Seminar on Teaching Mathematics 
2004-05: Mondays 5:10pm-6:30pm, 3088 East Hall, U of M  


The seminar is organized jointly by Deborah Ball, Hyman Bass, and Al Taylor. For more information contact us at dball@umich.edu, hybass@umich.edu, or taylor@umich.edu.


Schedule for Fall, 2004 talks:
(Talks from previous terms follow these.)

DATE and TIME  SPEAKER(S)  TITLE 
September 13 
Monday, 5:10pm-6:30pm 
No meeting this week.
 
September 20 
Monday, 5:10pm-6:30pm 
No meeting this week

 
 
September 27  
Monday, 5:10pm -6:30pm  
No meeting this week
 

 
October 4  
Monday, 5:10pm -6:30pm  
Gavin Larose
Department of Mathematics  
A Data Analysis of Michigan's
On-line Gateway Testing System
 
October 11  
Monday, 5:10pm-6:30pm  
To be announced  
 
 
October 18  
Monday, 5:10pm-6:30pm 
WINTER BREAK  
 
 
October 26  
Tuesday, 5:10pm-6:30pm  NOTE CHANGE OF DATE
FOR THIS WEEK
Professor George Andrews
Penn State University  
 
Research Mathematicians and
Mathematics Education  
November 1  
Monday, 5:10pm-6:30pm 
No meeting this week  
 
 
November 8  
Monday, 5:10pm-6:30pm 
No meeting this week.  
 
 
November 15  
Monday, 5:10pm-6:30pm 
No meeting this week.
 


 
November 22  
Monday, 5:15pm-6:30pm
 
No meeting this week.
 
 
 
November 29  
Monday, 5:10pm-6:30pm 
No meeting this week.  
 
 
December 6  
Monday, 5:10pm-6:30pm 
Matt Kaplan
Associate Director,
Center for Research on
Learning and Teaching  
 
What Research Tells Us About
Student Ratings of Instruction  
December 13  
Monday, 5:10pm-6:30pm 
To be announced
 
 

 

ABSTRACTS FOR FALL 2004 (in reverse chronological order):

Monday, December 6, 5:15-6:30 pm, 3088 East Hall
Seminar Leader: Matt Kaplan, Associate Director
Center for Research on Learning and Teaching

Title: What Research Tells Us About Student Ratings of Instruction

Abstract:
Student ratings of instruction are ubiquitous in higher education. Over the past thirty years an extensive literature on student ratings has developed. This presentation will provide an overview of the findings of this research. In particular, we will focus on issues of validity, reliability, bias, and the uses of ratings results.



Tuesday, October 26, 5:15-6:30 pm, 3088 East Hall
Seminar Leader: Professor George Andrews
Penn State University

Title: Research Mathematicians and Mathematics Education

Abstract:
In 2000, the American Matheamtical Society published a book entitled Mathematics Education Research: A Guide for the Research Mathematician. In speaking to the mathematics world generally at the end of their book, the authors say: "...we hope that they [i.e. research mathematicians] have an appreciation that mathematics education research is a serious field of scholarship and that research mathematicians and mathematics education researchers can enjoy mutual respect as fellow scientists." In 2001, I published a review of this book in the Amercian Mathematical Monthly. Succinctly, I tried to contrast the scientific approach to education described in the book under review with the ideas of E.F. Schumacher and Michael Polanyi. My conclusion was that a scientific approach to mathematics education is impossible.

In the Notices of the American Mathematical Society for April 2004. Tony Ralston provided a critique of many of the critics and criticisms of mathematics education research. In a section titled "Arrogance," we read: "The arrogance of mathematicians towards mathematics education manifests itself in various ways. Here are two:" The first item is a resounding blast at my review (described above). Subsequently Ralston adds: "If research mathematicians would engage in 'civil, constructive' criticism rather than, more often than not, arrogant putdowns, the result of the Math Wars would not be an endless battle to the detriment of school mathematics education in the U.S.."

In this talk, I shall examine Ralston's critique. My object will NOT be to bash back at Ralston. Rather I shall try to outline what I believe to be the philosophical abyss that makes the collaboration that Ralston longs for so difficult if not impossible.

