Introduction
In the educational
community, folklore has it that "The German education system
is quite similar to that of Austria," or "All post-communist
countries teach mathematics in the same way," and the like.
Sometimes these statements are based on an analysis
and comparison of national school structures, the curricula or
textbooks. Is it really possible to measure the similarity
between the countries? Usually, the phenomena of the
similarity of the national educational systems is descriptive and
subjective; their features are seldom measured and placed on
a scale. Data from the Third International Mathematics and
Science Study (TIMSS) provided the opportunity to search for
patterns
among nations in students' answers to the test items.
(Notes 3 and 4)
An attempt to group the
TIMSS participating countries had already been undertaken by
analyzing national curricula in mathematics and science
(Notes 1
and 2). The countries were grouped by a priori
geographic
and economic conditions, or by investigating statistically
some
patterns in the national math and science curricula. This
last
mentioned method of looking for statistical similarities is
close
to the method described in this article. The difference is
in the
nature of the data used: the curriculum analyses dealt with
the
intended curriculum whereas the emphasis in this article is
on
the achieved curriculum, i.e., what was actually learned by
the
students in the countries.
Conceptual
Framework
Figure 1 presents the
difficulty levels (p-values) of 20 items forming a part of
the
TIMSS mathematics test for three countries X, Y, and Z.
These
items have been ordered by their difficulty; that is, the
actual
percentage of students obtaining the right answer for each
item.
Figure 1. Item difficulties for 20 TIMSS items for countries
X, Y and Z.
It can be seen that the
students in countries X and Y performed this part of the
test
relatively similarly, despite the fact that country X had
higher
overall achievement than country Y. The students in these
two
countries performed in a similar way on the same items
relative
to other items. Country Z students performed in quite a
different
way: the overall students scores on this set of items were
about
the same as in Country X, but the relative national item
difficulties for these two countries were quite different.
This
fact becomes more evident if the items are re-ordered (see
Figure 2)
according
their difficulty for country X (forming "a
river" for
these two countries).
Figure 2. Item difficulties re-ordered for 20 TIMSS items
for countries X, Y and Z.
What is the meaning behind such a definition of similarity?
The simplest explanation
is that two countries were similar if the students in these
countries performed on the TIMSS math test in a similar way,
i.e., the same set of items were relatively more difficult
or more easy.
The value of such
comparisons of the countries lies in the identification of pairs
or groups of similar countries. Some of these pairs and groups
are well-known while some of them have remained somewhat hidden.
If there is similarity between two countries, the question of the
cause of such a phenomenon naturally arises; perhaps the
similarity is the result of a more general relationship between
countries based on common historical or linguistic similarities,
or it may be the result of the impact of educational reforms
undertaken, or it may be just a random occurrence. A brief look
at the groups of similar countries and an examination of the
matching pairs does not support the random character of such
groupings. Therefore, the naming of similar countries, on the one
hand, and countries performing in the quite different ways, on
the other hand, is a contribution not only to general knowledge,
but can also lead to the objective comparison of the curricula of
the particular countries, and provide new opportunities for
educational systems to learn from each other.
Method
The TIMSS mathematics
test contained a total of 157 items. The initial information
consisted of the difficulty levels (p-values) of every item in
every country, i.e., the percentage of the correct answers for
every item in every country. The range of values for each item
was from 0 to 100 (percent) and could be treated as the
countries profile in mathematics achievement
(measured 157
times, forming a 157-component vector). The simple correlation of
these values could be calculated between all pairs of countries.
However, this would not produce the desired result. The overall
international item difficulty would still play a primary role in
producing correlation among countries (instead of indicating some
specific trends), and the correlations between the countries
would be high: all countries performed better on easy items than
on difficult ones. Therefore, the effect of the item difficulty
should be removed. This can be done in two ways. The first would
involve a simple ranking of the participating countries from 1 to
41 according to their results on each item, and the vector of
such ranks could be defined as a country's profile.
This procedure would increase the distinguishing feature of the
variable (the distance between two country's results on the item
would be at least one), would take into account the results of
all TIMSS countries at the same time (the "room" for the top 10
is fixed: if one country enters the top 10, another must exit),
and would not be linked to the overall difficulties of the items.
These ranks are usually easy to explain, but this artificial
numbering (the minimal difference "1" in ranking might correspond
to either a very small difference in math achievement results or
a very large one) would result in a loss of information.
