TIMSS (Trends in International Mathematics and Science
Study) is an assessment of the maths and science skills of fourth grade and
eighth grade students around the world. The Mathematics data in the table below
are taken from TIMSS 2011Exhibit 2.2: Performance at the International
Benchmarks of Mathematics Achievement 4th Grade. http://timssandpirls.bc.edu/timss2011/downloads/T11_IR_M_Chapter2.pdf
GNI is gross national income. Thus GNI per capita is
the national income per person. The data in the the table below are from Wikipedia. http://en.wikipedia.org/wiki/List_of_countries_by_GNI_(PPP)_per_capita
Country
|
Maths
score
|
World Bank GNP per capita (PPP)
|
Notes
|
Singapore
|
43
|
59790
|
|
Korea, Rep. of
|
39
|
30290
|
|
Hong Kong SAR
|
37
|
51490
|
|
Chinese Taipei
|
34
|
41385
|
|
Japan
|
30
|
35510
|
|
Northern Ireland
|
24
|
36970
|
GNI per capita for UK, not Northern
Ireland
|
England
|
18
|
36970
|
GNI per capita for UK, not England
|
North Carolina, US
|
16
|
48890
|
GNI per capita for US, not North
Carolina
|
Florida, US
|
14
|
48890
|
GNI per capita for US, not Florida
|
Russian Federation
|
13
|
20050
|
|
United States
|
13
|
48890
|
|
Finland
|
12
|
37990
|
|
Australia
|
10
|
36910
|
|
Denmark
|
10
|
42350
|
|
Flanders, Belgium
|
10
|
39300
|
GNI per capita for Belgium, not
Flanders
|
Hungary
|
10
|
20380
|
|
Lithuania
|
10
|
19690
|
|
Ireland
|
9
|
33310
|
|
Serbia
|
9
|
11640
|
|
Portugal
|
8
|
24530
|
|
Kazakhstan
|
7
|
11310
|
|
Ontario, Canada
|
7
|
39,830
|
GNI per capita for Canada, not
Ontario
|
Romania
|
7
|
15140
|
|
Quebec, Canada
|
6
|
39,830
|
GNI per capita for Canada, not Quebec
|
Azerbaijan
|
5
|
9020
|
|
Dubai, UAE
|
5
|
48220
|
GNI per capita for UAE, not Dubai
|
Germany
|
5
|
40170
|
|
Italy
|
5
|
32350
|
|
Netherlands
|
5
|
43770
|
|
Slovak Republic
|
5
|
22610
|
|
Czech Republic
|
4
|
24190
|
|
Malta
|
4
|
24170
|
|
New Zealand
|
4
|
29140
|
|
Slovenia
|
4
|
27110
|
|
Turkey
|
4
|
16730
|
|
Alberta, Canada
|
3
|
39,830
|
GNI per capita for Canada, not
Alberta
|
Sweden
|
3
|
42350
|
|
Armenia
|
2
|
6140
|
|
Austria
|
2
|
41970
|
|
Chile
|
2
|
16160
|
|
Croatia
|
2
|
19330
|
|
Georgia
|
2
|
5390
|
|
Norway
|
2
|
58090
|
|
Poland
|
2
|
20450
|
|
Qatar
|
2
|
87030
|
|
Saudi Arabia
|
2
|
24870
|
|
United Arab Emirates
|
2
|
48220
|
|
Abu Dhabi, UAE
|
1
|
48220
|
GNI per capita for UAE, not Abu Dhabi
|
Bahrain
|
1
|
21240
|
|
Iran, Islamic Rep. of
|
1
|
11400
|
|
Oman
|
1
|
25770
|
|
Spain
|
1
|
31930
|
|
Thailand
|
1
|
8390
|
|
Botswana (Grade 6)
|
0
|
14560
|
|
Honduras (Grade 6)
|
0
|
3840
|
|
Kuwait
|
0
|
53820
|
|
Morocco
|
0
|
4910
|
|
Tunisia
|
0
|
9090
|
|
Yemen (Grade 4)
|
0
|
2180
|
|
Yemen (Grade 6)
|
0
|
2180
|
Three countries entered Grade 6 students for the
study. Somewhat confusingly Yemen provided Grade 4 and Grade 6 students. At
first glance, it seems unusual to lump Grade 6s in with Grade 4s, but on
reappraisal, what is Grade 4 anyway?
