The teacher provides examples which have the same concept and concept rule in common.
However, the concept rule IS NOT STATED. Students will attempt to find it through the examples near the end of the lesson.
The teacher, through questioning of the students, elicits
critical attributes and non-critical attributes, which are essential and non-essential characteristics of the concept. Through these exercises, students
should begin to understand the common concept which is found in all of the examples.
Students must categorize the examples or non-examples (those which do not show essential characteristics of the concept rule)
by explaining why they do or do not fit the concept rule they are discovering.
The students can either a) state the relationship found (in a guided lesson) or b) state relationships that they found, being allowed to differ from the rest of the group as needed (such as an unguided lesson).
Simple Example
The teacher shows the students examples of squares, possibly tables or objects in the classroom which have the desired qualities as well as
mathematical props.
The students, with guidance from the teacher, identify characteristics that must be present (CRITICAL ATTRIBUTES) for the object to be a square: a) the object has four sides
and b) the object's four sides are equal (i.e. all have sides which are 10 inches long, or 5 inches, etc).
The teacher then elicits the non-critical attributes of a square. (i.e. shape is non-critical or non-essential as long as it meets other characteristics,
meaning it could be 2 or 3 dimensional; size is also non-essential; weight is non-essential to the concept rule; etc.)
Students should be able to identify the concept rule being demonstrated.
The teacher shows more examples of a square, but mixes them in with rectangles (non-examples). Students must distinguish the difference and verbalize it.
If not already accomplished, the teacher should ask students to state the concept rule or the relationship(s) they found through the lesson.