Supporting Assessment in Undergraduate Mathematics

Lynn Arthur Steen, Bonnie Gold, Laurie Hopkins, Dick Jardine, William A. Marion (Editores)

Mathematical Association of America | 2006 | 239 páginas

on-line:
maa.org 

Like all college teachers of mathematics, I like to think that I am doing a good job. It is pleasant to think that the students that sit in my classes are getting quality instruction and that the course content is what it should be. While my beliefs are important, it is also necessary that I create the documentation to support this and satisfy the requirements known as assessment. While assessment does differ somewhat from institution to institution, the core of the requirements is essentially the same at every undergraduate institution.
Therefore, the papers in this book will be of value to you if you are currently going through an intensive assessment process. Some of the best ways to reduce the stress and workload of the process is to either borrow from others, cite the actions and consequences experienced by others or simply reading about the problems others have had. All of these and more are described in this book, and at many levels and locations. The editors have gone to great lengths to include articles by people in many different circumstances, so it is likely that you will find something appropriate to your circumstances. I have certainly found it helpful.

Mathematics

David Eugene Smith

Marshall Jones Company | 1923 | 175 páginas | rar-pdf | 8,62 Mb

on-line: quod.lib.umich.edu

link
link1

Descrição: Little book summarizing the contributions of Greece and Rome to mathematics.

Axiomatic Set Theory

Patrick Suppes


Dover Publications | 1972 | 265 páginas | pdf | 12 Mb

link
link1

djvu - 3 Mb
link
link1
link2

Descrição: In one of the finest treatments for upper undergraduate and graduate level students, Professor Suppes presents axiomatic set theory: the basic paradoxes and history of set theory, and advanced topics such as relations and functions, equipollence, finite sets and cardinal numbers, rational and real numbers and more.

A research companion to principles and standards for school mathematics

Jeremy Kilpatrick, W. Gary Martin, e Deborah Schifter (Editores)

National Council of Teachers of Mathmatics | 2003 | 413 páginas

O livro pode ser adquirido on-line em:

http://www.nctm.org/catalog/product.aspx?id=12341

De momento, estão disponíveis online, 16 dos capítulos do livro .

PDF - RAR - 12,4 Mb

Nenhum link disponível

Capítulos:
Contents (on-line: nctm.org)
Preface (on-line: nctm.org)
1 - Introdution
Jeremy Kilpatrick, W. Gary Martin e Deborah Schifter
2 - What research says about the NCTM standards
James Hiebert
3 - Making mathematics reasonable in school
Deborah Loewenberg Ball, Hyman Bass
(pdf | 1,83 Mb | on-line: personal.umich.edu)
ou (PDF | online: 393methods1)
4 - Teaching, teachers' knowledge, and their professional development
Denise S. Mewborn
5 - Classroom and large-scale assessment
Linda Dager Wilson, Patricia Ann Kenney
(PDF | online:393methods1)
6 - Developing mathematical power in whole number operations
Karen C. Fuson
(Parte do capítulo - pp. 78 - 94: PDF | online: math.wvu.edu)
7 - Fractions and multiplicative reasoning
Patrick W. Thompson, Luis A. Saldanha
(pdf | 100 kb | on-line: ite.sc.eduf)
8 - Facts and algorithms as products of students' own mathematical activity
Koeno Gravemeijer, Frans van Galen
(PDF | online : 393methods)
9 - On appreciating the cognitive complexity of school algebra: research on algebra learning and directions of curricular change
Daniel Chazan, Michal Yerushalmy
(online : PDF | 393methods1)
10 - Statis and change: integrating patterns, functions, and algebra throughout the K-12 curriculum
Erick Smith
11 - Teaching and learning geometry
Douglas H. Clements
(PDF | online: 393methods1)
12 - Developing understanding of measurement
Richard Lehrer
PDF | online: geometryandmeasurement)
13 - Reasoning about data
Clifford Konold, Traci L. Higgins
(PDF | online: 393methods1)
14 - Research on students' understanding of probability
J. Michael Shaughnessy
(PDF | online: 393methods1)
15 - Reasoning and proof
Erna Yackel, Gila Hanna
(PDF | online : 393methods1)
16 - Communication and language
Magdalene Lampert, Paul Cobb
(PDF | online: 393methods1)
17 - Representation in school mathematics: learning to graph and graphing to learn
Stephen Monk
(PDF | online : 393methods1)
18 -Representation in school mathematics: childrens' representations of problems
Stephen P. Smith
(PDF | online: 393methods1)
19 - Representation in school mathematics: a unifying research perspective
Gerald A. Goldin
20 - Implications of cognitive science research for mathematics education
Robert S. Siegler
(pdf | 330 Kb | on-line: psy.cmu.edu)
ou (PDF | online: 393methods1)
21 -  Situative research relevant to standards for school mathematics
James G. Greeno
(PDF | online: 393methods1)
22 - A sociocultural approach to mathematics reform: speaking, inscribing, and doing mathematics within communities of practice
Ellice Ann Forman
(PDF | online: 393methods1)
23 - Balancing the unbalanceable: the NCTM standards in light of theories of learning mathematics
Anna Sfard
24 - Using research in policy development: the case of the National Council of Teachers of Mathematics' Principles and standards for school mathematics
Joan Ferrini-Mundy, W. Gary Martin.