Therefore, another method was used: the difficulty levels
(national p-values) for the item were standardised within
countries and converted into z-scores. This allowed the
TIMSS countries to be ranked not by the natural numbers 1, 2, 3
etc., but by putting them on a continuous interval scale defined
by the countries achievement on the item. This procedure removes
the effect of the item difficulty. In order to avoid the effect
of the overall countries achievement on the test, the Pearson
correlation coefficient for these standardized difficulties of
the items was calculated to measure the similarity between the
countries.
After an examination of
the matrix of Pearson correlation coefficients of the countries
math profiles (i.e., the standardized items p-values for
countries), a hierarchical cluster analysis was undertaken. The
average linkage within groups method was used. This procedure was
used to identify groups of countries having similar
relationships
in the achievement profiles. The reliability of this
grouping was
based on the internal consistency of the group measured by
Cronbach's alpha coefficient. A cut-off point of 0.75
(of
the coefficient alpha) was taken for forming a group of
countries. The resultant group of countries was named and
factor
analysis was used later in order to extract the factors
which
were the specific profile factors of the group. This two-
step
procedure with the grouping of similar countries first and
the
factor analysis second was selected instead of the
straightforward use of factor analysis. This was done
because the
direct factor analysis would have taken into account the
effect
of a main factor in both directions, positive and negative.
This
would have led to the grouping of countries with strong
opposite
trends, and would result in it being quite difficult to
measure
the similarity later. The final analysis of the data
consisted of
an analysis of the similarities between the countries and
between
the groups of the countries.
One indicator of the
reliability of the method could be the comparison of the trends
of the same country calculated for two different grades. The
TIMSS study collected data about the students' achievement in two
adjacent grades called "lower" and "upper" (and for most
countries these were grades 7 and 8). The same procedure for the
standardization of the mathematics item difficulties was
undertaken for both data sets separately and the Pearson
correlation coefficients were calculated for every TIMSS country
pairing for both grades within a country. This analysis revealed
a very high similarity of profiles for these two grades within
countries. For mathematics, the coefficients were mostly above
0.80. The highest similarities were found for Singapore (Pearson
correlation coefficient, 0.95), Philippines (0.93), the USA
(0.91), Australia (0.92), Korea (0.92), Scotland (0.92), and the
lowest ones for Bulgaria (0.65), Austria (0.75), Greece
(0.76),
Spain (0.78). For science, these correlations were, for the most
part, even higher. These results provide evidence of the
high
stability of country trends and, at the same time, could
also be
regarded as evidence for the stability of the method.
Mathematics
Analysis of the
groups
Among all 41 countries
having taken the TIMSS mathematics test for the upper grade,
the
highest similarity of the mathematics achievement profiles
was
found for England and Scotland. The Pearson correlation
coefficient for this pair was 0.90. Quite close to these two
countries were New Zealand (correlation with Scotland 0.86,
with
England 0.85), and Australia (correlations with every of
these
three countries above 0.70). Therefore, these countries
could be
taken to form the core of the first group called
English-speaking countries. Using this language
designation, Canada, the USA, and Ireland could also be
included
in this group. The USA correlated most highly with Canada
but
these two North American countries also had much in common
with
the European-Australian group. The place of Ireland was
questionable: it was more highly correlated with Canada and
Scotland. The reliability analysis had about the same alpha
whether Ireland was included or removed from the group.
Therefore, all seven English-speaking countries were left in the
group. An analysis of the matrix of correlations presented below
showed that Ireland looked like a bridge between the
European-Australian group and the American one. Ireland was more
correlated with Canada than with neighboring England. The
reliability coefficient of 0.87 was quite high and showed some
homogeneity of the group, despite the fact that the USA was a
little to the side.
