Erin McNicholas: Teaching Portfolio
- Primary Instructor Responsibilities
- Sample Course Documents
- Teaching Team Member Experience
- Math in Modern Society Curriculum
- Introduction to Global Climate Change Curriculum
- High School Workshops
- Community Involvement
- High School Workshops & Visits
- Mentoring & Teaching Conferences
- Department Involvement
- Entry Level Committee
- Algebra ConcepTests Working Group
- First Year TA Mentoring
- Freshman Advising
- Statistical Summaries & Student Comments
My goal as an instructor is not only to provide students with an understanding of the mathematical concepts covered in class, but a sense of how mathematics ties into the world around them, and an appreciation for the breadth and beauty of the subject. To give students a solid understanding of the underlying theory, I stress the reasoning and logic behind the formulas and theorems covered in class. I believe it is important that students have a deep understanding of the concepts and are not merely learning to plug numbers into formulas or perform mindless algorithms. I believe that students must take an active role in their learning. To promote this, I use class discussion and group activities to develop class topics.
In addition to helping my students master the mathematical content and develop their critical thinking skills, I have specific goals for each course I teach. These goals usually depend on the course and the student demographic. In my business math courses I try to impress upon students the importance of math to their future business careers. I also try to improve their computer skills and professionalism. In Math in Modern Society, a non-prerequisite course, my primary goal is to improve students' confidence and enjoyment of the subject.
For more information on my pedagogical views, please see my Teaching Philosophy.
The following is a description of my teaching experience as a graduate student at the University of Arizona. Over the past five and a half years I've had the opportunity to work for both the math department and the Graduate Interdisciplinary Program. My responsibilities have ranged from primary instructor to teaching team member. I've had experience in both large (over 100 students) and small (35 students or fewer) lecture settings.
As primary instructor for several of the math department's undergraduate courses, my duties include: preparing and presenting all course lectures; assigning and grading student projects and homework; writing and grading all course exams; and assigning final grades.1 In addition, I had the opportunity to develop part of the curriculum for MATH 105: Math in Modern Society. A description of this curriculum development can be found in the Curriculum Development section. The enrollment in each of these math courses is capped at 35 students. Links to sample course documents as well as descriptions of the course and the teaching methods I used, are provided below. Student evaluations and feedback are provided in the Course Evaluations section.
- Math 110: College Algebra (Fall 2005 - 4 units)
Section Web Page; Section Calendar; Sample
Exam, ConcepTest Examples
College Algebra is a prerequisite course for Calculus, Business Mathematics, Statistics, and several science courses. Each semester there are 30 to 60 sections offered, and a common final is administered to all sections. I strive to maintain enough flexibility to respond to my students needs, while staying on schedule and preparing them for their future classes and the final exam. While many of the topics in this course have been introduced to students in high school, we stress a deep understanding of the subject rather than an algorithmic approach. To this end, I often use ConcepTests during the course lecture. These are multiple choice questions that require a deep understanding of the subject to answer correctly. Students hold up colored flash cards to signify their answer. This allows me to get a quick and accurate assessment of how many students have grasped the subject. I then have students discuss their answers in small groups, and after a few minutes I ask them to answer the question again. Students have responded remarkably well to this process. Circulating through the class and listening to their discussions, I am impressed by the level of their debates and mathematical reasoning. It gives students valuable practice expressing mathematical concepts verbally. Furthermore, there is no better way to learn a concept than to try and teach it to someone else. As students share their answers and ideas, their understanding is strengthened.
In response to poor pass rates amongst incoming Native American students, the university decided to enroll all incoming Native students taking College Algebra into the same section. Teaching this section has been a very rewarding experience. Because these students work closely together in many of their classes, they have brought a sense of community and collaborative learning to the class. Even my non-Native students seem to be working more in study groups and participating more in class. Several of the Native American students are enrolled in a program which promotes going to instructor office hours and tutoring lab hours. As a result I've had the opportunity to work extensively with these students one-on-one. I recruited two Native American math majors to work as preceptors for the course. They hold regular office hours and participate in class discussion sessions. These preceptors are an excellent resource for all my students, and provide valuable role models. For the most part, these Native American students are doing very well in this course. I fully expect a very high pass rate among these students.
