38
(6), 560-561. Access at www.ams.org/employment/chung.html.
Cobb, G. (2003). An Application of Markov Chain Monte Carlo to
Community Ecology. *The American Mathematical Monthly*, *110*
(4).

*What must surely be history's most acrimonious academic
exchange about the meaning of (0,1)-matrices provides a context for
introducing some ideas of Markov chain Monte Carlo. As the trigger for
three decades of vituperation among community ecologists, the matrices
record presence (1) and absence (0) on islands (rows) of various animal
species (columns). As a source of mathematics, these same matrices
serve as vertices of a very large graph, one whose order exceeds 1017.
Walking at random on the graph generates Markov chains whose limiting
behavior can be used for a variety of statistical purposes, such as
testing hypotheses. This article also includes some new variations on
these ideas, developed as part of a Research Experiences for
Undergraduates program at Mount Holyoke College. (From MAA Online: www.maa.org/pubs/monthly_apr03_toc.html).
*

COMAP, the
Consortium for Mathematics and Its Applications (www.comap.com) is a
non-profit organization whose mission is to improve mathematics
education for students of all ages by helping to create learning
environments where mathematics is used to investigate and model real
issues in our world. COMAP develops curriculum
materials and teacher development programs. COMAP's products are
developed in print, video, and multi-media formats. .

Conway, M. A. (1990). *Autobiographical Memory: An
introduction*. London, UK: Open University Press.

Cowen, C. (1991). Teaching and Testing Mathematical Reading. *The
American Mathematical Monthly*, *98*; 50-53.

Eisenberg, T. & T. Dreyfus. (1994). On Understanding How
Students Learn to Visualize Function Transformations.* *In
Dubinsky, E., Schoenfeld, A. & J. Kaput (Eds.), *Research in
Collegiate Mathematics Education I *(pp. 45-68). Washington, DC:
Conference Board of the Mathematical Sciences.

The authors report a teaching experiment with top Israeli
high school seniors on visualizing function transformations. While not
an unmitigated success, due to the game nature of the Green Globs
software used, they found a hierarchy from least to most difficult to
visualize. (From Research Sampler: mathforum.org/mathed/articles/selden.html).

Epp, S. (2003). The Role of Logic in Teaching Proof,.
The American Mathematical Monthly (to appear in the December issue).

This article offers a rationale for teaching the
reasoning principles that underlie mathematical proof and disproof.
The article proposes two hypotheses to explain some of the
reasons why so many students have difficulty with proof and disproof:
differences between mathematical language and the language of everyday
discourse, and the kinds of shortcuts and simplifications that have
been part of students' previous mathematical instruction. The
article describes research about whether instruction can help students
develop formal reasoning skills and suggests that such instruction can
be successful when done with appropriate parallel development of
transfer skills. The final sections discuss at what point the
principles of logic should be introduced and give a variety of
suggestions about how to teach them.

Ewing, J. (Ed.). (1999). *Towards Excellence: Leading a
Doctoral Mathematics Department in the 21*^{st} Century.
American Mathematical Society Task Force on Excellence. Providence, RI:
American Mathematical Society. (Available online at www.ams.org/towardsexcellence/).

Franzblau,
D.S., (1992) ’Giving Oral Presentations in Mathematics,â? PRIMUS, Vol.
II, no. 1.

Frid, S. (1994). Three Approaches to Calculus Instruction:
Their Nature and Potential Impact on Students’ Language Use and Sources
of Conviction. In Dubinsky, E., Schoenfeld, A. & J. Kaput (Eds.), *Research
in Collegiate Mathematics Education I* (pp. 69-100). Washington, DC:
Conference Board of the Mathematical Sciences.

Ganter
S., Changing Calculus: A Report on Evaluation Efforts and National
Impact from 1988-1998, MAA Notes, 2001.

Ganter
S. & J. Bookman. (In Press). The Impact of Technology in Calculus
on Long-term Student Performance.