Table 1
Correlations of Nations on TIMSS Mathematics Items
English-Speaking Group
|
Australia
|
AUS
|
***
|
|
|
|
|
alpha
|
0.87
|
|
Canada
|
CAN
|
0.44
|
***
|
|
|
|
|
|
|
England
|
ENG
|
0.76
|
0.34
|
***
|
|
|
|
|
|
Ireland
|
IRE
|
0.37
|
0.39
|
0.26
|
***
|
|
|
|
|
N.Zealand
|
NZL
|
0.79
|
0.43
|
0.85
|
0.32
|
***
|
|
|
|
Scotland
|
SCO
|
0.73
|
0.34
|
0.90
|
0.35
|
0.86
|
***
|
|
|
USA
|
USA
|
0.30
|
0.65
|
0.22
|
0.35
|
0.31
|
0.25
|
***
|
|
|
AUS
|
CAN
|
ENG
|
IRE
|
NZL
|
SCO
|
USA
|
Factor Analysis of Nations Correlations
|
communality
|
fac 1
|
fac 2
|
|
AUS
|
0.78
|
0.83
|
0.30
|
|
CAN
|
0.76
|
0.23
|
0.84
|
|
ENG
|
0.91
|
0.94
|
0.13
|
|
IRE
|
0.43
|
0.24
|
0.61
|
|
NZL
|
0.89
|
0.91
|
0.26
|
|
SCO
|
0.89
|
0.93
|
0.18
|
|
USA
|
0.76
|
0.07
|
0.87
|
|
|
f_UK
|
f_Am
|
There were no further
TIMSS countries the inclusion of which increased the homogeneity
of this group as measured by Cronbach's alpha. The factor
analysis for these seven countries resulted in two factors with
eigenvalues of 4.06 and 1.35, together explaining about 77.4
percent of the variation. After rotating these factors (the
varimax method was used), and examining the loadings, it was easy
to find the "right" names for them: the first could be
called English-speaking countries – United Kingdom
(f_UK), the second – English-speaking
countries--America (f_Am).
Table 2
Correlations of Nations--Post-Communist Group
|
Bulgaria
|
BGR
|
***
|
|
|
|
|
|
|
|
|
|
Czech R.
|
CZE
|
0.07
|
***
|
|
|
|
|
alpha
|
0.81
|
|
|
Hungary
|
HUN
|
0.13
|
0.35
|
***
|
|
|
|
|
|
|
|
Latvia
|
LVA
|
0.16
|
0.23
|
0.13
|
***
|
|
|
|
|
|
|
Lithuania
|
LTU
|
0.24
|
0.45
|
0.19
|
0.59
|
***
|
|
|
|
|
|
Romania
|
ROM
|
0.41
|
0.19
|
0.05
|
0.31
|
0.25
|
***
|
|
|
|
|
Russia
|
RUS
|
0.28
|
0.33
|
0.20
|
0.53
|
0.60
|
0.52
|
***
|
|
|
|
Slovakia
|
SVK
|
0.13
|
0.67
|
0.39
|
0.36
|
0.49
|
0.36
|
0.45
|
***
|
|
|
Slovenia
|
SLV
|
0.09
|
0.29
|
0.17
|
0.32
|
0.34
|
0.27
|
0.36
|
0.44
|
***
|
|
|
BGR
|
CZE
|
HUN
|
LVA
|
LTU
|
ROM
|
RUS
|
SVK
|
SLV
|
The second set of
candidates to form a group emerged clearly: all post-
communist
countries —Bulgaria, Czech Republic, Hungary, Latvia,
Lithuania, Romania, Russian Federation, Slovak Republic and
Slovenia (Central and Eastern Europe CEE
countries)—had
quite similar patterns in their math achievement profiles.
An
analysis of the correlation matrix showed about the same
picture
as for the English-speaking countries in that the place for
Hungary was similar to Ireland.
Table 3
Factor Analysis of Post-Communist Group
|
communality
|
fac 1
|
fac 2
|
|
BGR
|
0.44
|
-0.11
|
0.65
|
|
CZE
|
0.68
|
0.82
|
0.09
|
|
HUN
|
0.41
|
0.64
|
-0.07
|
|
LVA
|
0.49
|
0.34
|
0.62
|
|
LTU
|
0.59
|
0.54
|
0.55
|
|
ROM
|
0.59
|
0.07
|
0.77
|
|
RUS
|
0.68
|
0.38
|
0.74
|
|
SVK
|
0.74
|
0.81
|
0.29
|
|
SLV
|
0.35
|
0.49
|
0.33
|
|
|
f_CE
|
f_EE
|
The decision to include
Hungary in this group was based on the same consideration as
for
Ireland: it had no effect on Cronbach's alpha; and, it
made
sense from a geographical point of view and also allowed the
extraction of two factors later.
The factor analysis for
this group of these nine countries yielded two eigenvalues
above
one: 3.67 and 1.30, explaining 55.2 percent of the total
variance. The analysis of the loadings of the factors was
not so
simple as in the previous case: the impacts from the
countries
were somewhat mixed. The first factor was more linked to the
Czech Republic, Hungary, and the Slovak Republic, and the
second
to Bulgaria, Romania, and the Russian Federation. Countries
such
as Lithuania, Latvia and Slovenia were somewhere in between.
Therefore, the names Central Europe countries (f_CE),
and
Eastern Europe countries (f_EE) were chosen for these
two
factors.
