
Mathematics Instruction Colloquium
The UA Mathematics Instruction Colloquium is a forum for presentations and discussions of topics related to the teaching of mathematics at all levels, from elementary/secondary to the UA's entrylevel sequence and beyond.
The colloquium is an open forum; the public is invited to attend. Participants and attendees have included faculty and students from the UA's mathematics, applied mathematics, and mathematics education programs, as well as teachers and administrators from the Tucson Unified School District.
In the 20072008 academic year, the colloquium is being organized by Matthew Salomone and Nathan Carlson.
The colloquium is typically held on Tuesdays from 4:15  5:15 p.m. in Mathematics 501. Exceptions will be noted below. Refreshments in the form of coffee and cookies are usually provided.
You may click the title of any talk below to view its full abstract.
Schedule of Colloquia  Spring 2008
 Tuesday, January 22, 2008
 Dorin Dumitrascu, Department of Mathematics, University of Arizona
Reflections on the Teaching of Math XYZ
I will touch on some aspects of our Math 223 course. The first part is logistical in nature and is intended mainly for those that teach this particular class for the first time. I will share some of the things that I found useful teaching the course for 5 semesters: time management, use of handouts, software, manipulatives, concept tests, clickers etc. I hope that this discussion will also benefit those that are at the beginning of their teaching career.
In the second part I will present my attempt to incorporate formal mathematical writing in the Vector Calculus class. I believe that such an effort is necessary and extremely useful for students, and I will present arguments that support my belief. This is intended to be open ended, and I encourage participation from the audience.
 Tuesday, January 29, 2008
 Organizational Meeting for Spring 2008  All are invited
 Tuesday, February 5, 2008
 Deborah Hughes Hallett, Department of Mathematics, University of Arizona
Drugs and Drug Tests: Understanding through Multiple Representations
We all face the challenge of reaching classes of diverse learning styles and uneven preparation. A powerful technique to extend our reach to a wider group of students is the use of multiple representations. In this talk we will take a problem  drug testing of athletes  and analyze its effectiveness from multiple perspectives. We will see how a problem can be taught at different levels, using numbers, diagrams, algebra, or probability.
 Tuesday, February 12, 2008
 David Lomen, Department of Mathematics, University of Arizona
ConcepTests for Algebra  A Means for a More Interactive Classroom
ConcepTests  usually short multiple choice questions  have been developed for calculus, statistics, most of the sciences, and now for precalculus and algebra. The ones presented here are at the College Algebra level. The instructor presents a question, gives a short time for students to reason and vote, then have them interact with each other for a longer time and then vote again. The instructor then orchestrates a classwide discussion on the way (or ways) the students used to obtain the correct answer (or answers). ConcepTests may be used with or without technology  examples will be given.
 Tuesday, February 26, 2008
 Al Cuoco, Division of Mathematics Teaching & Learning, Educational Development Center, Inc. via IM&E
Some options for fourth year high school mathematics courses
With increasing calls for mandatory fourth year mathematics courses for all students, teachers and school districts are faced with finding or designing programs for high school seniors who may not want to or be prepared to take traditional precalculus or calculus courses. In this colloquium, we'll look at some examples of capstone courses for seniors that have been taught in Massachusetts and elsewhere, and we'll brainstorm other possibilities for such courses.
 Tuesday, March 4, 2008  Special Location: Math East 143
 Barbara Armenta, Department of Mathematics, Pima Community College
Autograph for Word, SmartBoard, and Interactive Use in the Classroom
Are you tired of sketching, describing or having students peer at a small calculator screens to "see" a mathematical concept? I was... until I discovered Autograph software.
Autograph was designed to help teachers and students visualize mathematics at the high school and college level. It was conceived and developed in the mathematics classrooms at the Oundle School, Peterborough, UK in 1990. Designed by teachers and continually improved, it is currently used worldwide and is available in 12 languages. Autograph operates in 3 modes:
1D  Statistics & probability
2D  Graphing, coordinates, transformations and bivariate data
3D  Graphing, coordinates and transformations.
The discussion will include a basic introduction some of the features in 2D and the applications to teaching mathematics; a demonstration of how to produce that "picture" you want in a Word Document; that concept you want to get across in the classroom (SmartBoard); and of course, its interactive use in the classroom using any projection system.
 Tuesday, March 11, 2008
 Virginia Bohme, Bruce MacMillan, Ann Modica, Department of Mathematics, University of Arizona
Engaging Students
Tips & ideas from three "mature" high school/college teachers with a combined 90plus years of experience
Participate in a handson activity, discuss effective tutoring techniques, and get tips for enjoyment of your teaching experience. This activity is especially applicable for Algebra II, Math 110, and Precalculus teachers.
 Tuesday, April 1, 2008  Special Time  4:30 p.m.
