Transcript Learning Studies in Sweden

LEARNING STUDIES IN SWEDEN
22 July 2015
SHORT DIVISION
22 July 2015
Öjersjö
 Öjersjö is a small village just outside Göteborg on
the west coast of Sweden. There are 700 students at
our school in the age of 6 to 16 years
Göteborg
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How it all started…
 In Öjersjö we have worked with Learning Study for
six years. In the beginning the University acted as
tutors, but now we manage on our own
Grade
Subject
The learning object
0-1
Mathematics
Half / Double
1
Mathematics
Equal sign, Area, Sub-traction with crossing tens
1-2
Mathematics
Length
4-5
Mathematics
Angles, Fraction, Algebra
6
English
Reading comprehension in English
6-7
Mathematics
Short division
7-8
Spanish
Pronoun
6-9
Mathematics
Negative numbers, Decimal number, Proportion
9
Social science
Inflation
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Our study
 This year our case study focuses on our experiences
from practising Learning Study in Mathematics on
the area of algorithms for division.
SHORT DIVISION
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Our study
 A tutor from our own school, not from the University
 Four teachers
 Four classes, grade 6-7 (age 12 – 13)
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The learning object
 Understanding the method and knowing how to use it
 Knowing when to use it
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The critical aspects
Too much respect for
the method
 Understanding the number system
 Which is the largest and the smallest of the ”memory
numbers” ?
 Analysing the relationship to multiplication
 The direction
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Method
Planning
Pretest
Posttest
Lesson
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Lesson 1
 Focusing on the direction. Comparison of the four
fundamental rules of arithmetic
3 starts from the right ( ”backwards”)
Only 1 starts from the left
836
836
836
836 =
* 2
+ 212
- 212
2
 When is division useful?
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Results after lesson 1
 The direction seems to be no problem at all
 The students understand division with the
”containerthinking”, not only ”dividing in parts”
 However, the value of each number, depending on its
position is still unclear
 How many tens are two hundreds?
Results table: Short division
Result
Lesson 1
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Lesson 2
Pretest
Posttest
20 %
55 %
Pretest
Lesson 3
Posttest
Pretest
Lesson 4
Posttest
Pretest
Posttest
Changes in lesson 2
 More student activities
 Focus on the value of each number (the number
system)
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Lesson 2
 We wrote three errors on the board and let the
students investigate the problems in group
discussions
535 = 101
535 = 17
535 = 161
5
5
5
 The number system, different values for different
numbers
 In how many ways can you explain 328?
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Results after lesson 2
 They understand the number system much better
 The students still, however, have difficulties with the
”memory digit” algorithm
Results table: Short division
Result
Lesson 1
Lesson 2
Lesson 3
Pretest
Posttest
Pretest
Posttest
20 %
55 %
29 %
52 %
Pretest
Lesson 4
Posttest
Pretest
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Posttest
Changes in lesson 3
 In how many ways can you say 328 SEK?
 The relationship between division and multiplication
 More analysis of the method
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Lesson 3
 The relationship between division and multiplication.
 The division 328 = 63
4
does not correspond, because 63 ∙ 4 ≠ 328
 Going through the method again, explaining the
algorithm
 The meaning of the “memory digit”
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Results after lesson 3
 The Swedish money system is useful for
understanding the number system if you use the
right values, i.e. 100, 10 and 1!
 The students gained an increased understanding of
the division algorithm.
Results table: Short division
Result
Lesson 1
Lesson 2
Lesson 3
Lesson 4
Pretest
Posttest
Pretest
Posttest
Pretest
Posttest
20 %
55 %
29 %
52 %
18 %
47 %
Pretest
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Posttest
Changes for lesson 4
 Student activities: throw the dice to decide numerator
and denominator
 More focus on the number system
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Lesson 4
 In what ways can you express
5328
(by using various thousands , hundreds , tens
and units)
 The students solved random tasks
 We used dices (0-9) and wrote the digits in the
squares
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Results
 The students understand and can use the algorithm
with a ”memory digit”
Results table: Short division
Result
Lesson 1
Lesson 2
Lesson 3
Lesson 4
Pretest
Posttest
Pretest
Posttest
Pretest
Posttest
Pretest
Posttest
20 %
55 %
29 %
52 %
18 %
47 %
13 %
75 %
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Difficulties during the study
 Problems to see what to focus on (unexperienced
teachers…)
 Lack of time. Result: We did not all agreed about
how to take the next step before we took it
 The vaccination programme disturbing lesson 2
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Conclusions
 Short division is considered difficult by many
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students and their parents, and therefore they show
more respect for the method than they really should
Understanding the number system is the key
The significance of the numbersystem for
understanding values.
The relation between numerator, denominator and
quotient.
Looking at division in two ways: ”dividing” and
”containing” helps to understand the method and
when it is useful
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The teacher experience – over the last
years
 Teachers try to work together on the critical aspects of
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an area - taking part of any previous Learning Study in
the area
We carefully define the goals of each area as precise
as possible
Clearer objectives and expectations for the students
Work with flexible student groups - sometimes
grouped by level of ability
Greater variety of working methods and examinations
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The student experience – over the last
years
 More enthusiastic teachers
 Positive experience with students grouped by level of
ability
 Positive experience from having several teachers
involved in appraisal of exams
 More variety in teaching
 The students are motivated and stimulated - every
lesson is important
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The student results have been
substantially improved over the last years
Year
# students
Exam %
”G”
Exam %
”VG”
Exam %
”MVG”
Exam %
”A”
2003
23
52
26
9
13
2004
50
56
26
8
10
2005
50
52
36
6
6
2006
49
56
24
20
0
2007
49
47
29
20
4
2008
54
38
41
19
2
Source: Department of school (2004-2007). Jens Gerhardsson and Tuula Maunula (2008)
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Recommendations for further studies:
 It is important that the variation theory is equally well
known by most of the group members
 Try to do more of the planning in the beginning of the
study
 Don’t make too many changes at a time
 Good circumstances around the lessons in the study are
important to achieve the most from the study
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Marianne Burenius
Lena Dahlen
Jenny Ljungberg
Tobias Sundin
Johanna Wallinder
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