Will at Work Learning

Mathemagenic Processing and Ernie Rothkopf

Mathemagenic Processing

In the mid-1960's, Rothkopf (1965, 1966), investigating the effects of questions placed into text passages, coined the term mathemagenic, meaning "to give birth to learning." His intention was to highlight the fact that it is something that learners do in processing (thinking about) learning material that causes learning and long-term retention of the learning material.

When learners are faced with learning materials, their attention to that learning material deteriorates with time. However, as Rothkopf (1982) illustrated, when the learning material is interspersed with questions on the material (even without answers), learners can maintain their attention at a relatively high level for long periods of time. The interspersed questions prompt learners to process the material in a manner that is more likely to give birth to learning.

Although the term mathemagenic was hot in the late 1960's and 1970's, it gradually faded from use as researchers lost interest in the study of adjunct questions and as critics complained that the word was too abstract and had little meaning beyond the operations of the research paradigm.

Despite having fallen into disfavor, the term—and the research it generated—have proven invaluable. The adjunct- question research showed us that test-like events are useful in helping learners to bolster memory for the information targeted by the question and to stay attentive to the most important aspects of the learning material. The concept of mathemagenic behavior is very much a central component in the way we think about learning. Who could doubt today that it's the manner in which learners process the learning material that makes all of the difference in learning.

Citations:

Rothkopf, E. Z. (1965). Some theoretical and experimental approaches to problems in written instruction. In J. D. Krumboltz (Ed.). Learning and the education process (pp. 193-221). Chicago: Rand McNally.

Rothkopf, E. Z. (1966). Learning from written instructive materials: An exploration of the control of inspection behavior by test-like events. American Educational Research Journal, 3, 241-249.

Rothkopf, E. Z. (1982). Adjunct aids and the control of mathemagenic activities during purposeful reading. In W. Otto & S. White (Eds.) Reading expository material. New York: Academic Press.

Research Review: Zechmeister & Shaughnessy (1980)

Here's the title of the research article:

When you know that you know and when you think that you know but you don't.

Great title. Much more colorful than most academic research articles. The thing for us to realize is that the "you" in the title of this classic research study is OUR LEARNERS. Sometimes our learners can become overly optimistic about their ability to remember. Oh no. If we believe---even a little bit---the adult-learning-theory mantra that our learners always know best (an incorrect assumption by the way), then we might be setting our learners up for failure.

The research these folks did was designed to look at the spacing effect, the finding that widely-spaced repetitions are more effective than narrowly-spaced repetitions. As the authors say, the spacing effect "has been obtained in a wide variety of memory paradigms, suggesting that it reflects the operation of a fundamental property of the memory system."

Here's What They Did

They had people study lists of words some of which were repeated. They repeated some of the words immediately and some of them after 3 to 5 other words. Notice that the spacings we're talking about here are rather small. For some of the words, they asked the subjects to rate how likely they would be to remember the words if asked about them later.

Here's What They Found

1. Learners were pretty good at estimating which words they would be able to recall. The one's they rated most likely to recall, they recalled 66% of the time on a later test. The one's they rated least likely to recall, they recalled only 35% of the time.
2. Learners recalled words they were asked to rate better than words they were not asked to rate. Rated words were recalled 52% of the time, non-rated words were recalled 40% of the time. This shows that extra processing, especially meaningful processing, improves learning results. Learners had an extra six seconds per word to do the rating.
3. Learners recalled repeated items better than items that were not repeated. This is the repetition effect. Non-repeated items were recalled 39% of the time. Repeated items were recalled 49% of the time.
4. Perhaps what is most intriguing about the data is that narrowly-spaced repetitions gave learners greater confidence (that they would be able to recall a particular word) than widely-spaced repetitions, BUT they actually recalled narrowly-spaced repetitions less highly than the widely-spaced repetitions. Narrowly-spaced repetitions were recalled at a rate of 49% compared with widely-space repetitions, which were recalled at a rate of 62%.

Is This Study Relevant to Me?

This is the generalizability question. Although the research had learners study words in a free-recall experimental design, instead of using complex knowledge in a more ecologically valid cued-recall design (real-world memory retrieval is almost always cued recall), there is no reason to think that the research results aren't widely applicable. The spacing effect is one of the most replicated phenomenon in learning research. Widely-spaced repetitions minimize forgetting, whereas immediate repetitions cannot. And because the spacing effect is such a fundamental learning mechanism, the college-student-as-subject problem is not relevant.

Practical Recommendations

1. Repeat key learning points.
2. Use spaced repetitions when logistically possible. Even these short spacings made a big difference in the learning results.
3. Consider prompting your learners to do additional processing of key learning points, especially if that processing is meaningful.
4. Challenge your learners (within reason) by showing them that their memory is fallible, and that forgetting is likely if they avoid additional learning time.

Citation

Zechmeister, E. B., & Shaughnessy, J. J. (1980). When you know that you know and when you think that you know but you don't. Bulletin of the Psychonomic Society, 15(1), 41-44.