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This monograph reports on an analysis of a small part of the mathematics curriculum, the definitions given to quadrilaterals. This kind of research, which we call micro-curricular analysis, is often undertaken by those who create curriculum, but it is not usually done systematically and it is rarely published.Many terms in mathematics education can be found to have different definitions in mathematics books. Among these are “natural number,” “parallel lines” and “congruent triangles,” “trapezoid” and “isosceles trapezoid,” the formal definitions of the trigonometric functions and absolute value, and implicit definitions of the arithmetic operations addition, subtraction, multiplication, and division.Yet many teachers and students do not realize there is a choice of definitions for mathematical terms. And even those who realize there is a choice may not know who decides which definition of any mathematical term is better, and under what criteria. Finally, rarely are the mathematical implications of various choices discussed. As a result, many students misuse and otherwise do not understand the role of definition in mathematics.We have chosen in this monograph to examine a bit of mathematics for its definitions: the quadrilaterals. We do so because there is some disagreement in the definitions and, consequently, in the ways in which quadrilaterals are classified and relate to each other. The issues underlying these differences have engaged students, teachers, mathematics educators, and mathematicians. There have been several articles and a number of essays on the definitions and classification of quadrilaterals. But primarily we chose this specific area of definition in mathematics because it demonstrates how broad mathematical issues revolving around definitions become reflected in curricular materials. While we were undertaking this research, we found that the area of quadrilaterals supplied grist for broader and richer discussions than we had first anticipated.The intended audience includes curriculum developers, researchers, teachers, teacher trainers, and anyone interested in language and its use.

This monograph reports on an analysis of a small part of the mathematics curriculum, the definitions given to quadrilaterals. This kind of research, which we call micro-curricular analysis, is often undertaken by those who create curriculum, but it is not usually done systematically and it is rarely published.Many terms in mathematics education can be found to have different definitions in mathematics books. Among these are “natural number,” “parallel lines” and “congruent triangles,” “trapezoid” and “isosceles trapezoid,” the formal definitions of the trigonometric functions and absolute value, and implicit definitions of the arithmetic operations addition, subtraction, multiplication, and division.Yet many teachers and students do not realize there is a choice of definitions for mathematical terms. And even those who realize there is a choice may not know who decides which definition of any mathematical term is better, and under what criteria. Finally, rarely are the mathematical implications of various choices discussed. As a result, many students misuse and otherwise do not understand the role of definition in mathematics.We have chosen in this monograph to examine a bit of mathematics for its definitions: the quadrilaterals. We do so because there is some disagreement in the definitions and, consequently, in the ways in which quadrilaterals are classified and relate to each other. The issues underlying these differences have engaged students, teachers, mathematics educators, and mathematicians. There have been several articles and a number of essays on the definitions and classification of quadrilaterals. But primarily we chose this specific area of definition in mathematics because it demonstrates how broad mathematical issues revolving around definitions become reflected in curricular materials. While we were undertaking this research, we found that the area of quadrilaterals supplied grist for broader and richer discussions than we had first anticipated.The intended audience includes curriculum developers, researchers, teachers, teacher trainers, and anyone interested in language and its use.

This volume contains the proceedings of the First International Curriculum Conference sponsored by the Center for the Study of Mathematics Curriculum (CSMC). The CSMC is one of the National Science Foundation Centers for Learning and Teaching (Award No. ESI-0333879). The countries—China, Japan, Korea, and Singapore (in alphabetical order, which also happens to be the order of their populations)—have each been in the news because of their performance on international testsand/or their economic performance and potential. They also have centralized education ministries that create a single mathematics curriculum framework followed in the entire country. In all these countries, curricula are differentiated for students with different interests, usually around Grade 10 or 11. We think the reader will agree that the papers are of very high quality, befitting the standing of the individuals who were invited, but particularly notable for our international speakers because in three of these countries, English is not the speaker’s first language. Following each paper, we have included a short biography of the author(s), so that the reader can understand the perspective of the paper’s author.

