There are many appealing strengths to the idea that learning should be organized around authentic problems and projects that are frequently encountered in nonschool settings: in John Dewey’s vision, “School should be less about preparation for life and more like life itself.”

there is an infinite number of numbers between any two rational numbers

Gradually, students come to ask self-regulatory questions themselves as the teacher fades out. At the end of each of the problem-solving sessions, students and teacher alternate in characterizing major themes by analyzing what they did and why. The recapitulations highlight the generalizable features of the critical decisions and actions and focus on strategic levels rather than on the specific solutions

Tests of transfer that use graduated prompting provide more fine-grained analysis of learning and its effects on transfer than simple one-shot assessments of whether or not transfer occurs

For example, a group of Orange County homemakers did very well at making supermarket best-buy calculations despite doing poorly on equivalent school-like paper-and-pencil mathematics problems (Lave, 1988). Similarly, some Brazilian street children could perform mathematics when making sales in the street but were unable to answer similar problems presented in a school contex

e.g., a person may be performance oriented in mathematics but learning oriented in science and social studies or vice versa).

A number of studies converge on the conclusion that transfer is enhanced by helping students see potential transfer implications of what they are learning

Understanding when, where, and why to use new knowledge can be enhanced through the use of “contrasting cases,” a concept from the field of perceptual learning (see, e.g., Gagné and Gibson, 1947; Garner, 1974; Gibson and Gibson, 1955). Appropriately arranged contrasts can help people notice new features that previously escaped their attention and learn which features are relevant or irrelevant to a particular concept

In the rote method, students were taught to drop a perpendicular and then apply the memorized solution formula.Transfer Both groups performed well on typical problems asking for the area of parallelograms; however, only the understanding group could transfer to novel problems, such as finding the area of the figures below.or distinguishing between solvable and unsolvable problems such asThe response of the “rote” group to novel problems was, “We haven’t had that yet.”

The concept of adaptive expertise (Hatano and Inagaki, 1986) provides an important model of successful learning. Adaptive experts are able to approach new situations flexibly and to learn throughout their lifetimes. They not only use what they have learned, they are metacognitive and continually question their current levels of expertise and attempt to move beyond them. They don’t simply attempt to do the same things more efficiently; they attempt to do things better. A major challenge for theories of learning is to understand how particular kinds of learning experiences develop adaptive expertise or “virtuosos.”

Sometimes, however, students can solve sets of practice problems but fail to conditionalize their knowledge because they know which chapter the problems came from and so automatically use this information to decide which concepts and formulas are relevant. Practice problems that are organized into very structured worksheets can also cause this proble

Experts usually mentioned the major principle(s) or law(s) that were applicable to the problem, together with a rationale for why those laws applied to the problem and how one could apply them (Chi et al., 1981). In contrast, competent beginners rarely referred to major principles and laws in physics; instead, they typically described which equations they would use and how those equations would be manipulated

Research shows that students who think that intelligence is a fixed entity are more likely to be performance oriented than learning oriented—they want to look good rather than risk making mistakes while learning. These students are especially likely to bail out when tasks become difficult

There is no universal best teaching practice.

This will require active coordination of the curriculum across school years.

Experts are also able to fluently access relevant knowledge because their understanding of subject matter allows them to quickly identify what is relevant. Hence, their attention is not overtaxed by complex events.

A common misconception regarding “constructivist” theories of knowing (that existing knowledge is used to build new knowledge) is that teachers should never tell students anything directly but, instead, should always allow them to construct knowledge for themselves.

In the most general sense, the contemporary view of learning is that people construct new knowledge and understandings based on what they already know and believe (e.g., Cobb, 1994; Piaget, 1952, 1973a,b, 1977, 1978; Vygotsky, 1962, 1978). A classic children’s book illustrates this point; see Box 1.2. A logical extension of the view that new knowledge must be constructed from existing knowledge is that teachers need to pay attention to the incomplete understandings, the false beliefs, and the naive renditions of concepts that learners bring with them to a given subject.

At the same time, students often have limited opportunities to understand or make sense of topics because many curricula have emphasized memory rather than under- Page 9 Share Cite Suggested Citation: "1 Learning: From Speculation to Science." National Research Council. How People Learn: Brain, Mind, Experience, and School: Expanded Edition. Washington, DC: The National Academies Press, 2000. doi:10.17226/9853. × Save Cancel standing.

Fundamental understanding about subjects, including how to frame and ask meaningful questions about various subject areas, contributes to individuals’ more basic understanding of principles of learning that can assist them in becoming self-sustaining, lifelong learners.