The Role of Graphing Calculators in Students' Algebraic Thinking

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Author :
Publisher : ProQuest
ISBN 13 : 9780549811756
Total Pages : pages
Book Rating : 4.8/5 (117 download)

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Book Synopsis The Role of Graphing Calculators in Students' Algebraic Thinking by : Sandy Margaret Spitzer

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.

How Students Think When Doing Algebra

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Author :
Publisher : IAP
ISBN 13 : 1641134135
Total Pages : 351 pages
Book Rating : 4.6/5 (411 download)

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Book Synopsis How Students Think When Doing Algebra by : Steve Rhine

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.

Lessons for Algebraic Thinking

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Author :
Publisher : Math Solutions
ISBN 13 : 0941355497
Total Pages : 278 pages
Book Rating : 4.9/5 (413 download)

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Book Synopsis Lessons for Algebraic Thinking by : Ann Lawrence

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.

Applying Algebraic Thinking to Data

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Author :
Publisher : Kendall Hunt
ISBN 13 : 9780757503887
Total Pages : 674 pages
Book Rating : 4.5/5 (38 download)

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Book Synopsis Applying Algebraic Thinking to Data by : Phil DeMarois

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:

Student Understanding of Functions and the Use of the Graphing Calculator in a College Algebra Course

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Publisher :
ISBN 13 :
Total Pages : 414 pages
Book Rating : 4.:/5 (466 download)

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Book Synopsis Student Understanding of Functions and the Use of the Graphing Calculator in a College Algebra Course by : Patrick J. Averbeck

Download or read book Student Understanding of Functions and the Use of the Graphing Calculator in a College Algebra Course written by Patrick J. Averbeck and published by . This book was released on 2000 with total page 414 pages. Available in PDF, EPUB and Kindle. Book excerpt: The purpose of the study was to investigate students' learning of the function concept and the role of the graphing calculator in a College Algebra course. Differences between students with high symbolic manipulation skills. and students with low symbolic manipulation skills were also examined. On the basis of an algebraic skills test administered by the instructor (high/low) and students' academic majors (math & science, business, and liberal arts), 25 students from one College Algebra class were placed into six categories. To gather data on students' understanding of functions, a pretest and posttest were administered. The Function Test consisted of four identification questions given in each of the representations, three questions asking for the definition, an example, and a nonexample of functions, and 15 questions consisting of three problem situations given in the numerical, graphical, and symbolic representations. To gather data on the role of the graphing calculator, daily classroom observations were conducted. To verify students' responses and classroom observations, formal interviews with students and informal interviews with the instructor were conducted. Students' personal definition progressed towards the formal definition of functions. Yet, students had difficulties with the univalence requirement in three areas: (a) order of domain and range, (b) preference for simple algorithms, and (c) the restriction that functions were one-to-one. Compared to students with low symbolic manipulation skills, students with high symbolic manipulation skills were more flexible working between representations of functions. Half of the interviewed students with low symbolic manipulation skills perceived a single function given in numerical, graphical, and symbolic representations as separate entities. The graphing calculator played a role in all phases of the solution process. During the initial phases, students used calculators to develop a symbolic approach. The prime motivation for using graphing calculators during the solution-execution phase was to avoid careless errors. The most common use of graphing calculators was to check answers during the solution-monitoring phase. However, graphing calculators created difficulties for students who accepted graphs at face value. Interpreting the truncated graph shown by the calculator, students determined that exponential functions possessed a bounded domain because they did not explore the graph.

Fostering Algebraic Thinking with Casio Technology

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Publisher :
ISBN 13 :
Total Pages : 334 pages
Book Rating : 4.:/5 (89 download)

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Book Synopsis Fostering Algebraic Thinking with Casio Technology by : Sonja L. Goerdt

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:

Mathematical Investigations

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Publisher :
ISBN 13 : 9780065023824
Total Pages : 244 pages
Book Rating : 4.0/5 (238 download)

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Book Synopsis Mathematical Investigations by : Phil DeMarois

Download or read book Mathematical Investigations written by Phil DeMarois and published by . This book was released on 1996 with total page 244 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Graphing Calculator Strategies: Middle School Math

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Publisher : Teacher Created Materials
ISBN 13 : 1425890660
Total Pages : 225 pages
Book Rating : 4.4/5 (258 download)

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Book Synopsis Graphing Calculator Strategies: Middle School Math by : Donna Erdman

Download or read book Graphing Calculator Strategies: Middle School Math written by Donna Erdman and published by Teacher Created Materials. This book was released on 2006-12-15 with total page 225 pages. Available in PDF, EPUB and Kindle. Book excerpt: Integrate TI Graphing Calculator technology into your mathematics instruction with this award-winning resource book. Perfect for grades 6-8, this resource includes lessons, problem-solving practice, and step-by-step instructions for using graphing calculator technology. 224pp 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.

