Ratio and Proportional Reasoning of Double-Accelerated Middle School Math Students PDF Download
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Author: Donna Wynkoop
Publisher:
ISBN:
Category :
Languages : en
Pages : 0
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Book Description
Ratio and proportional reasoning are critical concepts for students to understand to be successful in higher-level mathematics. In 1989, the National Council of Teachers of Mathematics (NCTM) published the Curriculum and Evaluation Standards for School Mathematics stating that the ability to reason proportionally is of "such great importance that it merits whatever time and effort that must be expended to assure its careful development" (NCTM, 1989, p. 82). According to the Common Core State Standards -- Mathematics (CCSS-M), the development of these concepts begins in kindergarten and culminates in grades six and seven, where they are separate domains. The participants in this study took Pre-Algebra in the sixth grade and Algebra I in the seventh grade, rather than the district CCSS-M based math curriculum and are considered double-accelerated students. Because of this acceleration they did not receive instruction in the domain of Ratio and Proportional Reasoning as set forth in the CCSS-M. The NCTM 2016 Position Statement on Providing Opportunities for Students with Exceptional Mathematical Promise states, "When considering opportunities for acceleration in mathematics, care must be taken to ensure that opportunities are available to each and every prepared student and that no critical concepts are rushed or skipped ..." (page 1). The critical concept of Ratio and Proportional Reasoning may have been rushed or skipped for these participants. Therefore, this case study sought to characterize the conceptual and Essential Understandings of Ratio and Proportional Reasoning of these double-accelerated participants. Participants were a convenience sample of eighth-grade students enrolled in a suburban middle school in south-central Pennsylvania. Data was predominantly collected via written documentation including pretest, instructional response, post-test, and limited participant journals. Researcher notes were transcribed to capture participant discussion and interaction with the researcher. Pretest and post-data were then analyzed and coded using researcher-created codes based on NCTM's Essential Understandings of Ratio and Proportional Reasoning Grades 6-8 and relevant conceptual understandings based on the literature. These double-accelerated participants demonstrated many of the same understandings as found in prior research conducted with on-grade level and lower-performing students. The implications of this study are that more care must be taken when accelerating students so that they develop deep, conceptual understandings in all areas of mathematics, but particularly in Ratio and Proportional Reasoning. The findings of this study call for more research into acceleration practices and curriculum development for accelerated students to ensure those students with exceptional mathematics promise have the understanding necessary to continue onto more advanced math topics.
Author: Donna Wynkoop
Publisher:
ISBN:
Category :
Languages : en
Pages : 0
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Book Description
Ratio and proportional reasoning are critical concepts for students to understand to be successful in higher-level mathematics. In 1989, the National Council of Teachers of Mathematics (NCTM) published the Curriculum and Evaluation Standards for School Mathematics stating that the ability to reason proportionally is of "such great importance that it merits whatever time and effort that must be expended to assure its careful development" (NCTM, 1989, p. 82). According to the Common Core State Standards -- Mathematics (CCSS-M), the development of these concepts begins in kindergarten and culminates in grades six and seven, where they are separate domains. The participants in this study took Pre-Algebra in the sixth grade and Algebra I in the seventh grade, rather than the district CCSS-M based math curriculum and are considered double-accelerated students. Because of this acceleration they did not receive instruction in the domain of Ratio and Proportional Reasoning as set forth in the CCSS-M. The NCTM 2016 Position Statement on Providing Opportunities for Students with Exceptional Mathematical Promise states, "When considering opportunities for acceleration in mathematics, care must be taken to ensure that opportunities are available to each and every prepared student and that no critical concepts are rushed or skipped ..." (page 1). The critical concept of Ratio and Proportional Reasoning may have been rushed or skipped for these participants. Therefore, this case study sought to characterize the conceptual and Essential Understandings of Ratio and Proportional Reasoning of these double-accelerated participants. Participants were a convenience sample of eighth-grade students enrolled in a suburban middle school in south-central Pennsylvania. Data was predominantly collected via written documentation including pretest, instructional response, post-test, and limited participant journals. Researcher notes were transcribed to capture participant discussion and interaction with the researcher. Pretest and post-data were then analyzed and coded using researcher-created codes based on NCTM's Essential Understandings of Ratio and Proportional Reasoning Grades 6-8 and relevant conceptual understandings based on the literature. These double-accelerated participants demonstrated many of the same understandings as found in prior research conducted with on-grade level and lower-performing students. The implications of this study are that more care must be taken when accelerating students so that they develop deep, conceptual understandings in all areas of mathematics, but particularly in Ratio and Proportional Reasoning. The findings of this study call for more research into acceleration practices and curriculum development for accelerated students to ensure those students with exceptional mathematics promise have the understanding necessary to continue onto more advanced math topics.
Author: Marjorie M. Petit
Publisher: Routledge
ISBN: 1000071448
Category : Education
Languages : en
Pages : 242
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Book Description
This resource offers a groundbreaking effort to make mathematics education research on ratios and proportions readily accessible and understandable to preservice and in-service teachers of grades 6 to 8. Using extensive annotated samples of student work and based on research gathered in the Ongoing Assessment Project (OGAP), A Focus on Ratios and Proportions teaches readers how students develop understanding and fluency involving ratio and proportion concepts. Special features include: A close focus on student work, including 150+ annotated pieces of student work, to help teachers improve their ability to recognize, assess and monitor their students’ errors and misconceptions, as well as their developing conceptual understanding. A focus on the OGAP Ratios and Proportions Progression, based on research conducted with hundreds of teachers and thousands of pieces of student work. Sections on how Common Core State Standards for Math (CCSSM) are supported by math education research. Student work samples and vignettes to illuminate the research, as well as end of chapter Looking Back questions and Instructional Links, which allow teachers to analyze evidence of student thinking and strategies and consider instructional responses. An accompanying eResource, available online, offers an answer key as well as extensive explanation of the Looking Back questions. Like A Focus on Multiplication and Division and A Focus on Fractions, this book is designed to bridge the gap between what math education researchers know and what teachers need to know in order to better understand evidence in student work and make effective instructional decisions.
