Sequence: Volume 32, Number 5

Release Date: September/October 1997

Introduction

Compared with students enrolled in conventionally taught courses, students who are provided regular access to well-crafted computer-mediated instructional (CMI) materials generally achieve higher scores on summary examinations (improved learner effectiveness), learn their lessons in less time (increased learner efficiency), like their classes more (greater learner engagement) and develop more positive attitudes toward the discipline under inquiry (enhanced learner interest). These results hold for a broad range of students, stretching from elementary to college students, studying across a broad range of disciplines, from mathematics to the social sciences to the humanities. The findings also hold for students who vary greatly in terms of their prior knowledge, educational experiences, preferences for particular types of instructional assistance and English language proficiency. The empirical data substantiating these findings are to be found in a steady stream of studies published since 1990, summarizing the experimental results obtained by a large number of researchers (Anderson, et. al., 1995; Ayersman, 1996; Boettcher, 1993; Fletcher-Flinn, 1995; Hannafin, et. al., 1996; Khalili and Shashaani, 1994; Kulik and Kulik, 1991; Kulik, 1994; McCoy, 1996; Schofield, 1995; and Weller, 1996). The experimental data has been subjected to a range of meta-analytic techniques, specifically designed to enable researchers to contrast and compare research findings across an breadth of instructional environments, implementation models and evaluation methods (Glass, 1976; Glass, McGraw and Smith, 1981; Hunter, 1990; Kulik and Kulik, 1989; Straf, 1990).

Despite the effectiveness of CMI materials relatively little use is made of technology in mainstream college teaching. Whole-class, lock-step synchronous teaching continues as the predominant teaching method, particularly in entry-level courses in mathematics, the basic sciences and engineering. Not even the National Research Council's (NRC) periodic pleas that greater use be made of technology to meet the learning assistance needs of an increasingly diverse student population, has succeeded in reducing higher education's reliance upon conventional teaching methods (NRC, 1989, 1990a, 1990b, 1991 and 1996). What accounts for this chasm between today's usage patterns and the promise of technology?

One obvious place to look for an answer to this question are the CMI materials featured in the meta-analytical reviews. When we took a closer look at these software materials we discovered that they could be characterized by the following five attributes:

Narrowly conceptualized. In the large majority of instances, the featured materials were designed and programmed by individual faculty or graduate students, typically working alone. This individualistic, entrepreneurial approach has led the NRC to refer to these campus-based software developers as "Lone Rangers." In the main, the objective of these development efforts was not to supply comprehensive instructional support for learners, but to aid the investigation of a particular cognitive phenomena, to test the efficacy of a few lessons in an experimental laboratory-like setting, or to examine of the potential usefulness of new programming languages and authoring tools.

Limited in their scope. The featured materials corresponded to only a small fraction of the topics, lessons, learning objectives and teaching activities one would expect to find in a typical college course. This outcome is not surprising since few of these development efforts were intended to function as agents of transformative change and improvement.

Theoretically chaotic. The featured materials were rarely informed by a well-articulated, rigorous and consistent theory of computer-mediated instruction and learning, the two notable exceptions being CMI materials produced by proponents of intelligent tutoring systems and commercial developers of classic approaches to computer assisted instruction. However, even in these cases, the underlying theory of instruction informing the design of these two approaches imagineds the student as the recipient of tightly-structured, highly-ordered CMI materials and the instructor as somewhat marginal to the teaching and learning enterprise.

Non-transformative. The featured materials were for the most part bolted-on to existent classroom teaching methods, leaving the traditional curriculum, learning objectives, teaching strategies and student learning activities more or less intact. By being bolted on to the teaching and learning enterprise as we now know it, the use of these materials provided little information on how computer-mediated instruction could be employed to increase learner productivity in a cost-effective manner.

Pedagogically confusing. The featured materials were rarely, if ever, accompanied by a "user's manual," explaining what new teaching methods and options they made possible for instructors, or what new learning strategies and methods they made possible for learners. Again, this outcome is not surprising since few of development these efforts were intended to stimulate transformative thinking on the part of instructors and their students regarding the nature and character of technology-mediated teaching and learning.

