Seminar on Teaching Mathematics F09

The seminar usually meets Mondays, 5:15-6:30pm, in East Hall 3096. Any exceptions to this are noted below.

Previous semesters' seminar schedules may be found below. Schedules predating these may be found on the older seminar page. For other seminars in the Mathematics Department, see the Math Department seminars page.

Abstracts

• The Calculus Concept Inventory--What does it tell us?, Karen Rhea, Department of Mathematics, University of Michigan
  In the fall semester 2008, we administered the Calculus Concept Inventory to all sections of Math 115. The results (indicating a gain in understanding) were phenomenal, according to the developer of that inventory. What can we infer from those results? In the spirit of this semester's theme for the Math/Ed seminar, we will explore methods (and ask for input) to investigate what we can and can't definitively tell from this type of assessment.
• Leveraging Resources to Improve Mathematics Instruction in Detroit: A Proposed Design, Daniel Burns, UM Math Dept.; Edward St. John, UM Center for the Study of Higher and Post Secondary Ed.; Nkem Khumbah, UM Comprehensive Studies Program; Mark Thames, Dept of Educational Studies
  In today’s world, the problems schools face are daunting, especially in cities with failing economies, political disarray, and social disparity — such as Detroit. What is the role and responsibility of a research university in relation to this problem? What can we contribute? However mindful of the context, the core problem of improving instructional interactions in the classroom remains. We propose an approach that fits the specific resources found here at the University of Michigan to key resources for the improvement of teaching and learning in Detroit. In this presentation, we describe this design as developed in a recent Mathematics and Science Partnership proposal submitted to the National Science Foundation.
• Research, Evaluation, and Proof in Mathematics Education, Deborah Ball, UM School of Education
  This seminar will examine approaches to disciplined inquiry in mathematics education, considering difference among kinds of questions, methods of seeking answers, and what it means to "know" or to "prove" something in education. We will use examples to illustrate. Time will be allotted for discussion of seminar participants' questions or issues.
  Optional reading: Boaler, J., Ball, D. L., & Even, R. (2003). Preparing researchers for disciplined inquiry: Learning from, in, and for practice. In A. Bishop & J. Kilpatrick (Eds.), International Handbook of Mathematics Education (491-521). Dordrecht: Kluwer. (Most relevant section is pp. 491- 516.) This reading is available for download: reading.
• Understanding Mathematical Proofs, Keith Weber, Rutgers Univ.
  Proof is widely recognized as a central activity in mathematical practice that should play an important role throughout the mathematics curriculum. Although there is a great deal of research on proof, most of this work examines either students' beliefs about proof or their construction of proof. There has been almost no research on how students understand the arguments and proofs of others. This presentation has two parts. The first will present an analysis of what it means to understand a proof. This analysis is based on readings from the mathematics education, philosophical, and reading comprehension literature, as well as interviews with 17 mathematicians. The second will present data from a study in which undergraduate mathematics majors were observed reading proofs.

Seminar Schedules from Previous Semesters

• 2008-09 Theme: Transitions in the Mathematical Development of Students and Curriculum
  Winter 2009  |  Fall 2008
• Winter 2008  |  Fall 2007
• Winter 2007  |  Fall 2006
• Winter 2006  |  Fall 2005
• Winter 2005

Schedule for Winter 2009

Abstracts

• Teaching proof in an IBL format to pre-service teachers, Alejandro Uribe and Katherine Walker, Department of Mathematics, University of Michigan
  Abstract: We will describe our experiences teaching Math 489, Topics in Elementary Mathematics, using Inquiry Based Learning methods. In particular we will discuss our efforts to teach proof as a foundation for the course, and some of our successes and difficulties. We hope to generate a discussion about our approach to teaching this and other similar courses.
  
• Analysis Of Classroom Objectives: Conception to Perception, Matt Elsey and Jeff Meyer, Department of Mathematics, University of Michigan
  When planning a lesson, teachers are advised to begin by identifying their objectives for that lesson. To better understand how these objectives are understood by students at the end of the lesson, we analyzed several introductory mathematics classes at the University of Michigan. Our analysis included interviewing the teacher before the lesson, observing the lesson, and then questioning students after the lesson. Our findings point to frequent discrepancies between the objectives of the teacher and the objectives perceived by the students. We discuss these results, and possible ways to ensure that students' understandings more closely match the teacher's objectives.
  
• Teachers and Teacher Education: Results from The National Mathematics Advisory Panel Report and Implications for Our Directions at the University of Michigan, Deborah Ball, School of Education, University of Michigan
  In this session, I will give some background on the National Mathematics Advisory Panel Report, on which I served as a member. I will explain the Panel's charge, provide a snapshot of the report's overall headlines, and then focus on what is said in particular about content preparation, professional education, teacher pay, and elementary mathematics "specialists." I will then offer some thoughts about what we are positioned to do to contribute to the improvement of mathematics teacher education here at U-M.
  
• What is worth focusing on in math courses for elementary teachers, and why?, Sybilla Beckman, University of Georgia
  We want elementary school teachers to develop a deep and coherent understanding of the mathematics they will teach. But what does this deep and coherent understanding consist of and how do we help teachers acquire it? In order to encourage depth and coherence in the elementary and middle grades, the National Council of Teachers of Mathematics has published Curriculum Focal Points for Prekindergarten through Grade 8 Mathematics and the National Math Panel has described critical foundations for algebra. In this talk I will present my view of the key topics on which mathematics courses for prospective elementary teachers should focus and the rationale for this view. I will also raise questions for empirical study.
• The Mathematical Transitions Project: Lessons and Issues for Collegiate Mathematics Educators, Jack Smith, Michigan State University
  The Mathematical Transitions Project was a multi-year examination of how beginning high school and college students navigated the shift into programs of school/collegiate mathematics that were quite different from their immediately previous experience. The background to this study was the perception that both pre-college and college curricula (Standards-based and "reform calculus" materials) and associated aspects of teaching make quite different demands on students than more traditionally constructed materials. The project followed about 50 students either out of or into programs using Standards-based or "reform calculus" materials, half starting in the 9th grade and half starting as college freshmen. The analysis tracked their achievement, disposition, how they saw differences between their "old" and "new" programs, and their approach to learning. Results generally showed effects for both curriculum type and educational level (high school vs. college). The results will describe the concepts and measures used in the study; some results, particularly at the collegiate level; and some issues that remain with me years after the completion of the work.

Schedule for Fall 2008

Abstracts

• Teaching Math Majors How To Teach. Yvonne Lai, Department of Mathematics, University of Michigan
  Abstract: This project was motivated by a desire to understand how students, in particular math majors, view teaching and learning how to teach. We report on a small seminar program in which a few mathematics undergraduates worked with graduate students at a weekend outreach program for high school students. During the pilot year 2007, we found that the undergraduate participants were uniformly surprised that teaching requires mathematical and pedagogical foresight. Additionally, while they were curious about techniques such as group work, in practice, they were hesitant to use them out of lack of confidence. These observations informed the design of the 2008 seminar. We will discuss the designs of the 2007 and 2008 seminars and share some stories about the undergraduate participants' insights into the process of becoming teachers. (Joint work with Hillel Raz, UC Davis)
• Michigan Calculus Achievement Program (M-CAP): Overview and Prospects. Nkem Khumbah, Comprehensive Studies Program, University of Michigan
  Abstract: Drawing from the implementation structure of Michigan's introductory mathematics program, the Comprehensive Studies Program and the Mathematics Department started the Michigan Calculus Achievement Program (M-CAP) with Martin Luther King High School in Detroit two years ago, in an effort to familiarize students from the Detroit Public Schools with the rigor and expectations of programs similar to Michigan. I will discuss our experiences and prospects.
• An Overview of the Douglass Houghton Scholars Program: Goals and Anecdotes, Mark Conger, UM Math Dept.
  Abstract: The Douglass Houghton Scholars Program (DHSP) is based on the Emerging Scholars Program developed by Uri Treisman at Berkeley and the University of Texas. DHSP is in its third year, and enrolls students taking Math 115 (calculus I), who take an additional workshop in which they tackle hard calculus problems for four hours a week. The goals of the program will be discussed, as will the manner in which the program seeks to accomplish them. These will be illustrated with specific examples of the activities students work on, their achievements, and observations of the success of the workshop.
• Elementary Algebra for Teachers, Scott Baldridge, Louisiana State University
  Abstract: My textbook, Elementary Mathematics for Teachers, with Tom Parker is about the development of real numbers and the real number line in Grades K-7. In Elementary Geometry for Teachers, two of the main goals are careful developments of measurement and the coordinate plane. In this talk I will describe some of the thinking that went into both books, and how the trajectory of the books naturally leads to a third course to help prospective elementary and middle school teachers understand algebra in a way that they can implement in their classrooms.
• Institutional Barriers to Math Achievement, Dilip Das, UM Provost's Office
  Abstract: President Coleman was a prominent member of the Lt. Governor Cherry Commission on Higher Education and Economic Growth in 2004. The Governor appointed the Commission in response to the unprecedented and rapid conversion from a manufacturing economy in Michigan to one necessarily grounded in technological and informational innovation. One of the many recommendations of the Commission was to double the number of postsecondary degrees in the state. One pathway for this increase is transfer from two-year to four year universities. This discussion will focus on the multiple barriers to student success in both two year and four year institutions.

Schedule for Winter 2008

Abstracts

• Assessment of the Effect of Introducing On-line Homework to Calculus II. Gavin LaRose, et al., Department of Mathematics, University of Michigan
  Abstract: In this talk we will present data from the implementation of on-line homework in Calculus II at the University of Michigan in Fall 2007. We will compare students' work in classes without and with on-line homework, their performance in the class, and the extent to which any differences in performance can be attributed to the on-line homework. In addition, we will consider instructors' sense of the success of the homework and how their management of the course and coverage of material was affected by their use of the on-line homework.
• TBA. Patricio Herbst, School of Education, University of Michigan
  Abstract: TBA

Schedule for Fall 2007

Abstracts

• IBL (Inquiry Based Learning) Teaching in Mathematics at the University of Michigan. Mort Brown, Carl Mummert, Kyle Petersen, Ralf Spatzier, Department of Mathematics, University of Michigan
  Abstract: Inquiry-based learning refers to any methodology that replaces traditional lectures and textbooks with some form of student-centered activities. Instructors typically supply students with a carefully crafted course guide consisting of a sequence of definitions, problems and theorems. Instructors then serve as mentors, by listening to the students, reading their work, and giving them the minimal information they need to understand the defined concepts, solve the problems, and prove the theorems. The Mathematics Department is in its third year of offering about 6 courses per year in this general style. We will describe the program and instructor experience in the classroom.
  
• Social Psychological Factors that Influence Women's Math Outcomes. Denise Sekaquaptewa, Department of Psychology, University of Michigan
  Abstract: In this talk I present research that addresses the under-representation of women in math-intensive fields. Women in math-intensive fields may encounter both negative stereotypes about women's ability in math, as well as a lack of female colleagues. I will present research showing that being one of few or the only woman in a testing situation lowers the performance of women compared to when other women are present. Negative gender stereotypes contribute to this effect. Implications of this research for developing effective programs and interventions designed to improve women's representation in math-intensive fields will be discussed.
  
• Intervention Strategy for Improving Success Rates in Calculus. Darryl Koch, Office of Student Affairs and Multicultural Engineering Programs Office, University of Michigan
  Abstrct: Engineering students at the University of Michigan are required to pass a set of core courses in mathematics and science during their first and second years before selecting a specific engineering department as their major. Success in these core courses is a critical factor for retention. In particular, our data suggests that success in Calculus I is very strongly correlated to eventual graduation in engineering. Entering first-year students are recommended for pre-calculus or calculus based on high school profile information (high school GPA and college test scores) and a placement exam administered by the Mathematics Department. Even though great care is involved in placing students in the correct course, it is possible that students may enroll in calculus without being adequately prepared, or a combination of other factors (heavy courseload, inadequate study skills, etc.) may prevent them from achieving success in that critical course. To improve the success rate in calculus for engineering students, the College, in collaboration with the Mathematics Department, recently instituted an “early warning” approach. If a student performs poorly on the first exam in Calculus I, he or she has the option of switching into an intensive precalculus course at midterm, with no penalty, before re-enrolling in calculus the following term. This intensive precalculus course is designed to help students develop the math skills and necessary study skills to ensure their success in calculus in the following term. In this paper, we will present the data that describes the correlation between success in Calculus I and eventual graduation, the logistics required to quickly identify students who may require this intervention and enroll them in a half-term course, the details of the course, and the effect of such an intervention on the success rate in calculus.
• Women in the STEM Disciplines: Why Do We Need Institutional Transformation? Abigail Stewart, Psychology Dept., University of Michigan
  Abstract: Drawing on social science research on the recruitment and retention of women in STEM fields, I will discuss the reasons that an approach that emphasizes institutional transformation is essential to changing the representation and success of women in these disciplines. I will outline not only some of the efforts underway at Michigan under the aegis of the ADVANCE program, but those underway at many other institutions with support from the National Science Foundation. The direct implications of these transformative efforts for teaching math will be an important topic for discussion.

Schedule for Winter 2007

Schedule for Fall 2006

Abstracts

• Situating Our Local Work on Mathematics Teaching and Learning within the Contemporary Context, Deborah Ball
  In this opening seminar of the year, we will discuss the larger issues underlying the conversation about mathematics education. These include issues about accountability for outcomes in undergraduate education, the critical shortage of trained mathematics teachers in our nation's schools, problems with our system of teacher education, and the demand that all students learn algebra in ways that prepare them to be both mathematically literate and prepared for success in college mathematics. The seminar on mathematics teaching and learning here at UM, now entering its fifth year, offers a site for deliberately engaging these issues, mobilizing and informing our own efforts to tackle them, rigorously studying our efforts, and strategically connecting our work to the broader context.
  Four recent reports are important in this broader context:
  1. The quality of undergraduate education and the critical need to improve it: The "Spellings Report": The Commission on the Future of Higher Education. A pre-publication version is available on-line.
  2. The national crisis in mathematics and science: A new report from the National Academy of Science: Rising Above the Gathering Storm: Energizing and Employing America for a Brighter Economic Future. Report on-line
  3. The quality of precollege mathematics education: The National Mathematics Advisory Panel, a presidential commission charged with focusing on K-12 with a special emphasis on algebra learning: Panel report.
  4. The serious problems with teacher education: "Educating Schoolteachers": a new report that offers a scathing indictment of modal teacher education in the U.S., led by Arthur Levine, former president of Teachers College at Columbia University: Released findings.
• On the road to being a teacher of college mathematics: Graduate students' knowledge and beliefs about student thinking in calculus, Natasha Speer, Michigan State University
  The past several decades have brought advances in what the mathematics education community knows about how undergraduate students think about and learn foundational concepts in calculus such as limit and derivative. In addition, researchers have examined the ways that students' understanding of more elementary concepts (such as function) interacts with the learning of calculus. Experienced teachers of college mathematics have knowledge of these ways that students think and make use of it as they plan and carry out instruction. What is unknown, however, is when and how this knowledge develops. This presentation reports on research done to investigate the nature of the knowledge of student thinking possessed by beginning college teachers as well as beliefs that influence their use of that knowledge. Using problems from (and modeled after) the problems used in research on students' thinking, mathematics graduate students were interviewed about typical strategies and difficulties students might exhibit while working on the problems. Implications for professional development and further research will also be discussed.
• Challenges in the Teaching and Learning of Mathematical Reasoning, Structure, and Language: Anecdotal Reflections, Hyman Bass
  (Abstract unavailable.)
• Mathematical Knowledge for Teaching Geometry: The Case of Math 431
  I will report some preliminary findings from a study of Math 431 ("Topics in Geometry for Teachers"), a math department course required for all preservice secondary mathematics teachers at U-M. In particular, I will discuss the role that specialized mathematical knowledge and experiences can play in the teaching of high school geometry, and the role that a course like Math 431 could play in helping to prepare preservice teachers for the challenges they will face in their future practice.

Schedule for Winter 2006

Abstracts

• What is the Answer? Contrasting Undergraduate Calculus Textbook Content, Vilma Mesa
  In this presentation I want to discuss preliminary results of an analysis of introductory calculus textbooks that looks at strategies available to students for (1) determining whether an action was relevant when solving a problem and (2) deciding that the problem was solved. This is known as the control structure (Balacheff, 2005). The books chosen differ in terms of audience (Honors, Regular, Applied) and in terms of degree of influence by the calculus reform movement. The study describes the control strategies that are present in lessons and examples associated with the notion of derivative and establishes differences across textbooks. Sociological and hermeneutic lenses are being used to analyze the texts. There are two main hypotheses in this study: (1) Control strategies tend to rely more on content at stake in books intended for honors students, and (2) Reform oriented textbooks provide the control structure more explicitly. Next steps will be discussed.
  Reference :  Balacheff, N. (2005). "Conception, propriete du systeme sujet/milieu" [Conception: A property of the learner-milieu system]. In Noirfalise R., Perrin-Glorian M.-J. (Eds.) Actes de la VII^o Ecole d'ete de didactique des mathematiques (pp.215-229). Clermont-Ferrand: IREM de Clermont-Ferrand.
  
• Assessing the Effectiveness of Homework: What are the Questions? How Are They Answered?, Gavin LaRose, Dale Winter, Karen Rhea
  This seminar will be an informal presentation of some assessment that has been done on the impact of (on-line) homework in mathematics classes at the University of Michigan. We will discuss what the appropriate assessment questions are, how they might be answered, and what next steps we might want to take. We will include a discussion with seminar participants to elucidate and expand on the presented material.

Schedule for Fall 2005

Abstracts

• Mathematicians' conceptions of Computer Algebra Systems (CAS) assisted mathematics teaching, Zsolt Lavicza
  In the past year, I conducted an exploratory study to examine university teachers' conceptions of CAS-assisted teaching. I interviewed academics, observed classes, and collected course material at a range of universities in Hungary, United Kingdom, and United States. In my talk, I shall share the findings of this study and highlight the differences between mathematicians' and school teachers' CAS-related conceptions as well as the variations in mathematicians' thinking about CAS in the participating countries. In addition, I am currently developing a large-scale quantitative study to examine CAS integration in university mathematics education. Finally, I would like to share and discuss my preliminary questionnaire design and sampling strategy with the audience.
  
• Mathematicians are from Mars; Math Educators are from Venus: The Story of a Successful Collaboration, Alan Sultan and Alice Artzt, Queens College of the City University of New York
  We will discuss the trials and tribulations associated with the collaboration between two dedicated professors who come from different worlds. Valuable lessons were learned from negotiating the content-driven perspective of a mathematician and the pedagogical perspective of a mathematics educator as they planned and implemented a calculus course for prospective secondary teachers.
  

Schedule for Winter 2005

Abstracts

• Can Emotions Enhance the Cognitive Outcomes of Learning?, Matt DeLong, Taylor University
  Our objective for this talk is to describe a rationale for using basic emotion responses as devices for enhancing students' learning of emotion-free subject matter, such as introductory college mathematics. We will use case studies of college mathematics teaching to suggest ways in which student emotional arousal can play a useful role for instruction, review research on basic emotions that suggest potential educational applications and report the results of a preliminary investigation of the possible effects of emotional arousal on learning.
  
• Describing the Use of and Assessing Perceived Effectiveness of Technology in Calculus III, Gavin LaRose, University of Michigan
  In third-semester (multivariable) calculus at the University of Michigan, a Computer Algebra System (Maple) is used for short in-class demonstrations. It is expected that these uses of technology facilitate students' understanding of the material and their ability to visualize the mathematical concepts considered in the course. In this talk we discuss the objective description of the use of the demonstrations in Calculus III and the degree to which student and faculty perceptions of their effectiveness and objective are consistent.
  
• Mathematicians are from Mars; Math Educators are from Venus: The Story of a Successful Collaboration, Alan Sultan and Alice Artzt, Queens College of the City University of New York
  This talk will discuss the trials and tribulations associated with the collaboration between two dedicated professors who come from different worlds. Valuable lessons were learned from negotiating the content-driven perspective of a mathematician and the pedagogical perspective of a mathematics educator.
  
• Assumptions About Knowledge Implicit in Math Reform Literature, Helen Burn, University of Michigan
  Helen will talk about assumptions about the relationship between procedural and conceptual knowledge and about transfer of knowledge that are implicit in calls for reform of introductory college mathematics courses (non-remedial courses below the level of calculus). She explores the extent to which these assumptions are grounded in the literature on student learning in undergraduate mathematics. The calls for reform include AMATYC's Crossroads in Mathematics (1995/2005), MAA's Curriculum Guide 2004, and NRC's Transforming Undergraduate Education in Science, Mathematics, Engineering and Technology (1999).
  
• Factors in High School Affecting Success in College Mathematics, Richard Hill and Jon Star, Michigan State University
  We are about to embark on a study to determine what kinds of high school experiences prepare students well for different colleges' experiences in mathematics. Recent studies by Adelman at the US Dept. of Education and by the Bridge Project at Stanford have explored this type of issue for the high school to college transition generally, but little research has focused specifically on students' mathematics experiences in high school and college. We feel that there is great interest and potential for exploring this important question.
     We will soon begin collecting data from high schools in the Genesee Intermediate School District and five or six Michigan public universities. We first will identify target participants, specifically students who graduated from any Geneseee ISD high school and then subsequently entered one of the participating universities in the years 2000 - 2004. From these students' high schools, we will obtain the math courses that each student took in grades 8 - 12, his/her grades in each course, descriptions of each course (including information about textbook and topic coverage), and standardized test data (8th grade MEAP scores; AP test scores, when applicable). At the school level, we will interview counselors and principals to determine school policies about placement into (and out of) math courses and course sequences.
     At each participating university, we will obtain data that parallels what we collect at each high school. For each student, we will gather information about college course taking, course grades, overall GPA, and placement test scores. We will also obtain descriptions of each course (syllabi, text, topic coverage) and details about procedures for placing incoming first-year students into appropriate mathematics courses.
     At the talk we will give more details on our procedures, the questions that we are seeking to answer, and the current status of the project. We look forward to some additional insight and suggestions from audience members.