the K-14 Curriculum," on May 27 and 28, 1997, at the National Academy of Sciences in Washington, D.C.

Author : Thomas A. Romberg
Publisher : Routledge
ISBN 13 : 1136476296
Total Pages : 363 pages
Book Rating : 4.97/5 ( download)

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Download or read book Integrating Research on the Graphical Representation of Functions written by Thomas A. Romberg and published by Routledge. This book was released on 2012-10-12 with total page 363 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume focuses on the important mathematical idea of functions that, with the technology of computers and calculators, can be dynamically represented in ways that have not been possible previously. The book's editors contend that as result of recent technological developments combined with the integrated knowledge available from research on teaching, instruction, students' thinking, and assessment, curriculum developers, researchers, and teacher educators are faced with an unprecedented opportunity for making dramatic changes. The book presents content considerations that occur when the mathematics of graphs and functions relate to curriculum. It also examines content in a carefully considered integration of research that conveys where the field stands and where it might go. Drawing heavily on their own work, the chapter authors reconceptualize research in their specific areas so that this knowledge is integrated with the others' strands. This model for synthesizing research can serve as a paradigm for how research in mathematics education can -- and probably should -- proceed.