Investigating the Story of Curriculum and Pedagogy: Conceptualizing and Comparing Educational Practices

Abstract

A teacher in an eighth grade mathematics class in Spain asks for the students’ attention and announces that there are exercises to correct. Requesting numbers from some students’ homework, the teacher recreates an exercise on the blackboard and reviews the concepts of positive and negative slope. As students correct their homework the teacher also asks a few questions to gauge students’ comprehension.

Completing the correction of homework the teacher tells students to turn to the appropriate textbook page and read along with him. Again, he draws on the blackboard to illustrate directly proportional linear functions. The teacher points out that students have seen this type of equation in their science class. He illustrates by drawing on the blackboard a physics example regarding the velocity of a vehicle.

Similarly, the concept of inverse proportionality is introduced, explained and illustrated with examples. Students are asked several times whether an illustration is an example of direct or inverse proportionality. After considerable explanation and discussion, the teacher writes an equation on the blackboard and asks students to copy and make a representation of it in their notebooks. He moves around the room observing students’ work occasionally addressing the class to correct common errors. As the lesson concludes, the teacher assigns homework for the next lesson and reminds students of an upcoming quiz.

A teacher in Switzerland begins his eighth grade mathematics class by asking students to gather in a circle in the middle of the room. He appoints one student secretary and explains that they are going to construct two-sided stairs out of little blocks and examine the relationship between the stairs’ height and the number of blocks used. Different students are asked to create stairs and the secretary records the height and number of blocks involved each time. After several sets of stairs have been constructed, the teacher asks students what the general rule is. The general relationship is summarized as n→n² on the blackboard. One more set of stairs is built to confirm the accuracy of this relationship. Students then build stairs to discover the relationship between the stairs’ height and the number of surfaces on which one could step and generalize the relationship.

Next the teacher has students physically form various polygons and count the number of diagonals. In groups of six, with students as the corners of a hexagon, string is used to form all the diagonals. After several different polygons have been constructed this way, the teacher leads a class discussion to discover the relationship between the number of sides of a polygon and the number of diagonals and to summarize this in a general formula. Several ideas are suggested and tested before one is finally adopted.

The teacher concludes the class by asking students to return to their seats and open their exercise books. He assigns a number of problems that will be due in two days. The next day they will have the option to work on any task they choose so this assignment may be completed at home or at school.