Mathematics in the Nordic schools * trends and changes

Report
Mathematics in the Nordic countries – Trends and challenges in students’
achievement in Norway, Sweden, Finland and Denmark
Liv Sissel Grønmo, Inger Christin Borge and Arne Hole
ILS, University of Oslo, Norway
Available data
• Most of the analyses presented are based on data
for Grade 8 in Norway and Sweden because we
have most data available for this grade level and
for these two Nordic countries.
• Limitations in data availability for Finland and
Denmark significantly limited the possibility to
conduct a number of analyses and comparisons
with these two Nordic countries.
Research questions
1. Why has Norway had an increase in
mathematics achievement level while there has
been a decrease in Sweden and Finland?
2. What characterises school mathematics in the
Nordic countries?
3. To what degree do students in the Nordic
countries have an Opportunity to Learn (OTL)
mathematics?
Trends in students’ achievement in Norway, Sweden and Finland in lower secondary
school in TIMSS from 1995 to 2011
Students in Norway and Finland have the same age, while students in Sweden are one year older.
Finland
Norway
Sweden
580
560
540
520
500
Scale
Scale
Centerpoint
Centerpoint
480
460
440
420
1995
1999
2003
2007
2011
In Grade 4 we have trend data for Norway, Sweden and Denmark. An increase in achievement in Norway and
Denmark from 2007 to 2011 – no change in Sweden.
Comparing primary school students with the same age in 2011 – conclusion:
Norway (549) and Finland (545) on the same level, Denmark (537) a little lower, Sweden (504) much lower
We have concentrated on Norway and Sweden:
Possible explanations for the positive trend in Norway –
and still a negative trend in Sweden
Much debate about weak
performances
School politics and society
have put more emphasis on
education
New curriculum with
emphasis on knowledge
and learning outcome
”A common lift”!
Has not had that much
debate
No new curriculum at that
time
Difficult to get the nation to
join in a common ”school lift”
Decentralization, private
schools, free school choice
Mathematics Performance and
School Emphasis on Academic Success (SEAS)
How would you characterize each of the following within your school?
• Teachers’ understanding of the school’s curricular goals
• Teachers’ degree of success in implementing the school’s
curriculum
• Teachers’ expectations for student achievement
• Parental support for student achievement
• Parental involvement in school activities
The collective aspect is important:
• Students’ regard for school property
• Students’ desire to do well in school
-
In Grade 8 in Norway there was a
positive change in all seven questions
- This was NOT the case in:
- Grade 4 in Norway
A two-level analysis was carried out using Structural Equation Modelling
(SEM) and Confirmatory Factor Analysis (CFA)
- Grade 4 and 8 in Sweden
(Nilsen, Grønmo & Hole, 2013).
Main findings concerning SEAS
Grade 8 in Norway and Sweden
SEAS has had a positive influence on mathematics
achievement in both Norway and Sweden
The increase in SEAS from 2007 to 2011 in Norway can explain
the observed increase in mathematics performance in Norway
from 2007 to 2011
For Sweden, no significant change was found in SEAS from
2007 to 2011, implying that this factor cannot be used to
explain the decrease in Sweden from 2007 to 2011
(Nilsen, Grønmo & Hole, 2013)
Profiles in mathematics
Based on analyses of data from TIMSS, PISA and TIMSS Advanced
Four different groups of countries (profiles) that are
stable
- over time and at different levels in school
- in different studies with different framework
 A Nordic group
 An English-speaking group
 An East European group
 An East Asian group
What characterises different profiles
Based on analysis of data from TIMSS, PISA, TIMSS Advanced, TEDS-M
East Asian and East European countries perform
relatively best in classical, pure, and abstract
mathematics as algebra and geometry
Nordic and English-speaking countries perform
relatively best on mathematics items closer to daily
life like estimation and rounding of numbers, lower
on items in classical, abstract mathematics like
fractions, exact calculations with numbers and
manipulations in algebra
What constitutes mathematics in school?
Simplification
REAL
ABSTRACT
Real world
problem
situation
Solution within
the model
Validation
Interpretation
Problem
formulationn
Mathematization
n
Transformation
Mathematical
model
TIMSS?
PISA?
We do not have data available to do the same in-depth analysis for Finland as we have for
Norway and Sweden – but it is worth reflecting upon reasons for the decrease in Finland.
“One reason for the increase of poor standards in the matriculation exam and
in the beginning of university studies is, undoubtedly, the weakness of the
foundation received in the comprehensive school. New, more difficult
concepts are hard to learn because still in upper secondary school much
energy is spent in reviewing concepts that should have been learned in the
comprehensive school. This vicious circle continues in tertiary education: the
high-school concepts are not properly learned, and further learning becomes
more difficult. The PISA survey provides us with useful information regarding
the mathematical literacy needed in everyday life and the ability to solve
simple problems. These skills are simply not enough in a world which uses
and utilizes mathematics more and more.”
(Astala et al, 2005 on behalf of more than 200 mathematicians in Finland, retrieved 24.03.2014)
Students’ Opportunity to Learn (OTL) Mathematics – Grade 8
How much instructional time teachers have spent on the various content domains in mathematics
in Grade 8 TIMSS 2011
Numbers
Algebra
Geometry
Statistics
Other topics
Int.mean
Finland
Norway
Sweden
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
Students’ Opportunity to Learn (OTL) Mathematics – Grade 8
Teachers’ reports on percentages of the total number of mathematical topics taught in each
domain in Grade 8 in TIMSS 2011
Sweden
Norway
Finland
Int.mean
120
Percent
100
80
60
40
20
0
Numbers
Algebra
Geometry
Statistics
Some results – TIMSS Advanced 2008
TIMSS Advanced gave us the opportunity to see
mathematics in primary school, lower secondary school and
upper secondary school as a whole –
AND
this gave us a consistent view of mathematics in school at all
levels
One step back
Advanced Mathematics and Physics in Norway
700
600
TIMSS Adv. Scale Centerpoint
500
Mathematics
400
Physics
300
1995/1998*
The results for Sweden were similar
2008
Possible reasons for the decline in performance in
upper secondary school?
• The decline in performance in both mathematics and physics
seems to be related to lack of basic skills in mathematics.
• This regards skills in arithmetic, in algebra, and in the basics
of calculus.
• Mathematics is both a subject in its own right, and a tool for
other subjects.
This is related to mathematics at lower levels in school – primary and lower
secondary – just as pointed out by mathematicians in Finland
Mathematics as an important tool
• Mathematics is an important tool in daily life – YES
AND
• Mathematics is an important tool in subjects and professions such
as physics, biology, economy, computer science, engineering, ...
Both these aspects have to be addressed both in primary
and in lower and upper secondary school
NOT NECESSARILY COPY ANYBODY
but
LEARN FROM EVERYBODY
Some things are better in the Nordic countries
Some things are better in the English-speaking countries
Some things are better in East Asian countries or the
East European countries
PISA, TIMSS and TIMSS Advanced are complementary studies
No single study – regardless of how good it is – provides all
the information we need
Further research and cooperation in the
Nordic countries
•
TIMSS 2015 – primary and lower secondary school
•
PISA 2015 – the end of lower secondary school
•
TIMSS Advanced 2015 – “the experts”: final year of upper secondary
•
Participation on a regular basis from all the Nordic countries in
international comparative studies in mathematics at different levels
in school is likely to significantly improve our possibility for further
research into factors that positively influence students’ performance
in mathematics.
•
More extensive analyses – follow-up studies – important to have a
large data bank
Thank you for your attention!
Liv Sissel Grønmo, Inger Christin Borge and Arne Hole

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