The commenter “m” did some calculations to work out the relative performance of different countries in PISA vs. TIMSS, and in Math vs. Science.
Dimension 1 is overall performance across all 4 (PISA Math, PISA Science, TIMMS Math, TIMMS science). Everything goes up with this dimension. Highest performers: Singapore, Chinese Taipei, Japan. Weakest performers: Turkey, UAE, Malta.
Dimension 2 separates stronger performers on TIMMS vs PISA: strongest performers on TIMMS relative to PISA are in order: Turkey, Korea, Russia, Hungary, United Arab Emirates, while strongest performers on PISA relative to TIMMS are: New Zealand, Canada, Australia, Norway, Italy. The five most balanced countries in the tradeoff are roughly: Slovenia, England, Hong Kong, Japan, USA.
Overperformance in TIMSS relative to PISA can arguably be used as a proxy for schooling quality, since it’s more dependent on academic/curricular skills than on raw intelligence. I am not surprised by the good figures for Korea, Russia, and to a lesser extent, the rest of East Asia and the post-Communist world. However, the UAE and Turkey are surprising.
Dimension 3 separates out Science nations vs Math nations: Most heavily Science vs Math: Slovenia, England, USA, New Zealand, Turkey and most heavily Math vs Science: Hong Kong, Malta, Korea, Italy, Norway.
As much as including TIMMS might be a worse proxy of “IQ” than just PISA, I have included in the above graphic a measure of using the PC1 overall performance score to convert to IQ, based on the assumption that England is 100 and Japan 104.3 as in your PISA conversion. There’s a bit of swing, not too much, compared to PISA alone.
Singapore’s the biggest relative loser when the skills measure is rolled in as well, with the least advantage on PIAAC skills relative to TIMMS / PISA. Most other countries gain compared to the other PCA, as they are more advantaged relative to England and the East Asians on young people’s life skills than they are on young people’s education measures.