MATH FOR A NEW MILLENNIUM
The College of Idaho began planning to revise its lower-level curriculum in response to various pressures, including changes in student demographics and interest as well as the nationwide rise in the ubiquity of computing technology. Cruz notes, “We realized they did not seem to serve the purpose they were intended for-to prepare students to take Calculus. Most of the students taking these pre-calculus courses ended up not taking Calculus. Even in the Calculus courses, the curriculum was designed to teach skills which could be done by a computer.” Thus, the department returned to the basics of course design: “What is the purpose of this course? What do we want students to take from this course?”
They spent months reading current research and contemplating the changes; they looked at what other math departments were doing. Then, three years ago, they embarked on a project to reimagine lower-level mathematics as a whole. Recognizing that the mathematical tools once considered mandatory in the 1960s were no longer relevant, they asked themselves, “What do students need for this next century?”
Interestingly, Cruz has been considering these questions since she attended a party in the 80s. She met an engineer who “loved calculus” and even saved the textbook from the course. When she started talking specifics, however, about what was being used from the calculus classes in engineering, she was shocked to discover that what she thought she was “teaching for the engineers” was not actually used by the engineers.
They realized they needed more time to “justify why something had to be taught,” which is a different process-of course-than how something could best be taught. Faculty members had to make the case for “what would be useful for students in problem solving,” in order to connect the skills being taught in any subject to their larger goals as a department.
They also took the time to speak to other departments and address the skills that would presumably “serve students in other classes” once they completed their lower-level math courses. The department members realized, in the course of their conversations, that they could use multiple methods to teach one skill, and there might be certain methods that would prove more beneficial in the long run. Furthermore, they were then able to verbalize the long-term benefits for students as well as the ways students would apply that knowledge in their later coursework.
Though acknowledging it is difficult to do something radically different from what has been the norm, Cruz notes they made progress and continue to make progress each year. Next year, they hope to address ways to improve remediation. Cruz, along with the rest of her department, recognizes that students will be better served in the long run, and the faculty members will also be happier knowing “what they are teaching will really serve the students.”
Colleague Ann Koga, in the Biology department, recalls a time Cruz approached a Macalester College Math professor who had led reform within his own institution. Beyond just gathering advice from him, Cruz asked that he be brought to their campus for a series of workshops. Koga notes, “Within a year the Math department had completely revised their curriculum which had been the same for decades.”
Dr. Dave Rosoff, who is fairly new to the Mathematics department, became quickly involved in the new curriculum planning. Rosoff calls Cruz a passionate educator “who is admirably dedicated to improving the lives of her students,” and he believes her work in redesigning the math curriculum may be her “most lasting contribution to The College of Idaho.”
Feeling privileged to be part of the departmental efforts to re-envision their classes, Rosoff praises this “complete reimagining” of what the lower-level courses in mathematics should accomplish. He also notes that these curricular reforms speak to Cruz’s innovation as well as her pragmatic spirit, in addition to highlighting her “commitment to interdisciplinary collaboration.” Because the new courses were developed after collaboration with other departments, a move that “some might have balked at,” Rosoff notes that it was typical of Cruz to “find a solution that promises to improve the educational experience of all students, whether they major in mathematics or take just a single course.”
Dr. Robert Hamilton, now at UCLA in a Medical/Engineering field, was in Cruz’s Precalculus class several years ago. As a “3-2 engineering student,” Hamilton completed three years at the College of Idaho and two years at an affiliate school for engineering-a program in place for smaller schools that can’t support a full engineering program. His first class, as a first-generation college student no less, was Dr. Cruz’s. He shares, “I would come to find out that Dr. Cruz was very thorough in her teaching (and grading) of calculus.” Though Hamilton admits that thoroughness was daunting in his early weeks, he quickly recognized that he was being set on a course that would ultimately take him through his doctoral studies in engineering. He adds, “Her attention to detail truly shaped how I went about both math and engineering. I will never forget to define my variable on my integrals.”
Hamilton also recalls not only the time and effort Cruz put into her students’ progress but also how fully invested she was in their success. He remembers a painstaking search through code to find an error on a computer programming test, and her excitement when he finally cracked it. He recalls, “The level of compassion and care for my work was something that I will always remember.”
Johanna Mori was one of the students who experienced the “new” Calculus course with Cruz, after the redesign. Mori notes, “She’s a little different than any math teacher I’ve ever had, but she made everything seem so understandable. She got me as a brand-new freshman, off of a very sketchy high school math background.” Mori also praises Cruz for introducing her to a staggering number of ideas that she came across in later math classes. She notes that the coverage Cruz managed has helped her navigate those classes with more ease. Mori also shares that as a new student to college, she had nothing to compare Cruz to other than her high school teachers-yet, now that she has moved further through her schooling, she can fully appreciate how “progressive” Cruz was as an educator.
Mori also recognizes that her high school math background was shaky and that she showed up with “a rather incomplete grasp of just about everything above long division.” She most appreciates Cruz for spending all that extra time to make sure Mori could keep up with her peers without ever leaving Mori feeling overwhelmed. “I never felt like I was drowning in material with no shore in sight,” Mori adds. “She challenged me, but I never felt like I couldn’t rise to the challenge.”