Author: Judith Flowers
Publisher:
ISBN:
Category :
Languages : en
Pages : 338
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Book Description
Author: Matthew Randall Clark
Publisher:
ISBN:
Category :
Languages : en
Pages : 171
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Book Description
Keywords: mathematics education, proportional reasoning, ratios.
Author: Carmen Whitman
Publisher: Math Solutions
ISBN: 9781935099246
Category : Education
Languages : en
Pages : 271
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Book Description
"Presents 18 proportional reasoning lessons for middle-school students; each lesson contains standards correlations, vocabulary, teacher notes, student connections, and reproducible pages, with the goal of seeing inclusive proportionality as the big idea that helps educators to make a unifying connection across all mathematics strands"--Provided by publisher.
Author: Robert Kaplinsky
Publisher: Taylor & Francis
ISBN: 1003839886
Category : Education
Languages : en
Pages : 193
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Book Description
This book is an amazing resource for teachers who are struggling to help students develop both procedural fluency and conceptual understanding.. --Dr. Margaret (Peg) Smith, co-author of5 Practices for Orchestrating Productive Mathematical Discussions Robert Kaplinsky, the co-creator of Open Middle math problems, brings hisnew class of tasks designed to stimulate deeper thinking and lively discussion among middle and high school students in Open Middle Math: Problems That Unlock Student Thinking, Grades 6-12. The problems are characterized by a closed beginning,- meaning all students start with the same initial problem, and a closed end,- meaning there is only one correct or optimal answer. The key is that the middle is open- in the sense that there are multiple ways to approach and ultimately solve the problem. These tasks have proven enormously popular with teachers looking to assess and deepen student understanding, build student stamina, and energize their classrooms. Professional Learning Resource for Teachers: Open Middle Math is an indispensable resource for educators interested in teaching student-centered mathematics in middle and high schools consistent with the national and state standards. Sample Problems at Each Grade: The book demonstrates the Open Middle concept with sample problems ranging from dividing fractions at 6th grade to algebra, trigonometry, and calculus. Teaching Tips for Student-Centered Math Classrooms: Kaplinsky shares guidance on choosing problems, designing your own math problems, and teaching for multiple purposes, including formative assessment, identifying misconceptions, procedural fluency, and conceptual understanding. Adaptable and Accessible Math: The tasks can be solved using various strategies at different levels of sophistication, which means all students can access the problems and participate in the conversation. Open Middle Math will help math teachers transform the 6th -12th grade classroom into an environment focused on problem solving, student dialogue, and critical thinking.
Author: Peter Sheppard
Publisher: Rowman & Littlefield
ISBN: 1475847491
Category : Education
Languages : en
Pages : 187
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Book Description
This work seeks to contribute to the national dialogue regarding best practices in teaching middle school mathematics. The authors are committed to improving mathematics achievement and opportunities for students whose inherited circumstances place them at a perceptible disadvantage. Most refer to said students as “risks.” We hold the position that these students, irrespective of their backgrounds, possess Hidden or Unmet Potential and the unveiling of their potential can be accelerated when they are exposed to high-quality mathematics teaching. This book is a practitioner’s guide to creative mathematics activities centered on algebraic, proportional, and geometric reasoning aligned with mathematics standards. This approach has the potential to accelerate the mathematical confidence and accentuate the mathematical proficiencies of students.
Author: Cathy L. Seeley
Publisher: Math Solutions
ISBN: 1935099035
Category : Mathematics
Languages : en
Pages : 277
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Book Description
Nctm Past President Cathy L. Seeley shares her messages on today's most relevant topics and issues in education. Based on Cathy L. Seeley's award-winning nctm President's Messages, and including dozens of new messages, this must-have k-12 resource offers straight talk and common sense about some of today's most important, thought-provoking issues in education. With topics ranging from the impact of rising expectations and the trap of timed tests to the role of technology and the phenomenon of jumping on bandwagons, this book provides a base for lively discussion among elementary, middle, and high school teachers; leaders; policy makers; and families. This book contains 41 messages included in three sections: (1) School Mathematics for the 21st Century: Elementary and Secondary Mathematics in America; (2) Great Ideas Whose Time Has Come (and Gone?): Mathematics Issues Facing Schools and Districts; and (3) Real Students and Real Teachers: Mathematics in Today's Classroom. This book also contains the following: (1) Foreword by Marilyn Burns; (2) Introduction; (3) How to Use This Book; (4) Afterword: The Sum of the Parts Is Greater than Some of the Parts; (5) Acknowledgments; (6) Readings and References; (7) Index; and (8) About the Author.
Author: Rod Clement
Publisher: Gareth Stevens Publishing LLLP
ISBN: 9780836803587
Category : Juvenile Nonfiction
Languages : en
Pages : 36
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Book Description
A boy and his dog present amusing counting, size comparison, and mathematical facts.
Author: Travis Olson
Publisher: National Council of Teachers of English
ISBN: 9780873537179
Category : Ratio and proportion
Languages : en
Pages : 0
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Book Description
Focuses on the specialized pedagogical content knowledge that you need to teach ratios and proportions effectively in grades 6-8. The authors demonstrate how to use this multifaceted knowledge to address the big ideas and essential understandings that students must develop for success with ratios and proportions.
