Sporting a brand new Ph.D. in mathematics, I arrived at LMU in 1973 along with the very first freshman class to enter the newly merged Loyola University and Marymount College. I took my place in the mathematics department as a beginning assistant professor teaching the then standard 12-hour load each semester that typically consisted of four courses and three preparations. There were nine tenured/tenure-track math faculty in the department, none of them women. The following historical tour of my teaching career proceeds chronologically within major thematic areas.

The first few years

A hallmark of our department was that we passed courses around rather than monopolizing the upper division course most closely related to our area of expertise. By the time I applied for full professor in 1984, I had taught 25 different courses in the math curriculum. The pedagogical technique we all used was described as lecture-discussion. Keys to success were being well prepared, enthusiastic and capturing the students interest. Relating well to students and being available to help was important then as it is now. I recall that my approach focused on good explanations, examples and insights. Phrases such as: Here let me make it clearer for you, This is a good way to look at it, and Heres how I remember that important formula, probably sprinkled my lectures in those days. Conversations with and support from colleagues, Scott Wright and Dennis Zill, in particular, were critical to my development as a teacher in those first few years.

Technology

The earliest hand held calculators were arriving on the scene as I began teaching. But at first the cost ($600+) was more than I could afford on a beginning assistant professors salary. Two years later, they dropped in price and, because I was teaching statistics for the first time, I bought one. They became a standard tool for teaching mathematics, but not without debates about when and how much to use them.

The next technological advance was bringing the computer into the classroom. I am probably too proud of having been the first in the department to use the computer for classroom demonstrations (beating out Scott Wright by only a week). It was the Fall of 1977. Getting the computer into the classroom required wheeling in a teletype terminal, and bringing along an old-fashioned telephone with a long cord to obtain a phone line hook-up to the Data General Nova computer that was Paul Rudes pride and joy. When I taught numerical analysis (before our expert numerical analyst Dave Smith arrive), students keypunched cards to run their programs on the mainframe computer (an IBM 1620, as I recall) in the basement of St. Roberts. Then microcomputers arrived on the scene and I wrote a successful proposal for Seaver grant monies to purchase the departments first mobile microcomputer unit for classroom demonstration. This consisted of an Apple II microcomputer on a moveable audiovisual stand with a large monitor on top. In addition to its frequent use for calculus demonstrations, this equipment made possible the incorporation of a computer literacy component into the Math for Elementary Teachers. It was 1983 when I developed that component, including worksheets and an instructors manual, so that future teachers could learn the history of computing, how to evaluate educational software, and experience the mathematical microworlds that the computer language Logo afforded students of all ages. My sabbatical projects in 1983 and in 1990 involved Logo, first in its role in developing the computer literacy of future elementary teachers and later in its ability to present interesting open-ended mathematical situations to math majors.

In the 1990s I embraced email as a new way of communicating with students and found that weekly writing prompts were an effective way of promoting student self-reflection about their learning.

The next big technological advance was the Internet. It has profoundly affected the way students approach the mathematical research papers I assign to students at all levels, from the freshman in MATH 190/191 Mathematics Workshop to the seniors in MATH 490 History of Mathematics. The challenges of teaching students to use the Internet appropriately far exceed those of teaching students to use calculators appropriately.

I am just beginning this year to embrace the use of the digital camera and Blackboard in my courses. Pictures taken while on the Summer 2004 Mathematical Association of America Math Study Tour of England are enriching my MATH 490 History of Math course.

I really must include one more bit of technological history. For many years, the departments copying machine was a hand-crank ditto machine that produced those old-fashioned purple copies from ditto masters. (If you are too young to know what I am talking about here, lucky you!) Because of the difficulties in fixing a typo on a ditto, it was not frowned upon to hand-write an exam. (Computers and word processors have changed all of that.) I recall how delighted I was to find a pink ditto master that I could use to produce two-color copies to better illustrate certain geometric concepts in calculus. I used the pink master sparingly (I only ever had one or two) repositioning it as needed to transfer ink from unused sections. I know that we were still using the ditto machine to reproduce some things in 1986 (at quite a savings of departmental funds), because we moved it to our new offices in Doolan. I recall that several department members were grateful that my dad, visiting from out of town, had been able to fix some problem it had (again saving money). When copying first became available on campus, it meant a trip over to Duplicating in the basement of St. Roberts. Before that, letters, reports and documents were typed (not word processed) by secretaries and/or faculty and copies were carbon copies, and limited in number by their very nature.