When examining the other
TIMSS countries there were no further large groups of
countries
like the two above. Searching for some smaller groups one
could
think of a Nordic group (Denmark, Iceland, Norway, Sweden),
an
East Asian group (Hong Kong, Japan, Korea, Singapore), and
possibly about some group from Western Europe such as
Austria,
Belgium, Germany, Greece, France, Spain or Portugal.
Unfortunately, this last set of countries proved to be very
heterogeneous: it was possible to identify only pairs of
countries (like Austria--Germany, French speaking
part of
Belgium--France), but not more. The Nordic countries
were
quite homogenous (see the table of correlations
below).
Table 4
Correlations of Nations--Nordic Group
|
Denmark
|
DEN
|
***
|
|
alpha
|
0.82
|
|
DEN
|
0.49
|
0.70
|
|
Iceland
|
ICE
|
0.46
|
***
|
|
|
|
ICE
|
0.67
|
0.82
|
|
Norway
|
NOR
|
0.47
|
0.55
|
***
|
|
|
NOR
|
0.72
|
0.85
|
|
Sweden
|
SWE
|
0.41
|
0.62
|
0.68
|
***
|
|
SWE
|
0.73
|
0.85
|
|
|
DEN
|
ICE
|
NOR
|
SWE
|
|
|
communality
|
factor
|
It was possible to
identify two other countries that were near to the four
Nordic
countries, namely the Netherlands and Switzerland. By adding
them
to the group there was no increase in the alpha coefficient
for
the group but both of them were quite highly correlated with
the
Nordic group as well as with the UK part from the
English-speaking group. These two countries form another
bridge
between the Nordic and English-speaking – UK groups
and
hence the Netherlands and Switzerland were not included in
either
of these groups. The factor analysis of the Nordic group
yielded
one large eigenvalue of 2.6, giving one factor, and
explaining
about 65 percent of variation.
The Eastern Asian group,
formed by Hong Kong, Japan, Korea and Singapore, was
homogeneous,
and each of these four countries contributed about the same
amount to the Asian factor (one large eigenvalue of 2.4
explaining about 60 percent of the variation).
Table 5
Correlations and
Factor Analysis of Nations--Eastern Asian Group
|
Hong Kong
|
HNK
|
***
|
|
alpha
|
0.82
|
|
HNK
|
0.71
|
0.84
|
|
Japan
|
JAP
|
0.54
|
***
|
|
|
|
JAP
|
0.63
|
0.79
|
|
Korea
|
KOR
|
0.37
|
0.48
|
***
|
|
|
KOR
|
0.46
|
0.68
|
|
Singapore
|
SIN
|
0.64
|
0.42
|
0.33
|
***
|
|
SIN
|
0.61
|
0.78
|
|
|
HNK
|
JAP
|
KOR
|
SIN
|
|
|
communality
|
factor
|
Each of
these four countries performed very well on the TIMSS test
(Singapore was ranked first in overall math achievement,
followed by the other three). It is interesting to note that
there was one country—South Africa— with the
lowest
score of all countries that had a similar profile to the
Asian
group. The math achievement profile of South Africa was
quite
similar to Singapore (correlation coefficient 0.48), to Hong
Kong
(0.41), and Japan (0.34). The inclusion of South Africa in
this
group would not affect the Cronbach's alpha
coefficient of
the group. Considering both the geographical location of
these
countries and the statistical considerations, only four
Asian
countries were left to form this group. From another point
of
view, this similarity could be somewhat artificial because
of the
method used to measure the similarity of pairs of countries
with
stable trends. In other words, a country that performed
extremely
well on the test could have a similar profile to a country
that
performed extremely poorly on the test because on most items
country ranks had no diversity; they were always on the top,
or
always on the bottom of the international list. Despite
this, it
can be seen that the method worked well for "average"
countries.
There were no TIMSS countries performing excellently or
poorly on
every test item, and, therefore, the method worked
reasonably
well to measure the similarity of the top (bottom) ranked
countries taking into account the patterns of the similarity
rather the overall achievement results.
The four groups above
were defined according the students' achievement on
more
than 150 math items. These items represented different areas
in
mathematics: fractions, algebra, geometry, and the like. The
countries traditions in mathematics education placed unequal
emphasis on these subtopics in the curriculum, and as a
consequence of this the students' achievements were
also
quite different. The similarities of profiles for sub-scales
are
briefly commented on below.
