CONCEPTUAL UNDERSTANDING IN
A TECHNO-PEDAGOGIC
CONTENT KNOWLEDGE CONTEXT
The following activities can be used by teachers to stimulate the cognitive processes needed to develop a conceptual understanding of physics:
- Use multiple representations. A representation may be linguistic, abstract, symbolic, pictorial, or concrete. Using many different representations for the same knowledge, and having students translate between representations, helps the student to inter-relate knowledge types and relate the knowledge to physical experience. It encourages the formation of links between knowledge elements and promotes a rich clustering of knowledge.
- Make forward and backward references. Concepts require a long time to be formed. Thus, you cannot wait for students to completely learn one topic before moving on to the next. By making forward references, you prepare the student for new material. By making backward references, you associate new material with established (or partially established) material, thus making knowledge interwoven and interconnected, rather than linear.
- Explore extended contexts. Concepts can be extremely context dependent and do not become globally useful until they are abstracted. Investigating a broad context of applicability helps the student to refine and abstract concepts. It also avoids incorrect or oversimplified generalizations.
- Compare and contrast. Essential to the process of structuring (or re-structuring) knowledge is the classification and inter-relation of knowledge elements. Comparisons and contrasts sensitize students to categories and relationships, and helps students perceive the commonalities and distinctions needed to organize their knowledge store.
- Categorize and classify. In parallel with comparisons and contrasts, students must be aware of categories and classification systems. Students must also practice creating and recognizing categorization systems. By requiring students to classify items, to choose names for their categories, and to explain their system, we can help students re-structure their knowledge store.
- Predict & Show (inadequacy of old model). Carefully selected demonstrations and experiments can be used to bring out inconsistencies in student models. Students should be shown a set-up or experimental apparatus and should be asked to predict what will happen when something is done. It is important that students make predictions beforehand, thus making them aware of their own model. Students will consider alternate conceptions only if their own fails. Requiring students to use their models and showing them how their models are inconsistent or inadequate will prepare them to create better (though still their own) models.
- Explain (summarize, describe, discuss, define, etc.). Standard problems seldom tell the teacher what students don't understand. Even when students get a problem right, there can still be confusion about the applicability of the equations used. Requiring students to explain how they will solve a problem exposes misunderstandings and misconceptions, and helps students reorganize their knowledge store. In addition, students seldom see in standard demonstrations and experiments what experts see. Students should explain and discuss what they think they've seen (during Predict & Show, for example), so that the teacher can interact with the students' models. Furthermore, the process of explaining (or summarizing, describing, discussing, etc.) helps students become aware of their own models as well as the models of other students.
- Generate multiple solutions. Efficient problem-solving cannot occur unless students choose from a set of valid solution paths. By solving problems in more than one way, students learn to prioritize elements of their Strategic Knowledge.
- Plan, justify, and strategize. Very few relationships in physics are always valid. To avoid equation manipulation, students should be asked to plan (and then explain) how they will solve problems. Students must learn how to determine which concepts are relevant (and which are irrelevant) for any particular problem situation and how to implement the relevant concepts to solve that problem. Having students generate their own strategies helps them to learn how concepts are used to solve problems.
- Reflect (evaluate, integrate, extend, generalize, etc.) After completing most activities, students benefit from looking back on what they've done. What patterns have they perceived? What general rules can be constructed? Other types of activities give students the pieces needed to create a coherent picture of physics, but some sort of reflective activity is usually needed to "put the pieces together".
- Meta-communicate about the learning process. To learn physics (or any other complex subject), students must become self-invested. They must be exposed to other people's (teacher's and student's) models. They must be warned that precision in communication is essential; they must be informed of common pitfalls and misinterpretations; and they must be told that they should re-structure their knowledge. Students must learn how they learn best. (COURTESY TO
Knowledge Structure
A qualitative model for the storage of domain-specific knowledge and its implications for problem-solvinghttp://www.srri.umass.edu)Extracted from a booklet accompanying a workshop for high school science teachers.
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