Is it an internationally recognized standard unit like the kilogram or the
ampere? Actually, no. Finns and Croatians start Primary School (Grade School) at
7 years old, while English and Australian children start Primary School at age
5. (Data from the World Bank: http://data.worldbank.org/indicator/SE.PRM.AGES)
Some of the data are for entire countries while others
are for, using TIMSS own terminology, ‘benchmarking participants.’ All of the benchmarking
participants (e.g. , North Carolina) are sub-units of sovereign states (eg
United States of America) , but (confusingly) not every sub-unit (eg North
Ireland) is classified as a ‘benchmarking
participant.’ (Well, it provides a possible
lesson digression on Venn diagrams.)
The original table (TIMSS 2011Exhibit 2.2) actually
provides four different benchmarks (Advanced, High, Intermediate and Low) for
each country or ‘benchmarking participant’. The original table also gives the standard
error for each data point. Completely arbitrarily, I chose just the ‘Advanced’
benchmark and omitted the standard error.
The choice of economic data was, again, arbitrary. What
choices did I have? For one, I might have used either ‘GDP per capita’ or ‘GNP
per capita’ instead of GNI per capita. Secondly,
the data I used are not ‘raw’ data but have been ‘put into a blender- chopped,
diced and reassembled’ as purchasing power parity (PPP) data using
‘international dollars’. PPP is an expression of the belief that countries
manipulate their currency’s exchange rate relative to the US dollar. Therefore,
another option would have been to use actual GNI per capita (without PPP). For another thing, the data are not equally
up-to-date. Australia’s GNI data are given as “2009 or 2010” whereas
most of the other countries GNI data is for 2011. For another, England and North Ireland have
separate entries for the TIMSS data, but are a single entity (both are part of
the United Kingdom) in the Wikipedia economic data. I could go on and on, but
my last point will be that some countries are given more weight than others in
my data. For example, both the USA and
Canada get three times the weight of Lithuania. The USA is counted as itself
and again as North Carolina and Florida. Canada, as such, does not appear in
the table but gets entries for Alberta, Ontario and Quebec.
Enough with the caveats, what does the data
actually look like?
Remarkably, there does appear to be a correlation
between the Mathematics benchmark at Grade 4 and the GNI per capita. Using my Excel spreadsheet, I calculate the
regression coefficient to be r = 0.34. Statisticians would generally consider
this to be an example of ‘weak’ correlation.
They almost certainly would go on to calculate r2, which
would allow them to say that the “mathematics benchmark” explains 12% of
the “GNI per capita.”
Remember, ‘explains’ does not mean ‘causes.’ Today’s Grade 4 Maths students cannot possibly
determine the size of today’s economy! Of
course the present Grade 4s could be a proxy for the Grade 4s of one or two generations
ago. The mathematics ability of Grade 4s of the 1970s could be a determiner of today's GNI. Another possibility is that the causation works in the other direction.
Rich economies might spend more on Grade 4 education and better paid teachers
might teach in such a way that the children do better on a standardized test of
Mathematics. Or there may be a third
variable that causes both of the graphed variables.
Unlike
the data comparing height and shoe size (yesterday’s blog), there should be plenty
to think about. How big is the leap from
the impersonal “How much maths education should country X provide to its
citizens to ensure its economic success?” to the much more personal “How much
maths education do I need to do ensure my
economic success?” Students might even
wonder if substituting “musical ability” or “prowess in sports” in Grade 4 in
place of “maths” would have produced a higher correlation coefficient. I do think it is unlikely that most students
would they take the same line as the Guardian newspaper. The Guardian appears unwilling
to takes sides but instead errs on the side of caution by writing “The IEA's studies, much like similar intermittent
league tables compiled by the OECD, generally contain so much data as to
support a series of different, even contradictory, arguments.”
In the
light of the weak correlation seen in the data, does it make sense for
politicians to push for better maths and science scores and for more STEM (science,
technology, engineering, and mathematics) grads? Brian Vastag who is a science reporter at The
Washington Post doesn’t think so. In a story entitled “U.S. pushes for more
scientists, but the jobs aren’t there” he writes: “There
are too many laboratory scientists for too few jobs.” Taking the
pharmaceutical industry as an example he goes on to say: “Since 2000, U.S. drug
firms have slashed 300,000 jobs, according to an analysis by consulting firm
Challenger, Gray & Christmas. In the latest closure, Roche last month
announced it is shuttering its storied Nutley, N.J., campus — where Valium was
invented — and shedding another 1,000 research jobs.” “(http://www.washingtonpost.com/national/health-science/us-pushes-for-more-scientists-but-the-jobs-arent-there/2012/07/07/gJQAZJpQUW_story.html)