Advances in child development and behavior

Volume 16
Hayne W. Reese e L. P. Lipsett (Editores)

Academic Press | 1982 | 336 páginas | rar -pdf | 15,75 Mb

link

Com particular interesse o capítulo (pp. 242-312):
The development of numerical understandings
R. S. Siegler e M. Robinson
On-line: pdf1 e pdf2

Para outros trabalhos de Siegler, veja a página do autor:
psy.cmu.edu

The development of mathematical skills

Chris Donlan (Editor)

Psychology Press | 2000 | 338 páginas

De momento apenas um dos capítulos do livro está disponível.

Capítulos
Section 1: Pre-school mathematical understanding
Numerical competence in infants
Karen Wynn
A developmental perspective on children's countingCatherine Sophian
Symbolic function in pre-schoolersPenny Munn
Section 2: Mathematical understanding and mathematical performance.
The relationship between conceptual and procedural knowledge in learning mathematics: A review
B. Rittle-Johnson e R. S. Siegler
( pdf | 2,1 M | on-line: psy.cmu.edu)
Doing mathematics as situated practiceNaoki Ueno
Mathematics across national boundaries: Cultural and linguistic perspectives on numerical competenceJohn Towse e Matthew Saxton
Section 3: Working memory and mental calculation: Effects of age and anxiety
Children's mental arithmetic and working memoryJohn W. Adams e Graham J. Hitch
On the cognitive consequences of mathematics anxietyMark H. Ashcraft, Elizabeth P. Kirk, e Derek Hopko
Section 4: Sources of individual difference in mathematical development
Cognitive neuropyschology and developmental dyscalculiaPaul Macaruso e Scott M. Sokol
Is hearing impairment a cause of difficulties in learning mathematics?Terezinha Nunes e Constanza Moreno
Number without language? Studies of children with specific language impairmentsChris Donlan
Individual differences in normal arithmetical developmentAnn Dowker

Descrição: Current research into the psychology of children's mathematics is extremely diverse. The present volume reflects this diversity; it is unique in its breadth, bringing together accounts of cutting-edge research from widely differing, sometimes opposing viewpoints. The reader with a grounding in developmental psychology but no knowledge of mathematical development will enjoy a wide ranging and challenging summary of current trends. Those already familiar with some of the work may take the opportunity to broaden their knowledge base and to evaluate new methodologies and the insights they offer.
The opening chapters describe studies of number awareness and numerical knowledge in infancy and early childhood. Contrasting nativist and socially-oriented accounts are presented. The second section of the book examines the broad principles underlying the acquisition of mathematical knowledge, the intricate effects of cultural context and the reflexive relation between mathematical activities and the situations within which they occur. A central section examines the working memory system, its role in arithmetical development and its vulnerability to effects of anxiety. Finally, individual differences in mathematical skills are explored through novel and contrasting perspectives including case studies in cognitive neuropsychology, and group studies of hearing-impaired children and children with specific language impairments. The final chapter gives a salutary reminder of the tremendous variation in patterns of mathematical learning to be found in unselected samples of children in mainstream education.
The book is an invitation to explore a complex set of phenomena for which no unitary explanation can be offered. It aims to show that apparently disparate research perspectives may be complementary to each other, and to suggest that progress towards a comprehensive account of mathematical skills may require a broad-based understanding of research from more than one viewpoint.

