The world is flat! Countries around the world affect one another, no matter their economic structures, thoughts, beliefs, or values. Therefore, we know that no country or person can be independent. Acknowledging the situations and trends of other countries is thus essential. According to this view, the international Trends in International Mathematics and Science Study (TIMSS) and the Programme for International Student Assessment (PISA) enable different nations to understand one another's educational situations.
Results from the TIMSS and PISA studies reveal that there are significant differences among countries in mathematics competency (National Center for Education Statistics [NCES], 2009; Organisation for Economic Co-operation and Development [OECD], 2007). These include mathematics knowledge and its application, analysis and problem solving, and model utilization and augmentation, among other proficiencies (OECD, 2007). In addition, these studies indicate that different countries have different curricula, a fact that might constitute the reason for various students' significant levels of difference. However, these indications are the total of our current interpretations; we still do not know how and in what way this difference of curricula affects our students' vast differences in knowledge.
To understand the factors that can affect students' levels of achievements, the TIMSS 1999 video study (NCES, 2003) focused on three aspects of mathematics teaching: the way lessons are organized, the nature of content implemented in lessons, and instructional practices. The study found that there were detectable differences in the relative emphasis or arrangement by mathematics teachers in different countries. It further suggested that teaching methods should align with what teachers want their students to IEArn and that one cannot say which teaching method may be best to implement in a given country.
In these three aspects, a common latent factor is noticed-the quality of teachers. Many studies have shown that teacher quality is the most important school-related factor influencing student achievement (Goe, 2007; Kaplan & Owings, 2001; Rice, 2003). Some also have found that the methods and content used by teachers have a definite influence on their students' learning (Abell Foundation, 2001; Fetler, 1999; Goldhaber & Brewer, 2000).
Various nations have therefore established teacher certification to control the quality of teachers (e.g., NCES, 1999; see also Goldhaber & Anthony, 2004). Different certifications thus exist in order to assess candidates' different types of knowledge for mathematics teaching. Among these different types of knowledge are subject matter knowledge, subject-specific knowledge for teaching, and pedagogical knowledge, all of which enjoy considerable favor in modern certifications, such as the Praxis Series (Hill, Sleep, Lewis, & Ball, 2007; NCES, 1999). These types of knowledge have also gained attention in academic circles (Hill et al., 2007). Many researchers further claim that a given teacher's knowledge of mathematics and knowledge of how to translate mathematics into a form that can be understood by students play the most important role in effective teaching (Ferrini-Mundy, Floden, McCrory, Burrill, & Sandow, 2005). These two types of knowledge are indeed consistent with, if not identical to, the two of Shulman's categories for teachers' knowledge that are applicable to mathematics, namely, mathematics content knowledge and mathematics pedagogical content knowledge (Shulman, 1987).
How a country can guarantee that its teacher quality is high has been a seriously considered issue. One straightforward inference is to guarantee the quality of the basic learning environment in which we train and equip our future teachers, that is, teacher education programs (TEPs). The different features and practices involved in TEPs are therefore worth investigating. …