Precalculus Students' Achievement When Learning Functions PDF Download
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Author: Laura Hauser
Publisher:
ISBN:
Category : Education
Languages : en
Pages :
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Book Description
The concept of function is one of the essential topics in the teaching and learning of secondary mathematics because of the central and unifying role it plays within secondary and college level mathematics. Organizations, such as the National Council of Teachers of Mathematics, suggest students should be able to make connections across multiple representations of mathematical functions by the time they complete high school. Despite the prominent role functions play in secondary mathematics curriculum, students continue to struggle with the complex notion of functions and especially have difficulty using the different representations that are inherent to functions (algebraic, graphical and tabular). Technology is often considered an effective tool in raising student achievement, especially in learning functions where the different representations of a graphing calculator are analogous to the different representations of a function. Opportunity to learn is another important consideration when examining achievement and is generally considered one of, if not the most important, factor in student achievement. Opportunity to learn, or the measure of to what extent students have had an opportunity to learn or review a concept, is often measured with self-reports of content coverage. This study examined the relationship between opportunity to learn, students'; use of graphing calculators, and achievement within a curriculum that supports integrated use of technology and focuses on conceptual understanding of mathematical concepts. The research questions focused on what opportunities students had to learn functions from the enacted curriculum, what calculator strategies students used when solving function problems, how both opportunity to learn and calculator strategies influenced student achievement, and what relationships exist between opportunity to learn, use of calculator strategies, and student achievement.
Author: Laura Hauser
Publisher:
ISBN:
Category : Education
Languages : en
Pages :
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Book Description
The concept of function is one of the essential topics in the teaching and learning of secondary mathematics because of the central and unifying role it plays within secondary and college level mathematics. Organizations, such as the National Council of Teachers of Mathematics, suggest students should be able to make connections across multiple representations of mathematical functions by the time they complete high school. Despite the prominent role functions play in secondary mathematics curriculum, students continue to struggle with the complex notion of functions and especially have difficulty using the different representations that are inherent to functions (algebraic, graphical and tabular). Technology is often considered an effective tool in raising student achievement, especially in learning functions where the different representations of a graphing calculator are analogous to the different representations of a function. Opportunity to learn is another important consideration when examining achievement and is generally considered one of, if not the most important, factor in student achievement. Opportunity to learn, or the measure of to what extent students have had an opportunity to learn or review a concept, is often measured with self-reports of content coverage. This study examined the relationship between opportunity to learn, students'; use of graphing calculators, and achievement within a curriculum that supports integrated use of technology and focuses on conceptual understanding of mathematical concepts. The research questions focused on what opportunities students had to learn functions from the enacted curriculum, what calculator strategies students used when solving function problems, how both opportunity to learn and calculator strategies influenced student achievement, and what relationships exist between opportunity to learn, use of calculator strategies, and student achievement.
Author: Anthony Wayne Wagner
Publisher:
ISBN:
Category : Academic achievement
Languages : en
Pages : 164
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Book Description
Author: Douglas W. Nance
Publisher:
ISBN:
Category : Calculus
Languages : en
Pages : 342
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Book Description
Author: Libby Knott
Publisher: IAP
ISBN: 1607522845
Category : Education
Languages : en
Pages : 242
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Book Description
The intent of this monograph is to showcase successful implementation of mathematical discourse in the classroom. Some questions that might be addressed are: * How does a teacher begin to learn about using discourse purposefully to improve mathematics teaching and learning? * How is discourse interwoven into professional development content courses to provide teachers with the tools necessary to begin using discourse in their own classrooms? * What does a discourse-rich classroom look like and how is it different from other classrooms, from both the teacher's and the students' perspectives? * How can teachers of pre-service teachers integrate discourse into their content and methods courses? * How can we use discourse research to inform work with teachers, both pre- and in-service, for example, to help them know how to respond to elicited knowledge from students in their classrooms? * What are the discourse challenges in on-line mathematics courses offered for professional development? Can on-line classrooms also be discourse-rich? What would that look like? * In what ways does mathematical discourse differ from discourse in general?
Author: Anne L. Rothstein
Publisher: Guilford Publications
ISBN: 1462539130
Category : Social Science
Languages : en
Pages : 321
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Book Description
Providing clear-cut steps for producing each section of a competitive grant proposal, this hands-on book is filled with examples from actual RFPs and proposals, practical tools, and writing tips. Prominent educator and successful proposal writer Anne L. Rothstein shares a systematic process created over decades of experience in the field. She details how to: achieve group consensus around a project; identify likely funding sources; establish need; develop objectives; assemble a Master Project Table and other needed tables, figures, and charts; create an effective logic model; prepare an evaluation; put together a budget; tailor the proposal to meet the requirements of funders; and avoid common errors. Purchasers get access to a Web page where they can download and print the book's 14 reproducible templates in a convenient 8 1/2" x 11" size.
Author: Cynthia H. Pilipczuk
Publisher:
ISBN: 9780542723995
Category : Academic achievement
Languages : en
Pages :
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Book Description
Author: Wendy M. Smith
Publisher: American Mathematical Soc.
ISBN: 1470463776
Category : Education
Languages : en
Pages : 348
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Book Description
The purpose of this handbook is to help launch institutional transformations in mathematics departments to improve student success. We report findings from the Student Engagement in Mathematics through an Institutional Network for Active Learning (SEMINAL) study. SEMINAL's purpose is to help change agents, those looking to (or currently attempting to) enact change within mathematics departments and beyond—trying to reform the instruction of their lower division mathematics courses in order to promote high achievement for all students. SEMINAL specifically studies the change mechanisms that allow postsecondary institutions to incorporate and sustain active learning in Precalculus to Calculus 2 learning environments. Out of the approximately 2.5 million students enrolled in collegiate mathematics courses each year, over 90% are enrolled in Precalculus to Calculus 2 courses. Forty-four percent of mathematics departments think active learning mathematics strategies are important for Precalculus to Calculus 2 courses, but only 15 percnt state that they are very successful at implementing them. Therefore, insights into the following research question will help with institutional transformations: What conditions, strategies, interventions and actions at the departmental and classroom levels contribute to the initiation, implementation, and institutional sustainability of active learning in the undergraduate calculus sequence (Precalculus to Calculus 2) across varied institutions?
