TIMSS, PISA, and other similar studies have provided consistent evidence that students in the US are falling steadily behind their counterparts in East Asian countries and in European Union countries. A report on PISA 2012 revealed that 15-year-old students’ performance in the United States ranked 27^th in mathematics out of 34 OECD member countries and they scored 481, which was 13 points below the OECD math mean score (i.e., 494). Furthermore, many of the nation's most talented students in science, technology, engineering, and mathematics (STEM) are not entering these academic fields, or are leaving at some point during their post-academic careers (National Science Foundation, 2006a; 2006b; 2006c; 2008). The number of engineering degrees awarded since 1985 has decreased 20% domestically (Froschauer, 2006). This has ultimately resulted in the decline of scientific literacy among our citizenry. All of this has occurred at an inopportune time when our society is becoming increasingly dependent on advanced technologies.

Among all the 34 OECD countries, Korean students were the highest performing students. The same report (i.e., the PISA 2012) revealed that 15-year-old students’ performance in the country of Korea ranked top in mathematics and ranked 5^th out of all 65 countries and economies. In addition, students in Switzerland performed the best in math among all European countries. They ranked 1^st in Europe and ranked 9^th out of all participating countries.

Another study conducted in Korea, however, shows that diminishing interest in science or mathematics-related subjects at the high school level leads to the avoidance of science-related careers and students’ preference toward science and mathematics decreases as they get older (Korea Science Foundation, 2003). According to the findings from this research, the percent of high school senior students who have applied to science or technology-related colleges noticeably decreased from 42.4 percent (1998) to 30.3 percent (2003). This research was conducted by a national scale internet survey, which was a large scale study whose participants (N=1,670,000) amounted to 22 percent of all Korean student population.

Comparing the PISA result between the US, Korea (i.e., Far-East Asian country), and Switzerland (i.e., European country) would be meaningful because this could give them an opportunity to learn from each other. Instead of just looking at the overall achievements, more in-depth investigation on the factors which will have an effect on students’ achievement at multiple levels will be required and the result of this investigation might suggest a possible answer to the current problems. In addition to the effect of student level characteristics, this research will examine the impact of school climate, such as school level effects of parents' education level, living environment, students' attitude toward math subject, and math teacher on the students’ math achievement revealed in PISA 2012 using hierarchical linear modeling (HLM) and Latent Class Analysis (LCA). This will provide deep insight into the students’ achievement which the report on the average numbers failed to explain to us. Using both hierarchical linear modeling analysis and multilevel mixture modeling methods, this study’s research questions will be as follows:

1. How much do student-level and group-level variables predict student math achievement?
2. How many latent classes at student level can be inferred from the data?
3. Are there any differences in the relationship between each latent class and their math achievement?

Clogg, C. C. (1995). Latent class models. In G. Arminger, C. C. Clogg, & M. E. Sobel (Eds.), Handbook of statistical modeling for the social and behavioral sciences (Ch. 6; pp. 311-359). New York: Plenum. Goodman, L. A. Exploratory latent structure analysis using both identifiable and unidentifiable models. Biometrika, 1974, 61, 215-231. Heinen, T. (1996). Latent class and discrete latent trait models: Similarities and differences. Thousand Oaks, California: Sage. Kelly, D., Nord, C. W., Jenkins, F., Chan, J. Y., & Kastberg, D. (2013). Performance of US 15-Year-Old Students in Mathematics, Science, and Reading Literacy in an International Context. First Look at PISA 2012. NCES 2014-024. National Center for Education Statistics. National Research Council (2002). Learning and Understanding: Improving Advanced Study of Mathematics and Science in U.S. Schools. Washington D.C.: National Academies Press. National Science Board (2004). Science and Engineering Indicators 2004. Arlington, VA: National Science Foundation, Division of Science Resources Statistics (NSB 04-01). Nezlek, J. B., & Zyzniewski, L. E. (1998). Using hierarchical linear modeling to analyze grouped data. Group Dynamics: Theory, Research, and Practice, 2(4), 313. Raudenbush, S. W., & Bryk, A. S. (2002). Hierarchical linear models: Applications and data analysis methods (Vol. 1). Sage. Raudenbush, S. W. (2004). HLM 6: Hierarchical linear and nonlinear modeling. Scientific Software International. Rost J, Langeheine R. A guide through latent structure models for categorical data. In J. Rost & R. Langeheine (Eds.), Applications of latent trait and latent class models in the social sciences. New York: Waxmann, 1997. In fact, this entire book is a good introductory resource. It includes many papers that illustrate applications of LCA in various areas. The papers, written mainly by methodologists, convey the "state of the art" for use of LCA.