 Tina Schuster, Department of Mathematics, University of Arizona
Facilitating the Transition between High School and College Math, Part II
There are differences between high school and college math courses that may not seem obvious to an incoming freshman student. The UA Math Department has invited local high school math faculty to participate in discussion with Math Department faculty, lecturers, course coordinators, and administrators to address some of these differences. Our intent is to hear from the high school math community, try to answer questions, and to generate discussion about how to help transition students.
There will be no formal presentation, just a question and answer format.
 Tuesday, April 8, 2008
 David Kukla, Sabino High School
Graphing Families of Curves with Function Transformations: A Discovery Approach for Building Graphical Thinkers
In which the real title should be: "Phew, my kids can graph now," and the ones who learned from someone else always complain, "your way is soooo cool and easy, why didn't we learn that?"
 Tuesday, April 15, 2008
 Phil Grizzard, Department of Mathematics, University of Arizona
 Thursday, April 17, 2008  Special Thursday colloquium, 2:00 p.m.
 Paul Zeitz, Department of Mathematics, University of San Francisco
Enrichment for the AlreadyEnriched vs. Enrichment for the Unenriched
A discussion of various San Francisco Bay Area Math Circles, some of which attempt to target underrepresented populations. We will talk about what works, what doesn't work, what we know, and what we don't know.
 Tuesday, April 22, 2008
 Jeff Bennett, Author, science education consultant
Mathematics for Life: Are You Teaching Students What They Really Need?
Make a list of mathematical skills and concepts crucial to daily life in modern society. Does it match the content of your core mathematics requirement for liberal arts students? Sadly, most college professors answer "no." Moreover, even when course content does seem applicable to daily life, many students don't seem to see the importance.
We can trace the roots of these problems to two simple facts: First, most liberal arts students are still thrown into courses that were originally designed to prepare students for further work in mathematics (such as college algebra or developmental courses), when in reality this will almost certainly be the last mathematics course they ever take. Second, most of the students in these required courses will selfidentify themselves either as "math phobics" (they're afraid of math) or "math loathers" (they don't like math). Clearly, such predispositions are an impediment to teaching.
Fortunately, the solution to both problems is equally simple, at least in principle: Create a course that focuses on concepts and skills that your students will actually use for the rest of their lives, and teach it in a way that shows them the context and relevance so clearly that they cannot help but become engaged. The particular course that I will describe, which I originally developed for the University of Colorado, fits both the AMATYC standards and MAA guidelines for quantitative reasoning. Note: This talk is updated and adapted from an article I coauthored in AMATYC Review.
 Tuesday, April 29, 2008  CANCELLED
 Tuesday, May 6, 2008
 Matthew Salomone, Department of Mathematics, University of Arizona
Writing About Mathematics
For all the times we ask our students to "show their work," how often do we ask them to "show their thoughts?" Sometimes, even students that are capable of writing an impeccably correct sequence of equations to solve a problem are incapable of explaining their thought process in going from one step to the next.
In this talk, I suggest that there is value not only in asking students to write mathematics, but also to write about mathematics, including but not limited to their thought processes, preconceived notions, understandings, and even reactions to the mathematics they are learning. Examples will be taken both from others' case studies, as well as my own experience teaching the notoriouslymisunderstood subject of infinite series in calculus.
Schedule of Colloquia  Fall 2007
 Monday, August 27, 2007
 Organizational Meeting, Math East Lobby, 4:00 p.m. (Note this is an unusual day, time, and place.)
 Tuesday, September 4, 2007
 Guershon Harel, Department of Mathematics, University of California  San Diego
The Necessity Principle and Its Implementation in Mathematics Instruction
The Necessity Principle states: For students to learn they must see a need for what we intend to teach them, where by "need" it is meant intellectual need, not social or economic need. Most students, even those who are eager to succeed in school, are intellectually aimless in mathematics classes because their teachers fail to help them realize an intellectual need for what they intend to teach them.
In this talk I will discuss the Necessity Principle and give examples of its implementation in mathematics instruction, focusing in particular on the teaching of proof.
 Tuesday, September 11, 2007
 Bill McCallum, Department of Mathematics, University of Arizona
The Institute for Mathematics and Education, A Year Later
I will give a report on the activities of the Institute for Mathematics and Education in its first year, and solicit ideas from the audience for future activities.
 Tuesday, September 18, 2007
 Stephen Gagola, Department of Mathematics, University of Arizona
Brainstorming an MAA Special Session
With so much wonderful pedagogy and ideas flowing out of the Math Instruction Colloquium, we would like to test the waters and propose to lead a special session at the 2009 AMS/MAA joint meetings. What theme could it take, and what contributions would you like to make?
Collaborators and friends of the UA Teaching Postdocs are invited to come to an informal brainstorming session, aimed at formulating a proposal for the MAA by December of this year.
