Initial Planning Reflection for - An Activity Sequence on Logic



Possible Related Concepts

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What instructional theory and learning theory should be used to begin to facilitate student learning for these ideas?

I would want to begin with exploration so the students will learn through their own actions and reactions in a new situation.  If they explore new materials and new ideas with minimal guidance or expectation of specific accomplishments, the new experience should raise questions they cannot answer with their present ideas and patterns of reasoning.  Having made an effort that most likely will not be completely successful, they should be motivated to ask questions and begin to look for ideas that will lead them to self-regulation. Meanwhile, I will have collected enough assessment data to begin to know what they understand and where I might begin to facilitate their learning in the second phase: invention.

What activities could be used for the first activity with students for   Suppose you are responsible for teaching elementary logic in which you want students to be able to translate ordinary language argument into symbolic language used in text.  Students are able to determine what phrases to consider as “propositions” and what not to count as “propositions.”  Now they need to learn to distinguish between kinds of expressions used to show logical relationships between propositions to determine what operator to use in their symbolic formula for various forms of argument.

Activities Review a resource file or a list of possible activities that would fit the concepts and generalization.

List of possible activities

What would you consider to be a useful exercise for introduction to the logical operations?  Rank the following:

1.     Present the students a list of the operations you are going to work with (e.g., converse, inverse, negation, etc), a definition of each operation, truth-values of the propositions in each operation.  Have them memorize the definitions and do exercises in applying them to a variety of passages containing argument.

2.     Provide a list, like 1 above with examples of ordinary expressions that fit the definitions of each operation.  Have student add other examples to include as many ordinary language expressions as they can think of.

3.     Have the students make a list of English expressions that they think are used to show relationships between propositions.  Have them work in small groups to classify those expressions according to the kind of relationship.  Then have describe each kind in the form of some sort of definition and provide a heading for each kind.  Compare groupings and their “definitions” with each other’s and with that presented in any text material, and consolidate.

4.     Give students a list of about a dozen common expressions which sort readily into two or three operation “kinds” and have them sort and define as in c above, but as a whole classroom, while you record the groupings they suggest.  Compare groupings with in the text.

5.     Give students examples of sentences showing the propositional relations you are concerned with and tell them which ones are alike and how you can characterize the relationships in terms of truth-values.  (Make sure your grouping and definitions are similar to those presented in the text.)

Making a decision

Review what resources are needed for each activity and the preparation of students needed for each activity. Eliminate activities that wouldn't fit the availability of resources and the readiness of students (mixtures). Then think about how each would or would not be good to use as the first activity.choice.  When you have done that, compare the ideas below with yours, and if possible, with those of others.

Certainly many factors would influence your choices in ranking these ways of proceeding.  Compare our comments below with yours and, if possible, with others.        

  1. This procedure is probably used in most textbooks and therefore is probably most used by teachers.  However, it prevents students from asking their own questions and, therefore seeing the relevance of the definitional categories other than they are in the book.  Usually students are not encouraged to ask why it’s that way.  Hence they have little opportunity to judge different methods of classification presented I different texts.  Applying definitions to specific sentences is likely to become an algorithmic exercise with success resting mainly on the students’ ability to memorize a list of expressions for each operator.  Relying on rote memory, rather than understanding students will eventually meet relational expressions which were not included in the lists presented and difficulty will result.
  2. Although this has most of the same limitations as above, the addition of the procedure of having students expand the lists of expressions that exemplify the defined operations is a significant advantage.  By way of this exercise, students will be actively engaged in building at least portions of the categories themselves and, in a format in which they must explain their additions, it would afford the teacher helpful access to the students’ reasoning.  How much of an advantage over this would be would depend a great deal on how much I  class time was devoted to this part of the exercise—too little time to afford the students peer and teacher feedback about their reasoning in classifying could make it relatively useless and frustrating experiences enough time must be given to allow all students but especially concrete operational students to explore expressions of their ordinary language for nuances of various relationships to find sense in classifying them.
  3. We prefer this way of proceeding, providing there is  adequate time to allow the students to do the initial sorting and to get some sort of characterization that is acceptable in their groups and to gain feedback from comparison to sort has the advantage of providing a greater variety of expressions for them to consider.  Although the sorting will take more time, they will be more likely to formulate useful definitions having contrastive, as well as comparative features.  The operation of sorting and defining can be extremely helpful for students if they are required to formulate rationale for each sort they do.  3, therefore, has the advantage over 4, because working in small groups, rather than as a whole classroom, several students can be gaining experience at the same time.  Also, the tendency to submit to the teacher’s characterizations and valuations of suggestions is not liable to get in the way of the student’s own reasoning activities, when their major confrontations are with their peers in the small groups.  (Teachers, of course, can eavesdrop on the groups to get access to the students’ reasoning and provide suggestions based on student’s ideas prior to an impose if one occurs.
  4. In the face of serious limitations on in-class time, making 3 impractical, this is the procedure we recommend next.  By limiting the variety with which students must deal in their in-class sorting, they can complete the groupings in a relatively short time.  But their characterizations of the ‘kinds’ are liable to be in more general terms, since there will be fewer kinds with which they have had to contrast each group.  As a means of promoting flexibility in handling a greater variety of expressions, one might assign “Revise your system”-tasks to be done out of class time, but it will be less helpful to those who have no access to classmates outside the class, because they will lack important opportunities for self-regulation provided by working with others.
  5. This approach relates the operations which the students must learn with example-sentences that they may relate to their own experiences with their language.  Its disadvantage is that the students are left to find their own rationale for the groupings and for the definitions.  If the teacher has no way of getting access to the students’ reasoning and so has no adequate way of being sure that the students understand the principles sufficiently to handle a variety of problems for themselves. 

Reflect on the positives and negatives for each and make a decision as to what you believe might be the best before continuing.

In our preferred approach, three, one can allow for the experiences necessary to learn new concepts while the teacher gains data on the students’ reasoning processes along the way.

The exercise of sorting out expressions of relationships between propositions focuses the student’s attention on part of his language behavior that has become automatic to him.  Since it engages them in exploring purposefully parts of his/her language that he uses with confidence, he/she is able to share his expertise in small group work with his peers.  And there he can gain the feedback he needs for self-regulation when she/he encounters something that doesn’t work well for others.

Dr. Robert Sweetland's Notes ©