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ANNOTATED BIBLIOGRAPHY

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Note: Italicized descriptions are quoted from other sources.

American Mathematical Association of Two-Year Colleges. (1995) Crossroads in Mathematics: Standards for Introductory College Mathematics Before Calculus, http:www.amatyc.org/Crossroads/CrsrdsXS.html .

This document was developed by AMATYC to establish standards for the mathematics programs that bridge the gap between high school mathematics and college calculus and that satisfy the needs of students whose educational plans do not include calculus. AMATYC is the only national organization exclusively devoted to improving mathematics in the first two years of college, and its work was made possible by funding from the National Science Foundation and Exxon Education foundation. Participating in the effort were representatives from the American Mathematical Society, the Mathematical Association of America, the National Association of Developmental Education, and the National Council of Teachers of Mathematics plus many educators from all levels of postsecondary education. The major goals of Crossroads in Mathematics are to improve mathematics education in two-year colleges and at the lower division of four-year colleges and universities and to encourage more students to study more mathematics. In 2003 a review of Crossroads in Mathematics was initiated by AMATYC with a view to possible updating.

Angelo, T.A. & K.P. Cross. (1993). Classroom Assessment Techniques: A Handbook for College Teachers. Second edition. San Francisco: Jossey-Bass Publishers. (ERIC Digest: ED422345).

This revised and greatly expanded edition of the 1988 handbook offers teachers at all levels of experience detailed, how-to advice on classroom assessment’from what it is and how it works to planning, implementing, and analyzing assessment projects. The authors illustrate their approach through twelve case studies that detail the real-life classroom experiences of teachers carrying out successful classroom assessment projects (From Wiley website: www.wiley.com/cda/product/0,,1555425003|desc|2855,00.html).

Angelo and Cross define effective teaching with two important questions in this volume: How well are students learning? and how well are teachers teaching? The answers, they say, come from classroom research and classroom assessment. Classroom research involves teachers becoming systematic on sensitive observers of learning as it takes place each day in their classroom. A major component of this research is classroom assessment in which students and teacher continuously monitor the students' learning. This provides both feedback to the teacher's effectiveness and a measure of progress to the students. This is a reference book to assist in both classroom research and classroom assessment. It draws on years of experience and practical workshops from the Classroom Research Project containing fifty different classroom assessment techniques. The handbook includes case studies, descriptions of assessment techniques and examples. (From CTL Bookshelf: www.usyd.edu.au/su/ctl/Synergy/Synergy7/bookshf7.htm).

Baxter, N., Dubinsky, E., & G. Levin. (1989). Learning Discrete Mathematics with ISETL. New York: Springer-Verlag.

ISETL (Interactive SET Language) is an interpreted, interactive, high-level computer language whose syntax is very close to mathematical notation. It contains the usual collection of statements common to procedural languages, but a richer set of expressions. The objects of ISETL include finite and heterogeneous sets and tuples, numbers, functions, strings. It was developed to enhance the teaching and learning of abstract mathematical concepts by Gary Levin, Ed Dubinsky, and Nancy Hood Baxter. Because its syntax is close to standard mathematical notation (as well as having the usual constructs common to programming languages), it is easy to learn and it is excellent for teaching and learning discrete mathematics, abstract algebra, abstract linear algebra, introductory computer science. All data types are "first-class" and this implies that sets, numbers, tuples, functions, strings can be parameters to be passed in functions and also may be returned by functions. Therefore you can have functions that take sets and returns a function, and so on. This permits a high-level modeling of abstract concepts such as functions (expressed as sets of ordered pairs or as "formulae" like f:= |x -> some expression| or as "processes" which may require a more complicated programmatic description). (From Münch, Donald L. (St. John Fisher College, Rochester, NY, USA) ICTCM talk: Teaching and learning mathematical concepts with ISETL euler.uni-koblenz.de/ictmt3/cd-rom/workshop.htm).

Although this book is currently not in print, Springer-Verlag has three other books in print that address using ISETL in Discrete Mathematics and Abstract Algebra (www.springer.de/search97cgi/s97_cgi). Dubinsky is a co-author on these three books.

Berger, T. & H. Pollatsek (Eds.). (2001). Mathematics and Mathematical Sciences in 2010: What Should Students Know? Washington, DC: Mathematical Association of America.