Gibson,
D. (1998). Students’ Use of Diagrams to Develop Proofs in an
Introductory Analysis Course In Schoenfeld, A., Kaput, J. & E.
Dubinsky (Eds.), *Research in Collegiate Mathematics Education III *(pp.
284-307). Washington, DC: Conference Board of the Mathematical Sciences.

Gillman, L. (1990). Teaching Programs that Work. *Focus:
The Newsletter of the Mathematical Association of America,* *10 *(1),
7-10.

Gold
B., Marion W. & S. Keith (1999). *Assessment Practices in
Undergraduate Mathematics.* MAA Notes, 49. Washington, DC:
Mathematical Association of America.

This Notes publication presents a series of articles that
address assessment and evaluation from many perspectives and contains
over seventy case studies of assessment at institutions across the
U.S. It provides a rich and diverse source of examples to
illustrate how assessment can be achieved in practice. This
publication includes an introduction by Lynn Steen, an overview by
Bernard Madison, a ’How to Use This Bookâ? section, and 72 contributed
papers under the four major areas of Assessing the Major, Assessment in
the Individual Classroom, Departmental Assessment Initiatives, and
Assessing Teaching. Also included is an ’Articles Arranged by
Topicâ? listing which is extremely useful for the reader to quickly
identify pertinent articles of interest.

Gordon, S. and F. Gordon (Eds.), (1992) *Statistics for the
21st Century*, MAA Notes, 26. Washington, DC: Mathematical
Association of America.

*Teachers of
introductory statistics courses will find ideas in this book that
suggest innovative ways of bringing a course in statistics to life. All
of the articles focus on major innovative themes that pervade
significant portions of an introductory statistics course. Learn about
current developments in the field and how you can make the subject
attractive and relevant to your students. All articles are written by
individuals who are innovative teachers themselves. They provide
suggestions, ideas, and a list of resources for faculty teaching a wide
variety of introductory statistics courses.*

Harel,
G. & E. Dubinsky (Eds.). (1992). *The Concept of Function:
Aspects of Epistemology and Pedagogy, *MAA Notes, 25. Washington,
DC: Mathematical Association of America.

The
editors of this volume hoped to contribute to the research in learning
the concept of function and to provide a resource for mathematics
teachers to assist in instructional approaches. The major themes that
emerge are: conceptions (and misconceptions) of functions held by
students and teachers; research methodology; the roles of theoretical
analyses, empirical investigations and teaching practices; and the use
of computers.

Harel,
G. & L. Sowder. (1998). Students’ Proof Schemes: Results From
Exploratory Studies*. *In Schoenfeld, A., Kaput, J. & E.
Dubinsky (Eds.), *Research in Collegiate Mathematics Education III *(pp.
234-283). Washington, DC: Conference Board of the Mathematical Sciences.

Henriksen,
M. (1990). You Can and Should Get Your Students To Write In Sentences.
In A. Sterrett (Ed). *Using Writing to Teach Mathematics*, MAA
Notes, 16, 50-52. Washington DC: Mathematical Association of America.

Hoaglin,
D.C. & D.S. Moore (1991). *Perspectives on Contemporary
Statistics*, MAA Notes, 21, Washington, DC: Mathematical Association
of America.

This
expository volume seeks to refocus the content of introductory
statistics courses to align instruction with current statistical
research and practice.

Holton,
Derek (Ed.). (2001). *The
Teaching and Learning of Mathematics at University Level: An ICMI Study*.
Dordrecht: Kluwer Publishers.