 Tuesday, September 25, 2007
 Ji Li, Department of Mathematics, University of Arizona
Everything You Wanted to Know About Math Tutoring (but Didn't Know to Ask)
In my graduate years at Brandeis University, I got involved a lot in math tutoring. That does not make me a "tutoring expert" by any chances, but it does give me something to share with you, such as the structure of public tutoring at Brandeis, the different groups of students that I tutored, how the experience of tutoring benefitted my
lecturing, and some thoughts of what makes a good tutor, etc.
Please
feel free to bring with you good patience  for listening to me, good
material on tutoring  math or not  for discussion's purposes, and a
good appetite  for some afternoon cookies and tea!
 Tuesday, October 2, 2007
 James Cossey, Department of Mathematics, University of Arizona
Summer TIME in the City
For the last two summers (and continuing next summer) Dr. Rebecca McGraw has organized the Teacher Improvement through Mathematics
Education (TIME) program here in Tucson, a joint project between the math
department and the Tucson Unified School District. This is a 23 week
summer program designed to help 4th through 8th grade math teachers
improve their content knowledge and model some classroom techniques. I
will talk about my experiences as an instructor in this program and
discuss some of the interesting things that happened.
 Tuesday, October 9, 2007
 Tal Sutton, Department of Mathematics, University of Arizona
What Counts as Math?
Several NSFfunded Centers for Learning and Teaching (CLTs) are working together to share and distill what they are learning in their respective fields of research, about how outofschooltime STEM learning can contribute to and expand student participation in STEM learning. One project that is in development is to explore the question: What counts as math and science? I will talk about the current status of this project, possible future directions, and applications.
 Tuesday, October 16, 2007
 Bill McCallum, Department of Mathematics, University of Arizona
Town hall meeting on improving the firstyear teaching experience for TAs
Presenters: The S_STEM Team (Nick Ercolani, Josh Chesler, Bill McCallum, Tina Deemer, Dan Madden, Alain Goriely, Ken McLaughlin)
As a result of a recent S_STEM grant, the department is considering
new models for the first year teaching experience for TAs. The purpose
of this meeting is to get input from the department, particularly
graduate students, about what would constitute a truly formative
experience, providing the best possible professional development and
preparation for teaching.
 Tuesday, October 23, 2007  4:30 p.m., Education 353
 Tina Schuster, UA Math Placement and Readiness Test Coordinator
Facilitating the Transition between High School and College Math: An Open Panel Discussion
There are differences between high school and college math courses that may not seem obvious to an
incoming freshman student. The UA Math Department has invited local high school math faculty to participate in an open panel discussion with Math Department faculty, lecturers, course coordinators, and administrators to address some of these differences. Our intent is to provide an opportunity for educators at both the high school and college level to understand these issues and be better prepared to assist students with the transition.
 Tuesday, November 6, 2007
 Liana Dawson, Department of Mathematics, University of Arizona
HandsOn Calculus Activities (PowerPoint Slides)
I will outline various handson and nontraditional activities that can be used in calculus courses, and we will actually try a few of the less involved activities. Most of the activities I learned at a Project NExT workshop this past summer. I would like to end the talk with a discussion about what classes these activities might be appropriate in, if any, and any other activities that people have used, so bring ideas you might have.
 Tuesday, November 13, 2007
 Virginia Bohme and Bruce MacMillan, Department of Mathematics, University of Arizona
Modeling Damped Harmonic Motion: A Data Collection Activity for the Precalculus Class
Data will be collected using a motion detector (CalculatorBased Ranger) and transmitted to each participant's graphing calculator. As participants are actively involved in determining the model for the collected data, they will be introduced to powerful graphing calculator features.
Instructors of the advanced algebra, precalculus, and calculus courses at the high school, community college, and university levels are encouraged to attend.
Bring your TI83/84 graphing calculator; calculators will be available for those who wish to borrow one.
 Tuesday, December 4, 2007 (in MATH EAST 141)
 Michelle Cirillo, Department of Mathematics, Iowa State University
On Becoming a Geometry Teacher: A Longitudinal Case Study of One Teacher Learning to Teach Proof
Currently, exposure to proof at the K12 level is mainly limited to a brief topic taught in the tenthgrade. In addition, research has shown that students' beliefs about proof are often unproductive and unsupportive of a positive disposition toward writing proofs. Thus, the teacher and the activities designed by the teacher are critical components to students' understanding of proof. In this study, I look into one novice teacher's classroom to understand how he cultivates the notion of proof and proving in his high school geometry class. I seek to explore how and why this teacher's proofrelated discourse practices changed across three years. In this talk, I will first discuss some of the literature that I am using to ground this work. Second, I will provide some context to the study. Finally, I will discuss how I am analyzing the data and some preliminary findings of this study.