Integrating Research on the Graphical Representation of Functions

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Author :
Publisher : Routledge
ISBN 13 : 1136476369
Total Pages : 364 pages
Book Rating : 4.1/5 (364 download)

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Book Synopsis Integrating Research on the Graphical Representation of Functions by : Thomas A. Romberg

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 364 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.

The Nature and Role of Algebra in the K-14 Curriculum

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Author :
Publisher : National Academies Press
ISBN 13 : 030917368X
Total Pages : 206 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis The Nature and Role of Algebra in the K-14 Curriculum by : National Research Council

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.

The Utilization of Graphing Calculators in Algebra I Instruction for Low-SES Students

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Publisher :
ISBN 13 :
Total Pages : 278 pages
Book Rating : 4.:/5 (773 download)

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Book Synopsis The Utilization of Graphing Calculators in Algebra I Instruction for Low-SES Students by : Edna Horton Flores

Download or read book The Utilization of Graphing Calculators in Algebra I Instruction for Low-SES Students written by Edna Horton Flores and published by . This book was released on 2009 with total page 278 pages. Available in PDF, EPUB and Kindle. Book excerpt: The National Council of Teachers of Mathematics (NCTM) asserts that a goal of mathematics education, in Prekindergarten through grade 12, is to develop mathematical power for all students, and that educational equity is the nucleus of this goal. Nevertheless, researchers have found that equity for all students in mathematics education has not been fully realized. African American students, especially those of low socioeconomic status (SES), are consistently shortchanged in the mathematics education they receive. According to NCTM, calculators can enhance the achievement of equity in mathematics education. The usage of graphing calculators in the teaching and learning of mathematics is advocated by NCTM and the National Research Council. A plethora of research shows that the use of graphing calculators has positive effects on students learning mathematics. Numerous studies have focused on the use of graphing calculators in secondary school mathematics. In particular, research has been conducted on the use of graphing calculators in Algebra I and Algebra II. A vast majority of students in these studies were White. The purpose of this descriptive study was to examine the use of graphing calculators in the teaching and learning of Algebra I for low-SES African American students. Specifically, this study investigated the similarities/difference in instruction, where graphing calculators were used and where they were not used, of a ninth-grade Algebra I unit on linear functions. This study used data from observations, interviews, and documents to examine teachers intended and implemented curriculum. Findings showed that teachers who used graphing calculators in instruction made connections between the different representations of functions. Teachers who did not use graphing calculators did not make connections between various ways to represent linear functions. Characteristics of standards-based instruction were observed in both groups.

The Nature and Role of Algebra in the K-14 Curriculum

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Author :
Publisher : National Academies Press
ISBN 13 : 0309061474
Total Pages : 206 pages
Book Rating : 4.3/5 (9 download)

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Book Synopsis The Nature and Role of Algebra in the K-14 Curriculum by : National Research Council

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.

Pak

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Publisher :
ISBN 13 : 9780757559365
Total Pages : 724 pages
Book Rating : 4.5/5 (593 download)

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Book Synopsis Pak by : De Marios

Download or read book Pak written by De Marios and published by . This book was released on 2010-01-05 with total page 724 pages. Available in PDF, EPUB and Kindle. Book excerpt:

The Impact of Using Graphing Calculators as an Aid for the Teaching and Learning of Precalculus in a University Setting

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Publisher :
ISBN 13 :
Total Pages : 348 pages
Book Rating : 4.3/5 (129 download)

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Book Synopsis The Impact of Using Graphing Calculators as an Aid for the Teaching and Learning of Precalculus in a University Setting by : Carl Wallace Norris

Download or read book The Impact of Using Graphing Calculators as an Aid for the Teaching and Learning of Precalculus in a University Setting written by Carl Wallace Norris and published by . This book was released on 1994 with total page 348 pages. Available in PDF, EPUB and Kindle. Book excerpt:

The Impact of Using Technology on Student Achievement

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Publisher :
ISBN 13 :
Total Pages : 498 pages
Book Rating : 4.:/5 (785 download)

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Book Synopsis The Impact of Using Technology on Student Achievement by : Barbara Renee Buckner