The Cambridge Handbook of Thinking and Reasoning

Keith J. Holyoak, Robert G. Morrison (Editores)

Cambridge University Press | 2005 | 872 páginas | pdf

link

Com particular interesse o capítulo (pp. 559-588) :
Mathematical cognition
C. R. Gallistel e Rochel Gelman
On-line: ruccs.rutgers.edu

Descrição: The Cambridge Handbook of Thinking and Reasoning is the first comprehensive and authoritative handbook covering all the core topics of the field of thinking and reasoning. Written by the foremost experts from cognitive psychology, cognitive science, and cognitive neuroscience, individual chapters summarize basic concepts and findings for a major topic, sketch its history, and give a sense of the directions in which research is currently heading. The volume also includes work related to developmental, social and clinical psychology, philosophy, economics, artificial intelligence, linguistics, education, law, and medicine. Scholars and students in all these fields and others will find this to be a valuable collection.

Focal points

Curriculum focal points for prekinderkarten through grade 8 mathematicsNational Council of Teachers of Mathematics | 2006 | 41 páginas | PDF - 4,11 Mb

link

Descrição: Curriculum Focal Points for Prekindergarten through Grade 8 Mathematics:A Quest for Coherence provides a rationale for focal points for each grade level, prekindergarten 8. Focal points are important mathematical topics that represent major areas of content emphasis. Building on Principles and Standards for School Mathematics, this publication is presented to begin a dialogue on what is important at particular levels of instruction and as an initial step toward a more coherent, focused curriculum. Each focal point topic is a key area of mathematics and is identified in depth. Three focal points for each level, prekindergarten 8, are presented, with connections to supporting content areas.

Quantitative literacy. Why numeracy matters for schools and colleges.

Proceedings of the National Forum on Quantitative Literacy held at the National Academy of Sciences in Washington, D.C. on December 1-2, 2001.
Bernard L. Madison e Lynn Arthur Steen, Editors

National Council on Education and the Disciplines | 2003

on-line: maa.org (em capítulos)

Mathematics and democracy. The case for quantitative literacy

Lynn Arthur Steen

The National Council on Education and the Discipline | 2001

on-line: maa.org (pdf)

Capítulos:
Preface: Mathematics, Numeracy, and Democracy
Robert Orrill
The Case for Quantitative Literacy
The Quantitative Literacy Design Team
The Emergence of Numeracy
Patricia Cline Cohen
Connecting Mathematics with Reason
Joan L. Richards
Numeracy, Mathematics, and General Education
An Interview with Peter T. Ewell
Reflections on an Impoverished Education
Alan H. Schoenfeld
The Emperor’s Vanishing Clothes
Dan Kennedy
Numerical Common Sense for All
Wade Ellis, Jr.
Mathematics and Numeracy: Mutual Reinforcement
Alfred B. Manaster
Connecting Theory and Practice
An Interview with James H. Stith
Quantitative Literacy for the Next Generation
Zalman Usiskin
Encouraging Progressive Pedagogy
Larry Cuban
Achieving Numeracy:The Challenge of Implementation
Deborah Hughes-Hallett
Setting Greater Expectations for Quantitative Learning
Carol Geary Schneider
Epilogue: Embracing Numeracy
Lynn Arthur Steen

Assessment and realistic mathematics education

Marja van den Heuvel-Panhuizen
(tese)

University of Utrecht | 1996

on-line: igitur-archive.library.uu.nl (em capítulos)
igitur-archive.library.uu.nl (um único capítulo em pdf)