Another technological advance is worth a brief mention because it has proven controversial in the math departmentthe white boards. Some of us love them and some of us hate them and some of us do both. (Im in the both category.) They are great for the color options they provide, especially for drawing graphs. The vibrant colors stand out much more than even the very best quality color chalk. But, especially at first, the markers had a toxic smell and they dried out so fast that we would use up a marker in a single hour. The grime they left on hands and clothes did not wash off as easily as chalk dust. So when we moved to University Hall, most of us put white boards in our offices and they went in the computer room, but the classrooms and the Student Study area got blackboards. Unfortunately the quality of these blackboards was very poor. They were hard to erase and after the first use of the day in an 8 AM class, it got harder for students to see what you were writing as the day and more layers of chalk went on. It actually took real effort to drag the chalk across the surface. By contrast the boards in Pereira were smooth and easy to erase. We knew what we had wasnt right. It took a couple years, but finally we got new (green) boards and they are sooo smoooth! Its a pleasure to write on them!! I am sure the students thought we were all nuts in the Fall of 2004 when we oohed and sighed the first few times we faculty used them.

Interdisciplinary studies

In 1973 my first committee assignment was to chair the Biomathematics Committee with the charge to investigate the feasibility of starting such a program at LMU. We surveyed all institutions granting graduate degrees in biomathematics for their required and desired pre-requisites. Based on these survey results, a curriculum was designed and a proposal written for a biomathematics option within our major. It was determined that utilizing the Individualizes Studies Program would be the best way to initiate the program. The biomathematics degree option has continued to this day, attracting a small number of very strong students, a large percentage of whom go on to doctoral programs. In the first 5 or 6 years of the program I advised all six students in the program. Early graduates from this program and students that I had the pleasure to teach include, Dr. Paul Pfaffinger, a researcher at Johns Hopkins and Dr. Terry Tong, Mathematics Department Chair, Cal Lutheran College. A later graduate of this program, Dr. Sonia Castillo, a researcher at the US Food and Drug Administration, is believed to have been the first Latina to get a doctorate in biomathematics in the United States. This committee assignment piqued my interest in the field, and I attended two NSF Chatauqua Short courses on mathematical modeling of biological and environmental systems and developed a senior seminar course on Mathematical Modeling Theory. My initial work in this area has been greatly superceded by the significant contributions of my colleagues Drs. Michael Cullen (who passed away in 1999), Thomas Zachariah, and Ben Fitzpatrick.

I made another foray into interdisciplinary studies in the 1980s when my research into the under-representation of women in math-related fields led me to develop a math/science course for non-majors. These were called Science/Technology courses in those days. The course combined a study of the biographies of 9 women mathematicians from the 4th to the 20th century with study of mathematical topics related to the work of thew women. It offered students the opportunities to participate in hands-on mathematical activities. In addition, to placing certain topics and figures in a historical perspective, the course also had the goal of improving students attitudes towards mathematics. After some debate (along the lines of If theres enough math in it to be an ST course, there cant be enough about gender issues to be a womens studies course and vice versa), it was agreed that the course could be cross-listed with Womens Studies. The course and its main clientele group have evolved over the years, but my interest and involvement in this area continues unabated. With the change in the math core to MATH 102, the current clientele for the Women and Math course consists primarily of future K-12 teachers, and the gender issues portion of the course has been re-focused for them, by attending to gender equity issues in K-12 education.

Involving students in research and appropriate pre-professional work

Early on in my teaching career I incorporated term projects and research reports into many of my courses, such as, our sophomore level statistics course for biology students (MATH 223 which is no longer offered), the senior seminars I taught, and the original Women and Math class (labeled Scientific Thought ST 206). In my early years with the biomath students, my work with senior biomathematics majors involved a research project that prepared them for successful graduate work. I am currently working with a senior math major who intends to pursue graduate work to prepare a paper on the Arithmetic-Geometric Mean for the spring meeting of the Southern Section of the Mathematical Association of America.

As a frequent teacher of the MATH 190/191 Mathematics Workshop I/II course sequence, I have the pleasure of preparing the freshman to write, and present orally, their first mathematics research papers in the fall semester and to make poster presentations to the entire department in the spring semester. It is a challenging task for all of us. One of these freshmen subsequently presented her paper at the local section meeting of the MAA. Others, having learned in MATH 191 what makes a poster paper look good, have gone on to advanced work with other faculty and presented good-looking posters as seniors at the national mathematics meetings.