Any number of possible explanations could account for these nonsystematic efforts. Higher education does not properly reward faculty who are interested in developing comprehensive, instructionally effective CMI materials. The development of CMI materials corresponding to a broad range of topics and lessons within a single disciplinary area is technologically and organizationally complex, and, therefore, is beyond the expertise and experiences of most faculty. Individual colleges and universities cannot afford to shoulder the financial risks of developing the enabling technologies necessary to support the development of instructionally effective CMI materials. State and federal agencies are uninterested in providing support for efforts intended to transmute promising research results into everyday instructional practices. It is still too early in the technological and theoretical life cycle for researchers to have reached agreement on a consistent theory of computer-mediated instruction and learning. It is easier to "bolt-on" CMI materials to traditional teaching environments than to reconceptualize the entire teaching and learning enterprise for a relatively small amount of curriculum materials. Finally, textbook publishers, higher education's traditional supplier of instructional materials has yet to come up with a viable economic model for commercializing the distribution of CMI materials. Some textbook publishers fear the potential impact of CMI materials on their existing business operations.

However one accounts for the failure of technology to materially impact teaching practices, there should be no confusion over the possible detrimental impact of technology's marginal status in the teaching mainstream. The chasm between the promise and potential of computer-mediated instruction will continue to remain immense as long as nothing is done to radically alter the conditions and circumstances that currently typify campus-based efforts to design, develop and implement CMI materials.

This was the conclusion reached by the one of the authors (Gifford), following a three-year stint as Apple Computer's first ever vice president for education. The position at Apple - held by Gifford while on a three-year leave from his faculty position at Berkeley - -afforded Gifford the opportunity to observe the efforts of campus-based, faculty-led teams of CMI materials developers on more than one hundred US colleges and universities. More important, these visits permitted Gifford to witness first-hand some of the obstacles to serious CMI materials development, we described above. Gifford's observations and insights also informed the efforts of the other two authors of this article (Baker and Hale) in their reading and interpretation of the research literature on the utilization and impact of CMI materials. In addition to our joint efforts to develop a better understanding of the impediments that appear to be thwarting the use of CMI materials to increase learner productivity, each of us has drawn upon our own individual experiences and observations of the materials development process on our respective campuses.

The origins and goals of Mediated Learning

In 1992 one of the authors (Gifford) founded Academic Systems, to develop, implement and continuously improve new approaches to using technology to improve learner productivity. The company's first task was to prototype the Mediated Learning model, an approach to embedding CMI materials within a computer-mediated, communications-rich instructional environment, in which the teaching, learning and assessment functions are fully integrated with each other through the use of especially created instructional software applications. The basic idea behind the creation of Academic Systems was to bring together under one roof: i) the enabling technologies necessary to develop instructionally effective CMI materials; ii) the organizational infrastructure, procedures and disciplined behaviors necessary to develop these CMI materials on a regular, predictable schedule; and iii) the sensibilities, expertise and commitment to collaboration necessary to make these CMI materials attractive and useful to instructors and their students and the acumen to achieve these complex objectives while building an organization capable of making effective use of its limited supply of equity capital. 1

The basic idea behind Mediated Learning was to employ technology to provide instructor's more teaching options and to provide students more options to secure more forms of instructional assistance. More specifically, in the case of instructors this means more opportunities to engage students in small-group instruction, more opportunities to offer students one-on-one tutoring sessions, and more opportunities to engage in what some cognitive scientists have referred to as scaffolded instruction, including coaching, mentoring and modeling activities. Similarly, in the case of learners this would mean that more students would have more opportunities to secure different types of instructional assistance, as well as the means to exercise greater control over the pacing and sequencing of their own learning. Finally, and most importantly, the idea was to pursue these objectives in a manner that would not require technology to be bolted on to the conventional lecture-presentation.

Consistent with Academic Systems' interest in forging strong collaborative partnerships with leading higher education institutions, and consistent with CSU-SLO's interest in forging closer relationships with the private sector, particularly leading edge instructional technology firms, Academic Systems and CSU-SLO began their collaborative efforts in the later part of 1992. By early 1993, representatives from three other CSU campuses had joined in the effort to help move the goals and objectives of Mediated Learning from the drawing board to the classroom. This attempt to make the transition from possibility thinking to prototype to implementation was motivated by policy, pedagogical, theoretical and economic considerations.