- Math 115A: Business Math I (Summer 2005, Spring 2004, and Spring 2002 - 3 units each)
Section Web Page, Section Policies, Outline of Project #2, Guidelines for Project #2 Write-Up
Developed here at the University of Arizona, the materials for this course have been published and distributed by the MAA. This is an in-depth interdisciplinary course coalescing topics from computer science, mathematics, and business. The electronic course textbook consists of interlinked PowerPoint presentations. Students spend the semester working in groups on two, involved, term projects. In the first project, students perform an in-depth statistical analysis of historical bank loan records in order to determine whether or not they should foreclose on a particular borrower. In the second project, they determine a fair market price for a European call option. Mathematical concepts and computer skills are developed and presented in the context of these projects. Topics covered in this course include: basic probability and statistics; probability density functions; cumulative distribution functions; and Bayes' Theorem. In addition to teaching students the mathematical content of the course, I taught them the business applications of that content, and how to use advanced Excel and PowerPoint features. These classes are taught in the Integrated Learning Center where all classrooms are equipped with computer projectors, document cameras, and lap tops for the students. Thus, I was able to demonstrate the computer skills in class and have students practice them on their laptops. For each project, students submitted a written and oral report. All student work was word-processed and all student presentations were delivered using PowerPoint. Samples of student work can be provided upon request.
The first time I taught this class, I worked hard to prepare and present the lectures in PowerPoint in order to provide students with a model for their own presentations. After having taught the course once, I felt that presenting the lectures in PowerPoint had distanced the students. I found they were far too content to sit back and watch, rather than take notes, question, and become actively involved in the class. To promote active learning instead of passive listening, I decided to use board work to present the mathematical content of the course. This gave me greater flexibility. I was able to lead students to the relevant mathematical concepts through examples and discussion. I continue to use the computer projection system to demonstrate various Excel, Word, and PowerPoint features. Using StarBoard software, I am able to make annotations directly on the screen.
- Math 115B: Business Math II (Fall 2002 - 3 units)
Section Web Page, Sample Lecture Notes
This is the second course in the two semester Business Math sequence. Like Business Math I, it uses an electronic text and encompasses topics from business, computer science, and mathematics. The mathematical and computer content of the course is developed around two term projects. In the first project students use marketing data to determine the demand function for a new product and find the price which will maximize profit. In the second project, students determine a bidding strategy to use in an oil lease auction. In this course I taught students to perform more advanced simulations using Excel. I also built on the presentation and report writing skills they gained in Business Math I. The mathematical content of the course includes basic differentiation and integration.
I was awarded the Eller Business and Public Administration Student Council Certificate of Appreciation for my work teaching this course.
- Math 105: Math in Modern Society (Fall 2003 - 3 units)
Section Web Page, Project 2 Options, Lecture Notes (Modular Arithmetic), Lecture Notes (Cryptography), Sample Student Report
While Math 105 satisfies the University's math requirement for graduation, it is not a prerequisite for any additional math or science courses. Thus, there is greater freedom in choosing the mathematical content. The course is divided into four units: Surveys & Statistics; Consumer Finance; and two units chosen from the topics covered in Peter Tannenbaum's Excursions in Modern Mathematics, 5th ed. Students in this course are predominately from the College of Fine Arts. Many students started the semester with little to no mathematical confidence, and some were openly hostile to the subject. These are bright, creative people, but their mathematical background is often weak. Because the majority of my students were Art or Music majors, I selected topics for the two open units which would emphasize the beauty of pure mathematics. I wanted topics that students had not been exposed to before. Having struggled through math classes in high school, several students felt behind before the semester even started. By choosing topics that would be new to everyone, I wanted to instill in them the feeling that they were all starting on the same footing, that their success in this course would not be hindered by previous failures.
I worked with Jill Newby, the mathematics librarian, to create a resource web page for students. During the semester, students produced two term projects, and I was very impressed with their work. It was rewarding to see students applying the concepts covered in class to topics related to their major. For more information about student reports, please see the Curriculum Development section.
- Math 111: Trigonometry (Fall 2000, and Spring 2001 - 2 units each)
Teaching Trigonometry was my first experience as a primary instructor. This class is a prerequisite for Calculus, and a requirement for students in the College of Architecture. For most lectures, I combined board work with class discussion. I assigned small, in-class, group projects incorporating calculator experiments and mathematical modeling. I then had students present their results to the class. Using a TI graphing calculator and view screen, I was able to instantly graph functions and point out relationships to students.
- NATS 101: Introduction to Global Climate Change (Fall 2004)
Course Web Page
The general education requirements at the University of Arizona include various interdisciplinary courses. Competitive TA-ships offered through the Graduate Interdisciplinary Program (GIDP) provide funding for graduate students wishing to assist in the teaching of these large courses. Working with Dr. Hirschboeck from the tree ring department, I gained first hand experience developing interdisciplinary course activities and working with undergraduate preceptors.
