Figure 1a.  PISA Math Scores, 2003 to 2015: 20 Developed Nations
NCES, Highlights PISA 2003,  p. 14       NCES, Highlights PISA 2009,  p. 18
NCES, Highlights PISA 2006,  p. 12       NCES, PISA 2012, Math        v
NCES, PISA 2015, Math

Korea and Japan are in light blue; Asia: Asian cities and city-states (C & C-S) is in light orange (see below for a breakout of the components of this category); Scandinavian nations + Switzerland are in dark blue; Anglo-Saxon nations in orange; France, Germany, Belgium and Poland in green; Italy, Portugal and Spain in red; the United States in yellow.

Of the European nations omitted from this graph, Croatia, Greece, Romania, Bulgaria, and Cyprus scored below the United States in math.  Ahead of the United States but not shown are Estonia, Slovenia, Ireland, Austria, Russian Federation, Czech Republic, Iceland, Luxembourg, Latvia, Malta, Lithuania, Hungary, and the Slovak Republic.
Figure 1b.  A Closer Look
Asia: Nations and City-States enables us to clarify certain issues regarding test score comparability.  Singapore, Hong Kong, Macao China, and Chinese Taipei ought to be thought of as city-states.  Their population densities of around 5,000 persons per square kilometer, compared with European population densities of two to three hundred persons per square km, makes this clear.  "China" was previously only Shanghai; now what is listed in the PISA report under "China" is Beijing, Shanghai, Jiangsu, and Guangdong (B-S-J-G).  The precipitous decline of more than 80 points is no doubt primarily a result of the addition of the industrial areas of Jiangsu and Guangdong.  The decline of Vietnam's score is likely due to the expanded geographical scope of the administration of the test.

Losers lets us see more clearly what's what among geographically stable test areas.