On the policy front, we wanted to test the hypothesis that, compared to teaching methods that currently typify college-level instruction in entry-level mathematics courses, distributed computing technologies could be employed to make the mathematics teaching enterprise more effective, efficient and accessible to a broader range of students. We were particularl y interested in the potential of Mediated Learning for improving the learning productivity of students who historically have not been well served by conventional teaching methods, especially students who require more opportunities to learn to achieve the same level of academic success as their peers and non-native English speaking students, who may require more language-rich, communications-intensive instructional settings to achieve a level of academic success commensurate with their demonstrated potential.

On the pedagogical front, we wanted to gather more empirical evidence regarding how one might go about employing technology to: i) provide more opportunities for students to obtain lesson-specific instructional assistance than possible in settings constrained by the traditional academic calendar, which limits the timing, duration, scope and quantity of instructional assistance available to students beyond regularly scheduled hours; ii) accommodate instructors interested in employing a greater range of teaching methods than possible in traditional classrooms, such as small-group instruction and more modeling, mentoring and coaching activities; iii) extend the reach of the teaching enterprise to students located beyond the physical boundaries of the location-specific classroom; and iv) foster location-independent electronic communications between and among instructors and their students.

On the theoretical front, we started with the assumption that the theories of direct classroom instruction that have informed and guided teaching strategies in location-specific settings would have to be revisited, to take into account the greater range of instructor and learner strategies and behaviors afforded by Mediated Learning. We also assumed that the process of developing a more contemporary theory of instruction consistent with the options afforded in distributed instruction settings, would have to address the issue of how technology compels us to revisit all of our standard assumptions and understandings of the nature and character of instructional work.

Last, but certainly not least in terms of importance, we knew we would have to address the issue of the cost-effectiveness. It was understood that unless we could come up with an uncomplicated metric that could be used to make first-order comparisons of the cost-effectiveness of technology-mediated and conventional instruction, the first three objectives on our agenda for reform and improvement would be meaningless in terms of the long-term impact of technology on mathematics teaching practices at CSU-SLO and the other three CSU campuses who advised Academic Systems' content specialists, instructional designers and software engineers during the early stages of the collaborative.

The infrastructure of the first version of Mediated Learning consisted of four key components.

1) A comprehensive collection of computer-mediated instructional (CMI) materials, incorporating many different media formats, including electronic text, digital video and audio, learner-controlled simulations and interactive dynamic representations. Modularly organized, these representation- and tool-rich materials are sufficiently broad in their scope and coverage to correspond to the topics and lessons one would expect to find in a typical college course.

2) A customized sophisticated relational database application tightly coupled to the CMI materials. Here the objective was to make it possible for instructors to closely monitor the progress being made by their students, and to provide lesson-specific advice to students in need of special learning assistance. Providing timely information to students on their own learning also makes it possible for students to exercise greater control over the pace at which they use the materials to support their own learning, as well as the pathways they take in navigating through the materials.

3) Computer networking technologies with sufficient bandwidth to enable instructors and their students to access these students over local area networks of personalcomputers, thereby facilitating individual or group access to these materials at any time.

4) Communications technologies capable of supporting synchronous and asynchronous communications between and among instructors and students.

The decision was made try the Mediated Learning approach in the area of introductory and intermediate college algebra. The intention here was to support students whose substandard scores on CSU's Entry-Level Mathematics (ELM) examination had resulted in their being placed in remedial mathematics courses. Currently, between 40 and 70 percent of the nearly 60,000 students who enter CSU each year are required to enroll in at least one remedial mathematics course.

CSU students enrolled in remedial mathematics courses are more likely than their peers to be members of minority racial, ethnic or language groups, to be the first in their families to attend college, to be older than their peers, to attend college part-time, to take coursework intermittently, to work full-time while attending college full-time and to have pressing family obligations. The students who end up in remedial or developmental mathematics courses are also much more likely to have attended high schools where they were not well-served by existing teaching practices. Currently, three population groups - black students, non Chinese/Japanese/Korean Asian students and Hispanic students - are disproportionately represented in CSU's remedial mathematics courses.

The challenge of providing effective remedial instruction is not unique to CSU. In California's public community colleges, which enroll more than 1.3 million students, nearly 90 percent of all entry-level students are required to take at least one remedial course in mathematics; more than 60 percent are required to take two courses. In both CSU and in the California community colleges, student passing rates in these courses frequently fail to top 50 percent. These trends are discouraging, and they are not unique to California. The flow of underprepared entry-level college students into remedial mathematics courses, and their subsequent high rates of failure in these courses, is a national phenomenon, and has been so for nearly 25 years (Alberts, et. al., 1994).

