Psychologist Examines Retention of Mathematical Knowledge
Harry P. Bahrick, director of the memory-research program at Ohio Wesleyan University, has made several long-term studies of the links between memory and learning.
In a recent paper, entitled "Lifetime Maintenance of High School Mathematics Content," which he discussed during a recent forum held by the American Psychological Association at the National Press Club, he argues that by extending the period of time over which students acquire mathematical knowledge, the amount of knowledge retained over a lifetime may be increased dramatically.
To compile the data for the study, Mr. Bahrick administered multiple-choice questions on algebra and plane geometry to a group of 1,726 individuals, ranging in age from students to senior citizens, to determine their level of mathematical knowledge. He then compared the test results with responses to questionnaires and student records to determine how much information the various groups retained.
He discussed his findings, and their implications for precollegiate educators, with Staff Writer Peter West.
Q. What led you to study the retention of mathematical capabilities?
A. I think it's terribly important for educators to find out more about what will make knowledge last longer.
Presently, we have good reason to be6lieve that even a month or two after [students] take exams there are very substantial declines in [their] performance.
So you spend a lot of time, and effort, and money, and you get results that last a few months.
The entire cost-benefit ratio of education is a function of what will make the knowledge last. We need to know what these tradeoffs are so that we can make intelligent decisions about what to teach.
Q. Could you explain the relevance of your findings to precollegiate education?
A. One very relevant finding is there is a greater retention of material that is taught [both] in pre-algebra and algebra than the material that is taught only in pre-algebra. That indicates that with substantially more rehearsal, or practice, the yield per hour would go up by a very large factor indeed.
I'm fairly confident that if nothing were done except [scheduling classes] fewer times a week for more years, the resulting longevity of knowledge would be far, far longer.
In quasi-experimental work that I have done with languages, I've found that longer exposure to knowledge yielded a far larger residue [of knowledge] over a longer period of time.
Q. Are the findings of your research1papplicable across-the-board to students of all levels of ability?
A. The rate of forgetting over time does not appear to be a factor of ability. The slope of the retention functions is very much influenced by the conditions that we can influence, not by ability, or achievement, or aptitude.
Q. In your presentation you indicated that your research is unusual because it violates generally held beliefs about valid psychological techniques. What are the implications of those differences for those who would apply your research findings?
A. Memory experiments typically are done over minutes, hours, days, or, occasionally, weeks, and, as a result, the only kinds of material that you can examine are those you can learn in a laboratory.
But that method excludes study of virtually all [long-term] learning. The retention intervals have to be years, and you can't control what the person does over these years. It simply can't be done. So the choice is not to do it or to do it with non-experimental methods.
It was difficult to get money for this originally, but I believe that the prevailing climate is now more permissive.
Q. What are the implications for precollegiate policymakers who wish to improve the quality of mathematics instruction and the amount of knowledge retained by their students?
A. I would increase the percentage of the content from higher [level] courses that is also taught in the lower [level] courses. And I would search for [knowledge] that can be introduced earlier and repeated that way.
I would also spread the instruction out over a few years and try to have the courses meet less frequently during the week.
You also could run [courses such as] geometry and algebra in parallel. I see no reason why we couldn't start with both in the 9th grade.
Some subject matter is sequential and does not permit parallel teaching, but, where it is possible, I would run them in parallel and run them over two or three years.
If we did that, I'm fairly certain that the quality of the knowledge would be noticeably improved and the knowledge retained over a longer period.