Author: Courtney Rose Nagle
Publisher:
ISBN:
Category :
Languages : en
Pages : 227
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Book Description
The limit concept plays a foundational role in calculus, appearing in the definitions of the two main ideas of introductory calculus, derivatives and integrals. Previous research has focused on three stages of students' development of limit ideas: the premathematical stage, the introductory calculus stage, and the transition from introductory calculus to the formal definition of the limit concept. Fairly little is known about the gulf between the premathematical stage and the introductory calculus stage. This study fills the void in research by investigating the knowledge components for limits developed during precalculus mathematics. One-hundred fifty high school and college precalculus students were engaged in a series of tasks designed to investigate students' ability to reason about limits. These tasks were designed based on the notion of predicting function values and required no prior knowledge of limits or calculus.^The tasks included both graphical and numerical representations of various functional behaviors, including linear, non-linear, unbounded, piecewise, and oscillating functions. Students' solutions to the limit tasks were coded using the qualitative technique of grounded theory in order to develop a list of knowledge components demonstrated in students' solutions to the tasks. Five knowledge themes emerged from the coding of knowledge components: finding patterns, functions, reading and extrapolating graphs, notions of closeness and approaching, and unexpected function behaviors. Results showed that students scored better on functional tasks represented in graphical form compared with the same functional tasks represented in numerical form.^A learning trajectory for the limit concept should provide a description of the desired outcome (a formal understanding of the limit concept), the stages of students' cognitive development, and instructional activities intended to advance students through the various stages. Additional statistical analyses contributed to informing a learning trajectory for limits. In particular, factor analysis showed that the numerical tasks and graphical tasks each measured a single underlying construct. Correlations between students' use of the various numerical and graphical knowledge components were used to identify simplex models and Guttman scalograms which supported developmental progressions. In particular, the developmental progressions supported knowledge of finding patterns, defining functions, reading and extrapolating graphs, and notions of the mathematical meaning of closeness and approaching as important prerequisites for developing additional, more advanced knowledge components.^Results of the regression analysis showed that students' knowledge of approaching a value as well as their ability to recognize unexpected function behaviors predicted their achievement on the limit tasks. The notion of approaching was distinct from the other knowledge components in terms of its importance as both a prerequisite for other concepts and its power for predicting student achievement. The findings of this study support precalculus instruction that builds students' understanding of the mathematical meaning of closeness as a building block for introductory calculus instruction, which extends the idea to approaching via arbitrary closeness. The results also support an emphasis on multiple representations of functions so that students can build covariational reasoning that supports recognizing various graphical behaviors as illustrations of a relationship between two covarying quantities.^The results corroborate previous findings that students struggle to interpret non-linear relationships, particularly when considering numerical representations. The findings are synthesized into a theory for how students develop notions of limit over time as well as into pedagogical suggestions for how precalculus and introductory calculus instruction can improve students' development of rich concept images.
Author: Yeping Li
Publisher: Springer Science & Business Media
ISBN: 9400775601
Category : Education
Languages : en
Pages : 651
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Book Description
Mathematics curriculum, which is often a focus in education reforms, has not received extensive research attention until recently. Ongoing mathematics curriculum changes in many education systems call for further research and sharing of effective curriculum policies and practices that can help lead to the improvement of school education. This book provides a unique international perspective on diverse curriculum issues and practices in different education systems, offering a comprehensive picture of various stages along curriculum transformation from the intended to the achieved, and showing how curriculum changes in various stages contribute to mathematics teaching and learning in different educational systems and cultural contexts. The book is organized to help readers learn not only from reading individual chapters, but also from reading across chapters and sections to explore broader themes, including: Identifying what is important in mathematics for teaching and learning in different education systems; Understanding mathematics curriculum and its changes that are valued over time in different education systems; Identifying and analyzing effective curriculum practices; Probing effective infrastructure for curriculum development and implementation. Mathematics Curriculum in School Education brings new insights into curriculum policies and practices to the international community of mathematics education, with 29 chapters and four section prefaces contributed by 56 scholars from 14 different education systems. This rich collection is indispensable reading for mathematics educators, researchers, curriculum developers, and graduate students interested in learning about recent curriculum development, research, and practices in different education systems. It will help readers to reflect on curriculum policies and practices in their own education systems, and also inspire them to identify and further explore new areas of curriculum research for improving mathematics teaching and learning.
Author: Benjamin Rott
Publisher: Springer
ISBN: 3030012735
Category : Education
Languages : en
Pages : 253
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Book Description
The book is made up of 21 chapters from 25 presentations at the 23rd MAVI conference in Essen, which featured Alan Schoenfeld as keynote speaker. Of major interest to MAVI participants is the relationship between teachers’ professed beliefs and classroom practice. The first section is dedicated to classroom practices and beliefs regarding those practices, taking a look at prospective or practicing teachers’ views of different practices such as decision-making, the roles of explanations, problem-solving, patterning, and the use of play. The focus of the second section in this book deals with teacher change, which is notoriously difficult, even when the teachers themselves are interested in changing their practice. The third section of this book centers on the undercurrents of teaching and learning mathematics, what rises in various situations, causing tensions and inconsistencies. The last section of this book takes a look at emerging themes in affect-related research. In this section, papers discuss attitudes towards assessment.