Results: Increased Passing Rates and Enduring Impact

Now that it has been in use for a few years and information on student achievement has been analyzed by faculty on more than three dozen campuses, including CSU-SLO and eight other CSU campuses, the Mediated Learning approach can now be judged on its potential to improve student learning productivity. For this analysis we have chosen to focus on the impact of Mediated Learning on a specific measure of student learning productivity, course passing rates. The importance of course passing rates in a discussion about results is vital because the mathematics courses currently being supported by Mediated Learning - courses in introductory, intermediate and college algebra - are usually offered as part of a two- or three-course sequence. When course passing rates are low, students churn through courses over and over again, until they either pass or drop out. An instructional approach that significantly increases course passing rates could than justify the additional costs of making it happen

On some campuses, students who were enrolled in Mediated Learning courses consistently passed their courses at high rates than their peers enrolled in traditionally taught algebra courses. On other campuses, the results were more mixed. In no instance, however, did the students supported by Mediated Learning fare more poorly than their peers enrolled in traditionally taught courses. On some of the more successful campuses, compared to traditionally taught courses, the employment of Mediated Learning has regularly resulted in 15 to 25 percent increases in student passing rates, reducing student "churning" in these courses to the point where it becomes possible to finance the incremental costs of Mediated Learning expenses out of cost savings.

In Table 1, we attempt to make more vivid the economic implications of increased course passing rates on the economics of instruction, by focusing on the relationship between course passing rates and selected student churning variables. The table contains data simulating the impact of a 20 percent increase in passing rates on the course taking dynamics of a 1200 student cohort, enrolled in a three-course sequence. In generating the simulation we assume that students drop out following two consecutive failures of the same course. In a cohort where the passing rate is 40 percent - a typical rate in many conventionally taught college-level algebra courses - 315 of the students would complete the entire three-course sequence. Increase this passing rate by 20 percent, and the number of students completing the three course sequences jumps to 711, an rather dramatic increase of 126 percent.2

Table 1: Student performance indicators for a 1200 student cohort taking a three-course sequence, at course passing rates of 40 and 60 percent, where students drop out following two consecutive failures

Course passing rates (%) Cumulative enrollment Students who repeat courses Students who drop out Students completing sequence 40 3,935 1,475 885 315 60 4,277 1,222 489 711 Change 342 (253) (396) 396 % change 8.7 % (17.2 %) (44.7 %) 126 %

While encouraging, the fact that Mediated Learning course enrollment could be positively linked to significant increases in course passing rates, was not considered sufficiently persuasive to declare the approach a success. We were also interested in looking at the enduring impact of Mediated Learning.

Following the spring quarters of the 1994-95 and 1995-96 academic-years, we collected performance data on all 476 students enrolled in CSU-SLO's precalculus courses. The question we wanted to answer was: "Do students taught algebra in Mediated Learning courses do as well in subsequent traditionally-taught precauculus courses as their peers, who were taught algebra in conventionally taught courses, in which individual instructors prepare their own quizzes, mid-term and final examinations, and are responsible for assessing student performance handing out their own letter grades?" Once we completed our data collection efforts, we sorted the data in accordance with the scheme depicted in Figure 1. That is, we catagorized students into the six distinct groups depicted in Figure 4, in accordance with their own past mathematics course taking behaviors, prior to enrolling in precalculus:

Group 1. This group includes students who did not require any prerequisite coursework in algebra. The assumption by the mathematics department was that these students were ready for precalculus immediately upon enrollment.

Group 2. This group includes students whose scores on the college's entry-level mathematics (ELM) examination indicated that they needed to take the equivalent of one course in Intermediate Algebra before enrolling in Precalculus. Students who met this requirement by enrolling in a traditionally-taught Intermediate Algebra course comprise this group.

Group 3. In terms of mathematics background knowledge, Group 3 is more or less identical to Group 2, with one major difference. Group 3 students met their Intermediate Algebra requirement by enrolling in the Mediated Learning course, Interactive Algebra II.