This
book arose from the ICMI Study on the teaching and learning of
mathematics at university level that began with a conference in
Singapore in 1998. The book looks at tertiary mathematics and its
teaching from a number of aspects including practice, research,
mathematics and other disciplines, technology, assessment, and teacher
education. *Over 50 authors, all international experts in their
field, combined to produce a text that contains the latest in thinking
and the best in practice. It therefore provides in one book a
state-of-the-art statement on tertiary teaching from a
multi-perspective standpoint. No previous book has attempted to take
such a wide view of the topic. The book will be of special interest to
academic mathematicians, mathematics educators, and educational
researchers.* (From Kluwer site: www.wkap.nl/prod/b/0-7923-7191-7).

Howe,
R. & W. Barker. (2000). *Continuous Symmetry: From Euclid to
Einstein*. Undergraduate text; unpublished manuscript.

Katz,
V.J. & A. Tucker. (2003). Preparing Mathematicians to Educate
Teachers (PMET). *Focus: The Newsletter of the Mathematical
Association of America, 23* (3).

The
MAA is expecting funding to initiate a multifaceted project entitled
Preparing Mathematicians to Educate Teachers (PMET) in response to
numerous national reports calling for better preparation of the
nation's mathematics teachers. These reports are sparking growing
interest among college and university mathematicians to do more to help
improve school mathematics teaching. The PMET project, directed by Alan
Tucker and Bernie Madison, will help nurture and support this interest
by providing a broad array of educational, organizational and financial
assistance to mathematicians. (Available at www.maa.org/internal-archive?url=/internal-archive?url=/pmet/focus.html).

Kenney,
P. A., & J.M. Kallison, Jr. (1994). Research studies on the
effectiveness of Supplemental Instruction in mathematics. In Martin, D.
C. & D. Arendale (Eds.), *Supplemental Instruction: Increasing
Achievement And Retention* (pp. 75-82). San Francisco, CA:
Jossey-Bass.

Recent
documents from the National Council of Teachers of Mathematics
(NCTM,1989) and the National Research Council (NRC, 1991) have
emphasized the need for mathematical literacy. Yet, for many
undergraduate students mathematics has become a filter rather than a
pump in that lack of success in mathematics often prevents students
from entering scientific and professional careers. In a document that
advocates sweeping changes in the way undergraduate mathematics is
taught, the members of the Committee on Mathematical Sciences in the
Year 2000 present an action plan that promulgates effective
instructional models that foster learning about learning and involving
students actively in the learning process (NRC, 1991). A Supplemental
Instruction (SI) program has the potential to provide academic support
for students in entry-level undergraduate mathematics courses that
aligns with the goals for change in mathematics instruction. This
chapter begins with a brief summary of the theoretical foundations of
the SI model and then details results from research studies on the
effectiveness of SI programs with an emphasis on studies in
college-level mathematics. (From www.umkc.edu/centers/cad/si/sidocs/jbmth194.htm).

Kilpatrick,
J., Swafford, J. & B. Findell (Eds.). (2001). *Adding it up:
Helping children learn mathematics. *Mathematics Learning Study
Committee, Center for Education. Washington, DC: National Academy
Press.

Adding
it All Up explores how students in pre-K through 8th grade learn
mathematics and recommends how teaching, curricula, and teacher
education should change to improve mathematics learning during these
critical years. The committee identifies five interdependent components
of mathematics proficiency in the domain of number and describes how
students develop these proficiencies. With examples and illustrations,
the book presents a portrait of mathematics learning:

Klein,
K. & A. Boals. (2001). The Relationship Of Life Event Stress And
Working Memory Capacity. *Applied Cognitive Psychology*, 15,
565-579.

The
effects of life stress on both physical and psychological functioning
are well known within the psychology domain (Baum and Poslunszy, 1999).
Previous studies looking at differences in life stress have linked it
with problem solving and information processing. Baradell and Klein
(1993), for example have shown that with increased life stress,
individual's performance on an analogical reasoning task have
decreased. It has also been suggested that these effects involve active
information processing. This is noted to be due to the fact that while
sentence verification tasks are associated with life stress, implicit
and explicit memory tasks are not (Yee et al, 1996). The present study
investigates the idea that cognitions related to life stress, and
working memory, compete for the same resources. (From authors’ site: www.lancs.ac.uk/ug/hattersj/homepage.html).