As I began to teach courses for future teachers, I incorporated assignments and reports that would increase their awareness of resources for teachers and professional organizations. I prepared many future teachers to present workshops at the Expanding Your Horizon Career Day for junior high girls. I have served as off-site supervisor for internship opportunities at a variety of local schools for many years. Over a several year period in the 1990s, more than 20 future teachers served as my teaching assistants in special programs such as Math for Girls, Great Math, and Family Math at St. Jeromes School in Westchester (where my own children were in attendance). My work with the Los Angeles Collaborative for Teacher Excellence provided and institutionalized additional opportunities to train the teacher-leaders of tomorrow. Many of my former students are now role model teachers who make presentations at the Future Teachers Conference and the Meet the Teachers Roundtable.

Grant writing

Over my teaching career I have written a number of successful (and unsuccessful) grant proposals, all of which related somehow to my teaching. The very first proposal, funded by the California Mathematics Council in 1980, enabled me to buy math manipulatives and hands-on materials for my Counteracting Math Anxiety Workshop and for my courses for future teachers.

In 1980 I co-authored (with Mel Bertolozzi and Susan Manning) the Study Skills Section of LMUs first Title III grant proposal. This coincided with the expansion of the Study Skills Center into the Learning Resource Center. In 1981-82 I worked with Scott Wright on the Basic Skills in Mathematics component of the Title III grant to develop a mastery approach basic math course, select the first Math Specialist for the Learning Resource Center, and develop a new Mathematics Placement Exam along with scoring and advising procedures. Then we undertook a validation study which showed that students who went against the Placement Exam recommendations and enrolled in a higher level course were twice as likely to be unsuccessful (that is, get a D, F or withdraw) than students who were placed into the higher course.

In 1995 LMU joined nine other universities to form the Los Angeles Collaborative for Teacher Excellence (LACTE), a six-year $5.5 million dollar project funded by the National Science Foundation to improve K-12 teacher preparation programs. A legacy of LACTE at LMU is an increase in Liberal Studies majors concentrating in mathematics (and science), paid internship opportunities at the California Science Center, and new math (and science) courses for these students. The math department now boasts more than a dozen future elementary teachers concentrating in mathematics (up from zero before LACTE). I frequently advise these students about courses, conferences to attend, and scholarships.

I am team leader on a 2004 SENCER grant from the Association of American Colleges and Universities (AAC&U) to support an interdisciplinary faculty team to develop a version of MATH 102, the current math core course, based on modeling environmental problems in Los Angeles. SENCER stands for Science Education for New Civic Engagements and Responsibilities, which is AAC&U's NSF-funded initiative to improve science education by teaching math and science through real-world problems.

Course development

Given that teaching was far and away the major part of a faculty members responsibilities in my early years at the university (when the teaching load was 12-hours per semester), developing new courses was a primary means of intellectual enrichment and life for faculty. Over the years I have developed the following new courses (listed chronologically): a senior seminar on mathematical modeling, a course in Algebraic Topology (for the now defunct M.A. in Mathematics program), a mastery approach to basic mathematics with a focus on word problems (with Scott Wright), a course on women and mathematics initially designed to meet the old science/technology core requirement (and cross-listed as an elective for Womens Studies) and later revised to serve future teachers, a hands-on laboratory course to accompany the mathematics for elementary teachers course, a senior seminar on problem solving, a two-semester sequence for freshman mathematics majors (with Suzanne Larson and Thomas Zachariah), a course on the history of calculus (for the MAT in Mathematics program), and a course on the mathematics of decision making (also for the MAT in Mathematics program). Two of these projects stand out above the others as having been extremely satisfying and having had a long lasting impact: the women and mathematics course and the workshop course sequence for freshmen mathematics majors.