Group 4. This group includes students whose scores on the ELM test indicated that they needed to take the equivalent of one course in introductory algebra and one course in Intermediate Algebra before enrolling in Precalculus. Students who met this requirement by enrolling in traditionally-taught courses in Introductory and Intermediate Algebra are included in this group.

Group 5. In terms of mathematics background knowledge, Group 5 is more or less identical to Group 4, with one major difference. Group 5 students fulfilled the two-algebra-course requirement in either of two ways: by enrolling in the traditionally-taught course in Introductory Algebra and following this course byenrolling in Mediated Learning Intermediate Algebra, or by first taking the Mediated Learning algebra course and then taking traditional Intermediate Algebra.

Group 6. In terms of mathematics background knowledge, Group 6 is more or less identical to Groups 4 and 5, with one major difference. Group 6 students met the two-algebra-course requirement by enrolling in Interactive Algebra I and II.

In Table 2, the six groups are further sub-divided according to the final grades students received in their precalculus courses. The commonly-used grades A through F are provided in the table, but also note the grades of W, U and I. W stands for "withdrawal," U for "unauthorized withdrawal," meaning that a student attended class for a short period of time at the beginning of the term, did not drop the class, but never took any exams or other diagnostic exercises (otherwise an F would be given), and I for "incomplete." Finally, the letter G is used to represent a given grade range.

Table 2: Grade distribution (by number of students) of six student groups

Grade Range (G) Group 1 Group 2 Group 3 Group 4 Group 5 Group 6 Total C<G<A 110 67 61 15 12 44 309 G<C or G=W,U, or I 55 47 12 30 13 10 167 Total 165 114 73 45 25 54 476

To complete this analysis, first we had to convert the categorical letter grade data to their numerical equivalents. We accomplished this by setting the following numerical grade-equivalent scores for each letter grade, in accordance with the following conversion factors: A = 91 through 100, A- = 87.5 through 90, B+ = 85 through 87.4, B = 80 through 84, B- = 77.5 through 79, C+ = 75 through 77.4, C = 70 through 74, C- = 67.5 through 69, D+ = 65 through 67.4, D = 60 through 64, D- = 57.5 through 59, F = 0 through 57.4, W = 0 through 57.4, U = 0 through 57.4, I = 0 through 100. We then transformed the categorical grade data by employing a random number generator to produce the same number of grade-equivalent scores as the frequency with which students obtained the grade in question.

Table 3 Performance of students enrolled in conventionally taught and Mediated Learning precalculus mathematics courses at California Polytechnic State University, Saint Luis Obispo

Student Cohort Group SLO algebra courses taken by students prior to enrolling in precalculus courses Sample size Percent of students grades >C Results of Chi-Square analysis Comparison groups Chi-square Value Significant at < 0.01? 1 None 165 66.7 1 and 2 1.812 No 2 Conventional Intermediate Algebra 114 58.6 1and 3 7.142 Yes 3 Mediated Learning Intermediate Algebra 73 83.6 1 and 4 16.306 Yes 4 Conventional Introductory & Intermediate Algebra 45 33.3 1 and 5 3.292 No 5 Mixture of Mediated Learning & Conventional Introductory & Intermediate Algebra 25 48.0 1 and 6 4.278 No 6 Mediated Learning Introductory & Intermediate Algebra 54 81.5 2 and 3 12.663 Yes 4 and 5 1.459 No 4 and 6 26.631 Yes 5 and 6 9.282 Yes

Once we completed this conversion and transformation process, we then proceeded to subject the data to chi-square analyses and one-way analysis of variance (ANOVA) tests. The results of the chi-square analysis are presented in Table 3. Both tests indicate that students who took one Mediated Learning algebra class before enrolling in Precalculus (Group 3) earned a higher proportion of grades of C or better in Precalculus than did students who entered precalculus directly (Group 1). By contrast, the proportions of grades of C or better in Precalculus did not differ between students who took one traditional preparatory algebra class (Group 2) and those who enrolled directly in precalculus (Group 1). Students who entered precalculus directly (Group 1) were more likely to receive grades of C or better than were students who took two preparatory courses in the traditional form (Group 4), whereas there was no statistically significant difference in receiving grades of C or better between students who were prep ared to enroll directly in precalculus (Group 1) and those who took two preparatory courses, one of which was in the Mediated Learning form (Group 5). Of students who were required to take two algebra classes prior to precalculus, those who took both courses in the Mediated Learning form (Group 6) received a higher proportion of grades of C or better than their peers who took both courses in a traditional format (Group 4). Those who took both courses in the Mediated Learning form (Group 6) also received a higher proportion of grades of C or better than their peers who took one course in the traditional form and one in the Mediated Learning form (Group 5). The general pattern presented by the chi-square analyses is that, far from being hindered in their progress by having to take Mediated Learning algebra courses at CSU-SLO, students who take and pass these courses are more likely than others to receive grades that enable them to pursue further study of mathematics.

