Attitudes and Teaching Philosophy
At the root of this ten-year commitment to implementing reform in the college algebra course at UHD are the reformers' attitudes and teaching philosophy (defn). What values made this reform happen? Playing the skeptic, we asked if the purpose of reform was to make the course more appealing to students-a somewhat superficial objective for using technology. One of the reformers who answered provided some interesting insights into his classroom teaching principles (defn):

I don't think we were thinking of using technology to make the course sexier; that was in the back our mind. They [the students] come in with weak skills, so we were using the technology as kind of a skill replacement. We wanted to do more relevant problems. We wanted to present the material in a different way. We didn't want them to be repeating their high school algebra class. Technology really gives you an opportunity to sort of remake the course. We call it reinventing the course, so it gives you something to structure your syllabus around. (Bill Waller, Faculty)

We also inquired about using technology to interact and communicate with students, in light of the fact that many students are working long hours outside UHD. Another reformer answered:

We don't use technology as a communications tool; we use it mainly to teach content. One great thing about the technology is that it really gives you a good context for interaction. So if the students are doing something in class, for example making a graph, it gives you a good opportunity to talk with them about that graph or have them ask you questions about it. It really helps bring the instructor and the student closer together. (Bill Waller, Faculty)

The road to reform has had its bumps, in the form of criticisms from faculty outside UHD who use the curriculum materials developed for the course and also from faculty within the UHD Department of Computer and Mathematical Sciences who have not adapted the materials. Both groups have expressed concern about the scope of the new course. As a result, the reformers have had to make a case for reducing some of the content and skills that are taught in the traditional course. They questioned the old paradigm of teaching students every detailed step in the mathematical solutions to canonical examples, and, in line with the national reform movement, they included in their curriculum problems with real-world relevance. Here is how they made their case:

In many cases, people say, "you didn't teach students the step-by-step way of solving a three-by-three system of equations, which is a standard part of the curriculum." People who have used our material off campus have complained about that, but it's a decision that you make, and here is why you might come to that sort of conclusion. When you're teaching students to solve a three-by-three system by hand, what are you really trying to teach? There is something useful there--the whole idea of substitutions. What else is there about solving a system of equations that's truly useful? What happens often in algebra courses is that it's never pointed out to students that algebra is a problem-solving method that's useful in other areas as well. It merely becomes a blue box in a book: "Follow these steps to solve a system of equations." When it becomes that rote, all the value of the method is missing, but all the pitfalls are still there, the arithmetic mistakes, all the things that frustrate students. So we thought that what students learn by us teaching them elimination is not worth it at this point. We'll just let them solve the system with the computer, which is the way they're going to do it in practice anyway. They're probably not often going to do it by hand with a realistic system of equations, maybe only for small systems like a 2 x 2. So those are the kinds of decisions that we were facing throughout the curriculum. We asked, "What's really important about this problem?" And then, "How important are the manipulative skills that you must have to carry out to the next level?" (Bill Waller, Faculty)

A faculty collaborator reinforces the case for reform by commenting on his experience teaching a reformed linear algebra course at UHD:

My experience so far teaching this class has been relatively successful. In a course like linear algebra, from my point of view, if I were to do it the traditional way--the theorem proof type of thing--it wouldn't be of value to our students and they wouldn't appreciate it. But in the interactive setting that they have, they're creating something of their own; they have to create their own examples. The examples are there, but they can change the examples and try to conjecture from them what's going on. They can derive some of the concepts, but proofs are very minimal in this course. So that's basically what I do in this linear algebra course. (Elias Deeba, Faculty)

When this same collaborator was asked why he continued down the reform path even though he faced a series of daunting challenges (increased workload, technical difficulties, etc.), he replied:

Yes, I could have quit, but I felt a value in it for me, because I saw the utility of these [software] packages--in particular, in my case, Maple. I saw how important it was for me to make a presentation and create a dynamic environment in the classroom using these software packages. (Elias Deeba, Faculty)

In reflecting on the last few years of reform, one instructor considers the many benefits of including technology-based activities in the college algebra curriculum:

People who are thinking about using technology may just be wondering what it offers. It really allows you to open up in the classroom and gives you a lot of avenues for discussion. Sometimes when you're lecturing and you're so focused on finishing up five examples, or whatever you had planned for that day, you're really just reciting the material. You ask for questions, but it's kind of perfunctory, and of course the students don't ask anything. They're willing just to sit there and let you regurgitate the material. But when you're trying to do examples with technology, when you're making graphs in a math class or showing graphs, it always raises points of discussion. There's always something that you see in the graph that suggests a point that maybe you hadn't thought about. When you're doing more complicated examples than before, it brings up the whole question of "What's the meaning of the example? What's going on here?" (Bill Waller, Faculty)

Peer Support
At educational institutions, even those that are teaching-focused, there is limited financial gain for faculty who engage in curricular reform. Often the institutions provide financial support or other types of resources (e.g., additional space) only after external foundations, such as NSF, have approved a project. Hence peer support is a key element that usually keeps reformers engaged and motivated in the initial stages of their work. A variety of factors (such as the Interactive Math Text Project [IMTP] workshops in the early 90's) resulted in the UHD college algebra reformers receiving external support early on. Thus peer support was important, not to get the project started, but to continue its implementation for almost a decade. One should remember that this reform project relied upon a close working relationship among three faculty members for nearly ten years. UHD's environment encouraged this collaboration and allowed the relationship to flourish. Nevertheless, one reformer spoke about the commitment required to continually build support from departmental colleagues. Here is some advice for future adapters:

You have to constantly sell yourself. Give it a chance. There will be times you'll be lost, there will be times you'll be confused, but if you're patient and keep trying, then things will get better. It's not always smooth sailing; it's constantly trying to convince them that it will work in the long run. (Linda Becerra, Faculty)

The environment at UHD is unusual in that faculty are free to experiment with small curriculum segments, as long as they do not attempt to impose these changes on their colleagues. While departmental support per se was not strong, the changes implemented in college algebra were also not opposed by the department.

Well, the department doesn't require that we do things in a certain way; so it's been supportive in the sense that we can pretty much try anything that we want. We've streamlined the curriculum, we've brought in technology, we've tried collaborative learning, and we've never been told to stop doing something. (Linda Becerra, Faculty)