English-speaking
countries . These countries were more
similar on Proportionality (Cronbach's alpha
coefficient is 0.91) than on Measurement (0.73). It
should
be pointed out that there was high similarity between the
USA and
Ireland on Proportionality compared with the rest of
the
countries of this group (USA – New Zealand 0.69,
Ireland
– Scotland 0.80), and the differences on
Measurement
(the pair Australia – Ireland had a negative
correlation of
-0.31). The most interesting figures from the other
subscales
were the 0.64 and 0.69 for the pair USA and England on
Geometry and Data representation respectively
(compared with 0.10 for Algebra).
CEE
countries. The analysis of the
subscales pointed to the exceptional place of Hungary in
this
group having only negative correlations with the other
countries
in this group on Geometry (up to -0.62 with
Romania!).
Some negative correlations were found in other subscales,
such as
in Fractions Bulgaria – Czech Republic -0.20,
in
Algebra Czech Republic – Latvia -0.16, in
Measurement Latvia – Romania -0.25, in
Proportionality Lithuania – Romania -0.28.
Generally, the Cronbach alpha coefficients for this group
ranged
from 0.55 in Geometry (the Hungarian effect), to 0.85
in
Data representation. In Geometry Hungary was
most
similar to the English-speaking countries group
(correlation with England 0.63, with New Zealand 0.71, with
USA
0.45).
Nordic
countries. The group is quite
homogenious in all subscales: there were no negative
correlations. The Cronbach alpha coefficients ranged from
0.71
(Measurement), to 0.87
(Proportionality).
East Asian
countries. The interesting subscale for
this group was Proportionality, where the alpha
coefficient fell to 0.38 (the correlation for the pair
Singapore
– Hong Kong was 0.71, and with all the rest it was
about
zero). In this subscale Japan was more similar to the
Philippines
(0.79), Korea – to Greece (0.74) or USA (0.68). This
subscale was one of the shortest with 12 items only which
might
account for the diversity. Other subscales worked in a
relatively
stable manner with the alpha coefficients ranging from 0.67
(Algebra) to 0.86 (Geometry,
Measurement).
Another noteworthy
finding from the subscale analysis was unexpected and
concerns
the difference between Measurement and
Proportionality. Both of these subscales included
more
application type items involving use in real-life
situations.
Thus, it was expected that countries would teach them in a
fairly
similar way, whereas larger differences would be found in
topics
such as Algebra, Geometry orData
representation.
To summarize, four
groups of similar countries were identified among 41 TIMSS
countries. The relationship between these four groups are
presented below. Since rotation was used in the factor-analysis,
at least two pairs of factors in the first two groups should
be
perpendicular. In order to understand the overall picture
for all
four groups together, an examination of the correlation
matrix
below should be made.
Table 6
Correlations Among the Factors
|
f_UK
|
***
|
|
|
|
|
|
|
f_Am
|
0.00
|
***
|
|
|
|
|
|
f_CE
|
-0.32
|
-0.07
|
***
|
|
|
|
|
f_EE
|
-0.49
|
-0.44
|
0.00
|
***
|
|
|
|
f_Nord
|
0.50
|
0.10
|
-0.20
|
-0.52
|
***
|
|
|
f_Asia
|
-0.25
|
0.21
|
-0.32
|
0.24
|
-0.44
|
***
|
|
f_UK
|
f_Am
|
f_CE
|
f_EE
|
f_Nord
|
f_Asia
|
The Nordic group
countries were quite similar to the UK group (correlation
coefficient 0.50), but not so similar to the USA and Canada group
(0.10), and were opposite to the Eastern European (-0.52) and
Asian groups (-0.44). Note the Asian group's relationships
with UK/USA and Central/Eastern European groups. In both cases
the correlation coefficients were positive with one subgroup and
negative with another. Thus the behavior of the Asian group could
serve as an indication that the splitting these two large groups
into parts was done correctly.
Science
Analysis of the
groups
Table 7
Factor Analysis for Science Items
English-Speaking Group
|
communality
|
fac
1
|
fac
2
|
|
AUS
|
0.64
|
0.48
|
0.64
|
|
CAN
|
0.72
|
0.22
|
0.82
|
|
ENG
|
0.81
|
0.88
|
0.19
|
|
IRE
|
0.61
|
0.76
|
0.17
|
|
NZL
|
0.66
|
0.64
|
0.50
|
|
SCO
|
0.80
|
0.87
|
0.19
|
|
USA
|
0.75
|
0.09
|
0.86
|
|
|
f_UK
|
f_Am
|
The same four groups of
countries for mathematics were also tested for Science. Two of
them were stable enough to be kept for science (English speaking
countries' group – Australia, Canada, England,
Ireland, New Zealand, Scotland, USA, and the Nordic
group--Denmark, Iceland, Norway, Sweden). Relationships in the
other two
groups were more complex and not strong enough to permit keeping
the countries together, i.e., the CEE countries group (Bulgaria,
Czech Republic, Hungary, Latvia, Lithuania, Romania, Russian
Federation, Slovak Republic, Slovenia), and the Eastern Asian
group (Hong Kong, Japan, Korea, Singapore). One reason for this
could be some heterogeneity in the school subject called science:
in the CEE countries groups, science is taught as separate
courses (Geography, Biology, Chemistry, Physics).