Future Goals

Efforts are now underway to expand the applicability of Mediated Learning to other disciplinary areas. CSU-SLO and four other CSU campuses are now beta-testing a course in basic writing. As part of this effort, the relational database used to support mathematics instruction has been upgraded to support the maintenance of portfolios containing student writing samples, including written commentary of student peer reviewers. This would permit writing instructors to review writing samples generated by individual students over the course of a full semester of instruction. In addition to these changes, the instructional architecture for the CMI materials supporting the basic writing course is being structured to support more extensive modes of communications between and among students and instructors, including real-time chat, peer review and whole group access to the same interface.

Efforts are also underway to extend the Mediated Learning approach to the Internet. This is in line with our view that technology should be used to redistribute the focus of teaching and learning activities from individual learners, functioning inside of hermetically sealed, self-contained classrooms to larger learning communities that networked CMI materials afford to individual students, their peers and their instructors. Put another way, knowledge is situated in, and distributed across the activities and the cognitive tools that afford these activities in the classroom and in the world beyond classroom and campus boundaries. This objective was also intended to focus attention on the notion that, with the creation of the appropriate database application, the network itself could serve as a dynamic repository of the history of the exchanges and interactions among students and their peers, students and instructors, and students and instructional materials, and that this repository should be made accessible to students and instructors outside of traditional classroom hours.

To illustrate the usefulness of passing rates, as a means for computing the cost-effectiveness of conventional and computer-mediated instruction, we constructed Figure I-1, which traces the progress of single cohort of 1200 students through a sequence of three mathematics courses. We selected this particular sequence because of its broad applicability to the circumstances of many publicly financed two- and four-year colleges. In these colleges, a significant proportion entry-level students enter college underprepared in the area of mathematics, necessitating their enrollment in one to two remedial mathematics courses (Alberts, et. al. 1992).

As evidenced by the complexity of the Figure 2, tracking a 1200 student cohort over six full terms of instruction is not entirely a trivial analytical exercise. There are 29 different cells depicted in the figure. There would be even more cells if we did not assume that, after a student fails a course twice in a row, he or she will drop out. Figure I-1 also serves to highlight the fact that there are seven different pathways a student can takebefore being accepting failure and dropping out, and eight distinct pathways leading to academic success. That there are so many different pathways for individual students in our 1200 student cohort to take on the way to failure or success would appear to underscore the need for measures similar to the Mediated Learning approach, which attempts to take into account a student's prior learning experiences, including his or her past failures and successes, and is also by the belief that effective learning is more likely to result when students are given the means to assume greater control over their own learning (National Research Council, 1989, 1991).

We demonstrate the analytical implications of Figure I-1 in Table 1, by showing how relatively modest increases in course passing rates can generate rather dramatic increases in the overall learning productivity of the lager teaching and learning enterprise. Notice the impact of an increase in passing rates from 40 to 60 percent. From the perspective of faculty employed in publicly-financed institutions of higher education, where campus revenues tend to be driven by student enrollment, the impact of this level of increase in student passing rates actually increases the demand for instruction; in this instance a twenty percent increase in student passing rates generates an increase in enrollment of 342 students, or 8.7percent. This finding runs counter to the popular wisdom that the use of technology to increase learner productivity must necessarily lead to decreases in the demand for faculty. It is also interesting to note that the number of students repeater the same course one or more times declines from 1,475 to 1,222 students, a drop of 253 students, or 17.1 percent. Similarly, the number of students dropping out following two consecutive course failures falls from 885 to 489 students, a decline of 396 students, or 44.5 percent. Finally, and most important of all, are the totals in the last column of Table 1, which indicates that by increasing student passing rates from 40 to 60 percent, the total number of students completing the three course sequence over the six-term period our 1200 student is making its way through the teaching pipeline jumps form 315 to 711 students, an increase of 126 percent. Some of these impacts are illustrated in Figure I-1.

