One does not teach children how to think merely by imparting information, nor do any subjects or courses automatically teach thinking. Different strategies must, therefore, be used to teach the thinking process. Some of these techniques are included here.
Concept mapping is a technique that can teach students how to learn based on the work of David Ausubel. This asserts that concepts derive their meaning through connections with other concepts, and that meaningful learning occurs when new knowledge is linked to existing concepts. Concept maps are a visible relationship of cognitive structure consisting of concepts, relationships, hierarchy and cross-links. Concepts are tied to one another through linking words to form a proposition. Propositions are developed in a hierarchy from the most general concept at the top of the map to progressively more specific concepts at the bottom of the map. (Cross-links are used when possible to show the relationships that can be made between concepts in different domains on the map.) Concept maps may be developed in a variety of ways and can represent a personalized view of a given area of knowledge.
There are six steps to concept map making.
In evaluating concept maps, one might make a qualitative judgment about a student's progress, or one might look for specific components of the map. Concerning the propositions, there should be a meaningful and valid relationship between the two concepts indicated by the connecting line. The map should show the hierarchy, with each subordinate concept more specific than the concept drawn above it. The map should also show meaningful connections between one segment of the concept hierarchy and another segment in the form of cross-links. Point values may be assigned to each of these components to determine an overall grade.
Concept attainment is based on the work of Jerome Bruner and is the process of defining concepts by determining the characteristics that are absolutely essential to the meaning of the concept and disregarding those that are not. It is also concerned with learning what is and what is not an example of the concept. Only use when teaching a concept in a process-oriented manner. To qualify as a concept, an item has to have a name, examples, attributes, and attribute value (some things are essential for meaning and some are not).
There are three stages to planning a concept attainment lesson. First, select a concept that meets the criteria given above. Next, select the characteristics, or examples, that define the concept. Last, develop positive and negative examples of the concept and arrange them in a sequence to be used in presentation. The examples may be actual objects, pictures of the concept, or words that illustrate the concept.
To present a concept attainment lesson, the teacher must take the learners through four phases. During phase one, the teacher explains the goal of the activity and the methods to be used to determine the concept. Positive (Yes) and negative (No) examples are then presented, always beginning with a positive example. During phase two, students are asked to give other positive examples of the concept and to try to develop a concept rule or definition for the concept. Only when this has been successfully completed is the name of the concept given. For phase three, the students are asked to analyze the thinking process they used in determining the concept rule. Questions that might be asked are:
The final phase of the presentation is an evaluation of the activity. It can be deemed successful when students can identify additional examples of the concept, identify essential attributes of the concept, determine a concept rule, and relate the concept to other valid concepts.
Cooperative learning is an extremely valuable technique to be used in empowering nontraditional students. It is different from traditional group work, which is often the work of only one or two members of a larger group. It can be described as a group of no more than six members who ALL work together to complete instructional activities. It embodies five essential elements:
Cooperative learning has been found to be especially effective because it meets the needs for belonging, for love, for power, for freedom, and for having fun that all students have. William Glasser and others have found that classrooms that use this technique are more successful. Any teacher who wishes to enhance learning for nontraditional math and science students should become proficient in use of cooperative learning.
Students are paired and each student is given a different set of problems or questions and the answers to the other person's questions. Students work on their own questions and after each one is finished the two students discuss the correct answers. This requires students to write and verbalize and is a good technique to use for unit reviews.
Suchman Inquiry is based on the premise that the intellectual strategies used by scientists and mathematicians to solve problems can be taught to students. By using the students' natural curiosity, they can be trained and disciplined in the procedures of inquiry. It will help students:
This model differs from other inquiry models in the way data are presented. Students gather data in a simulated process through questioning rather than actual manipulation of data. Inquiry training has five phases. The first phase is the student's confrontation with a puzzling situation. Phases two and three are the data-gathering operations that use verification and experimentation. In the data-gathering phase, the students ask a series of questions that the teacher answers with a yes or no. Students may also ask the teacher to engage in experimentation that will enable them to obtain information through observation rather than through inference. In the fourth phase, students organize the information obtained so that they can derive an explanation for the puzzling event. Finally, the students are asked to analyze the problem-solving strategies they used. During this operation the teacher's role is to construct the problem situation, to referee the inquiry procedures, to respond to students' inquiry probes with the necessary information, to help students establish a focus in their inquiry, and to facilitate discussion of the problem situation among the students.
Concept development is based on the work of Hilda Taba. It builds on basic concepts which are part of the learner's prior knowledge, and, as conceptual interrelationships develop, a framework for new understandings is established. The model teaches students to make observations, form different types of inferences from these observations, group data on the basis of perceived similarities, then form categories and labels for the data; thus producing a conceptual system. In so doing, students develop thinking skills.
This model is effective with objectives related to contrasting, applying, categorizing, and analyzing data. Three inductive thinking tasks are utilized. The first is concept formation. The second is interpretation of data. The third is the application of principles. The steps in each phase are initiated by teacher questions.
During concept formation, students identify and list ideas, associations, and concepts through questions such as "What do you see? Notice? Find?" They then group the items based on similarity. Next, they develop categories and labels for the groups.
In the interpretation of data stage, critical or different relationships are established through questions such as: "What did you notice?" "Could some of these belong in more than one group?" The relationships are then explored and regrouping is done if possible. Lastly, students are asked to find implications, extrapolate, and synthesize the information. This may be done through questions such as: "What does this mean?" "What would you conclude?" "Can someone say in one sentence something about all these groups?"
Students may apply the principles by predicting consequences, explaining unfamiliar phenomena, and hypothesizing. This may be done through a question such as "What would happen if ...?" They can then explain or support the predictions and hypotheses by asking: "Why do you think this would happen?" Lastly, students can verify their prediction by asking: "What would it take for this to be generally true or probably true?"