Knuth,
E.J. (2002). Teachers’ Conception of Proof. *Journal for Research in
Mathematics Education*, 33 (5), 379-405. Reston, VA: National
Council of Teachers of Mathematics.

Recent
reform efforts call on secondary school mathematics teachers to provide
*all* students with rich opportunities and experiences
with proof *throughout* the secondary school mathematics
curriculum ’ opportunities and experiences that reflect the nature and
role of proof in the discipline of mathematics. Teachers’ success in
responding to this call, however, depends largely on their own
conceptions of proof. This study examined 16 in-service secondary
school mathematics teachers’ conceptions of proof. Data were gathered
from a series of interviews and teachers’ written responses to
researcher-designed tasks focusing on proof. The results of this study
suggest that teachers recognize the variety of roles that proof plays
in mathematics; noticeable absent, however, was a view of proof as a
tool for learning mathematics. The results also suggest that many of
the teachers hold limited views of the nature of proof in mathematics
and demonstrated inadequate understandings of what constitutes proof.

Kyungmee
P. & K. Travers. (1996). A Comparataive Study of a Computer-Based
and a Standard College first Year Calculus Course. In Kaput, J.,
Schoenfeld, A. & E. Dubinsky (Eds.), *Research in Collegiate
Mathematics Education II*. Washington, DC: Conference Board of the
Mathematical Sciences.

Leitzel,
J.R.C. (1991). *A Call for Change: Recommendations for the
Mathematical Preparation of Teachers of Mathematics. *Washington,
DC: Mathematical Association of America.

How
can we improve the teaching and learning of mathematics in our schools
to better prepare our students for the future? We can begin by making
some changes in the way our teachers learn and teach mathematics. *A
Call For Change*, an MAA Report, offers a set of recommendations
that come from a vision of ideal mathematics teachers in classrooms of
the 1990s and beyond. The report describes the collegiate mathematical
experiences that a teacher needs in order to meet this vision. (From
MAA Online: MAA Bookstore main page.)

Lenker,
S. (1998). *Exemplary Programs in Introductory College Mathematics.*
MAA Notes, 47. Washington, DC: Mathematical Association of America.

This
handbook is a result of the first competition of the INPUT (Innovative
Programs Using Technology) Project. Project descriptions offer insights
into innovations in Introductory College Mathematics that use
technology. The handbook highlights twenty projects ’ the five top
award winners, the next ten projects and five additional notable
projects. Projects focus on one of five areas; Business Mathematics,
Developmental Mathematics, Precalculus/College Algebra and
Trigonometry, Statistics, and Quantitative Literacy/Special Topics.

Ma, L.
(1999). *Knowing and teaching elementary mathematics: Teachers'
understanding of fundamental mathematics in China and the United States.*
Mahwah, NJ: Lawrence Erlbaum Associates.

Liping
Ma's book, *Knowing and teaching elementary mathematics*, appears
in the series Studies in Mathematical Thinking and Learning published
by Lawrence Erlbaum Associates. ’This is a very unusual book, in which
Ma examines the mathematical content and pedagogical knowledge of
Chinese and U.S. teachers of elementary mathematics. It is the only
book I know that has won high praise from people on both sides of the
"math wars." Ma explains in detail the basis of teachers' mathematical
competency, a "profound understanding of fundamental mathematics." Many
world class mathematicians are delighted with the book, for it makes
the case that teachers' mathematical knowledge is essential. But
reformers love it as well, because the book shows that it's not just
*more* knowledge that matters: what matters is having a deeply
connected understanding of what elementary mathematics really is. If
you want to understand the kind of knowledge it takes to teach
elementary mathematics really well, you need to read this book.â? (Alan
Shoenfeld on HallEducation.com: halleducation.com/education/857.shtml.
Book review located at www.ams.org/notices/199908/rev-howe.pdf.)