Therefore, the similarities found for one subject were not
valid
for another subject.
Table 8
Correlations for Science
English-Speaking Group
|
Australia
|
AUS
|
***
|
|
|
|
|
alpha
|
0.86
|
|
Canada
|
CAN
|
0.48
|
***
|
|
|
|
|
|
|
England
|
ENG
|
0.53
|
0.38
|
***
|
|
|
|
|
|
Ireland
|
IRE
|
0.34
|
0.31
|
0.62
|
***
|
|
|
|
|
N.Zealand
|
NZL
|
0.67
|
0.51
|
0.59
|
0.44
|
***
|
|
|
|
Scotland
|
SCO
|
0.50
|
0.38
|
0.74
|
0.60
|
0.59
|
***
|
|
|
USA
|
USA
|
0.49
|
0.59
|
0.25
|
0.35
|
0.37
|
0.27
|
***
|
|
|
AUS
|
CAN
|
ENG
|
IRE
|
NZL
|
SCO
|
USA
|
The link
England–Scotland (correlation coefficient 0.74)
remained
the strongest in all TIMSS countries (with an increase up to
0.82
for Life science, and a decrease to 0.56 for
Physics). This group was more stable for science than
for
mathematics: Ireland had more weight, and the link
USA–Australia was also strengthened. As a consequence,
the
group became more homogeneous, especially in Life
science
where the alpha coefficient was 0.89. Physics was a
weaker
area for this group, but still the similarities between the
countries were strong enough to keep the group together (the
alpha was 0.79).
The factor analysis for
these 7 countries yielded two factors with eigenvalues of
3.88
and 1.12, explaining 71.4 percent of the variation. After
rotation (varimax method was used), an analysis of the
loadings
yielded the names English-speaking countries - United
Kingdom (f_UK) for the first factor, and English-
speaking
countries - America (f_Am) for the second, as was found
in
the mathematics achievement results.
The four Nordic
countries of Iceland, Denmark, Norway and Sweden formed the
second group. The links between three countries in this
group
were about the same for all science sub scales with the
exception
of Environment and nature of science (the alpha was
only
0.40), where Iceland stood out (all correlations with the
three
other Nordic countries were negative!). This country was the
weakest member of the group in Earth science and in
Chemistry, where quite strong links to New Zealand
(0.64),
and the Netherlands (0.58) were found. The factor analysis
for
these 4 countries yielded an eigenvalue of 2.16 explaining
about
54 percent of the variation in the Nordics group.
Table 9
Correlations and Factor Analysis for Science
Nordic Group
|
Denmark
|
DEN
|
***
|
|
alpha
|
0.71
|
|
DEN
|
0.60
|
0.77
|
|
Iceland
|
ICE
|
0.36
|
***
|
|
|
|
ICE
|
0.33
|
0.58
|
|
Norway
|
NOR
|
0.43
|
0.31
|
***
|
|
|
NOR
|
0.63
|
0.80
|
|
Sweden
|
SWE
|
0.46
|
0.20
|
0.54
|
***
|
|
SWE
|
0.59
|
0.77
|
|
|
DEN
|
ICE
|
NOR
|
SWE
|
|
|
communality
|
factor
|
As was mentioned
earlier, the other two groups of countries had scattered
patterns. The East Asian group with Hong Kong, Japan, Korea
and
Singapore split into two pairs: Hong Kong – Singapore
(on
the total science scale the correlation was 0.26, in
Physics 0.55, and in Chemistry -0.23!), and
Japan
– Korea (0.36, in Chemistry 0.66, compared with
-0.11 for Earth science). The Cronbach alpha for the
total
science scale was 0.47, but it ranged from -0.08 for
Environment and Nature of science to 0.57 for Life
science and 0.53 for Chemistry. Nevertheless,
these
figures were too low to coalesce the countries into one
group.
The eight CEE countries
formed a group in mathematics, but for science the situation
was
more complex.