Each fall there are approximately 150 students enrolled in Introduction to Global Climate Change, which is taught in the Integrated Learning Center. To promote student involvement we used wireless responders, allowing students to answer questions posed during the lecture. The responses to these multiple choice questions were displayed using PowerPoint. Incorporating responders into the lecture made it possible for us to determine how well students were grasping subjects covered in class. It also allowed us to pose more philosophical questions to the class and get a sense of how the students felt about various issues. The class was divided into 20 groups, each containing seven to ten students. Students discussed, debated, and performed experiments with their teams. Undergraduate preceptors were recruited from the class. Dr. Hirschboeck, myself, and three other graduate TAs worked closely with these preceptors outside of class, preparing them to lead group discussions and facilitate lab experiments. In addition to working with undergraduate preceptors, my duties included performing class demonstrations, grading assigned papers and projects, and holding regular office hours.
During the spring of 2005, I was awarded a GIDP assistantship to work with Dr. Hirschboeck on improving the course content. I proposed a reorganization of course topics, and developed new projects and activities. These changes were adopted and are currently being implemented. For more information on this work, see the Curriculum Development section below.
- Math 527: Principles of Analysis (Fall 2003 & Spring 2004 - 1 unit each)
As a teaching assistant for the Applied Mathematics Program's graduate analysis course, I held weekly recitation sections and office hours. I prepared and delivered mini-lectures on background material relevant to course topics, and helped students work through challenging problems.
- Math 263: BioStatistics (Spring 2005)
Assisting Dr. Kim, I prepared and presented several lectures in his absence. I also created homework keys and graded class assignments. These assignments included a series of projects performed using Minitab.
I've been fortunate to have the opportunity to develop curriculum for several courses and workshops. I have always been interested in curriculum development, particularly in the development of interdisciplinary courses and projects. I took the University's Teaching with Technology (TTE 501) course, where I developed projects and lesson plans aimed at the high school and undergraduate level. These projects and lesson plans were based on NCTM Standards and incorporated technology and science applications. Through this course, I learned how to perform class experiments using the TI View Screen and associated Calculator Based Laboratory accessories. I also learned to use Geometer's sketchpad, Hyperstudio, Graphmaster, and several other math education software packages. While I believe technology can be an effective tool for facilitating student understanding and interest, it needs to be implemented with care. I try to use calculators and other tools to help students explore relationships and concepts covered in class. At the same time, I stress the limitations of this technology and the importance of understanding the underlying theory when interpreting the output of these devices.
Below is a description of the projects, course documents, and lessons I've developed for the Math in Modern Society course, the Introduction to Global Climate Change course, and the high school workshops on Cryptography and SETI.
Since the majority of my students in this course were art or music majors, I wanted to choose topics which would stress the symmetry and beauty of mathematics, while simultaneously strengthening students' logic and reasoning skills. I decided to do a unit on Graph Theory, and one on Groups, Fields, Symmetries, & Codes. Since this second unit is not covered in the course text book, I obtained permission from the department to deviate from the text. In addition to developing the content of this unit, I created supplemental course documents for student reference.
My students responded extremely well to this unit on Groups, Fields, Symmetries, & Codes. Their interest and involvement in the class increased. For their second term project, I gave them a wide range of topic choices, but every student chose to do a project relating to this unit. The quality of their Project 2 reports was noticeably higher than their Project 1 reports. I've included a sample student report below. The author of this report was a music major. He researched the Fibonacci numbers and their appearance in music, and then applied what he had learned about modular groups to compose a piece of music using the Fibonacci sequence. Using his background in music, he analyzed the musical properties of his composition.
As part of this unit, I reserved a classroom for the evening and showed The Proof, a Nova episode describing Andrew Wiles proof of Fermat's last theorem. Attendance at this optional showing was high, and several students remarked afterwards how surprised they were to understand some of the mathematics discussed in the show. It was exciting and rewarding to see students working with and understanding advanced mathematical concepts such as modular groups and fields. I think the inclusion of this unit gave students a much better understanding of what mathematicians do and what the subject of mathematics encompasses.
- Sample Student Report
- Examples of Supplemental Course Documents
During the spring semester of 2004, I received a special Graduate Interdisciplinary Program TA-ship to work on curriculum development for the general education course, Introduction to Global Climate Change. Having served as a graduate teaching assistant for this course during the fall, I was familiar with the course content and format.