DEVELOPING FREE ONLINE MATH RESOURCES WITH WeBWorK
WeBWorK is an open-source online system for math and science homework. According to Cruz, “For math online homework systems, there are three main players, and WeBWorK is one of them.” Recalling even the earliest days of WeBWorK on campus at The College of Idaho, she notes that she and her colleagues were “astonished at how well the students took to it.” One of the clear benefits would be that students couldn’t spend an evening doing a set of problems the wrong way, only learning of their mistake once in class. There was no chance, for instance, of a student completing twenty quadratic formulas that would all ultimately prove to be wrong. In addition to being effective and immediately helpful to students, the tool is also free to use; with international translations available, it is now being used around the world.
Dr. Michael Gage at the University of Rochester, one of the original developers of WeBWorK, notes that there are currently more than 700 institutions using WeBWorK, and he believes that number will continue to grow, as WeBWorK continues to impact university-level mathematics as well as mathematics education in high schools and community colleges. Gage has known Cruz since 2002 when she set up a WeBWorK server at her institution. Gage shares that Cruz has remained a prolific contributor and a “central figure” of WeBWorK since that time, particularly at the precalculus level, where she has offered hundreds of recently developed problems. He shares that Cruz has helped to grow and nurture the community, while simultaneously increasing the effectiveness of the tool with the “imaginative and high quality precalculus homework questions which she has designed and field tested.”
Gage states, “When new features (such as using GeoGebra applets or essay Questions or making it easy to write problems using currency) become available, she is among the first to try them out, to analyze the features that do or do not work and to make helpful and innovative suggestions. Since many of the questions she and her colleagues create are for different courses and audience than those already in the OpenProblemLibrary, they have driven the creation of new software tools that make precalculus and statistics and other questions easier to write. Our forums are filled with posts from Robin identifying specific software issues or helping newcomers to WeBWorK figure out how to make it work smoothly.”
Rosoff is also quick to note that Cruz’s contributions to WeBWorK are a result of Cruz devoting hundreds of hours to “the arduous work of classifying, tagging, testing, and editing the thousands of problems in the Open Problem Library.”
Rosoff concludes that Cruz’s work with the project “exemplifies the quality of her long-term vision and planning,” in that the system offers clear benefits to both instructors and their students. Not only is the grading load reduced for instructors, but students are also provided immediate feedback. Rosoff states, “Robin was not content to use it in one or two calculus classes at her institution. Instead, she planned the years of work and change necessary to write an impressive collection of WeBWorK problems, so that it would be suitable for all of the introductory courses. These courses presently serve hundreds of students every semester.”
REACHING AT-RISK MIDDLE SCHOOL STUDENTS
After talking to local teachers in secondary schools near her institution, Cruz learned that over fifty percent of the middle schools were Latino, yet the high schools-serving those same geographic areas-did not have those same numbers. Clearly, they were losing kids before they could make it to high school; after reading research papers, she came to understand that students “tended to drop out of math and science after middle school.”
She wanted to start a summer enrichment program for middle school students, giving those kids a chance to see success before high school even started. After working together with Cruz on several unsuccessful grant proposals, the principal of one of the middle schools in Caldwell- inspired by Cruz’s passion-called her to say they would somehow find funding to pilot a program.
She covered the costs of 20 girls and 20 boys, students who could be determined high-risk, and they were “thrilled with the results” and the high level at which these students were performing. The students also learned quickly that this wasn’t a punishment; this was an opportunity. With Cruz serving as “coach and cheerleader,” the gamble paid off. Later that year, they submitted three grant proposals, which were all successful and secured funds to cover the following year with twice the number of students. When the grants ran out, the school district absorbed more of the costs. Finally, in the program’s fifth year, the new superintendent decided to include the program in the budget.
Dayne Filer, a graduate of College of Idaho who is now applying for medical school, worked for The Math and Science Summer Institute (MASSI) as a TA. Filer notes that Cruz “does an amazing job with the MASSI students-and they can be a very difficult bunch.” Filer shares that it’s not just the academic excellence that she shares with these students either; Cruz brings her energy and enthusiasm to the project as well. Filer adds, “Not many college professors would have the patience or even interest in working with a bunch of middle-school students, half of which could not care less, but she does. And she does it with a smile on.”
Cruz shares that Dr. Ann Koga, a member of the Biology department at College of Idaho, was also instrumental in developing MASSI. Koga recalls that they were working together several years back on the outreach component of a grant proposal for the Howard Hughes Medical Institute, when Cruz first developed the idea. Though that grant didn’t come through as they had hoped, Cruz didn’t let that deter her. She was able to secure a grant through The Mathematical Association of America. Koga states, “While Robin and I split the teaching responsibilities for the camp evenly, she does almost all of the planning and organizing. For example, we provide busing and meals for the kids. This requires a great deal of coordination and she does all of it for both the 7th and 8th grade groups.”
Because the 7th grade program Cruz and Koga developed together has an Epidemiology focus, Koga shares that they have been able to easily meld math and science. She adds, “It is Robin’s goal to encourage students to keep taking math and science courses and to bring them to a college campus so they can envision themselves going to college.” Koga admires Cruz’s spirit, her demeanor, and her ideas-that latter of which Cruz is determined to bring to fruition. She adds, “Robin’s motivations are pure: She does these things to provide a better educational experience for students and to help students from disadvantaged backgrounds see college as an achievable goal.”
Math colleague Rosoff adds that Cruz’s work with the project could stem from her “deep commitment to democratic values in education,” as she is tireless in improving opportunities for students, particularly students from less-privileged backgrounds. He recognizes that the MASSI program has stayed organized and funded only because of Cruz’s energy and passion in ensuring its survival.