Fractions – Knowledge Quartet

11Oct 2012 by Tracy Weston

RSI: Scenario 2

Scenario: Róisín teaching equivalence of fractions Country: Ireland Grade (student age): 3rd class (age 8-9) Contributed by: Dolores Corcoran, St Patrick’s College, Drumcondra, Ireland Context – national, curricular, professional, other The Irish primary curriculum proposes that “the child should be enabled to identify fractions and equivalent forms of fractions with denominators 2, 4, 8 and 10” first among a list of six objectives for children in third class. Róisín, who was a second year Bachelor of Education student, with a relatively strong background in mathematics devised an ambitious lesson to develop an understanding of equivalent fractions with this class of 21 girls in the third week of her spring teaching placement. The lesson lasted 40 minutes. Scenario Róisín set the lesson in a pizzeria, with five friends sharing a “ten…

11Oct 2012 by Tracy Weston No Comments

RSI: Scenario 4

Responding to students' ideas

Scenario: Hans teaching fractions greater than one Country: Norway Grade (student age): Year 5 (age 11-12) Contributed by: Bodil Kleve, Oslo and Akershus University College of Applied Sciences Context – national, curricular, professional, other In our present curriculum LK 06, competence aims for the subject are presented after year 2, year 4, year 7 and year 10. This lesson is from year five. With regard to fractions, competence aims after year 4 do not include any. After year 7 fractions are included in Competence aims for numbers and algebra: “The aim for the education is that the pupil shall be able to describe the place value system for decimal numbers, calculate with positive and negative whole numbers, decimal numbers, fractions and percentages, and place them on the real number line…

08Oct 2012 by Tracy Weston No Comments

AP: Scenario 1

Awareness of purpose

Scenario: Finding three fractions that adds up to one whole Country: Norway Grade (student age): Grade 7 (age 12-13) Contributed by: Ove Gunnar Drageset, University of Tromsoe, Norway Context The teacher has five years teaching experience. The lesson is halfway through grade seven. 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 competence goals regarding fractions after grade seven focuses on calculations using positive and negative fractions, and placing fractions on a number line. In this case the teacher asks the students in plenary of suggestions to a task that many found difficult. The task…

11Sep 2012 by Tracy Weston No Comments

AC: Scenario 1

Anticipation of complexity

Scenario: Find 5/3 when 9 is the whole Country: Norway Grade (student age): Year 5 (age 10-11) Contributed by: Ove Gunnar Drageset, University of Tromsoe, Norway Context The teacher has 16 years of teaching experience. The lesson is from fifth grade (students aged 10-11) in the middle of the year. The students have only met fractions like ½ and ¼ used in everyday situations prior to fifth grade. 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 competence goals regarding fractions after grade seven focuses on calculations using positive and negative fractions, and placing fractions on a number line. The following excerpt is from one of the first lessons on fractions, and the…

11Sep 2012 by Tracy Weston No Comments

AC: Scenario 3

Anticipation of complexity

Scenario: Nóirín teaching fraction concepts Country: Ireland Grade (student age): 5th Class (age 10-11) Contributed by: Dolores Corcoran, St Patrick’s College, Drumcondra, Ireland Context – national, curricular, professional, other Nóirín is an undergraduate student in her final year in a teacher education programme engaged in a Learning to Teach Mathematics Using Lesson Study elective course. This lesson was a ‘reteaching’ of a lesson which the group had amended following discussion of its first iteration. The initial lesson in a middle-class school was supported by a worksheet with six equal sized circles representing pizzas to be divided among a group of friends. On this occasion, in a designated disadvantaged setting, it was decided to use the same ‘problems’, but half the page was left blank so children could represent the problem…

10Sep 2012 by Tracy Weston No Comments

UIM: Scenario 1

Use of instructional materials

Scenario: Teaching of fractions Country: Norway Grade (student age): Year 5 (age 10-11) Contributed by: Ove Gunnar Drageset, University of Tromsoe, Norway Context The teacher has 35 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 competence goals regarding fractions after grade seven focus on calculations using positive and negative fractions, and placing fractions on a number line. The teacher writes 1/10 on the blackboard and asks if someone knows another fraction of equal size. A student answers 10/100, and the teacher writes ‘=10/100’ to the right of 1/10. Then the teacher chooses to illustrate this by…

10Sep 2012 by Tracy Weston No Comments

UIM: Scenario 2

Use of instructional materials

Scenario: Teaching of fractions Country: Norway Grade (student age): Example 1 - year 7 (age 12-13) Contributed by: Ove Gunnar Drageset, University of Tromsoe, Norway Context 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. …

11Aug 2012 by Tracy Weston No Comments

CUR: Scenario 3

Choice of representations

Scenario: Hans teaching fractions greater than one Country: Norway Grade (student age): Year 5 (age 11-12) Contributed by: Bodil Kleve, Oslo and Akershus University College of Applied Sciences Context – national, curricular, professional, other In our present curriculum LK 06, competence aims for the subject are presented after year 2, year 4, year 7 and year 10. This lesson is from year five. With regard to fractions, competence aims after year 4 do not include any. After year 7 fractions are included in Competence aims for numbers and algebra: “The aim for the education is that the pupil shall be able to describe the place value system for decimal numbers, calculate with positive and negative whole numbers, decimal numbers, fractions and percentages, and place them on the real number line…