April 22, 2023

April 22, 2023

April 22, 2023

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

April 22, 2023

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 object0-1 Mathematics Half / Double1 Mathematics Equal sign, Area, Sub-traction with

crossing tens1-2 Mathematics Length4-5 Mathematics Angles, Fraction, Algebra6 English Reading comprehension in English6-7 Mathematics Short division7-8 Spanish Pronoun 6-9 Mathematics Negative numbers, Decimal number,

Proportion9 Social science Inflation

April 22, 2023

Our study

This year our case study focuses on our experiences from practising Learning Study in Mathematics on the area of algorithms for division.

April 22, 2023

Our study

A tutor from our own school, not from the University Four teachers Four classes, grade 6-7 (age 12 – 13)

April 22, 2023

The learning object

Understanding the method and knowing how to use it Knowing when to use it

April 22, 2023

The critical aspects

Understanding the number system Which is the largest and the smallest of the ”memory

numbers” ? Analysing the relationship to multiplication

The direction

Too much respect for the method

April 22, 2023

Method

Pretest

Posttest

Planning

Lesson

April 22, 2023

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?

April 22, 2023

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

April 22, 2023

Changes in lesson 2

More student activities Focus on the value of each number (the number

system)

April 22, 2023

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?

April 22, 2023

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

April 22, 2023

Changes in lesson 3

In how many ways can you say 328 SEK? The relationship between division and multiplication More analysis of the method

April 22, 2023

Lesson 3

The relationship between division and multiplication. The division 328 = 63

4does not correspond, because 63 ∙ 4 ≠ 328

Going through the method again, explaining the algorithm

The meaning of the “memory digit”

April 22, 2023

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

April 22, 2023

Changes for lesson 4

Student activities: throw the dice to decide numerator and denominator

More focus on the number system

April 22, 2023

Lesson 4

In what ways can you express 5 3 2 8 (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

April 22, 2023

Results

The students understand and can use the algorithm with a ”memory digit”

Results table: Short division

April 22, 2023

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

April 22, 2023

Conclusions

Short division is considered difficult by many 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

April 22, 2023

The teacher experience – over the last years Teachers try to work together on the critical aspects of

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

April 22, 2023

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

April 22, 2023

The student results have been substantially improved over the last yearsYear #

students

Exam % ”G”

Exam % ”VG”

Exam % ”MVG”

Exam %”A”

2003 23 52 26 9 132004 50 56 26 8 102005 50 52 36 6 62006 49 56 24 20 02007 49 47 29 20 42008 54 38 41 19 2

Source: Department of school (2004-2007). Jens Gerhardsson and Tuula Maunula (2008)

April 22, 2023

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

April 22, 2023

Marianne BureniusLena Dahlen

Jenny LjungbergTobias Sundin

Johanna Wallinder