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

Proceedings of a National Symposium
(Compass Series)
National Council of Teachers of Mathematics, Mathematical Sciences Education Board, National Research Council

National Academies Press | 1998 | 206 páginas

on-line: nap.edu

Methods of effectively teaching algebraic thinking in elementary schools as well as secondary schools is the topic of the following 19 papers. Papers include: (1) "Transforming Algebra from an Engine of Inequity to an Engine of Mathematical Power by 'Algebrafying' the K-12 Curriculum" (J. Kaput); (2) "Developing a Coherent and Focused K-12 Algebra Curriculum" (E. Phillips); (3) "Enhancing Algebraic Reasoning with Technology" (G. Akst); (4) "Algebra for Everyone? With or Without Technology?" (M. Norman); (5) "How Might Technology Enhance Algebraic Reasoning?" (R. Zbiek); (6) "What Do We Know about K-14 Students' Learning of Algebra?" (J. Confrey); (7) "Algebra: What All Students Can Learn" (S. Williams and D. Molina); (8) "Improving K-14 Algebra Instruction: A Discussion of Teachers' Responsibilities and Students' Opportunities" (B. Moore-Harris); (9) "Capturing Patterns and Functions: Variables and Joint Variation" (G. Lappan); (10) "Functions and Relations: A Unifying Theme for School Algebra in Grades 9-12" (C. Hirsch); (11) "Middle School Algebra from a Modeling Perspective" (G. Kleiman); (12) "Why Modeling Matters" (L. Godbold); (13) "Modeling: Changing the Mathematics Experience in Postsecondary Classrooms" (R. Dance); (14) "Algebraic Structure in the Mathematics of Elementary-School Children" (C. Tierney); (15) "Structure in School Algebra (Middle School)" (M. van Reeuwijk); (16) "The Role of Algebraic Structure in the Mathematics Curriculum of Grades 11-14" (G. Foley); (17) "Language and Representation in Algebra: A View from the Middle" (R. Billstein); (18) "Teaching Algebra: Lessons Learned by a Curriculum Developer" (D. Resek); and (19) "The Nature and Role of Algebra: Language and Representation" (D. Hughes Hallett). (ASK)

Foundations of Geometry

David Hilbert

Open Court Publishing Company | 1971 | 226 páginas


on-line: gutenberg.org
on-line: archive.org

A History Of The Mathematical Theory Of Probability

A history of the mathematical theory of probability: From The Time Of Pascal to that of Laplace
Todhunter

London : Macmillan | 1865 |

on-line: archive.org
gallica.bnf.fr
ia600305.us.archive.org

Kessinger Publishing, LLC | 2007 | 640 páginas | rar - djvu | 29 Mb

Descrição: A thorough and standard work in the field. Isaac Todhunter (1820-1884) gave a close and carefully reasoned account of the difficulties involved and the solutions offered by each investigator. His studies and use of source materials were thorough and fully documented. His reputation rests on the contribution he made to the history of mathematics.

Helping Children Learn Mathematics

Jeremy Kilpatrick, Jane Swafford

National Academies Press | 2002 | 52 páginas

on-line: nap.edu

Results from national and international assessments indicate that school children in the United States are not learning mathematics well enough. Many students cannot correctly apply computational algorithms to solve problems. Their understanding and use of decimals and fractions are especially weak. Indeed, helping all children succeed in mathematics is an imperative national goal. However, for our youth to succeed, we need to change how we're teaching this discipline. Helping Children Learn Mathematics provides comprehensive and reliable information that will guide efforts to improve school mathematics from pre-kindergarten through eighth grade. The authors explain the five strands of mathematical proficiency and discuss the major changes that need to be made in mathematics instruction, instructional materials, assessments, teacher education, and the broader educational system and answers some of the frequently asked questions when it comes to mathematics instruction. The book concludes by providing recommended actions for parents and caregivers, teachers, administrators, and policy makers, stressing the importance that everyone work together to ensure a mathematically literate society.

High School Mathematics at Work: Essays and Examples for the Education of All Students

Mathematical Sciences Education Board, National Research Council

National Academies Press | 1998 | 192 páginas

on-line: books.nap.edu

PDF - 1,16 Mb

depositfiles.com

This book is a collection of thought-provoking essays that frame basic issues, provide background, and suggest ways to strengthen the mathematical education of all students. The essays present ideas for making mathematical education meaningful for all students--how to meet the practical needs of students entering the work force after high school as well as the needs of those going on to postsecondary education. The essays take up issues such as: finding common ground between science and mathematics education standards and improving the articulation from school to work. High School Mathematics at Work provides thoughtful views from mathematicians, educators, and other experts, and identifies rich possibilities for teaching mathematics and preparing students for the technological challenges of the future.

Mathematics Education in the Middle Grades: Teaching to Meet the Needs of Middle Grades Learners and to Maintain High Expectations

National Research Council, National Convocation on Mathematics Education in the Middle Grades

National Academy Press | 2000 | 270 páginas | pdf | 1,07 Mb

on-line: nap.edu

Bringing Out the Algebraic Character of Arithmetic: From Children’s Ideas to Classroom Practic

Analucia Dias Schliemann, David William Carraher, Barbara M. Brizuela,

Lawrence Erlbaum | 2006 | 144 páginas | pdf | 1,37 Mb

Versão draft

on-line: earlyalgebra.terc.edu

Referência em MathEdu

Bringing Out the Algebraic Character of Arithmetic contributes to a growing body of research relevant to efforts to make algebra an integral part of early mathematics instruction, an area of studies that has come to be known as Early Algebra. It provides both a rationale for promoting algebraic reasoning in the elementary school curriculum and empirical data to support it.

The authors regard Early Algebra not as accelerated instruction but as an approach to existing topics in the early mathematics curriculum that highlights their algebraic character. Each chapter shows young learners engaged in mathematics tasks where there has been a shift away from computations on specific amounts toward thinking about relations and functional dependencies. The authors show how young learners attempt to work with mathematical generalizations before they have learned formal algebraic notation.

The book, suitable as a text in undergraduate or graduate mathematics education courses, includes a CD-ROM with additional text and video footage on how students reason about addition and subtraction as functions; on how students understand multiplication when it is presented as a function; and on how children use notations in algebraic problems involving fractions. These three videopapers (written text with embedded video footage) present relevant discussions that help identify students' mathematical reasoning. The printed text in the book includes transcriptions of the video episodes in the CD-ROM.

Bringing Out the Algebraic Character of Arithmetic is aimed at researchers, practitioners, curriculum developers, policy makers and graduate students across the mathematics education community who wish to understand how young learners deal with algebra before they have learned about algebraic notation.

Contents: Preface: Rethinking Early Mathematics Education. Interpreting Research About Learning Algebra. Part I: Interview Studies. Young Children's Understanding of Equivalences. Can Young Students Solve Equations? Part II: Classroom Studies. Addition Operations as Functions. From Quantities to Ratio, Functions, and Algebraic Notation. On Children's Written Notation to Solve Problems. Discussion.