MacGregor,
J. (Ed). (1999). *Strengthening Learning Communities: Case Studies
from the National Learning Communities Dissemination Project (FIPSE)*.
Olympia, Washington: Washington Center for Improving the Quality of
Undergraduate Education.

*For the past 15 years, the Washington
Center for Improving the Quality of Undergraduate Education, a
grass-roots network of colleges in the State of Washington based at The
Evergreen State College, has supported the development of curricular
learning community approaches. In 1996, the Center began to serve as a
national resource for curricular learning community work. A
FIPSE-funded project (1996-99) engaged 19 campuses nationwide in
intensive assessment and other efforts to strengthen their learning
community programs. This project culminated in a national conference in
May 1999, and this book on lessons learned by the participating
campuses. (From learningcommons.evergreen.edu/02_nlcp_entry.asp). *

Madaus,
G., West, M., Harmon, M., Lomax, R.. & K. Viator. (1992). The
Influence of Testing on Teaching Math and Science in Grades 4-12. *National
Science Foundation News*, NSF PR 92-86.

Madison,
B. (2001). *Supporting Assessment in Undergraduate Mathematics (SAUM)*.
Grant proposal submitted to the National Science Foundation (NSF) and
available at /prep.

Mathematical
Sciences Education Board (MSEB). (1993). *Measuring What Counts.*
National Research Council. Washington, DC: National Academy Press.

To
achieve national goals for education, we must measure the things that
really count. Measuring What Counts establishes crucial research- based
connections between standards and assessment. Arguing for a better
balance between educational and measurement concerns in the development
and use of mathematics assessment, this book sets forth three
principles--related to content, learning, and equity--that can form the
basis for new assessments that support emerging national standards in
mathematics education. (From the National Academies Press: www.nap.edu/catalog/2235.html.)

Maurer,
S.J. (1991). Advice for Undergraduates on Special Aspects of Writing
Mathematics. *PRIMUS*, *1* (1), 9-28.

Meel,
D. (1998). Honors Students’ Calculus Understandings: Comparing
Calculus&Mathematica and Traditional Calculus Students. In
Schoenfeld, A., Kaput, J. & E. Dubinsky (Eds.), *Research in
Collegiate Mathematics Education III* (pp. 163-215). Washington, DC:
Conference Board of the Mathematical Sciences.

Meier,
J. & T. Rishel. (1998). *Writing in the Teaching and Learning of
Mathematics*, MAA Notes, 48. Washington, DC: Mathematical
Association of America.

Writing
in the Teaching and Learning of Mathematics discusses both how to
create effective writing assignments for mathematics classes, and why
instructors ought to consider using such assignments. The book is more
than just a user's manual for what some have termed "writing to learn
mathematics"; it is an argument for engaging students in a dialogue
about the mathematics they are trying to learn.

The
first section contains chapters addressing the nuts and bolts of how to
design, assign and calculate writing assignments. The second section,
Listening to Others, introduces ideas such as audience, narrative,
prewriting and process writing which our colleagues in writing
departments have found useful. Specific examples illustrate how these
are important for writing in mathematics classes. After discussing
Major Projects, the text concludes with Narrating Mathematics, a
section making explicit what is implicit in the rest of the text:
writing, speaking and thinking are all intertwined. By asking good
questions and critiquing students manuscripts in an open, yet rigorous
manner, instructors can get students at any level of ability and
background to a deeper awareness of the beauty and power of
mathematics. (From MAA Online: MAA Bookstore main page.)

Muench, D.L.
(1990). ISETL-Interactive Set Language. *Notices* of the American
Mathematical Society, 37 (3), 277-279.

Moore, T. L.
(Ed.) (2000), *Teaching Statistics: Resources for Undergraduate
Instructors*, MAA Notes, 52. Washington, DC: Mathematical
Association of America.