The initial women and mathematics course Mathematics: Contributions by Women (variously numbered ST 206, ST 215, and SCTC 260, cross-listed as WNST 221) was described above in the section entitled Interdisciplinary Studies. Here Ill say a few more words about the redesigned version MATH 398 Women and Mathematics. The course still combines a study of the lives and mathematical work of nine women mathematicians from Hypatia of Alexandria to Emmy Noether of modern times with an examination of gender equity issues in mathematics education and participation with the latter now focused on K-12 education. It continues to include a significant amount of mathematics at the appropriate level. Students typically enter the course unable to name a single woman mathematician. They exit with a significant increase in knowledge of womens contributions to mathematics and of the factors that will encourage school-aged girls (and boys) in their studies of mathematics. They are also better able to articulate what the discipline of mathematics entails. Those who are future teachers have prepared and presented a lesson plan for the grade level they intend to teach that includes information about a woman mathematician and mathematical ideas related to her work.

The initial idea that our department should develop a course that would address the skills and attitudes students needed to succeed in the math major belongs to my colleague Suzanne Larson. The department agreed and Suzanne Larson, Thomas Zachariah and myself began working on such a course. The result was MATH 190/191 Workshop course in Mathematics I/II, which I have taught frequently since its inception in Fall 1992. The course has 4 components: Problem Solving, Mathematical Communication and Study Skills, Modern Mathematics and Culture, Mathematical Careers and People. It is clear what the first two components are about. Through guest speakers and videos Modern Math and Culture shows students that math is a relevant and still developing field that has significant impact on society. Utilizing guest speakers, a biography assignment, MAA and AWM career booklets and Horizons magazine, and interviewing department faculty, Math Careers and People attempts to humanize the discipline and introduces students to many rewarding career paths open to a math major. We also want the workshop to build a sense of community and encourage study support groups. To aid in institutionalizing this course, the course development team wrote course materials and resources including a student manual and an instructor's course manual in print and on disk. This work was supported in part by a course development grant from the LACTE project. MATH 190/191 has been assessed in a number of ways both quantitative and qualitative using pre- and post-tests on problem solving, student surveys of attitudes, knowledge of potential careers, ability to name mathematicians, and end-of-course surveys. Most significantly, the dropout rate for students taking both semesters of the course during 1992-2000 was one-half of the dropout rate for LMU math majors during the preceding five years. One of the major advantages to teaching this course is the chance it affords the instructor to get to know and influence majors at the very beginning of their career here. I have found over the years when I teach this course that students in this course often consider me to be an extra advisor until they graduate. Years when I dont teach the course I feel like I am missing out on getting to know the new crop of majors. Seeing the progress students make in their understanding of mathematics over their years here is really the greatest reward of teaching. Teaching this course gives a faculty member the best possible view of that progress.

Scholarship of teaching and learning

During my teaching career there have been many forces at work both locally and nationally to mold me into a reflective and scholarly teacher. These include: (1) learning about how students of all ages learn mathematics as part of my increasing involvement over the years in teacher preparation; (2) interest in gender issues in mathematics education; (3) the national Calculus Reform movement; (4) dabbling in computer-assisted instruction design; (5) increasing emphasis nationally on the role of writing in mathematics both writing-to-learn and learning-to-write approaches; (6) studying mathematical problem solving and how to improve students skills in this critical area; (7) faculty development workshops offered through the LACTE grant that informed me about student learning styles, active learning strategies, and alternative/authentic assessment methods. The latter brought me in contact with the Lilly West Conferences on College Teaching and experts such as Laurie Richlin, Milton Cox and Craig Nelson. All of these experiences set the stage for my year as a Carnegie scholar in 2003-4 during which I became deeply immersed in the Scholarship of Teaching and Learning (SoTL) community of the Carnegie Academy for the Scholarship of Teaching and Learning.

SoTL is more than excellent teaching or reflective practice. The scholarship of teaching and learning occurs when faculty systematically investigate questions related to student learning for the two-fold purpose of improving their own classroom performance and for advancing the profession of teaching. It results in a formal, peer-reviewed communication in an appropriate media or venue and thereby becomes part of the knowledge base of teaching and learning in higher education. Here is a brief summary of some of the SoTL work done during the last year. My colleague, Dr. Curt Bennett, and I have adapted and expanded R. Shavelsons typology of scientific knowledge to create a new typology of mathematical knowledge that contains 6 cognitive dimensions and 2 affective dimensions of mathematical learning. Across these 8 dimensions we applied P. Alexanders Model of Domain Learning, a classroom-based theory of expertise, to create a Mathematical Knowledge Expertise Grid that provides a useful framework for thinking about my teaching and my students learning. This work has been presented as several national conferences and is being written up for publication. Faculty from areas as diverse as science, music, history and English have found that this framework speaks to their disciplines as well.