The question of what students should know is critical for the MAA Committee on the Undergraduate Program in Mathematics (CUPM) as it works to develop a new Curriculum Guide for departments, planned for late 2002. The situation today is much more complicated than in the decades when CUPM began formulating curricular recommendations. Institutions and students are more diverse, the number of mathematical sciences majors is falling, teacher shortages in mathematics and the sciences are becoming acute, the range of mathematics courses taught at the undergraduate level has increased dramatically, and the need for mathematical knowledge at the undergraduate level has grown significantly. The goal of the new Curriculum Guide is to help departments respond effectively to the current challenges in ways appropriate to their particular institutional settings and missions. Last summer, CUPM solicited a dozen position papers on the undergraduate mathematics curriculum, and in September 2000 it held a conference with the authors. A study document entitled Mathematics and Mathematical Sciences in 2010: What Should Students Know? includes the position papers and some preliminary recommendations resulting from the conference. It is available on MAA Online in .PDF format at www.maa.org/news/cupm_front.pdf; a print version may be ordered as an MAA Reports volume. Both the conference and the publication were funded by the Calculus Consortium for Higher Education (CCHE). (From MAA Online: maa.org/news/students2010.html).

Bonsangue, M. (1994). An Efficacy Study of the Calculus Workshop Model. In Dubinsky, E., Schonefelf, A. & J. Kaput (Eds.), Research in Collegiate Mathematics Education I (pp.117-138). Washington, DC: Conference Board of the Mathematical Sciences.

Bookman, J. & C. Friedman (1994). A Comparison of the Problem solving Performance of Students in a lab based on traditional Calculus. In Dubinsky, E., Schonefelf, A. & J. Kaput (Eds.), Research in Collegiate Mathematics Education I (pp.117-138). Washington, DC: Conference Board of the Mathematical Sciences.

Burmeister, S.L., Kenney, P.A. & D.L. Nice. (1996). Analysis of Effectiveness of SI Sessions for College Algebra, Calculus, and Statistics. In Kaput, J., Schoenfeld, A. & E. Dubinsky (Eds.), Research in Collegiate Mathematics Education II. Washington, DC: Conference Board of the Mathematical Sciences.

Carlson, M. (1998). A Cross-Sectional Investigation of the Development of the Function Concept. In Schoenfeld, A., Kaput, J. & E. Dubinsky (Eds.), Research in Collegiate Mathematics Education III (pp. 114-162). Washington, DC: Conference Board of the Mathematical Sciences.

This study investigates students' development of the function concept as they progress through undergraduate mathematics. An exam measuring students' understanding of major aspects of the function concept was developed and administered to students who had just received A's in college algebra, second-semester honors calculus, or first-year graduate mathematics courses. Follow-up interviews were conducted with five students from each of the three groups. Analyses of the exam results and interview transcripts reveal that even our best students do not completely understand concepts taught in a course, and when confronted with an unfamiliar problem, have difficulty accessing recently taught information. (From www.mste.uiuc.edu/indicators/research/articles/113_Carlson_P.html).

Conference Board of the Mathematical Sciences (2001). The Mathematical Education of Teachers. Washington, DC: Mathematical Association of America.

Now is a time of great interest in mathematics education. Student performance, curriculum, and teacher education are the subjects of much scrutiny and debate. Studies on the mathematical knowledge of prospective and practicing U. S. teachers suggest ways to improve their mathematical educations. It is often assumed that because the topics covered in K-12 mathematics are so basic, they should be easy to teach. However, research in mathematics education has shown that to teach well, substantial mathematical understanding is necessary--even to teach whole-number arithmetic. Prospective teachers need a solid understanding of mathematics so that they can teach it as a coherent, reasoned activity and communicate its elegance and power.

This volume gathers and reports current thinking on curriculum and policy issues affecting the mathematical education of teachers. It considers two general themes: (1) the intellectual substance in school mathematics; and (2) the special nature of the mathematical knowledge needed for teaching. The underlying study was funded by a grant from the U.S. Department of Education. The mathematical knowledge needed for teaching is quite different from that required by students pursuing other mathematics-related professions. Material here is geared toward stimulating efforts on individual campuses to improve programs for prospective teachers. This report contains general recommendations for all grades and extensive discussions of the specific mathematical knowledge required for teaching elementary, middle, and high-school grades, respectively. It is also designed to marshal efforts in the mathematical sciences community to back important national initiatives to improve mathematics education and to expand professional development opportunities. The book will be an important resource for mathematics faculty and other parties involved in the mathematical education of teachers. (http://www.cbmsweb.org/ or from AMS Bookstore: www.ams.org/bookstore?fn=20&arg1=cbmathseries&item=CBMATH-11).

Online version and information about ordering found at www.cbmsweb.org/MET_Document/index.htm.

Chung, F.R.K. (1991). Should You Prepare Differently for a Non-academic Career? In Notices of the American Mathematical Society, 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 21st 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.

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