Monday, October 4, 5:15-6:30 pm, 3088 East Hall
Seminar Leader: Gavin Larose
University of Michigan

Abstract:
Gateway tests are a formative assessment tool that provide a means of assuring that students in Precalculus and Calculus courses acquire the algebraic and computational skills needed in these and subsequent courses. At the University of Michigan we have used gateway tests in our reformed Precalculus, Calculus I and Calculus II courses since 1994, and have administered these tests on-line since Fall 2001. We have found a strong correlation between completion of a gateway test and student acquisition of tested skills [LaRose and Megginson, Primus XIII(4), 2003]. In this presentation we extend this assessment to a more general analysis of the data available from the gateway testing system, including the numbers of gateway attempts made by students, the timing of these attempts, their eventual course grades, and their course and gateway test pass rates. Our data support many of the expected correlations between student success between student performance on the gateway and other metrics for learning and skill acquisition, while also revealing some less expected results. Finally, we discuss how the results presented corroborate our conclusions as to the effectiveness of the on-line gateway tests and inform structure and administration of our testing program.

Schedule of Winter 2004 talks:
(Fall 2003 talks follow these.)
DATE and TIME  SPEAKER(S)  TITLE 
January 26 
Monday, 5:10pm-6:30pm 
Professor Deborah Ball,
Andreas Stylianides, Gabriel Stylianides
University of Michigan  
The Mathematical Preparation of
Elementary Teachers, Part I
February 2 
Monday, 5:10pm-6:30pm 
Carolyn Dean, Laurie Sleep
Hyman Bass, Deborah Ball
University of Michigan  
The Mathematical Preparation of
Elementary Teachers, Part II  
February 9  
Monday, 5:10pm -6:30pm  
Professor Tom Parker
Michigan State University  
A Focused Mathematics Course
for Elementary Teachers  
February 16  
Monday, 5:10pm -6:30pm  
Deborah Ball, Carolyn Dean
Alejandro Uribe  
The Mathematical Preparation of
Elementary Teachers, Part IV:
Discussion of Issues Raised in Last Three Seminars  
February 23  
Monday, 5:10pm-6:30pm  
WINTER BREAK  
 
 
March 1  
Monday, 5:10pm-6:30pm 
To be announced.  
 
 
March 8  
Monday, 5:10pm-6:30pm 
No meeting this week.  
 
 
March 15 
Monday, 5:10pm-6:30pm 
Deborah Ball, Hyman Bass,
Mark Hoover, and Laurie Sleep
University of Michigan  
 
Motivation for Learning Mathematics for Teaching  
March 22  
Monday, 5:10pm-6:30pm 
No meeting this week.  
 
 
March 29  
Monday, 5:10pm-6:30pm 
Prof. Raven Wallace (MSU);
Helen Siedel, Andreas Stylianides  
Mathematics Textbooks for Prospective
Elementary Teachers: The Case of
Integer Multiplication
 
April 7  
Wednesday, 5:15pm-6:30pm, Room 4088 East Hall
Note change of day and room for this week!  
Professor Guershon Harel
Univ. of California, San Diego  
 
On the Learning and Teaching of Proof.  
April 12  
Monday, 5:10pm-6:30pm 
No meeting this week.  
 
 
April 19  
Monday, 5:10pm-6:30pm 
No meeting this week.  
 
 
May 3  
Monday, 5:10pm-6:30pm 
Zsolt Lavicza
University of Michigan  
 
Assessing the use of Technology
in Teaching Mathematics III  

ABSTRACTS FOR WINTER 2004 (in reverse chronological order):

Monday, May 3, 5:15-6:30 pm, 3088 East Hall
Seminar Leader: Zsolt Lavicza
University of Michigan
 
    Title: Assessing the use of Technology in Teaching Mathematics III

Abstract:
Following the perception and attitude investigation in the fall semester, the math215 group conducted a video study in the past semester. Zsolt videotaped math 215 lectures in which instructors used Maple demos to illustrate the material for students. Using these records we would like to characterize teaching practices of instructors when they are using computers in the classroom to better understand the role of Maple demos in math215 lectures. In the seminar, we will watch and discuss sample clips from this video collection and try to select important elements from these movies.

Wednesday, April 7, 5:15-6:30 pm, 4088 East Hall
(Note change of time and date for this week only)
Prof. Geurshon Harel,
University of California, San Diego
 
    Title: On the Learning and Teaching of Proof.

