Abstract This research uses TIMSS 2003 data to test faucet theory in Taiwan, Singapore, South Korea, Hong Kong, Japan, Russia, United States, Scotland and Italy. It explores the relationships between frequency of homework, time of finishing homework, frequency of shadow education and mathematics achievement. Statistics methods such as descriptive statistics, one-way ANOVA, and regression analysis were used. Major findings of this research are described as follows: 1. For 8th grade pupils, homework and shadow education are common in these nine countries/areas. In terms of their impacts on mathematics achievement, there are similarities as well as differences across the nine countries/areas. 2. According to results of regression analysis, faucet theory is completely supported in Taiwan, but is only partially supported in other countries/areas. 3. From the correlations between shadow education and mathematics achievement in the nine countries/areas, different types of extra-school instruction can be discerned. 4. The effects of after-school learning (i.e., shadow education and homework) on mathematics achievement are close to that of socio-economic backgrounds in nine counties/areas. This paper also proposes the following suggestions for future studies: 1. Different type of shadow education will make faucet theory accepted or rejected. It is important to detect which type of shadow education a country has. 2. A substitutional effect is found between shadow education and homework in South Korea, but none of such effect exists in Russia, while both countries rely heavily on after-school learning. Further study on substitutional effect of after-school learning is needed. 3. The regression model explains a very small portion of variances of Japanese students’ achievement in mathematics. Further study to test the effects of shadow education in Japan is suggested.