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Learning Fundamental Principles, Generalizations, or Theories

Tomorrow's Teaching and Learning

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The importance of feedback can't be overstated. Students value feedback, as it confirms their understanding or misunderstanding while learning is still taking place. It's easier to learn things the right way the first time than try to unlearn and relearn it later.



The posting below looks at ways to help improve students comprehension of basic principles. It is IDEA Item #5 by Walt Wager, Florida State University and Marilla Svinicki, University of Texas at Austin and is from POD-IDEA Center Notes on Learning series. The series editor is Michael Theall, Youngstown State University. The IDEA Center. POD is the Professional and Organizational Development Network [] and the IDEA Center is a nonprofit organization whose mission is to serve colleges and universities committed to improving learning, teaching, and leadership performance.[] ©1999-2014 The IDEA Center. All rights reserved. Reprinted with permission.


Rick Reis

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Tomorrow's Teaching and Learning

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IDEA Objective #2: Learning Fundamental Principles, Generalizations, or Theories



Ms. Jones enters the classroom and gets the student's attention by pushing a chair across the front of the room. She asks the class how pushing this chair demonstrates Newton's third law of motion. Shenifa raises her hand and says, "Newton's third law is the one about an equal and opposite reaction. So when you push the chair, friction is pushing back and you have to apply a force that breaks that and other forces that are keeping the chair from moving."  "Very good, Shenifa," replies Ms. Jones, "How would you describe Newton's third law in your own words?"

In this example, Ms. Jones is working at getting the students to "comprehend" principles, theories and generalizations in science. Bloom (1) describes comprehension as a level of learning above knowledge or recall of information. Bloom states, "...when students are confronted with a communication, they are expected to know what is being communicated and to be able to make some use of the material or ideas contained in it" (1, p. 89). Shenifa had to do more than just memorize Newton's laws of motion in order to answer Ms. Jones's two questions; she had to understand them. To know what Bloom means by this we can look at some specifics.

How can students show they "comprehend" a principle, generalization or theory? Bloom (1) describes three ways. First, they can restate the principle, generalization or theory in their own words, which Bloom calls translation.  When asked what is Newton's third law of motion, the student might answer, "It's when two things hit each other, they push each other equally in opposite directions."

Bloom states that translation can take one of three forms: translation into the student's own words, as we've just seen; translation into symbolic form e.g., from verbal to graphical form (inserting arrows into a picture to depict the forces operating on the chair in the example above); translation from one verbal form to another, e.g., metaphor, analogy.

A second way to demonstrate understanding is what Bloom calls interpretation.  The student's response might be - "That's when two things push on each other in opposite directions, the forces are equal in both directions, like when you roll two pool balls at each other they hit and push on each other in opposite directions." Another form of interpretation might involve the student's recognition that the communication is describing the operation of a principle, like realizing that Newton's laws explain how it is possible for car to move forward on a road.

A third way to demonstrate understanding is extrapolation, which "...includes the making of predictions based on understanding of the trends, tendencies, or conditions described in the communication" (1, p. 90). For example, the communication might ask, "Why is it easier for three people to push a car than one person?" An acceptable answer might be that the car pushes back with a force equal to the force of the person pushing it, so with more people pushing, the force is distributed among the three. While there may be any number of acceptable responses, the answer would have to include the following components 1) a force, 2) an equal counter force, and 3) in the opposite direction.

Helpful Hints

So, what teaching techniques are appropriate for attaining these desired levels of understanding?

Gain and direct attention. Do something to focus the learner on the learning task at hand (2, 3). In the case of principles, the instructor might start with a question to pique the curiosity about the principle to be learned, and point to its application to the real world. This foreshadows the eventual focus on principles rather than facts. IDEA research has found that several instructional methods related to "stimulating student interest" are important to engaging the learner in the principles and theories addressed in courses (see POD-IDEA Center Note #4 "Demonstrated the importance and significance of the subject matter," #8 "Stimulated students to intellectual effort beyond that required by most courses," and #13 "Introduced stimulating ideas about the subject").

Make clear how each topic fits in the course (see POD-IDEA Note #6). In comprehension learning tasks, the student must understand the meaning of the component concepts, and the relationships among them.

Recall prerequisite learning and connect to new material. All new learning is hooked in some way into previous learning (2, 3). Comprehension involves bringing to mind previously learned knowledge related to the new learning. In this case it is likely that the student has encountered an explanation of Newton's first and second laws. So they are familiar with the concepts of inertia, mass, force, acceleration. If during instruction these laws are tied together such that an understanding of one can be used to support understanding of the next, the chances are good that the students will learn the similarities and differences among them, and will be able to differentiate the examples that represent each of the theories or principles. 

Theories of how concepts like these are learned suggest that, after reminding students of where they might have encountered this concept before (either personally or in a previous class), the instructor would give a good, clear definition of the concept followed by what is called a "paradigmatic example," which is simply the example that most people would think of if you asked for an example of the concept. For example, in the case of Newton's laws, the example of rolling a ball along a surface is the simplest example that would come to mind for most people. The instructor could even use bowling or soccer as a more concrete example that most students would recognize. (This example later serves as a benchmark against which to check every other example they think of, so it pays to think it through thoroughly.) Then the instructor or the students generate other examples of the principle. Seeing or even categorizing positive and negative instances (non-examples) of the concept helps the students to clarify their understanding. The instructor can illustrate different relationships or characteristics of the concept by moving on to more complex or related examples, for example, using the example of how different strengths of the bowler would cause the ball to roll faster or slower. In fact, the instructor could even invite the students to suggest other scenarios and what they might say about the concept.

