# Ellis, Amy B.

Overview
Works: 7 works in 19 publications in 2 languages and 433 library holdings Academic theses Author QA11.2, 372.7
Publication Timeline
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Most widely held works by Amy B Ellis
Developing essential understanding of ratios, proportions, and proportional reasoning for teaching mathematics in grades 6-8 by Joanne Lobato( Book )

6 editions published between 2010 and 2014 in English and held by 199 WorldCat member libraries worldwide

How do you refute the erroneous claim that all ratios are fractions? This book goes beyond a simple introduction to ratios, proportions, and proportional reasoning. It will help broaden and deepen your mathematical understanding of one of the most challenging topics for students and teachers to grasp. It will help you engage your students, anticipate their perplexities, help them avoid pitfalls, and dispel misconceptions. You will also learn to develop appropriate tasks, techniques, and tools for assessing your students understanding of the topic
Developing essential understanding of mathematical reasoning for teaching mathematics in prekindergarten-grade 8 by John K Lannin( Book )

4 editions published between 2011 and 2013 in English and held by 137 WorldCat member libraries worldwide

Developing essential understanding of proof and proving for teaching mathematics in grades 9-12 by Amy B Ellis( Book )

2 editions published in 2012 in English and held by 87 WorldCat member libraries worldwide

What is the difference between "proof" in mathematics and "proof" in science or a court of law? In mathematics, how does proof differ from other types of arguments? What forms can proof take besides the traditional two-column style? What activities constitute the process of proving? What roles do examples play in proving? Can examples ever prove a conjecture? Why does a single counterexample refute a conjecture? How much do you know, and how much do you need to know? Helping your students develop a robust understanding of mathematical proof and proving requires that you understand this aspect of mathematics deeply. But what does that mean? This book focuses on essential knowledge for teachers about proof and the process of proving. It is organized around five big ideas, supported by multiple smaller, interconnected ideas essential understandings. Taking you beyond a simple introduction to proof and the activities involved in proving, the book will broaden and deepen your mathematical understanding of one of the most challenging topics for students and teachers. It will help you engage your students, anticipate their perplexities, avoid pitfalls, and dispel misconceptions. You will also learn to develop appropriate tasks, techniques, and tools for assessing students' understanding of the topic. Focus on the ideas that you need to understand thoroughly to teach confidently. - Publisher
Relationships between generalizing and justifying : students' reasoning with linear functions by Amy B Ellis( )

4 editions published in 2004 in English and held by 7 WorldCat member libraries worldwide

This dissertation explicates the nature of the relationships between students' acts of generalizing and acts of justifying. A new generalization framework supports the development of these relationships. This cohesive categorization system differentiates the types of generalizations students construct when reasoning mathematically. The framework accounts for multiple levels of generalizing, and distinguishes between statements of generalization and the generalizing actions that lead to those statements. The framework, in concert with Harel and Sowder's (1998) taxonomy of proof schemes, generated direct links between types of generalizations and associated proof schemes, as well as more complex relationships revealing how the two acts mutually influence one another. Research examining students' ability to generalize and justify suggests that students experience severe difficulty in creating and using appropriate generalizations and proofs. A review of the rich body of literature documenting students' errors highlights the need to examine more thoroughly what students do understand to be general and convincing. This study extends Lobato's (2003) actor-oriented transfer perspective to examine the ways in which middle-school students generalized during units on linear functions. Qualitative analysis of clinical interviews and teaching-experiment data focused on identifying and categorizing students' generalizations, proof schemes, and the relationships between acts of generalizing and justifying. Results include six hypotheses of direct links between particular categories of generalizations and particular proof schemes. The study also identifies five dimensions across which students' generalizations and justifications mutually interact to support increasingly sophisticated reasoning: (a) cycles of generalizing actions and generalization products, (b) the role of students' attention focus, (c) generalizations that promote the transformational proof scheme, (d) the role of justification as explaining why, and (e) generalizations supported by justifying via the transformational proof scheme. The dimensions provide a way to account for the evolution of students' generalizing and justifying. Analysis of the data revealed that reasoning with emergent quantities constructed from ratios of two initial quantities is connected to more powerful generalizing and justifying than that seen when students reason with number patterns
Bi, birye, birye churon ui pilsu ihae( Book )

1 edition published in 2016 in Korean and held by 1 WorldCat member library worldwide

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1 edition published in 2014 in Korean and held by 1 WorldCat member library worldwide

The impact of the Community Partnership Schools model community school on graduation and attendance rates in one Florida high school by Amy B Ellis( )

1 edition published in 2019 in English and held by 1 WorldCat member library worldwide

Findings of this study, though mixed, suggest the Community Partnership Schools[superscript TM] model may have provided a positive environment for improvement in key measures at the targeted CPS high school. Though no definitive conclusions were reached, this study alongside other evaluations of the Community Partnership Schools[superscript TM] model may be helpful in informing decision makers regarding the potential positive influence of the CPS model on such measures as graduation and attendance rates

Audience Level
 0 1 Kids General Special

Related Identities
Languages
English (17)

Korean (2)