Table 10
Correlations for Science
Post-Communist Group
|
Bulgaria
|
BGR
|
***
|
|
|
|
|
|
|
|
|
|
Czech R.
|
CZE
|
0.07
|
***
|
|
|
|
alpha
|
0.71
|
|
|
|
Hungary
|
HUN
|
0.04
|
0.18
|
***
|
|
|
|
|
|
|
|
Latvia
|
LVA
|
0.14
|
-0.00
|
0.27
|
***
|
|
|
|
|
|
|
Lithuania
|
LTU
|
0.18
|
0.24
|
0.15
|
0.39
|
***
|
|
|
|
|
|
Romania
|
ROM
|
0.29
|
0.34
|
0.21
|
-0.03
|
0.30
|
***
|
|
|
|
|
Russia
|
RUS
|
0.24
|
0.24
|
0.12
|
0.32
|
0.48
|
0.44
|
***
|
|
|
|
Slovak R.
|
SVK
|
-0.05
|
0.51
|
0.18
|
0.01
|
0.09
|
0.28
|
0.22
|
***
|
|
|
Slovenia
|
SLV
|
0.03
|
0.32
|
0.22
|
0.25
|
0.16
|
0.33
|
0.12
|
0.31
|
***
|
|
|
BGR
|
CZE
|
HUN
|
LVA
|
LTU
|
ROM
|
RUS
|
SVK
|
SLV
|
Formally, the measure of
the homogeneity of the group – Cronbach's alpha
for
overall science scale – was quite high and was 0.71
(ranging from 0.68 for Physics, to 0.78 for
Chemistry). A cut-off point of 0.75 was defined for
alpha
to form a group. For the Nordics group and for the CEE
group, the
coefficients were somewhat lower than the cut-off point
–
0.71 in both cases. The Nordic countries were grouped, but
the
analysis of the matrix of the correlations for CEE countries
group showed large diversity among countries, especially in
the
relationships for the different subjects of science.
Firstly,
Bulgaria was different: in Physics this country was
similar to the Russian Federation (0.41) and Romania (0.41),
but
in Chemistry similar to Japan (0.49). The subscale
Environment and Nature of science disturbed this
grouping.
Also noteworthy are the links between the pairs Hungary
–
Germany (0.79), Lithuania – France (0.48), Russia
–
Greece (0.59), Slovakia – Greece (0.65) as well as
Lithuania– Slovenia (0.66), Russia – Slovakia
(0.74).
The factor analysis yielded three eigenvalues above 1, and
the
explanations of these three factors became quite complex.
Therefore, the decision was made not to form the CEE
countries
into one group.
Discussion
The process of the
grouping of countries indicated the high similarity between
some
countries, but from another point of view showed that some
countries were different from these groups. An examination
of
some of the countries not included in the groups has been
undertaken. The relationship of these countries with the
main
trends of groups, extracted by factor analysis above, is
mentioned first, followed by some analyses of the pairing of
countries.
Only two significant
links with factors could be seen for Austria: this
was in
mathematics with Central Europe countries f_CE (correlation
0.36), and with East Europe countries f_EE. (-0.23). Austria
was
most linked to its neighbor Germany (0.40 in math, 0.58 in
science, with 0.85 for Life science). Other
interesting
links were with Norway (0.51 in Algebra), Switzerland
(0.41 in science), Czech Republic (0.49 in Life
science),
Ireland (0.55 in Chemistry), Israel (0.52 in
Chemistry). For Earth science some obscure
relationships could be noted with Kuwait (0.55), and the
Philippines (0.44).
There were no
significant correlations for France with other
countries,
except a weak 0.22 in mathematics with Nordic countries
f_No. It
was not unexpected that France in mathematics was most
similar to
the French part of Belgium (Belgium took the part in TIMSS
education with two subsystems – Flemish and French,
according to the prevalent language used in education in the
country). The correlation coefficient was 0.33. Some of the
CEE
countries were traditionally influenced by French ideas in
mathematics education and this fact can be seen in the
analyses:
in the subscaleAlgebra, France was correlated with
the
Russian Federation (0.32), in Geometry with the Czech
Republic (0.49), and Lithuania (0.47). The French part of
Belgium
was most similar to France in Science (0.67, with an
increase to
0.87 in Chemistry). Some other interesting links were
in
Physics to Denmark (0.45) and in Chemistry to
Switzerland (0.69).
The most interesting
links for Germany were the negative relationships
with the
East Asian factor f_As (-0.51) and with East Europe factor
f_EE
(-0.32). At the same time, Germany was quite similar to the
United Kingdom part of the English-speaking countries group
(correlation with f_UK was 0.41). Germany, as was mentioned
above, was similar to Austria. In math some other links to
Switzerland (0.41), Norway (0.40), and in Algebra to
Greece (0.67), Portugal (0.56) could be mentioned too.
