“Answers are listed on the last page,” I said.
“But we don’t know if we’re getting to the answers the right way,” she replied.
“I write out examples in class. You’re supposed to apply what you learn by doing the problem set on your own.”
“The examples are tough to follow. I think we need stepwise procedures,” she suggested.
I was not convinced and decided to appeal to the scholarly teaching literature to support my position that studying pre-worked problems would result in inferior learning compared to working through problems on your own. I was surprised to discover that the weight of evidence was not in my favor.
Worked Problem Effect
The worked problem effect was reported by John Sweller and colleagues in 1985 and has been validated and elaborated upon many times in the years since. In one of the initial experiments, 22 students were taught how to solve several different types of algebra problems using generalized examples. The students were then separated into two groups. Both groups received a problem set in which each type of algebra problem was represented twice. The first of each problem type was worked for the worked problem group, but the control group was expected to solve all the problems themselves. Finally, a test containing each problem type was administered. The results showed that the worked problem group committed fewer errors and required less time per problem on both the problem set and the test, with a per-problem time nearly half that of the control group.
The researchers made sense of their results in the context of cognitive load theory, suggesting that having students struggle to solve unfamiliar math problems overloads their working memory, which can interfere with the procedural automation, pattern recognition, and rehearsal processes required for successful long-term learning of new material. In other words, if working memory is occupied just trying to work through arithmetic, it is not engaged in recognizing problem types and solution strategies. It is possible for students to navigate their way through many problems and never recognize the simple rules that underlie the solutions. The way to avoid this is to focus on the big picture initially, allowing students to become thoroughly familiar with the various kinds of problems they will encounter and to consider efficient ways to solve them (for example, by studying instructor-worked problems) before attempting the problems themselves.
When the Worked Problem Effect Fails
In perusing this body of research, it was interesting to me to read about situations in which the worked problem effect is not observed. First, students may lack adequate motivation to extract knowledge from a set containing only worked problems. Thus, it is preferable to alternate worked problems with practice problems because students will likely learn more from a worked problem if they know they will be using the information in a subsequent practice problem. Second, the worked problem effect is not observed if the cognitive load required for understanding the example problem is greater than the cognitive load of solving practice problems. For instance, it has been found that “non-integrated examples” have a high cognitive load, such as the use of an equation where the variables are defined in a separate location, or the use of a diagram that has separate descriptive text. A standalone diagram or standalone descriptive text will have a lower cognitive load because the student will not be required to integrate two different information streams. Third, there are no benefits from worked problems if the example problem is redundant. One way redundancy can occur is when a student already has a fairly good understanding of how to solve a particular type of problem. In this case, trying to comprehend an example problem would require a greater cognitive load than moving directly to practice problems. To avoid redundancy, pre-testing to gauge students’ prior knowledge may be required.
Beyond Math Problems
The implications of this research extend to more than just math. Principles for reducing cognitive load can be applied in the creation of teaching materials for any topic. Are diagrams self-contained? Are redundancies avoided? Are practice questions regularly incorporated to enhance student motivation and check understanding? Are learning activities appropriately scaffolded, meaning that supports (like worked problems) are provided until learners gain independence? Regardless of the subject matter, the cognitive load of our teaching approach can apparently have a big impact on whether students get a view of the whole forest of knowledge or get lost in the trees.
If you would like to contribute to The Faculty Development Blog, please contact Tyler Rose at firstname.lastname@example.org.
Tyler Rose, PhD
Associate Professor of Pharmaceutical Sciences
Roseman University of Health Sciences College of Pharmacy