Learning by Being Told or by Example

We can acquire new operators by being told about them or by observing someone else use them. These are examples of social learning. The first method is a uniquely human accomplish- ment because it depends on language. The second is a capacity thought to be common in primates: “Monkey see, monkey do.” However, the capacity of non- human primates for learning by imitation has often been overestimated.
It might seem that the most efficient way to learn new problem-solving op- erators would be simply to be told about them, but seeing an example is often at least as effective as being told what to do. Table 8.1 shows two forms of instruc- tion about an algebraic concept, called a pyramid expression, which is novel to most undergraduates. Students either study part (a), which gives a semiformal specification of what a pyramid expression is, or they study part (b), which gives the single example of a pyramid expression. After reading one instruction or the other, they are asked to evaluate pyramid expressions like
10$2
Which form of instruction do you think would be most useful? Carnegie Mellon undergraduates show comparable levels of learning from the single example in part (b) to what they learn from the specification in part (a). Sometimes, examples can be the superior means of instruction. For instance, Reed and Bolstad (1991) had participants learn to solve problems such as the following:
An expert can complete a technical task in five hours, but a novice requires seven hours to do the same task. When they work together, the novice works two hours more than the expert. How long does the expert work? (p. 765)
Participants received instruction in how to use the following equation to solve the problem:
rate1 3 time1 3 rate2 3 time2 5 tasks
The participants needed to acquire problem-solving operators for assigning values to the terms in this equation. The participants either received abstract

instruction about how to make these assignments or saw a simple example of how the assignments were made. There was also a condition in which participants saw both the abstract instruction and the example. Participants given the abstract instruction were able to solve only 13% of a set of later prob- lems; participants given an example solved 28% of the problems; and partici- pants given both instruction and an example were able to solve 40%.
It has now been shown many times that providing worked examples is one of the most effective methods of instruction for problem-solving skills like al- gebra (for a review, see Lee & Anderson, 2013). The worked examples provide expert solutions that students can emulate, and the worked examples are usu- ally alternated with problems so that the students can practice solving on their own. A large number of studies compared learning by worked examples with instructional explanation and without instructional explanation (see Wittwer & Renkl, 2010 for a review). Sometimes providing instruction in addition to exam- ples actually hurts, sometimes there is no effect, and sometimes it does help, as in the Reed and Bolstad study above. To the extent that students can explain for themselves how the examples work, they can benefit more by explaining it for themselves than by reading someone else’s explanation. However, sometimes ex- amples can be obscure and lead to incorrect conclusions without an explanation. A classic example from mathematics involves showing children an example like
3 3 2 1 5 5 6 1 5 5 11
and then asking them to solve
4 1 6 3 2 5 ?
Many children will give 20 as the answer, mistakenly adding 4 and 6 and then multiplying that by 2. Instruction can alert them to the fact that they should always perform multiplication first, rather than perform the first operation in the expression.
■ Problem-solving operators can be acquired by discovery, by mod- eling example problem solutions, or by direct instruction.