Abstract:
The presentation will address the following questions:  what are students' understandings of proof?  Are students' difficulties with proofs avoidable?  What can we learn from history about the difficulties students encounter with the concept of proof?  What sorts of experiences seem effective in shaping students' understandings of proof?  Are there promising frameworks for teaching the concept of proof so that students appreciate the value of justifying, the role of proof as a convincing argument, the need for rigor, and the possible insights gained from proof?

Guershon Harel is a professor of mathematics at the University of California, San Diego.  He joined UCSD in 2000 after eleven years at Purdue University.  He has research interest in cognition and epistemology of mathematics and their application in mathematics curricula and the education of mathematics teachers.  His research has focused on the concept of mathematical proof, the learning and teaching and linear algebra, and the development of proportional reasoning.  He currently is the PI of a three-year NSF-funded project entitled, "The Development of Mathematics Teachers' Knowledge Base Through DNR-Based Instruction: Focus on Proof in Algebra." Harel has served as an associate editor of the Mathematical Monthly, and he currently is an editor of the Collegiate Research in Mathematics Education Series, and a chair of the editorial board of the Journal for Research in Mathematics Education.

Monday, March 29, 5:10pm - 6:30pm
Prof. Raven Wallace (Michigan State University);
Helen Siedel, Andreas Stylianides

Title: Mathematics Textbooks for Prospective Elementary Teachers:
The Case of Integer Multiplication

Abstract:
Teacher preparation programs  often provide a sequence of mathematics courses designed especially for prospective elementary teachers.  Over the last decades, many textbooks have been written for use in such courses, some in multiple editions with revisions in response to changes in policies or standards.  In our study, we are analyzing the textbooks currently in print in an effort to understand what mathematics is being offered to prospective elementary teachers in their undergraduate education.  This is the first part of a larger study aimed at understanding the mathematical education of prospective elementary teachers, as well as how textbook authors conceptualize what mathematics is needed to teach this subject well. In this seminar, we will give an overview of the study, including a list of the books we are analyzing (20 books) and a description of our methods of analysis.  We will then focus on integer multiplication to illustrate the range of mathematical (and sometimes pedagogical) issues addressed in these texts, and engage the audience in thinking about what is important for prospective elementary teachers to know on this topic.   The seminar will include a short video segment from Deborah Ball's 3rd grade classroom, in which students are working on the problem 6 + -6.   We will also provide copies of pages from several of the textbooks for participants to work with during the seminar.

Monday, March 15, 5:10pm - 6:30pm
Deborah Ball, Hyman Bass, Mark Hoover, Laurie Sleep
University of Michigan

Title: Motivation for Learning Mathematics for Teaching

Abstract:
This seminar is intended to follow up on recent discussions we've had about how one can motivate prospective teachers to learn mathematics. Some different possible ways to do that will be presented. We will try some of the examples ourselves, and discuss other possibilities stimulated by thinking about this perennial problem.

Monday, February 16, 5:10pm - 6:30pm
Deborah Ball, Carolyn Dean, Alejandro Uribe
University of Michigan

Title: The Mathematical Preparation of Elementary Teachers, Part IV:
Discussion of Issues Raised in Last Three Seminars.

Abstract:
This week's seminar meeting will examine key issues raised across the last three weeks' presentations on courses here at UM, general ideas about the mathematical knowledge that teachers need, Tom Parker's textbook, and the desirable nature and scope of courses for prospective teachers. Seminar participants should come with questions.

Monday, February 9, 5:10pm - 6:30pm
Professor Tom Parker
Michigan State University

Title: A Focused Mathematics Course for Elementary Teachers

Abstract:
This is the third in a series of seminars focusing on the mathematics studies of prospective elementary teachers, one of three strands that we will be pursuing in the Mathematics Teaching Seminar this semester. Across the series, we will learn about and discuss some of the main issues involved in preparing elementary teachers to teach mathematics; features of and developments in the program here at UM, and how it compares with preparation programs elsewhere; textbooks designed for courses for prospective teachers; and assessment and research.