Switzerland was similar to Germany in science (0.54),
together
with France (0.50), Norway (0.49) in Chemistry and to
the
Netherlands in Physics (0.42).
There were
threecorrelations with factors for Israel:
two of
them negative (-0.22 with f_UK, and -0.30 with f_No), and
one
positive 0.21 with f_EE. The country most similar to Israel
in
mathematics was Cyprus (0.36), especially in Algebra
(0.60), and Geometry (0.53). There was also a high
correlation between Israel and the Russian Federation in
Geometry (0.55). It was difficult to identify
similarities
with Israel in science, except some links with Cyprus (0.44
in
Earth science), and Austria (0.52 in
Chemistry).
The
Netherlands was like
aninternational cross-roads: in mathematics +0.62
with
f_UK, –0.48 with f_EE, +0.45 with f_No, –0.32
with
f_CE. For science the relationships were weaker: 0.23 with
f_Am,
and 0.24 with f_No. In mathematics there were common
patterns
with Austria (0.52, with an increase to 0.66 in
Algebra),
England (0.56), New Zealand (0.60), Sweden (0.59), and in
Geometry to the USA (0.64). The neighbouring
education
system, Belgium-Flemish, was most similar in science (0.48,
with
increase till 0.57 in Physics, and even to 0.82 in
Chemistry). Some other interesting links were: in
Physics with Germany (0.42), in Chemistry with
Switzerland (0.64), in Earth science with Sweden
(0.51).
Spain had something in common in mathematics with f_CE
(0.26),
but was negatively correlated with Nordics and East Asian
countries (-0.22 with f_No, -0.28 with f_As). Spainin
mathematics was most similar to its neighbor Portugal (0.39,
with
an increase to 0.58 in Geometry), with a possible
link to
Slovenia (0.37), and some relationship with the USA (0.46 in
Geometry). The linguistic similarity had an impact on
science education: correlation with Colombia (0.27),
Portugal
(0.39, with an increase to 0.61 in Earth science).
Some
other similarities were with the USA (0.46 in
Physics),
Greece (0.62 in Chemistry), and Norway (0.59 in
Earth
science).
In mathematics the
pattern of Switzerland was interesting (+0.49 with
f_No,
–0.41 with f_EE, +0.29 with f_UK, –0.28 with
f_As),
and in science there was just one significant link (0.32
with
f_No). Switzerland was quite similar in mathematics to
Nordic
countries Norway (0.37) and Sweden (0.46), and had common
patterns in Geometry with New Zealand (0.58) and
Canada
(0.44). In science Switzerland was similar to Belgium-French
(0.41, with an increase to 0.67 for Physics, 0.78 for
Chemistry), as well as was linked with Austria (0.51
in
Life science), France (in Physics 0.43, in
Chemistry 0.69), the Netherlands (in Chemistry
0.64), Germany (in Earth science 0.63), Belgium-
Flemish
(in Chemistry 0.81).
This article could be
viewed as an attempt to measure something that some might say was
unmeasurable. It is impossible to measure everything in education
by converting the complexities and idiosyncrasies of nations into
figures. Tables with correlation coefficients presented in this
paper do not explain everything that is going in the schools of
these countries. But sometimes it is useful to see "well-known
truths" converted into the language of figures.
Notes
-
Many visions, many aims.
A cross-national investigation of curricular intentions in
school
mathematics. Kluwer, 1996.
- Many visions, many aims.
A cross-national investigation of curricular intentions in
school
science. Kluwer, 1996.
- Mathematics Achievement
in the Middle School Years: IEA's Third Intentional
Mathematics and Science Study (TIMSS). Boston College,
1996.
- Science Achievement in
the Middle School Years: IEA's Third Intentional
Mathematics and Science Study (TIMSS). Boston College,
1996.
About the Author
Dr. Algirdas
Zabulionis
Vilnius University, Lithuania
Email: algiz@nec.lt
Algirdas Zabulionis currently is a senior
researcher in the Centre for
Education Policy at Vilnius University.
Until September, 2001, he directed the National
examinations centre NEC
(http://www.nec.lt) and worked with large-scale
educational assessment projects.
His specializations are educational assessment,
statistics, and research
methodology. Zabulionis was the National Research
Coordinator for Lithuania of
the TIMSS-95 and TIMSS-99 studies.
|
times since September 14, 2001