Scenario: Teaching of fractions
Grade (student age): Example 1 - year 7 (age 12-13)
Contributed by: Ove Gunnar Drageset, University of Tromsoe, Norway
The teacher in example one has 25 years of experience as a teacher. The lesson is taught mid-way through the school year. The competence goals in the Norwegian curriculum are not formulated for each year, but are given after the completion of grade 4, 7 and 10. The students have only met fractions like ½ and ¼ used in everyday situations prior to fifth grade.
The teacher helps one student with the task of comparing and finding the smallest fraction of ¼ and 5/8. She sits down and tells him to find the fraction bars.
Then the teacher asks the student to find one fourth. After some searching, the student finds the yellow bar with fourths.
SM: Oh, there. (puts down the whole strip)
T: Can you take one fourth of that strip. Can you show me that?
SM: (Breaks off one piece)
T: Yes. Put it there (point at the desk). Like that. And then … (points at 5/8 that is written on a paper).
Then the student finds the green strip of fifths, and a dialogue follows where the teacher tells him to think what the denominator means. Then this follows:
SM: (Picks the stripe with eights and starts counting. Breaks off so that he has one strip of five eights and one of three eighths).
T: Then you put it next to.
SM: (Puts down the strip of three eighths)
T: Yes was that in a way that one?
SM: No (changes to the strip with five eighths)
T: There, yes. Can you see now that this (the five eights strip) is bigger than this (the one fourth)?
SM: Yes (nodding)
T: Or that one fourth is smaller than five eights. You have to do like this with all these tasks that you do. You have to build them as long as you can find strips here.
Knowledge Quartet Coding Commentary
Contributed by: Ove Gunnar Drageset, University of Tromsoe
Knowledge Quartet Dimension: Transformation
Knowledge Quartet Code: Use of instructional materials (UIM)
Scenario: Two examples from the teaching of fractions
In this example the teacher does the main part of the work. This way to use fraction strips are encouraged for all the students that does not see the answer immediately. The effect is that the fraction strips are used as a method (calculator) where the correct answer is found while the reason behind, or the steps of finding equivalent fractions so that fractions with common denominators can be compared, are hidden. This way to use instructional materials is limited to using it to solve tasks. This use seems to be connected to the desire to make mathematics simpler. The use of instructional material was dominated by the teacher, helping the student to avoid the difficult part and arrive at the answer. The result is also that the students work are simplified which probably also effects what they learn from such activities.