February 8, 2010
Attaining Quality Education Via Flexible Paths to Learning
By Daniel Bernstein, University of Kansas
Some years ago I served on a campus-wide faculty teaching committee, and we received a request from the physics department and an engineering department for money to teach their own calculus courses. Their faculties found students unprepared for major content courses even though they had completed the calculus prerequisite in the mathematics department, and they were losing course time to remedial mathematics. They were confident that their students would be properly prepared if they controlled the prerequisite courses.
Their inquiry led to extended conversations with mathematics faculty members who revealed some interesting internal data: students who received a C in the first calculus course had only a one in five chance of passing the second calculus course. When asked about these data, one person said, “Giving a C means please get out of math.” While acknowledging that students and colleagues in other fields may take a passing grade to mean that students are prepared for further study requiring skill in calculus, the mathematics faculty offered a more socially constructed account of grading. With firm expectations from their chair and other academic leaders that a large percentage of students in foundational service courses will pass, the calculus instructors took to using partial credit and extra credit on easier material as a substitute for actually mastering the course fundamentals.
My thoughts turned to my former mathematics colleagues as I listened to the opening plenary speakers at the recent AAC&U conference. One theme was repeated many times: our goal must be higher completion rates while also preserving the high quality of the education delivered. This message is repeated in the recent statement from the AACU Board of Directors, “The Quality Imperative", and it follows from the long standing AACU initiative on “Greater Expectations”. We are asked to achieve two goals simultaneously, both increasing substantially the percentage of Americans who complete an undergraduate degree and assuring that those students demonstrate the quality skills, knowledge and understanding essential for their futures and for the future of our country. How do we find a path that reconciles the ideals articulated by policy leaders with the teaching and learning challenges encountered by the faculty members who create and manage real learning environments?
At a very important level it is a reasonable position on grading being taken by those mathematicians (and echoed by faculty who teach required service courses in English, humanities, second languages, and science). One of the primary functions of giving grades is to differentiate among students, identifying who in each class learns the fastest and the deepest. In fact, faculty are constantly reminded about the problem of grade inflation and urged to restore some meaningful spread in grades so that students know whether or not continued study in a field is encouraged by knowledgeable instructors. We are also asked to give differentiating information so that employers, scholarship committees, and providers of further education can make informed decisions about scarce resources. In those contexts, it makes sense to use curve grading that reflects relative standing within a class of students.
A focus on comparison, however, ignores another of the primary functions of grading, namely certification of accomplishment. Passing a course or receiving a degree in a program also needs to certify that the person has demonstrated the qualities conventionally identified with an advanced level of skill, knowledge, and understanding. There needs to be some assurance that course and program completion indicates appropriate accomplishment by some intellectual criteria not based on relative standing alone. In some perhaps mythical past, our system presumed that the high standards for admission into post-secondary study meant that those in the middle of the curved distribution (the C students) were reasonably competent, even if not among those who show exceptional achievement with great promise. As we have properly moved to including most of our citizens in post-secondary education, many of us have discovered (as did the mathematicians) that being in the middle of a distribution does not by itself guarantee sufficient accomplishment to meet our conventional expectations for quality. Something else is needed in our system of learning and grading if we are to achieve the goals put before us by academic, governmental, and philanthropic leaders.
For me, analysis of this problem focuses on individual rates of learning. Our course sessions typically proceed through content and skill measurement at a rate suited to the average of our student population, with the result that some students could easily learn more and faster while another set of students cannot keep up and fall further behind until they fail. More than 40 years ago two notable educators (Benjamin Bloom and Fred Keller) addressed this problem by developing systems of individually paced learning, asserting that learning foundational skills well is necessary for successful continued learning. Their slightly different systems supported students in repeating topics until well learned before moving on to the next (perhaps more advanced) topic. Students work through the course at different rates, demonstrating their learning at different times. In this way of thinking, a grade reports the final level of accomplishment of intellectual work, rather than the relative rate of learning among students. In principle, every student could learn all the content well and receive a grade signifying a high degree of understanding and skill. Grades sacrifice their service in differentiation in favor of certification of achievement.
In the real world we all work in, how can this idea help us achieve the important dual goals of attainment and quality? If that were an easy task, it would have been done by now, so let us consider the hurdles. Our social, academic, and economic cultures will continue to demand some differentiation among students, so first we need to design programs that combine curve graded courses with courses in which high level learning is certified for all students who completed a course. The obvious candidates for mastery learning are the foundation courses (introductory knowledge, methods of knowing about a field, basic skills, core content areas), while more variation is acceptable and even useful in advanced and specialty courses. Given such a change in values, we then need to allocate human resources to redesign learning environments that are flexible enough to support individual rates of progress, including finding ways to help students increase their rates (learn to learn). This second hurdle means rethinking faculty work to allow people to spend more time on course design and on building systems for individual feedback, especially in large enrollment foundational courses. While this involves change, which is not always easy to produce, academic leaders can honor learning outcomes that are valuable to an institution. When it is in their self-interest, successful units will find ways to meet institutional goals.
Let me finish with a footnote from the mathematics department. One faculty member who took the internal data to heart looked for solutions to the problem of second course failure. After exploring the mastery course option, he concluded that it was too much change and too much work for him as an individual to redesign his entire course. Instead, he identified those parts of the course that were essential foundations for the next course and those parts that included elegant and beautiful mathematical ideas and skills that were not essential. He did individualized teaching and required high level mastery of the essential parts to get a C in his course. He taught the rest of the material in a conventional way, and the B’s and A’s went to those who successfully followed him into the more esoteric domains. It’s not a perfect solution, but I thought it was a very good first step. It showed real sensitivity to the issue at hand. It would be worthwhile for all of us to be clear what we mean when a student earns a C grade in one of our courses.
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