This volume contains the proceedings of the First International Curriculum Conference sponsored by the Center for the Study of Mathematics Curriculum (CSMC). The CSMC is one of the National Science Foundation Centers for Learning and Teaching (Award No. ESI-0333879). The countries—China, Japan, Korea, and Singapore (in alphabetical order, which also happens to be the order of their populations)—have each been in the news because of their performance on international testsand/or their economic performance and potential. They also have centralized education ministries that create a single mathematics curriculum framework followed in the entire country. In all these countries, curricula are differentiated for students with different interests, usually around Grade 10 or 11. We think the reader will agree that the papers are of very high quality, befitting the standing of the individuals who were invited, but particularly notable for our international speakers because in three of these countries, English is not the speaker’s first language. Following each paper, we have included a short biography of the author(s), so that the reader can understand the perspective of the paper’s author.

This monograph reports on an analysis of a small part of the mathematics curriculum, the definitions given to quadrilaterals. This kind of research, which we call micro-curricular analysis, is often undertaken by those who create curriculum, but it is not usually done systematically and it is rarely published.Many terms in mathematics education can be found to have different definitions in mathematics books. Among these are "e;natural number,"e; "e;parallel lines"e; and "e;congruent triangles,"e; "e;trapezoid"e; and "e;isosceles trapezoid,"e; the formal definitions of the trigonometric functions and absolute value, and implicit definitions of the arithmetic operations addition, subtraction, multiplication, and division.Yet many teachers and students do not realize there is a choice of definitions for mathematical terms. And even those who realize there is a choice may not know who decides which definition of any mathematical term is better, and under what criteria. Finally, rarely are the mathematical implications of various choices discussed. As a result, many students misuse and otherwise do not understand the role of definition in mathematics.We have chosen in this monograph to examine a bit of mathematics for its definitions: the quadrilaterals. We do so because there is some disagreement in the definitions and, consequently, in the ways in which quadrilaterals are classified and relate to each other. The issues underlying these differences have engaged students, teachers, mathematics educators, and mathematicians. There have been several articles and a number of essays on the definitions and classification of quadrilaterals. But primarily we chose this specific area of definition in mathematics because it demonstrates how broad mathematical issues revolving around definitions become reflected in curricular materials. While we were undertaking this research, we found that the area of quadrilaterals supplied grist for broader and richer discussions than we had first anticipated.The intended audience includes curriculum developers, researchers, teachers, teacher trainers, and anyone interested in language and its use.

This volume contains the proceedings of the First International Curriculum Conference sponsored by the Center for the Study of Mathematics Curriculum (CSMC). The CSMC is one of the National Science Foundation Centers for Learning and Teaching (Award No. ESI-0333879). The countries-China, Japan, Korea, and Singapore (in alphabetical order, which also happens to be the order of their populations)-have each been in the news because of their performance on international testsand/or their economic performance and potential. They also have centralized education ministries that create a single mathematics curriculum framework followed in the entire country. In all these countries, curricula are differentiated for students with different interests, usually around Grade 10 or 11. We think the reader will agree that the papers are of very high quality, befitting the standing of the individuals who were invited, but particularly notable for our international speakers because in three of these countries, English is not the speaker's first language. Following each paper, we have included a short biography of the author(s), so that the reader can understand the perspective of the paper's author.

This volume contains papers from the Second International Curriculum Conference sponsored by the Center for the Study of Mathematics Curriculum (CSMC). The intended audience includes policy makers, curriculum developers, researchers, teachers, teacher trainers, and anyone else interested in school mathematics curricula.

This volume is an outgrowth of the Conference on Research on the Enacted Mathematics Curriculum, funded by the National Science Foundation and held in Tampa, Florida in November 2010. The volume has the potential to be useful to a range of researchers, from established veterans in curriculum research to new researchers in this area of mathematics education. The chapters can be used to generate conversation about researching the enacted mathematics curriculum, including similarities and differences in the variables that can and should be studied across various curricula. As such, it might be used by a curriculum project team as it outlines a research agenda for curriculum or program evaluation. It might also be used as a text in a university graduate course on curriculum research and design.The chapters in this volume are a natural complement to those in Approaches to Studying the Enacted Mathematics Curriculum (Heck, Chval, Weiss, & Ziebarth, 2012), also published by Information Age Publishing. While the present volume focuses on a range of issues related to researching the enacted mathematics curriculum, including theoretical and conceptual issues, the volume by Heck et al. provides insights into different instrumentations used by groups of researchers to study curriculum enactment.

