For example, one teacher who participated in the Teaching for Understanding project was introducing the taxonomy of plants and animals. To probe the students' initial understanding of classification systems, she asked them to construct one. Almost everyone has a drawer full of junk at home - old pencils, can openers, nails, worn spoons. Her assignment for the students: They were to survey the contents of a junk drawer and create a classification system for its contents. How they did this made them more aware of classification as an enterprise, told the teacher what they understood so far, and allowed her to highlight some of the purposes and challenges of designing a classification system.

Much later on in developing the same theme, the teacher assigned a more traditional but also challenging task. The students were to use a "key" of critical features to classify organisms. If they could make the taxonomy work, this would show at least a partial understanding.

Two key ideas follow from these common-sense observations. First of all, to gauge a person's understanding-so-far, ask the person to do something that puts the understanding to work - explaining, solving a problem, building an argument, constructing a product. Second, what learners do in response not only shows their understanding-so-far but very likely advances it. By working through their understanding in response to a particular challenge, they come to understand better.

The notion that people recognize understanding through performance not only makes common sense but appears throughout a range of research in human cognition. The Swiss developmental psychologist Jean Piaget tested children's understanding of basic logical structures by setting tasks for them to perform, for instance seriating a collection of sticks from smallest to largest. Investigators of students' understanding of physics pose qualitative problems that ask students to think about the physics rather than turn a well-practiced quantitative crank. For instance, when an object is dropped from an airplane, will it hit the ground ahead of the plane, directly under the plane, or behind the plane, neglecting air friction? With no numbers in sight, students' answers and explanations reveal whether they understand the physical principles involved.

• What's the Teaching for Understanding Framework?

Information Contents Introduction What's Understanding?     - An Interactive Look at Understanding What's Teaching for Understanding?     - A Performance Criterion What's the TfU Framework     - Throughlines     - Generative Topics     - Understanding Goals     - Performances of Understanding     - Ongoing Assessment