Descrição: Assessment and Realistic Mathematics Education This book describes the consequences of Realistic Mathematics Education (RME) for assessing students’ understanding of mathematics in primary school. RME is the Dutch answer to the worldwide need to reform mathematics education.
Changed ideas about mathematics as a school subject, its goals, ideas about teaching and learning mathematics, require new forms of assessment. Within RME this means a preference for observation and individual interviews. However, written tests have not been abandoned within this approach. As this book makes clear, even written tests can give teachers valuable information concerning the learning processes of their students, if these tests are looked at in a new light.
The book has two sections. Part I forms the core of the work. Chapter one retraces the early years of the reform of mathematics education in the Netherlands, and provides a survey of how assessment was regarded at that time.
Chapter two concentrates on how the MORE research laid the foundation for further development of primary school mathematics assessment within RME. Originally, this research was a comparative study of the implementation and effects of different approaches to mathematics education.
Chapter three provides a general orientation of the present state of affairs within RME and presents a further elaboration of the RME theory for assessment. In the second half of the chapter the RME views on assessment are held up to the mirror of international assessment reform.
In chapter four, as a supplement to the general orientation, the focus is shifted to written tests. In particular, paper-and-pencil short-task problems and the potential enrichment of such problems through the application of RME theory are discussed.
Part II describes three assessment studies in detail. Chapter five focuses on one of the tests that was developed for the MORE research, namely the test for beginning first grade. It provides background information on the development of the test and describes its unexpected results, including some international findings on the test. Chapter six gives an account of a study into the opportunities for RME in special education. The heart of this study is a written test on ratio, similar to MORE tests. Chapter seven covers a developmental research project on assessment that was conducted within the framework of the “Mathematics in Context” project, an American middle school project. The chapter focuses on one particular assessment problem on percentage. The main issue here is the tension between openness and certainty that one meets if one moves to more open-ended problems in assessment.

The Assessment Challenge in Statistics Education

The Assessment Challenge in Statistics Education
I. Gal e J. B. Garfield (Editores)

IOS Press | 1997

on-line: stat.auckland.ac.nz

Capítulos:
Curricular Goals and Assessment Challenges in Statistics Education
Iddo Gal e Joan Garfield
Part I. Curricular Goals and Assessment Frameworks
Some Emerging Influences Underpinning Assessment in Statistics
Andy Begg
Authentic Assessment Models for Statistics Education
Shirley Colvin e Kenneth E Vos
Monitoring Attitudes and Beliefs in Statistics Education
Iddo Gal, Lynda Ginsburg e Candace Schau
Part II. Assessing Conceptual Understanding of Statistical Ideas
A Framework for Assessing Knowledge and Learning in Statistics (K-8)
Susan N. Friel, George W. Bright, Dargan Frierson, Gary D. Kader
Using "Real-Life" Problems to Prompt Students to Construct Conceptual Models for Statistical Reasoning
Richard Lesh, Miriam Amit, Roberta Y. Schorr
Simple Approaches to Assessing Underlying Understanding of Statistical Concepts
Anthony E. Kelly, Finbarr Sloane, Andrea Whittaker
Assessing Students' Connected Understanding of Statistical Relationships
Candace Schau, Nancy Mattern
Part III. Innovative Models for Classroom Assessment
Assessing Statistical Thinking Using the Media
Jane M. Watson
Assessing Students' Statistical Problem-solving Behaviors in a Small-group Setting
Frances R. Curcio, Alice F. Artzt
Assessing Student Projects
Susan Starkings
Assessing Project Work by External Examiners
Peter Holmes
Portfolio Assessment in Graduate Level Statistics Courses
Carolyn M. Keeler
Technologies for Assessing and Extending Statistical Learning
Susanne P. Lajoie
Issues in Constructing Assessment Instruments for the Classroom
Flavia Jolliffe
Assessment on a Budget: Using Traditional Methods Imaginatively
Chris Wild, Chris Triggs, Maxine Pfannkuch
Part IV. Assessing Understanding of Probability
Dimensions in the Assessment of Students’ Understanding and Application of Chance
Kathleen E. Metz
Combinatorial Reasoning and its Assessment
Carmen Batanero, Juan D. Godino, Virginia Navarro-Pelayo
Probability Distributions, Assessment and Instructional Software: Lessons Learned from an Evaluation of Curricular Software,
Steve Cohen, Richard A. Chechile