This volume is an outgrowth of the Conference on Research on the Enacted Mathematics Curriculum, funded by the National Science Foundation and held in Tampa, Florida in November 2010. The volume has the potential to be useful to a range of researchers, from established veterans in curriculum research to new researchers in this area of mathematics education. The chapters can be used to generate conversation about researching the enacted mathematics curriculum, including similarities and differences in the variables that can and should be studied across various curricula. As such, it might be used by a curriculum project team as it outlines a research agenda for curriculum or program evaluation. It might also be used as a text in a university graduate course on curriculum research and design.The chapters in this volume are a natural complement to those in Approaches to Studying the Enacted Mathematics Curriculum (Heck, Chval, Weiss, & Ziebarth, 2012), also published by Information Age Publishing. While the present volume focuses on a range of issues related to researching the enacted mathematics curriculum, including theoretical and conceptual issues, the volume by Heck et al. provides insights into different instrumentations used by groups of researchers to study curriculum enactment.

This volume is an outgrowth of the Conference on Research on the Enacted Mathematics Curriculum, funded by the National Science Foundation and held in Tampa, Florida in November 2010. The volume has the potential to be useful to a range of researchers, from established veterans in curriculum research to new researchers in this area of mathematics education. The chapters can be used to generate conversation about researching the enacted mathematics curriculum, including similarities and differences in the variables that can and should be studied across various curricula. As such, it might be used by a curriculum project team as it outlines a research agenda for curriculum or program evaluation. It might also be used as a text in a university graduate course on curriculum research and design.The chapters in this volume are a natural complement to those in Approaches to Studying the Enacted Mathematics Curriculum (Heck, Chval, Weiss, & Ziebarth, 2012), also published by Information Age Publishing. While the present volume focuses on a range of issues related to researching the enacted mathematics curriculum, including theoretical and conceptual issues, the volume by Heck et al. provides insights into different instrumentations used by groups of researchers to study curriculum enactment.

The mathematics curriculum – what mathematics is taught, to whom it is taught, and when it is taught – is the bedrock to understanding what mathematics students can, could, and should learn. Today’s digital technology influences the mathematics curriculum in two quite different ways. One influence is on the delivery of mathematics through hardware such as desktops, laptops, and tablets. Another influence is on the doing of mathematics using software available on this hardware, but also available on the internet, calculators, or smart phones.These developments, rapidly increasing in their availability and decreasing in their cost, raise fundamental questions regarding a mathematics curriculum that has traditionally been focused on paper-and-pencil work and taught in many places as a set of rules to be practiced and learned.This volume presents the talks given at a conference held in 2014 at the University of Chicago, sponsored by the Center for the Study of Mathematics Curriculum. The speakers – experts from around the world and inside the USA – were asked to discuss one or more of the following topics:• changes in the nature and creation of curricular materials available to students• transformations in how students learn and how they demonstrate their learning• rethinking the role of the teacher and how students and teachers interact within a classroom and across distances from each otherThe result is a set of articles that are interesting and captivating, and challenge us to examine how the learning of mathematics can and should be affected by today’s technology.

The mathematics curriculum – what mathematics is taught, to whom it is taught, and when it is taught – is the bedrock to understanding what mathematics students can, could, and should learn. Today’s digital technology influences the mathematics curriculum in two quite different ways. One influence is on the delivery of mathematics through hardware such as desktops, laptops, and tablets. Another influence is on the doing of mathematics using software available on this hardware, but also available on the internet, calculators, or smart phones.These developments, rapidly increasing in their availability and decreasing in their cost, raise fundamental questions regarding a mathematics curriculum that has traditionally been focused on paper-and-pencil work and taught in many places as a set of rules to be practiced and learned.This volume presents the talks given at a conference held in 2014 at the University of Chicago, sponsored by the Center for the Study of Mathematics Curriculum. The speakers – experts from around the world and inside the USA – were asked to discuss one or more of the following topics:• changes in the nature and creation of curricular materials available to students• transformations in how students learn and how they demonstrate their learning• rethinking the role of the teacher and how students and teachers interact within a classroom and across distances from each otherThe result is a set of articles that are interesting and captivating, and challenge us to examine how the learning of mathematics can and should be affected by today’s technology.