Download or read book The Impact of Using Technology on Student Achievement written by Barbara Renee Buckner and published by . This book was released on 2011 with total page 498 pages. Available in PDF, EPUB and Kindle. Book excerpt: The purpose of this study was to determine the effect of TI-Nspire graphing calculator use on student achievement and on teacher behavior variables of planning, teaching, and assessing. This study investigated the teaching of functions by teachers using the TI-Nspire graphing calculator versus teachers using a non-graphing scientific calculator. A review of the literature found that the emergence of calculators and computers has changed the way mathematics is both done and used (Ellington, 2006; Thorpe, 1989; & Kieran, 1992). Research also showed that students can effectively use a graphing calculator as an instructional tool to make and understand different types of representations (Choi-Koh, 2003; Colgan, 1993; and Drijvers & Doorman, 1996). Other studies have shown how graphing calculator use has engaged students in higher level thinking skills (Dessart, DeRidder, Charleen, & Ellington, 1999; Ellington, 2006; Graham & Thomas, 1998; Keller & Hirsch, 1998; Huntley, Rasmussen, Villarubi, Sangtong, & Fey, 2000; & Ronau et al., 2008). Since it is a relatively new tool, there is a limited amount of research on the classroom use of the TI-Nspire. The TI-Nspire is designed to link together multiple-representations within a single problem, so the concept of functions is an ideal context within which to study the impact of the TI-Nspire. This was a quasi-experimental study. The researcher gathered and analyzed pretest, post-test, and post post-test data on student performance on function concepts. The study included a 90 minute classroom observation of each class as well as document analysis of weekly questionnaires, daily lesson plans, and daily assessments. Vignettes employed classroom observations, document analysis, and thick description to triangulate the results of the qualitative analysis. During the summer prior to this study, all teachers attended 12 hours of training over the course of two days with a National Texas Instruments Instructor in which they were trained to use the TI-Nspire graphing calculator. Teachers were then given a TINspire, TI-Nspire emulator and access to online Atomic learning video training (Atomic Learning, 2011), to continue their exploration of the TI-Nspire. The week prior to the study, the teachers attended another day of professional development activity taught by a Texas Instruments Trained Cadre member. This "Function Focused Session" was six hours long and provided review on the TI-Nspire, specific training about teaching the function concept with the TI-Nspire, and time to create lesson plans and activities for this study. During the two weeks of treatment and two weeks of follow up, teachers met once a week for "Weekly Touchdown Sessions" a 90 minute meeting held after school to complete a weekly questionnaire, turn in lesson plans, assessments, and receive further professional development on the TI-Nspire. Providing a trained Texas Instruments Instructor on a weekly basis to answer questions, assist in providing direction for the following week, and meeting weekly with the teachers to complete questionnaires were vital strategies necessary to support teachers with this new technology tool and to assure their fidelity in treatment implementation and control maintenance. All professional development sessions were taught by Texas Instruments trained Instructors. The results from four teachers, each with one treatment class using the TI-Nspire and one control class using a non-graphing scientific calculator, were significant on the pre-test with the control group having a higher mean score than the treatment group and statistical significance on the post post-test with the treatment group having a higher mean score than the control group. While there was a statistically significant effect of Teacher Zeta on the post-post test in comparisons with the other teachers, most of the teacher effect was controlled for within the design of the study. To control for teacher effect, all teachers taught both a treatment and a control class. For each teacher, one of their two algebra classes was randomly assigned to treatment and the other was then assigned to control. There was not enough power in the data to properly analyze the effect of socioeconomic status and special education. This study supports the use of TI-Nspire graphing calculators in Algebra classrooms while studying the concept of functions. This study shows that, while using the TI-Nspire graphing calculator, the use of multiple representations and higher Depth of Knowledge activities can be used to improve student achievement, and impact classroom teaching, and lesson planning. While this study shows the impact of the TI-Nspire graphing calculator for the concept of functions, further research is needed to continue evaluating the impact of the TI-Nspire across additional mathematics topics.

The Nation's Report Card

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Author :
Publisher :
ISBN 13 :
Total Pages : 380 pages
Book Rating : 4.:/5 ( download)

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Book Synopsis The Nation's Report Card by :

Download or read book The Nation's Report Card written by and published by . This book was released on 2001 with total page 380 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Effects of Graphing Calculators on College Algebra Students' Understanding of Functions and Graphs

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Publisher :
ISBN 13 :
Total Pages : 236 pages
Book Rating : 4.:/5 (318 download)

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Book Synopsis Effects of Graphing Calculators on College Algebra Students' Understanding of Functions and Graphs by : Elizabeth Ann Nagel

Download or read book Effects of Graphing Calculators on College Algebra Students' Understanding of Functions and Graphs written by Elizabeth Ann Nagel and published by . This book was released on 1994 with total page 236 pages. Available in PDF, EPUB and Kindle. Book excerpt: