Seminar on Teaching Mathematics W08

The seminar usually meets Mondays, 5:15-6:30pm, in EH3088. Exceptions to this are noted below.

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

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

Seminar Schedules from Previous Semesters

• Fall 2007
• Winter 2007
• Fall 2006
• Winter 2006
• Fall 2005
• Winter 2005

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.