While serving as a TA for the course, I felt too much time was spent at the beginning of the semester covering the math and physics topics necessary to understand various processes of climate change. It was my impression that students started the course eager to discuss and learn about climate change, and this beginning background material had diminished their interest. I suggested we reorder the topics of the course, covering the math and physics concepts in the context of climate change, rather than as stand alone units. I felt this reorganization would provide students with motivation and a clear understanding of how physics and mathematics tie into the study of climate change. I reviewed each of Dr. Hirschboeck's PowerPoint lectures, determining which lectures would have to be altered to effect these changes. I provided Dr. Hirschboeck with specific suggestions on how these alterations might be made.
In addition to proposing a reorganization of course topics, I reworked existing class assignments and developed new projects and activities. I created a detailed syllabus outlining these changes. This syllabus laid out the lecture schedule, in-class activities, homework assignments and due dates. The changes I proposed, as well as the class activities and assignments I developed, were adopted and are currently being implemented.
Each semester, local high school math instructors are invited to bring their classes to campus for a day-long mathematics workshop. Each workshop is based on a particular mathematical subject or application, and has one to three high school classes in attendance. This program is run and organized by the graduate students in the department. Through a series of interactive lectures and hands-on activities, these workshops teach concepts not covered in high school courses. Each workshop has a lead person, several graduate student volunteers, and a number of undergraduate volunteers. The lead person develops the content of the workshop, organizes the volunteers, and leads various sections of the workshop. The remaining sections are led by graduate volunteers. Undergraduate volunteers help facilitate activities, and answer students' questions about college life. The purpose of these workshops is to encourage high school students to take higher level math courses and consider careers in mathematics. University recruitment is an added benefit.
During the spring 2003 and spring 2004 semesters, I organized and led workshops on Cryptography. These workshops covered Caesar, Playfair, and the ADFGVX ciphers, as well as one-time pads and the Vigenere square. Public Key Exchange methods and modern cryptographic practices were also discussed . In the process, students were introduced to matrices and modular arithmetic. Students had the opportunity to practice their newly acquired cryptographic skills through a series of activities and competitions.
While the cryptography workshops were highly successful, they contained units involving exponential functions which made them too advanced for some high school classes. During the spring 2005 semester I developed and led a workshop on SETI (the Search for Extraterrestrial Intelligence), which was designed to be accessible to Algebra I students. This workshop demonstrated that even the most hypothetical situations can lead to interesting mathematics. Students worked together to decode the Arecibo message which was broadcast into space in 1974. The length of this binary message is the product of two prime numbers (73 and 23). Arranging the message in an array of 73 rows and 23 columns reveals a pictogram conveying information about our planet, our genetic makeup, etc. In the process of decoding the Arecibo message, students were introduced to various topics in chemistry, astronomy, and biology. They reviewed prime and composite numbers, and learned ways of representing data. In particular, they learned how to represent molecules numerically using the information contained in the periodic table.
I believe the role of an effective instructor extends beyond the classroom. Universities serve not only their students, but the surrounding communities as well. It is our responsibility to create ties with that community and take part in pedagogical debates occurring at local and national levels.
- High School Workshops & Class Visits
During my time at the University of Arizona, I have organized and led three High School Workshops. These day-long workshops are held on the University of Arizona Campus, and are open to local high school students. These workshops emphasize the applications of mathematics and present topics not usually covered in the high school curriculum. For more information on these High School Workshops, see the Curriculum Development section above.
I've also taken part in the Calculus Class Visitation Project. Each year the department sends a professor, a graduate student, and an undergraduate math major to visit every AP high school Calculus class in Tucson. During these visits we talk to students about our experiences in mathematics, what mathematicians do, and how mathematics relates to various professions and careers. Having participated in the Student Internship Program at Sandia National Laboratory, I talk in detail about research experiences and internships available to high school and undergraduate students. The purpose of these visits is to encourage students to consider careers in mathematics, and to take more advanced mathematics courses when they come to the University.
- Mentoring & Teaching Conferences
I was a member of the student panel at the 2004 AMS-NSF Conference on Mentoring in Mathematics. As a panelist, I prepared and delivered a brief statement on what I believe makes someone an effective mentor. I also answered questions from the audience and had an opportunity to discuss undergraduate advising one on one with several of the conference attendees.
