Seminar on Teaching Mathematics


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.
DATE and TIME  SPEAKER(S)  TITLE  
September 13
Monday, 5:10pm6:30pm 
No meeting this week. 

September 20
Monday, 5:10pm6:30pm 
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 Online Gateway Testing System 

October 11
Monday, 5:10pm6:30pm 
To be announced


October 18
Monday, 5:10pm6:30pm 
WINTER BREAK


October 26
Tuesday, 5:10pm6:30pm NOTE CHANGE OF DATE FOR THIS WEEK 
Professor George Andrews Penn State University 
Research Mathematicians and Mathematics Education 

November 1
Monday, 5:10pm6:30pm 
No meeting this week


November 8
Monday, 5:10pm6:30pm 
No meeting this week.


November 15
Monday, 5:10pm6:30pm 
No meeting this week.   
November 22
Monday, 5:15pm6:30pm 
No meeting this week. 

November 29
Monday, 5:10pm6:30pm 
No meeting this week.


December 6
Monday, 5:10pm6:30pm 
Matt Kaplan Associate Director, Center for Research on Learning and Teaching 
What Research Tells Us About Student Ratings of Instruction 

December 13
Monday, 5:10pm6:30pm 
To be announced 

ABSTRACTS FOR FALL 2004 (in reverse chronological order):
Monday, December 6, 5:156:30 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, 5:156:30 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, 5:156:30 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 online 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 online 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, 5:10pm6:30pm 
Professor Deborah Ball, Andreas Stylianides, Gabriel Stylianides University of Michigan 
The Mathematical Preparation of Elementary Teachers, Part I  
February 2
Monday, 5:10pm6:30pm 
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, 5:10pm6:30pm 
WINTER BREAK


March 1
Monday, 5:10pm6:30pm 
To be announced.


March 8
Monday, 5:10pm6:30pm 
No meeting this week.


March 15
Monday, 5:10pm6:30pm 
Deborah Ball, Hyman Bass, Mark Hoover, and Laurie Sleep University of Michigan 
Motivation for Learning Mathematics for Teaching  
March 22
Monday, 5:10pm6:30pm 
No meeting this week.


March 29
Monday, 5:10pm6:30pm 
Prof. Raven Wallace (MSU); Helen Siedel, Andreas Stylianides  Mathematics Textbooks for Prospective Elementary Teachers: The Case of Integer Multiplication  
April 7
Wednesday, 5:15pm6:30pm, 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, 5:10pm6:30pm 
No meeting this week.


April 19
Monday, 5:10pm6:30pm 
No meeting this week.


May 3
Monday, 5:10pm6:30pm 
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, 5:156:30 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, 5:156:30 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 threeyear NSFfunded project entitled, "The
Development of Mathematics Teachers' Knowledge Base Through DNRBased
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 muchlauded 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, 5:10pm6:30pm
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, 5:10pm6:30pm 
Deborah Ball, Hyman Bass, and Teresa McMahon (U of M) 
The Center for Proficiency in Teaching Mathematics (See abstract below) 
Sept 29
Monday, 5:10pm6:30pm 
No meeting this week.


Oct 6
Monday, 5:10pm6:30pm 
No meeting this week.


Oct 13  NO SEMINAR  FALL BREAK 
Oct 20
Monday, 5:10pm6:30pm 
Deborah Ball and Hyman Bass
(Univ. of Michigan) 
Investigating students' ideas of the derivative. 
Oct 27
Monday, 5:10pm6:30pm 
No meeting this week


Nov 3
Monday, 5:10pm6:30pm 
Bill McCallum
(U of Arizona) 
The Ideas of Undergraduate Mathematics. 
Nov 10
Monday, 5:10pm6:30pm 
Richard Hill
(Michigan State U) 
Emerging scholars and the transition from HS to college in math. 
Nov 17
Monday, 5:10pm6:30pm 
No meeting this week


Nov 24
Monday, 5:10pm6:30pm 
No meeting this week.


Dec 1
Monday, 5:10pm6:30pm 
No meeting this week


Dec 8
Monday, 5:10pm6:30pm 
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, 5:106:30 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, 5:106:30 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 calculuslevel, integrated, underrepresented minority support program run in the Department of Mathematics. It is integrated with rural students who have a similar underperforming 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 calculuslevel 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 nittygritty 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 UMAA) 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. Thirtyfour high schools sent us the senioryear grades of students who came to MSU in 199699. 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, 5:106:30 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, 5:106:30pm 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 fiveyear 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::
To develop knowledge to support the effective education of teachers of mathematics in grades prekindergarten to 16 across their careers, helping them learn mathematics for teaching, and how to use that knowledge in teaching
To make instructional practice and its development the heart of teachers’ professional education.
To build connections among the different types of professionals, organizations, and institutions involved in supporting the learning of teachers of mathematics.
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.