In this seminar, Tom Parker will describe a course on prospective elementary teachers designed at Michigan State based on the textbook "Elementary Mathematics for Teachers" (which he wrote with S. Baldridge). After describing the challenges of designing such a course, he will explain his approach to creating a practical course which is of maximal benefit to the students while requiring minimal specialized knowledge by the instructors. The course integrates the textbook with the much-lauded elementary school textbooks from Singapore. The daily presence of the Singapore books enlivens classes, provides beautiful presentations of elementary mathematics, and has many other advantages. The talk will include examples of ideas learned from the Singapore books and incorporated into the course.

Monday, February 2, 5:10pm -6:30pm
3088 East Hall

The Mathematical Preparation of Elementary Teachers, Part II
Carolyn Dean, Laurie Sleep, Hyman Bass, Deborah Ball

This is the second in a series of seminars focusing on the mathematics studies of prospective elementary teachers, one of three strands that we will be pursuing in the Mathematics Teaching Seminar this semester.  Across the series, we will explore some of the main issues involved in preparing elementary teachers to teach mathematics; features of and developments in the program here at UM, and how it compares with preparation programs elsewhere;  textbooks designed for courses for prospective teachers; and assessment and research.

This second seminar will focus on the interface between "content" and "methods" in the mathematical education of teachers: Where is the boundary between mathematics and teaching?  What lies in the intersection of the two? Carolyn Dean (Mathematics) will talk about the work she did in the first content course, Math 385, providing a view of her work on one particular mathematical topic (combinatorics) and an opportunity to look at students' work on this topic.  Laurie Sleep, Deborah Ball, and Hyman Bass will provide an overview of the "methods" courses, and discuss some specific examples of the work on mathematics and pedagogy (algorithms, place value, and modeling) in ED 411.

Monday, January 26, 5:10pm-6:30pm
3088 East Hall

The Mathematical Preparation of Elementary Teachers, Part I
Deborah Ball, Andreas Stylianides, Gabriel Stylianides
University of Michigan

This is the first in a series of seminars focusing on the mathematics studies of prospective elementary teachers, one of three strands that we will be pursuing in the Mathematics Teaching Seminar this semester.  Across the series, we will learn about and discuss some of the main issues involved in preparing elementary teachers to teach mathematics; features of and developments in the program here at UM, and how it compares with preparation programs elsewhere;  textbooks designed for courses for prospective teachers; and assessment and research. This week's seminar will consist of two segments. In the first, Deborah Ball (SOE) will provide an overview of the issues involved in the mathematical preparation of teachers.  She will also offer a brief sketch of our current program, including what students learn in what parts of the program.  In the second segment of the seminar, we will learn about the course taught to students last summer by Andreas and Gabriel Stylianides to prospective teachers enrolled in the master's level teacher education program.

Schedule of Fall 2003 Seminars:
DATE and TIME  SPEAKER(S)  TITLE 
Sept 22 
Monday, 5:10pm-6:30pm 
Deborah Ball, Hyman Bass, and
Teresa McMahon 
(U of M) 
The Center for Proficiency in Teaching Mathematics
(See abstract below)  
Sept 29 
Monday, 5:10pm-6:30pm 
No meeting this week. 
 
 
Oct 6 
Monday, 5:10pm-6:30pm 
No meeting this week. 
 
 
Oct 13  NO SEMINAR  FALL BREAK 
Oct 20 
Monday, 5:10pm-6:30pm 
Deborah Ball and Hyman Bass 
(Univ. of Michigan) 
Investigating students' ideas of the derivative.  
Oct 27 
Monday, 5:10pm-6:30pm  
No meeting this week  
 
 
Nov 3 
Monday, 5:10pm-6:30pm 
Bill McCallum  
(U of Arizona) 
The Ideas of Undergraduate Mathematics.  
Nov 10 
Monday, 5:10pm-6:30pm 
Richard Hill  
(Michigan State U)  
Emerging scholars and the transition from HS to college in math.  
Nov 17 
Monday, 5:10pm-6:30pm 
No meeting this week 
 
 
Nov 24 
Monday, 5:10pm-6:30pm 
No meeting this week.  
 
 
Dec 1 
Monday, 5:10pm-6:30pm 
No meeting this week 
 
 
Dec 8 
Monday, 5:10pm-6:30pm 
Zsolt Lavicza (UM SOE),
Anton Dzhamay, and Gavin Larose (UM Math)  
 
The Assessment of Instructional Technology in Math 215  

ABSTRACTS (in reverse chronological order):

December 8, 5:10-6:30 in room 3088 East Hall
Speakers: Zsolt Lavicza, Anton Dzhamay, Gavin Larose
Title: The Assessment of Instructional Technology in Math 215.