During the 2006 AMS/MAA joint meetings in San Antonio, I took part in a panel discussion organized by the Young Mathematicians' Network (YMN) on making the transition from an undergraduate institution to graduate school.
Derek Habermass and I gave a talk at the 2006 MAA Southwest Sectional Meeting. In out talk, ConcepTests: Implementations & Examples from a Wide Range of Courses, we provided examples of conceptests and discussed our experiences using them.
I constantly strive to improve my teaching. Involvement in departmental activities gives me the opportunity to learn from my colleagues. Sharing classroom techniques and ideas, we are able to develop new and more effective ways of teaching our students. Furthermore, involvement gives me the chance to influence department policies while gaining a better sense of how my teaching efforts contribute to the department's overall mission.
- Entry Level Committee (2005-2006 Academic Year)
I am currently the graduate teaching assistant representative on the Entry Level Committee. This committee meets bi-monthly and works to improve the quality of entry level mathematics courses. These courses include Math in Modern Society, Algebra, Trigonometry, Pre-Calculus, Calculus, and the Business Math sequence. We examine the effectiveness of the currently adopted course text books and discuss other possible texts. We look at student pass rates in these courses, and their corresponding placement grades to determine whether our current methods of student placement are effective. We discuss ways of preparing new TAs, and discuss pedagogical issues which are common to all entry level courses (such as ways of improving students' basic algebra skills).
- Algebra ConcepTests Working Group (Fall 2005)
I am currently taking part in a working group to develop ConcepTests for the department's College Algebra course. ConcepTests were developed by Harvard professor Eric Mazur  to improve his students' conceptual understanding of Physics concepts. ConcepTests have since been developed for a variety of other courses, including Calculus . ConcepTests consist of challenging multiple choice problems which require a deep understanding of course concepts to answer correctly. Student are given a minute to think about their answer to the question, and then they respond using electronic responders, or by holding up flashcards. This gives the instructor immediate feedback on how well students are following course topics. After answering the question individually, students discuss their answers with their neighbors. Through these discussions, students engage in peer instruction while improving their communication and reasoning skills. After a few minutes of discussion, students answer the question again. Studies have shown that implementing ConcepTests in the classroom improves students' performance on both conceptual and algorithmic problems .
As part of the College Algebra ConcepTest Working Group led by Dr. Lomen, I meet weekly with other College Algebra instructors to develop ConcepTests and discuss our experiences implementing these tests in the classroom. I have been very impressed by my students' response. They are clearly engaged and interested in discussing their answers with their neighbors. I have noticed a marked improvement in my students' ability to express mathematical ideas verbally since implementing these tests.
- First Year TA Mentoring (Fall 2005)
Many graduate students begin their first semester teaching College Algebra or Trigonometry. While these graduate students undergo departmental and university TA training during their first year, it can be difficult to adjust to graduate courses while simultaneously teaching for the first time. In an attempt to better help these students become effective teachers, I was asked to sit in on several classes throughout the semester, and then meet with each graduate TA to discuss their teaching techniques and possible areas of improvement. After meeting with the TA, I meet with their faculty supervisor to discuss the TA's progress.
- Freshman Advising (Summer 2001)
Throughout the summer, incoming freshman come to campus for two day orientation and advising periods. During this time they take placement exams and enroll in courses for the fall. The department has two placement tests which are used to place incoming freshman who do not have advanced placement or college transfer credits in mathematics. At each of these orientation sessions, I met with freshman to discussed their placement exam results, and help them determine which math classes would be most appropriate given their placement scores and expected major.
While student evaluations are by no means a perfect measure of teaching effectiveness, I value the feedback of my students and take their comments and suggestions seriously. My student evaluations have been consistently high, even in the Business Math courses which traditionally receive lower evaluations. Each semester students fill out an anonymous scantron form provided by the university, and a short answer questionnaire developed by the mathematics department. Statistical summaries of these scantron results are provided below, as well as a sample of student comments from the department's questionnaire.
The scantron questionnaires for my Math in Modern Society course were lost. Since there is no statistical summary of student feedback for this course, I have included a PDF file containing all the student responses to the department's short answer form. These forms are unedited.
The following link contains a sampling of student comments received in letters, e-mails, and on the math department's anonymous, short answer questionnaire form.
- Sample of Student Comments (Coming Soon)
· Outstanding Graduate Teaching Assistant Award, College of Science (Spring 2004)
· Eller Business and Public Administration Student Council Certificate of Appreciation (Fall 2002)
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Last Updated October 1, 2006