BOX 3.5 Learning Algebra
Students taking regular algebra in a major school system received an average of 65 hours of instruction and homework during the year. In contrast, those taking honors algebra received approximately 250 hours of instruction and homework (John Anderson, personal communication). Clearly, it was recognized that significant learning takes major investments of time.
expertise occurs only with major investments of time, and the amount of time it takes to learn material is roughly proportional to the amount of material being learned (Singley and Anderson, 1989); see Box 3.5. Although many people believe that “talent” plays a role in who becomes an expert in a particular area, even seemingly talented individuals require a great deal of practice in order to develop their expertise (Ericsson et al., 1993).
Learners, especially in school settings, are often faced with tasks that do not have apparent meaning or logic (Klausmeier, 1985). It can be difficult for them to learn with understanding at the start; they may need to take time to explore underlying concepts and to generate connections to other information they possess. Attempts to cover too many topics too quickly may hinder learning and subsequent transfer because students (a) learn only isolated sets of facts that are not organized and connected or (b) are introduced to organizing principles that they cannot grasp because they lack enough specific knowledge to make them meaningful. Providing students with opportunities to first grapple with specific information relevant to a topic has been shown to create a “time for telling” that enables them to learn much more from an organizing lecture (as measured by subsequent abilities to transfer) than students who did not first have these specific opportunities; see Box 3.6.
Providing students with time to learn also includes providing enough time for them to process information. Pezdek and Miceli (1982) found that on one particular task, it took 3rd graders 15 seconds to integrate pictorial and verbal information; when given only 8 seconds, they couldn’t mentally integrate the information, probably due to short-term memory limitations. The implication is that learning cannot be rushed; the complex cognitive activity of information integration requires time.
It is clear that different ways of using one’s time have different effects on learning and transfer. A considerable amount is known about variables that affect learning. For example, learning is most effective when people engage