Table I-1: Enrollment totals for a 1200 student cohort completing a three-course sequence, as a function of course passing rates, assuming that students drop out following two consecutive failures in the same course

Course passing rates (%) Cumulative enrollment Students who repeat courses Students who drop out Students completing sequence 100 3,600 0 0 1,200 90 3,921 357 36 1,164 80 4,150 692 138 1,062 70 4,271 986 296 904 60 4,277 1,222 489 711 50 4,163 1,388 694 506 40 3,935 1,475 885 315 30 3,611 1,487 1,041 159 20 3,218 1,431 1,144 56 10 2,796 1,325 1,192 8 0 2,400 1,200 1,200 0

In Table I-2, we break down the information from Table I-1 even further, by depicting the number of students that successfully complete the three-course sequence from term three on, as a function of the student passing rate. When the passing rate is 40 percent, 77 students will complete the three-course sequence in the third term; 138 students in the fourth term; 84 students in the fifth term; and 16 students in the sixth term. In all, a total of 315 successful students after six full terms of instruction and learning. The comparable numbers for a 60 percent passing rate are: 259 students in the third term; 312 students in the fourth term; 123 students in the fifth term; and 17 students in the sixth term. In all, a total of 711 students. Not only do more students complete the sequence, they complete the sequence in less time when passing rates go up, a desirable outcome for everyone, since it lowers the opportunity costs for both students and the institutions they attend.

Table I-2 Number of students and percentage of original 1200 student cohort completing three-course sequence, as a function of course passing rates Course Number of students completing three-course sequence

Course Number of students completing three-course sequence Passing In three terms In four terms In five terms In six terms TOTAL Rate (%) Number % Number % Number % Number % Number % 100 1,200 100.0 0 0.0 0 0.0 0 0.0 1,200 100.0 90 875 72.9 261 21.8 27 2.3 1 0.1 1,164 97.0 80 614 51.2 369 30.8 75 6.3 5 0.4 1,063 88.6 70 412 34.3 369 30.8 111 9.3 11 0.9 903 75.3 60 259 21.6 312 26.0 123 10.3 17 1.4 711 59.3 50 150 12.5 225 18.8 114 9.5 19 1.6 508 42.3 40 77 604 138 11.5 84 7.0 16 1.4 315 26.3 30 32 2.7 69 5.8 45 4.0 11 0.9 160 13.3 20 10 0.8 24 2.0 18 1.5 5 0.4 57 4.8 10 1 0.1 3 0.3 3 0.3 1 0.1 8 0.7 0 0 0.0 0 0.0 0 0.0 0 0.0 0 0.0

Summing things up, the points being made here are clear, and we believe quite persuasive. Passing rates are an important metric of instructional productivity. When passing rates increase, more students succeed, more quickly. Getting back to Table I-1, when the passing rate is 40 percent, the ratio of successful students to the cumulative total enrollment is 315 divided by 3,935, or 0.080; at 60 percent passing rates, this ratio increase to 16.6, the ratio of 711 to 4,277. By any measure of change in instructional productivity, this is an impressive result.

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NOTES

1 The decision to seek private equity capital to finance Academic System's start-up research and development costs was made following the persistent failure of attempts by Gifford to launch a sustainable non-profit organization. Gifford's original intent was to create an market-sensitive, non-profit organization along the lines of the Children's Television Workshop (CTW). The producers of the popular children's television program Sesame Street, CTW has played a major role in pushing for improvements in educational television in the US and the world for more than three decades. CTW generates a large proportion of its operating budget from revenues generated by its product development and distribution partnerships with private sector companies. Many of the major federal agencies, philanthropic organizations and publicly financed systems of higher education were enthusiastic about the potential benefits of such an organization. However, none were able to imagine how they could involve themselves in such an entity.

2 A more detailed explanation of the impact of student passing rates on the demand for instruction is described in the insert: The impact of student passing rates on the demand for instruction.

Warren Baker is President and Thomas Hale is Professor and Chair of the Department of Mathematics at California Polytechnic State University - Saint Luis Obispo (CSU-SLO)

Bernard R. Gifford is Chief Instructional Officer at Academic Systems Corporation and Professor, of the Division of Education in Mathematics, Science and Technology at the University of California at Berkeley.