The portrait we have sketched of human learning and cognition emphasizes learning for in-depth comprehension. The major ideas that have transformed understanding of learning also have implications for teaching.
Teaching for In-Depth Learning
Traditional education has tended to emphasize memorization and mastery of text. Research on the development of expertise, however, indicates that more than a set of general problem-solving skills or memory for an array of facts is necessary to achieve deep understanding. Expertise requires well-organized knowledge of concepts, principles, and procedures of inquiry. Various subject disciplines are organized differently and require an array of approaches to inquiry. We presented a discussion of the three subject areas of history, mathematics, and science learning to illustrate how the structure of the knowledge domain guides both learning and teaching. Proponents of the new approaches to teaching engage students in a variety of different activities for constructing a knowledge base in the subject domain. Such approaches involve both a set of facts and clearly defined principles. The teacher’s goal is to develop students’ understanding of a given topic, as well as to help them develop into independent and thoughtful problem solvers. One way to do this is by showing students that they already have relevant knowledge. As students work through different prob- lems that a teacher presents, they develop their understanding into principles that govern the topic.
In mathematics for younger (first- and second-grade) students, for example, cognitively guided instruction uses a variety of classroom activities to bring number and counting principles into students’ awareness, including snack-time sharing for fractions, lunch count for number, and attendance for part-whole relationships. Through these activities, a teacher has many opportunities to observe what students know and how they approach solutions to problems, to introduce common misconceptions to challenge students’ thinking, and to present more advanced discussions when the students are ready.
For older students, model-based reasoning in mathematics is an effective approach. Beginning with the building of physical models, this approach develops abstract symbol system-based models, such as algebraic equations or geometry-based solutions. Model-based approaches entail selecting and exploring the properties of a model and then applying the model to answer a question that interests the student. This important approach emphasizes understanding over routine memorization and provides students with a learning tool that enables them to figure out new solutions as old ones become obsolete.
These new approaches to mathematics operate from knowledge that learning involves extending understanding to new situations, a guiding principle of transfer (Chapter 3); that young children come to school with early mathematics concepts (Chapter 4); that learners cannot always identify and call up relevant knowledge (Chapters 2, 3, and 4); and that learning is promoted by encouraging children to try out the ideas and strategies they bring with them to school-based learning (Chapter 6). Students in classes that use the new approaches do not begin learning mathematics by sitting at desks and only doing computational problems. Rather, they are encouraged to explore their own knowledge and to invent strategies for solving problems and to discuss with others why their strategies work or do not work. A key aspect of the new ways of teaching science is to focus on helping students overcome deeply rooted misconceptions that interfere with learning. Especially in people’s knowledge of the physical, it is clear that prior knowledge, constructed out of personal experiences and observations— such as the conception that heavy objects fall faster than light objects—can conflict with new learning. Casual observations are useful for explaining why a rock falls faster than a leaf, but they can lead to misconceptions that are difficult to overcome. Misconceptions, however, are also the starting point for new approaches to teaching scientific thinking. By probing students’ beliefs and helping them develop ways to resolve conflicting views, teachers can guide students to construct coherent and broad understandings of scientific concepts. This and other new approaches are major break- throughs in teaching science. Students can often answer fact-based questions on tests that imply understanding, but misconceptions will surface as the students are questioned about scientific concepts.
Chèche Konnen (“search for knowledge” in Haitian Creole) was presented as an example of new approaches to science learning for grade school children. The approach focuses upon students’ personal knowledge as the foundations of sense-making. Further, the approach emphasizes the role of the specialized functions of language, including the students’ own language for communication when it is other than English; the role of language in developing skills of how to “argue” the scientific “evidence” they arrive at; the role of dialogue in sharing information and learning from others; and finally, how the specialized, scientific language of the subject matter, including technical terms and definitions, promote deep understanding of the concepts. Teaching history for depth of understanding has generated new approaches that recognize that students need to learn about the assumptions any historian makes for connecting events and schemes into a narrative. The process involves learning that any historical account is a history and not the history. A core concept guiding history learning is how to determine, from all of the events possible to enumerate, the ones to single out as significant. The “rules for determining historical significance” become a lightening rod for class discussions in one innovative approach to teaching history. Through this process, students learn to understand the interpretative nature of history and to understand history as an evidentiary form of knowledge. Such an approach runs counter to the image of history as clusters of fixed names and dates that students need to memorize. As with the Chèche Konnen example of science learning, mastering the concepts of historical analysis, developing an evidentiary base, and debating the evidence all become tools in the history toolbox that students carry with them to analyze and solve new problems.
Expert teachers know the structure of the knowledge in their disciplines. This knowledge provides them with cognitive roadmaps to guide the assignments they give students, the assessments they use to gauge student progress, and the questions they ask in the give-and-take of classroom life. Expert teachers are sensitive to the aspects of the subject matter that are especially difficult and easy for students to grasp: they know the conceptual barriers that are likely to hinder learning, so they watch for these tell-tale signs of students’ misconceptions. In this way, both students’ prior knowledge and teachers’ knowledge of subject content become critical components of learners’ growth.
Subject-matter expertise requires well-organized knowledge of concepts and inquiry procedures. Similarly, studies of teaching conclude that expertise consists of more than a set of general methods that can be applied across all subject matter. These two sets of research-based findings contradict the common misconception about what teachers need to know in order to design effective learning environments for students. Both subject-matter knowledge and pedagogical knowledge are important for expert teaching because knowledge domains have unique structures and methods of inquiry associated with them.
Accomplished teachers also assess their own effectiveness with their students. They reflect on what goes on in the classroom and modify their teaching plans accordingly. Thinking about teaching is not an abstract or esoteric activity. It is a disciplined, systematic approach to professional development. By reflecting on and evaluating one’s own practices, either alone or in the company of a critical colleague, teachers develop ways to change and improve their practices, like any other opportunity for learning with feedback.
• Teachers need expertise in both subject matter content and in teaching.
• Teachers need to develop understanding of the theories of knowledge (epistemologies) that guide the subject-matter disciplines in which they work.
• Teachers need to develop an understanding of pedagogy as an intellectual discipline that reflects theories of learning, including knowledge of how cultural beliefs and the personal characteristics of learners influence learning.
• Teachers are learners and the principles of learning and transfer for student learners apply to teachers.
• Teachers need opportunities to learn about children’s cognitive development and children’s development of thought (children’s epistemologies) in order to know how teaching practices build on learners’ prior knowledge.
• Teachers need to develop models of their own professional development that are based on lifelong learning, rather than on an “updating” model of learning, in order to have frameworks to guide their career planning.