The Cambridge Handbook of the Learning Sciences

R. Keith Sawyer
Cambridge University Press | 2005 | 648 páginas | zip -pdf | 7,1 Mb

link

Com particular interesse o capítulo 23 (pp. 389-408):
Exploring Mathematics through Construction and Collaboration
Richard Noss e Celia Hoyles

Uma versão on-line deste capítulo em: PDF

Descrição: Learning sciences is an interdisciplinary field that studies teaching and learning. The sciences of learning include cognitive science, educational psychology, computer science, anthropology, sociology, neuroscience, and other fields. The Cambridge Handbook of the Learning Sciences shows how educators can use the learning sciences to design more effective learning environments - including school classrooms and also informal settings such as science centers or after-school clubs, on-line distance learning, and computer-based tutoring software. The chapters in this handbook each describe exciting new classroom environments, based on the latest science about how children learn. CHLS is a true handbook in that readers can use it to design the schools of the future - schools that will prepare graduates to participate in a global society that is increasingly based on knowledge and innovation.

Changing Minds: Computers, Learning, and Literacy

Andrea diSessa

The MIT Press | 2001 | 296 páginas | zip -pdf | 9 Mb

link

Descrição: Rejecting the notion that the computer is merely a tool for more efficient instruction, this book shows how computers can be the basis for a new literacy that will change how people think and learn. It discusses the learning theory that explains why computers can be such powerful catalysts for change in education, in particular, how intuitive knowledge is the platform on which students build scientific understanding. It also discusses the material and social reasons for the computer's potential and argues for "two-way literacies," where everyone is a creator as well as consumer of dynamic and interactive expressive forms. The author gives many examples from his work using the Boxer computer environment, an integrated software system designed to investigate computational literacies. Chapters cover:
(1) Computational Media and New Literacies--The Very Idea;
(2) How It Might Be;
(3) Snapshots: A Day in the Life;
(4) Foundations of Knowledge and Learning;
(5) Intuition and Activity Elaborated;
(6) Explaining Things, Explainable Things;
(7) Designing Computer Systems for People;
(8) More Snapshots: Kids Are Smart;
(9) Stepping Back, Looking Forward.

Reading, Writing, and Proving: A Closer Look at Mathematics

(Undergraduate Texts in Mathematics)
Ulrich Daepp, Pamela Gorkin

Springer | 2003 | 408 páginas

djvu - link; link1

PDF - 12 Mb
link direto
link

Descrição: This book, which is based on Pólya's method of problem solving, aids students in their transition from calculus (or precalculus) to higher-level mathematics. The book begins by providing a great deal of guidance on how to approach definitions, examples, and theorems in mathematics. It ends by providing projects for independent study. Students will follow Pólya's four step process: learn to understand the problem; devise a plan to solve the problem; carry out that plan; and look back and check what the results told them. Special emphasis is placed on reading carefully and writing well. The authors have included a wide variety of examples, exercises with solutions, problems, and over 40 illustrations, chosen to emphasize these goals. Historical connections are made throughout the text, and students are encouraged to use the rather extensive bibliography to begin making connections of their own. While standard texts in this area prepare students for future courses in algebra, this book also includes chapters on sequences, convergence, and metric spaces for those wanting to bridge the gap between the standard course in calculus and one in analysis.

The Nature of Mathematical Knowledge

Philip Kitcher


Oxford University Press, USA | 1985 | 300 páginas | pdf | 4 Mb

link
link1
philosophy.ru (link directo)
scribd.com

djvu - 2,5 Mb
link
link1

Descrição: This book argues against the view that mathematical knowledge is a priori, contending that mathematics is an empirical science and develops historically, just as natural sciences do. Kitcher presents a complete, systematic, and richly detailed account of the nature of mathematical knowledge and its historical development, focusing on such neglected issues as how and why mathematical language changes, why certain questions assume overriding importance, and how standards of proof are modified.