The mathematics curriculum - what mathematics is taught, to whom it is taught, and when it is taught - is the bedrock to understanding what mathematics students can, could, and should learn. Today's digital technology influences the mathematics curriculum in two quite different ways. One influence is on the delivery of mathematics through hardware such as desktops, laptops, and tablets. Another influence is on the doing of mathematics using software available on this hardware, but also available on the internet, calculators, or smart phones. These developments, rapidly increasing in their availability and decreasing in their cost, raise fundamental questions regarding a mathematics curriculum that has traditionally been focused on paper-and-pencil work and taught in many places as a set of rules to be practiced and learned. This volume presents the talks given at a conference held in 2014 at the University of Chicago, sponsored by the Center for the Study of Mathematics Curriculum. The speakers experts from around the world and inside the USA were asked to discuss one or more of the following topics: changes in the nature and creation of curricular materials available to students transformations in how students learn and how they demonstrate their learning rethinking the role of the teacher and how students and teachers interact within a classroom and across distances from each otherThe result is a set of articles that are interesting and captivating, and challenge us to examine how the learning of mathematics can and should be affected by today s technology.

The mathematics curriculum - what mathematics is taught, to whom it is taught, and when it is taught - is the bedrock to understanding what mathematics students can, could, and should learn. Today's digital technology influences the mathematics curriculum in two quite different ways. One influence is on the delivery of mathematics through hardware such as desktops, laptops, and tablets. Another influence is on the doing of mathematics using software available on this hardware, but also available on the internet, calculators, or smart phones. These developments, rapidly increasing in their availability and decreasing in their cost, raise fundamental questions regarding a mathematics curriculum that has traditionally been focused on paper-and-pencil work and taught in many places as a set of rules to be practiced and learned. This volume presents the talks given at a conference held in 2014 at the University of Chicago, sponsored by the Center for the Study of Mathematics Curriculum. The speakers experts from around the world and inside the USA were asked to discuss one or more of the following topics: changes in the nature and creation of curricular materials available to students transformations in how students learn and how they demonstrate their learning rethinking the role of the teacher and how students and teachers interact within a classroom and across distances from each otherThe result is a set of articles that are interesting and captivating, and challenge us to examine how the learning of mathematics can and should be affected by today s technology.

This volume is an outgrowth of the Conference on Research on the Enacted Mathematics Curriculum, funded by the National Science Foundation and held in Tampa, Florida in November 2010. The volume has the potential to be useful to a range of researchers, from established veterans in curriculum research to new researchers in this area of mathematics education. The chapters can be used to generate conversation about researching the enacted mathematics curriculum, including similarities and differences in the variables that can and should be studied across various curricula. As such, it might be used by a curriculum project team as it outlines a research agenda for curriculum or program evaluation. It might also be used as a text in a university graduate course on curriculum research and design.The chapters in this volume are a natural complement to those in Approaches to Studying the Enacted Mathematics Curriculum (Heck, Chval, Weiss, & Ziebarth, 2012), also published by Information Age Publishing. While the present volume focuses on a range of issues related to researching the enacted mathematics curriculum, including theoretical and conceptual issues, the volume by Heck et al. provides insights into different instrumentations used by groups of researchers to study curriculum enactment.

This volume contains papers from the Second International Curriculum Conference sponsored by the Center for the Study of Mathematics Curriculum (CSMC). The intended audience includes policy makers, curriculum developers, researchers, teachers, teacher trainers, and anyone else interested in school mathematics curricula.

This volume contains the proceedings of the First International Curriculum Conference sponsored by the Center for the Study of Mathematics Curriculum (CSMC). The CSMC is one of the National Science Foundation Centers for Learning and Teaching (Award No. ESI-0333879). The countries-China, Japan, Korea, and Singapore (in alphabetical order, which also happens to be the order of their populations)-have each been in the news because of their performance on international testsand/or their economic performance and potential. They also have centralized education ministries that create a single mathematics curriculum framework followed in the entire country. In all these countries, curricula are differentiated for students with different interests, usually around Grade 10 or 11. We think the reader will agree that the papers are of very high quality, befitting the standing of the individuals who were invited, but particularly notable for our international speakers because in three of these countries, English is not the speaker's first language. Following each paper, we have included a short biography of the author(s), so that the reader can understand the perspective of the paper's author.