Use the three modes of understanding (translation, interpretation, and extrapolation) in the examples given during instruction. The use of these three modes of understanding would represent learning guidance in the form of elaboration with a variety of examples of the concepts or principles being learned. Translation can be accomplished by having the students state the principles in their own terms; there could even be a contest to see who comes up with the best alternative statement of the principle or theory. For interpretation, the students could be asked to demonstrate the principle or draw a graph of it. For extrapolation, the teacher might demonstrate the interaction of two moving objects and ask the students what they think will happen if some variable changes. The teacher might explore the related concepts and principles at the same time, so the students might see how they relate to each other. 

Incorporate practice and feedback. One important component of learning at this level is practice and feedback. The principle just learned should become the foundation for learning future principles. Furthermore, the more the principle is used in future activities, the better and stronger the neural connections (4), and the easier it will be to recall and use. Unfortunately, research in the area of transfer has shown that many students fail to recognize that previously learned skills can be transferred to a new task situation unless they are prompted to do so (5).  However, the more often this type of spaced practice occurs, the higher the probability that learners will develop an orientation for transfer (6).

The students would get practice in the elaboration activity suggested above, and the results could be used by the teacher to reinforce correct understanding and remediate misunderstanding. Practice and feedback can be accomplished in many different ways, from collaborative activity to computerized tutorials and quizzes. Especially helpful are engaging activities where the students can practice putting things into their own words, giving examples of the principles or theories, illustrating with graphics or models, and/or, given a set of conditions, setting up a demonstration. This practice allows students to get feedback on their understanding.  

The importance of feedback can't be overstated. Students value feedback, as it confirms their understanding or misunderstanding while learning is still taking place. It's easier to learn things the right way the first time than try to unlearn and relearn it later.

Model intellectual skills. Consider employing the "cognitive apprenticeship" model. In this model the instructor acts as a master model to illustrate the intellectual skill being learned and then coaches the students as they practice solving real problems using those illustrated strategies (7).

Assessment Issues

Assessment of comprehension tasks follows the same pattern as the behaviors practiced in instruction. The student can be asked to identify relevant theories or principles when given a scenario, or be asked to translate, interpret or extrapolate a particular principle within a range of conditions. However, assessment of comprehension should stay within the parameters described in the statement of instructional outcomes. That is, if learning is at the comprehension level, assessment should not test application or evaluation of the principles or concepts.

Finally, instruction should include opportunities for lots of practice spaced out across the learning. Spaced practice is periodic use of the principles in dialog and other learning activities. Knowledge that is not practiced or used to support new knowledge quickly decays, and becomes inert knowledge. Reminding students in successive class periods of what they learned before and having them do something with that information will keep it fresh and eventually more solidly stored in long term memory. This is the principle behind a spiral curriculum, in which the instruction returns to earlier principles but in more complex situations. An example would be moving from comprehension to application of a principle in a subsequent class period. 

Comprehension of fundamental principles, generalizations, and theories is generally taught as a prerequisite for application level learning, where students are expected to demonstrate understanding by applying the knowledge they just learned to new situations they haven't encountered before. Instruction that teaches comprehension level learning should be followed as soon as possible with application level activities.  Application level learning strengthens the students' ability to recall the previously learned knowledge. Applications are potentially more meaningful and motivating to students, especially if they have a manipulative and or emotional component, because they reinforce the conceptual understanding associated with comprehension. Comprehension of fundamental principles, generalizations and theories can be an exciting and motivating part of learning, and it facilitates the students' future application of knowledge. Because of this, it is worth the time and effort to teach it.

                                                        References and Resources

Bloom, B. S. (Ed.). (1956). Taxonomy of educational objectives: The classification of educational goals handbook I: Cognitive domain. New York: David McKay Company, Inc.

Gagne, R. M. (1977). The conditions of learning, 3rd Ed. NY: Holt Rinehart & Winston

Gagne, R. M., Wager, W. W., Golas, K. C., & Keller, J. M. (2005). Principles of Instructional Design, 5th Ed. Stamford, CT: Wadsworth/Thomson.

Zull, J. E. (2002). The art of changing the brain. Sterling, VA: Stylus Publishing

Gick, M., & Holyoak, K. (1980) Analogical problem solving. Cognitive Psychology, 12, 306-355.

Bransford, J., Brown, A., & Cocking, R. (Eds.) (1999). How people learn: Brain, mind, experience and school.Washington, DC: National Academy Press.

Collins, A. (1991). Cognitive apprenticeship and instructional technology. In L. Idol & B.F. Jones (Eds.), Educational values and cognitive instruction: Implications for reform (pp. 121-138). Hillsdale, NJ: Lawrence Erlbaum Associates, Inc.

Related POD-IDEA Center Notes

IDEA Item #4 "Demonstrated the importance and significance of the subject matter," Nancy McClure

IDEA Item #6 "Made it clear how each topic fit into the course," Michael Theall

IDEA Item #8 "Stimulated students to intellectual effort beyond that required by most courses," Nancy McClure

IDEA Item #12 "Gave tests, projects, etc. that covered the most important parts of the course," Barbara E. Walvoord

IDEA Item #13 "Introduced stimulating ideas about the subject," Michael Theall

IDEA Item #15 "Inspired students to set and achieve goals which really challenged them," Todd Zakrajsek

Additional Resources

IDEA Paper No. 24: Improving Instructors' Speaking Skills, Goulden

IDEA Paper No. 41: Student Goal Orientation, Motivation, and Learning, Svinicki

©2006 The IDEA Center

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