Abstract: During the Mathematics Teaching and Learning Seminar the question of the evaluation of the technology used in the undergraduate curriculum, particularly in Math 215, was raised. In the summer of 2003 a small group planned a pilot investigation to be conducted in the fall semester. This investigation is examining students' perceptions and attitudes toward technology in Math 215, in order to understand what students value and dislike in the use of technology in the course. This pilot investigation will also help us develop a more focused study which will characterize current teaching practices in the course, how teachers use technology, and the nature of students' learning in this environment.

Our talk will discuss the results and implications of questionnaires administered in the fall semester and of a student focus group conducted in the same time. We will also discuss our plans for future investigation and the improvement of the course. Additionally, we would like to hear your feedback on our work and recommendations for the development of future assessment tools.

November 10, 5:10-6:30 in room 3088 East Hall
Speakers: Professor Richard Hill, Michigan State University
Title: Emerging scholars and the transition from HS to college in math.

Emerging Scholars is a calculus-level, integrated, underrepresented minority support program run in the Department of Mathematics. It is integrated with rural students who have a similar under-performing profile that underrepresented minority students have. It was started in the late 1970's at Berkeley by Uri Treisman, and it has spread to about 100 colleges and universities in the US. It has been running at MSU since 1992.

So far, the program has not worked all that well for precalculus students. But it has worked quite well, sometimes spectacularly well, for calculus-level students. For example, for the last two fall semesters, students taking Calculus 1 have had an overall average of 2.52 while the Emerging Scholars students (about 50 each year) averaged 3.19. (In fall, 2002, the minority Emerging Scholars students averaged 3.31.) Each year there are several Emerging Scholars students who end up as math majors. The reasons include doing well in mathematics and hence liking it, as well as getting lots of support from the department while in the program.

I will describe not only the nitty-gritty about how the program functions, but also some of the research by Treisman (and others at Berkeley) that led to his design. I will also present some of the research by Claude Steele (who holds a chair in psychology at Stanford and was previously at UM-AA) on women and minorities in math and how it relates to this program.

The difficulties with precalculus students was one of the motivating factors in our doing a study of students transitions from high school to Michigan State University. Thirty-four high schools sent us the senior-year grades of students who came to MSU in 1996-99. We compared these with standardized test scores, MSU math placement scores, and the math courses with grades they took at MSU. I will also present some of the interesting results of this study, in particular some of the results that have bearing on our ES students.

Short bio: Richard Hill has been on the faculty in the Department of Mathematics at MSU since 1967. He has done research in algebraic topology (PhD - Northwestern), numerical linear algebra, and recently in math education. He has been directing the Emerging Scholars Program since its beginning in 1992.

October 20, 5:10-6:30 in room 3088 East Hall
Speakers: Deborah Ball, Hyman Bass
Title: Investigating Students' ideas of the derivative.

ABSTRACT:

A continuation of the ongoing research project of the seminar, We will view and discuss student responses to a probe of their knowledge of the derivative.

September 22, 5:10-6:30pm in room 3088 East Hall
Speakers: Deborah Ball, Hyman Bass, and Teresa McMahon
Title: The Center for Proficiency in Teaching Mathematics

ABSTRACT:

The Center for Proficiency in Teaching Mathematics (CPTM) is a five-year project of the UM in partnership with the University of Georgia, funded by the National Science Foundation. The PIs at UM are Deborah Ball, Hy Bass, and Ed Silver. CPTM’s aims are::

Among the activities and programs sponsored by CPTM are: (a) the development of resources for the mathematical education of teachers; (b) summer institutes and workshops for teacher leaders, doctoral fellows, and postdoctoral fellows who teach mathematics to teachers; and (c) research on teachers’ learning of mathematics for teaching.

Mathematicians’ participation in the Center is a goal and will be encouraged in each of these strands of work. A summer institute, to be held here in Summer 2004, is one such opportunity. Other opportunities include a regular study group that focuses on mathematics courses for teachers, and includes faculty from several area universities, research on teachers’ mathematics knowledge for teaching. Several UM mathematicians are already involved in several of these activities, and others’ involvement is invited.