*A collection of classic and original articles on various
aspects of statistical education along with a collection of
descriptions of several of the more effective and innovative projects
that have surfaced in the past few years, often with major external
funding, many of which have become commercial products. Project
descriptions give the reader a clear introduction to the project
followed by "companion pieces" written by teachers who through their
experience with the project can give useful and practical advice on how
to use the project effectively.*

National
Council of Teachers of Mathematics. (2000). *Principles and
Standards for School Mathematics*. Reston, W.VA.: National Council
of Teachers of Mathematics.

(Information site at standards.nctm.org/.)

O’Shea,
D. & H. Pollatsek. (1997). Do We Need Prerequisites. *Notices *of
the American Mathematical Society.

(Posted
at http://www.ams.org/notices/199705/comm-holyoke.pdf)

Price,
J. J. (1989). Learning Mathematics Through Writing: Some Guidelines. *The
College Mathematics Journal*, 20 (5), 349-401.

Rogers,
R. (2002). *Using the Blackboard as Scratch Paper*. Available at
MAA Online at www.maa.org/t_and_l/exchange/ite8/scratchpaper.html.

Schoenfeld,
A. (Ed.). (1997). *Student Assessment in Calculus.* MAA Notes,
43. Washington, D.: Mathematical Association of America.

Selden,
a. & J. Selden. (2003). Validations of Proofs Considered as Texts:
Can Undergraduates Tell Whether an Argument Proves a Theorem. *Journal
for Research in Mathematics Education*, 34 (1), 4-36. Reston, VA:
National Council of Teachers of Mathematics.

This article reports on an exploratory study of the way that
eight mathematics and secondary education mathematics majors read and
reflected on four student-generated arguments purported to be proofs of
a single theorem. The results suggest that such undergraduates tend to
focus on surface features of arguments and that their ability to
determine whether arguments are proofs is very limited ’ perhaps more
so than either they or their instructors recognize. The article begins
by discussing arguments (purported proofs) regarded as texts and
validations of those arguments, that is, reflections of individuals
checking whether such arguments really are proofs of theorems. It
relates the mathematics research community’s views of proofs and their
validations to ideas from reading comprehension and literary theory.
Then, a detailed analysis of the four student-generated arguments is
given and the eight students’ validation of them are analysed.

Silver,
E., Momona-Downs, J. Leung, S.S. & Kenney, P.A. (1996). Posing
Mathematical Problems: An Exploratory Study. *Journal for Research
in Mathematics Education*, 27 (3), 293-309.

Stevens,
F., Lawrenz, F. & L. Sharpe. (1993). *The User-Friendly Handbook
on Program Evaluation.* Washington, DC: National Science Foundation.

Steen,
L.A. (Ed). (2001). *Mathematics and Democracy: The Case for
Quantitative Literacy*. The National Council on Education and the
Disciplines. Washington, DC: Mathematical Association of America.

"As
this book illustrates so well, the intelligent use of numbers is vital
to all aspects of our personal, professional, and public lives....
Without citizens who can understand and evaluate statistics and
surveys, balance risks and benefits, identify flawed or misleading
logic, and much more, our democracy clearly will be in trouble."
’William E. Kirwan, President Ohio State University

"Mathematics
and Democracy makes the case for a definition of literacy that
encompasses the ability to work with numbers and understand another’s
use of numbers and data, as well s reading, writing, and speaking. The
opening salvo and continuing theme is that mathematics and numeracy, or
quantitative literacy, are not the same thing; that mathematics is more
formal, more abstract, more symbolic than quantitative literacy, which
is contextual, intuitive, and integrated."

