Without specific guidance from teachers, students may fail to connect everyday knowledge to subjects taught in school.

Sometimes, however, prompting is necessary. With prompting, transfer can improve quite dramatically

explain their blueprints to a group of outside experts who held them to very high standards

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

It is important to be realistic about the amount of time it takes to learn complex subject matter.

For example, young children often erroneously believe that they can remember information and hence fail to use effective strategies, such as rehearsal.

Expert teachers know the kinds of difficulties that students are likely to face; they know how to tap into students’ existing knowledge in order to make new information meaningful;

One way to help students learn about conditions of applicability is to assign word problems that require students to use appropriate concepts and formulas (Lesgold, 1984, 1988; Simon, 1980). If well designed, these problems can help students learn when, where, and why to use the knowledge they are learning.

Often there is only superficial coverage of facts before moving on to the next topic; there is little time to develop important, organizing ideas.

In mathematics, experts are more likely than novices to first try to understand problems, rather than simply attempt to plug numbers into formulas.

The principles are relevant as well when we consider other groups, such as policy makers and the public, whose learning is also required for educational practice to change.

Superficial coverage of all topics in a subject area must be replaced with in-depth coverage of fewer topics that allows key concepts in that discipline to be understood. The goal of coverage need not be abandoned entirely, of course. But there must be a sufficient number of cases of in-depth study to allow students to grasp the defining concepts in specific domains within a discipline. Moreover, in-depth study in a domain often requires that ideas be carried beyond a single school year before students can make the transition from informal to formal ideas. This will require active coordination of the curriculum across school years.

The model of the child as an empty vessel to be filled with knowledge provided by the teacher must be replaced. Instead, the teacher must actively inquire into students’ thinking, creating classroom tasks and conditions under which student thinking can be revealed. Students’ initial conceptions then provide the foundation on which the more formal understanding of the subject matter is built.

A “metacognitive” approach to instruction can help students learn to take control of their own learning by defining learning goals and monitoring their progress in achieving them.

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.

For example, imagine being asked to design an artificial artery—would it have to be elastic? Why or why not?

trial and error. Thorndike argued that rewards (e.g., food) increased the strength of connections between stimuli and responses.

better at selecting talent than developing it

rather, the goal of education is better conceived as helping students develop the intellectual tools and learning strategies needed to acquire the knowledge that allows people to think productively about history, science and technology, social phenomena, mathematics, and the arts.

Thoughtful participation in the democratic process has also become increasingly complicated as the locus of attention has shifted from local to national and global concerns.