The Classroom Story Unfolds: Observing the Implementation of Curricular and Pedagogical Intentions

Abstract

Students enter their eighth grade mathematics class in the United States stopping to check their paper “leaves” in the “garden” displayed on the back wall of the classroom to see how much of the “leaves” area has been destroyed by “insect activity” since the previous day. While students are recording their “leaf” data, the teacher puts assignments on the board: leaf project, expression simplification, and graphing equations. These projects were begun several days ago and each is to be completed on different days the following week.

As class begins, the teacher asks students how many have not completed the expression simplification worksheet. None have finished it so the teacher tells them to form groups of two or three to complete the worksheet. Students arrange themselves in groups and begin to discuss how to simplify and then solve each algebraic expression.

As the teacher moves about the room monitoring students’ progress, she realizes that some students do not understand how to complete the exercise. She asks all students who are having difficulty to join her in a group and she goes over the procedures with them. Once she has explained several exercises to the group, she lets them continue without her and resumes moving from group to group monitoring the students’ activity. After a brief time, she announces to the class that they will end this activity in a few minutes and move on to something else. She tells students that she will be in the room during lunch next week if they need further help in completing this assignment.

Later, with about 15 minutes remaining in the period, the teacher has students return to their seats and to turn their attention to the screen at the front of the room. The teacher enters an equation into her graphing calculator which then is projected onto the screen. The teacher leads the class in predicting how the graph of various equations will look. She asks students to tell something about the geometry of the lines the equations represent, how two lines are related to one another, and the difference in orientation of two lines represented by two different equations. Students appear to be thinking and often offer voluntary responses to the teacher’s prompts. This discussion continues until the signal is heard ending class.

In France, after correcting homework on the blackboard with the help of several students, the teacher began her eighth grade mathematics class by announcing the lesson’s title: “expansion and factorization”. She explains that expansion basically requires applying the distributive rule and after illustrating this with an example has a student demonstrate with another example. After this she explains that factoring is the opposite operation and illustrates this with an example. Having explained one example, the teacher has students work on two further examples.

After a brief time, the teacher has a student solve the two exercises on the blackboard. The teacher makes a few comments and then moves on to more complicated examples that entail using both expansion and factorization. She demonstrates how to work with this type of exercise and then has students work on a similar example. The teacher moves about the classroom monitoring students’ progress and indicating their errors.

After three minutes, the teacher asks a student to put the exercise on the board. The student writes the exercise on the board clearly labeled with the three steps presented earlier by the teacher: expand, factor, and proof. The teacher discusses the two exercises students have worked on and then assigns a few exercises to be completed for the next lesson.