"The
authors...all agree that currently we are not preparing young people to
function in a society that increasingly requires literacy in all forms.
Mathematicians, statisticians, teachers, and others are all responsible
for this state of affairs and this book makes it abundantly clear to
the reader that we all must solve the problem. The enormous value of
this book is that it sets the stage for the important discussion that
must take place now, not five years or 20 years from now." ’Margaret B.
Cozzens, Vice President, Colorado Institute of Technology

(From MAA Online: MAA Bookstore main page.)

Subcommittee
on Assessment, Committee on the Undergraduate Program in Mathematics
(1995). *CUPM Guidelines for Assessment of Student Learning.*
Washington, DC: Mathematical Association of America.

The Committee on the Undergraduate
Program in Mathematics established the Subcommittee on Assessment in
1990. This document, approved by CUPM in January 1995, arises from
requests from departments across the country struggling to find answers
to the important new questions in undergraduate mathematics education.
This report to the community is suggestive rather than prescriptive. It
provides samples of various principles, goals, areas of assessment, and
measurement methods and techniques. These samples are intended to seed
thoughtful discussions and should not be considered as recommended for
adoption in a particular program, certainly not in totality and not
exclusively. (From www.maa.org/internal-archive?url=/internal-archive?url=/saum/maanotes49/279.html.)

Szydlik, J. & S. Szydlik. (2002). *Exploring Changes in
Elementary Education Majors' Mathematical Beliefs Using a Model of the
Classroom as a Culture*, Paper presented at the meeting of the
Mathematical Association of America (SIGMAA on RUME), Burlington, VT.

*In this presentation, the authors described the culture
of a mathematics classroom for preservice elementary teachers that is
designed to establish sociomathematical norms that foster autonomy. The
authors provide evidence that students' mathematical beliefs changed
over the course of a semester and document how students attribute those
changes to specific classroom norms. The data provide both a
description of the classroom culture and elementary education students'
mathematical beliefs, and they reveal that student beliefs became more
consistent with autonomous behavior during the course. Interviewed
students attributed this change to specific social and
sociomathematical norms including aspects of small group work, work on
significant problems with underlying structures, a broadening in the
acceptable methods of solving problems, the focus on explanation and
argument, and the norm that the mathematics was generated by the
students and not the instructor. Data for this work includes classroom
videotape, and student survey responses and transcribed interviews from
both the beginning and end of the course.*

Stigler, J.
W. & Hiebert, J. (1999). *The Teaching Gap: Best Ideas From The
World’s Teachers For Improving Education In The Classroom*. New
York: The Free Press.

Thompson,
P.W. (1994). Students, Functions, and the Undergraduate Curriculum*.*
In Dubinsky, E., Schoenfeld, A. & J. Kaput (Eds.), *Research in
Collegiate Mathematics Education I *(pp. 21-44). Washington, DC:
Conference Board of the Mathematical Sciences.

Pat
Thompson's research review and synthesis of students' understanding of
function is an elaboration of his invited address to the 1993 Annual
Joint AMS/ MAA Meeting. He focuses on representation, student
cognition, and instructional obstacles, suggesting that the use of
multiple representations, as currently construed, may not be well
thought out. (From Research Sampler: mathforum.org/mathed/articles/selden.html).

Treisman, P.M. (1985). *A study of the mathematics
performance of black students at the University of California, Berkeley.*
Unpublished doctoral dissertation, University of California, Berkeley.

Tucker, A. (Ed.), 1995. *Models That Work: Case Studies in
Effective Undergraduate Mathematics Programs*. MAA Notes, 38.
Washington, DC: Mathematical Association of America.

*This publication is the culminating report of a case
studies project aimed at providing a resource for faculty seeking to
improve their undergraduate programs. The report summarizes effective
practices at a set of mathematics departments who are excelling at
attracting and training large numbers of mathematics majors, or
preparing students to pursue advance study in mathematics, or preparing
future school mathematics teachers, or attracting and training
underrepresented groups in mathematics. This notes volume examines the
common practices of effective programs, addresses each of the areas
where departments excel, and provides site visit reports on ten
departments.*