# Generating the angular velocities of planetary and annular gears

#### Generating the angular velocities of planetary and annular gears: When self-generating explanations helps learning

Tell me, how does a differential work? Can you explain it to me? All of us who drive or ride in cars rely on a differential to get us around corners under power, and yet not all of us know that a differential is “… a simple planetary gear train that has the property that the angular velocity of its carrier is the average of the angular velocities of its sun and annular gears.”

Let’s assume you didn’t know that already, and let’s assume the above picture doesn’t tell the full story. How would you best learn about how a differential functions?

One promising approach involves self-generated explanations, defined as the process of generating explanations for oneself in an attempt to make sense of new information. Crucially, explanations involve inferences that go beyond the given information: For example, looking at the above picture and reading the definition, you might infer something about planetary gears and angular velocities.

Generally speaking, the literature reveals positive effects of prompting students for self-explanation, as compared to studying the same information without self-explaining.

Self-explanation is thought to promote learning via two primary processes. First, it aids comprehension by promoting knowledge integration. Learners often link steps in the solution to their prior knowledge or other information. When new information conflicts with prior knowledge, learners are compelled to resolve the inconsistency, which in turn may also boost learning because of the additional required processing. Second, self-explanation forces learners to pay attention to structural features rather than surface attributes— when trying to explain a differential it is of little help to marvel at its shiny silver color.

But is it always the case that self-explanations assist learning? Or are there exceptions?

recent article in the Psychonomic Bulletin & Review tackled this question. Researchers Rittle-Johnson and Loehr examined the existing literature and identified several constraints on when self-generated explanations aid learning. The constraints are summarized in the table below:

1. Target outcomes and domains.

Self-explanation facilitates transfer of learning to new tasks. For example, when adults are prompted to self-explain a category learning task, they transferred the category learning better to new items than other participants who were asked to describe the items used in the task. However, this enhanced transfer—usually considered a good thing—comes at a cost: self-explaining participants had less memory for the details of study items. This reduced memory, in turn, may have adverse effects when the task involves recognition of exceptions or probabilistic rules of categorization.

For this reason, adult learners of English as a second language do not appear to benefit from self-articulating grammatical rules. Although they tend to be able to recite the rule better than people who did not self-explain, the two groups do not differ in their ability to apply the rule.

1. What is being explained.

The nature of what is being explained matters greatly. In general, self-explanation does not help if the information that is focused on is incorrect and the learner does not recognize its inaccuracy. This tends to happen when learners explain their own thinking, rather than a correct solution. Accordingly, in cases in which one’s own thinking is correct, self-explanation of one’s own actions is again beneficial.

Intriguingly, it is also frequently helpful if learners explain why incorrect explanations are wrong. The mere inclusion of incorrect examples may surprise learners and may therefore increase their motivation to understand the differences between correct and incorrect examples.

1. Explanation prompts.

In most practical situations, learners are not just asked to “explain” one thing or another without further guidance. Instead, learners may be given additional quite specific prompts. For example, in one study using problems in taxation law, participants received prompts such as “Why do you calculate the total possible outcome by multiplying?”

Rittle-Johnson and Loehr suggest that “why” prompts “promote inferences about causes behind outcomes, expanding comprehension of domain concepts (i.e., conceptual knowledge) because they focus attention on identifying relevant and underlying principles and regularities.”

However, because prompts direct attention to specific aspects of the task at the expense of others, care is advised in designing prompts: Rittle-Johnson and Loehr suggest that explanation prompts that focused attention on key concepts increased comprehension of domain principles, but also reduced success on transfer problems.

1. Relative effectiveness.

One common attribute of self-generating explanations is that they take a considerable amount of time. In one early study, self-generation took nearly twice as long as studying in a control condition in which the material was merely read.

It does not follow, however, that the self-generation advantage is due to extra time spent on task: In experiments in which timing is controlled—usually by asking participants in the control condition to use their own techniques for an amount of time equivalent to that used in the self-generation condition—the advantage of generation is still obtained.

A final question involves the utility of instructor-generated explanations: If you generate an explanation for a differential, will you learn more about cars than when an expert is explaining it to you? Rittle-Johnson and Loehr show that the evidence for this question is rather mixed, with some studies going one way and others the opposite way. On balance, however, there was no difference between those conditions—receiving an explanation from anywhere or anyone is better than studying without any guidance.

Just in case you still worry about the differential and haven’t generated an explanation yet, here is an animation. Watch it and then self-generate an explanation:

Article focused on in this post:

Rittle-Johnson, B., & Loehr, A. M. (2016). Eliciting explanations: Constraints on when self-explanation aids Learning. Psychonomic Bulletin & Review. DOI:10.3758/s13423-016-1079-5.