Research in Brief - May 2008 - Volume 108 (5)

Mathematical Preparation of Elementary School Teachers: Generalists versus Content Specialists

Yeping Li

It is now common knowledge to many that mathematics knowledge for teaching is key to the improvement of mathematics classroom instruction. Few would disagree that teacher preparation should also increase its emphasis on mathematics content training for prospective teachers. Yet, it is not clear what impact courses taken on mathematics content and methods may have on teacher preparation (Wilson, Floden, & Ferrini-Mundy, 2001). One approach is proposed to have elementary school teachers as content specialists (e.g., Fennell, 2006). In this way, we may expect that in-service teachers will be specialized in teaching different content subjects and prospective teachers will get adequate preparation in mathematics. But is this really a good idea? Will the preparation of content specialists be the solution for the long-standing concern about U.S. teachers' knowledge in mathematics and their performance in mathematics teaching (e.g., Li, 2007; Ma, 1999; Stigler & Hiebert, 1999)? In this brief, I aim to address this issue with reference to what we can learn from relevant practices in East Asia, highlight the differences evidenced in prospective teachers' mathematics performance cross-nationally, and conclude with possible suggestions obtained.

The idea of having elementary school teachers as content specialists was supported in part by findings from some cross-national studies on teachers' mathematics knowledge for teaching (e.g., An, Kulm, & Wu, 2004; Ma, 1999). In particular, Ma's study revealed that sampled Chinese elementary teachers had a profound understanding of the fundamental mathematics they teach, whereas U.S. teacher participants lacked a strong knowledge base in mathematics. As argued by Ma, the results provided a partial explanation for what contributes to Chinese students' achievement in school mathematics. They are also in alignment with current understanding that teachers and their teaching are key to the improvement of students' learning (e.g., National Commission on Teaching and America's Future [NCTAF], 1996; National Council of Teachers of Mathematics [NCTM], 1991). Paradoxically, according to Ma, Chinese elementary teachers actually received less formal education, in terms of the number of years spent before entering the teaching profession, than their U.S. counterparts in her study. The apparent cross-national discrepancy between teachers' knowledge and the number of years' training they received in the United States and China remains open to multiple interpretations. One interpretation is that Chinese elementary school teachers who teach mathematics are content specialists, whereas elementary school teachers in the United States are generalists who need to teach many different school subjects. The cross-national difference in teaching responsibility assignment suggests that being content specialists provides Chinese elementary mathematics teachers better opportunities to improve their mathematics knowledge for teaching over the years. The idea of having elementary teachers as content specialists is likely supported through Ma^#39;s study about the case of China. However, elementary school teachers as generalists are not necessarily poor in knowing and understanding school mathematics. In fact, a recent study (Li, Ma, & Pang, in press) revealed that Mainland China is the only one out of six education systems in East Asia (i.e., Hong Kong, Japan, Mainland China, Singapore, South Korea, and Taiwan) that have elementary school teachers concentrated on teaching a main school content subject, such as mathematics. Therefore, the practice of having elementary teachers as generalists is common and does not necessarily bring negative impact to teachers' knowledge and teaching in mathematics. The question of better having content specialists or generalists at the elementary school level is unlikely to have an absolute answer, and further inquiry about the question thus leads to teacher preparation.

In fact, another possible interpretation related to Ma's (1999) findings is that Chinese elementary teachers might enjoy a better start than their U.S. counterparts upon the completion of their teacher education programs. To expand such discussions, Li, Ma, and Pang (in press) provided an in-depth examination of elementary teacher preparation practices in Hong Kong, Japan, Mainland China, Singapore, South Korea, and Taiwan. One may expect that in-service teachers' instructional responsibility in different education systems would be consistent with the training they received through preparation programs. To our surprise, this is often not the case. For example, in Mainland China where in-service teachers often need to have a focal teaching subject, teacher preparation programs were traditionally set up to offer virtually the same curriculum of studies for all prospective elementary teachers in normal schools. In contrast, elementary teachers in the remaining five education systems need to teach many different school subjects. However, teacher preparation programs in these education systems often require prospective teachers to select a focal subject area through their program studies. Thus, elementary teacher preparation practices in East Asia do not support the idea of preparing mathematics content specialist at the elementary school level.

Now the question remains as what helps make elementary teachers in East Asia good at mathematics and why U.S. elementary teachers often show a deficiency in the mathematics they teach. In fact, Li, Ma, & Pang (in press) suggested that an emphasis on mathematics preparation is an important feature in elementary teacher preparation programs in several education systems in East Asia. It is not necessarily the preparation of content specialists, but the general emphasis placed on mathematical preparation of elementary teachers, that likely helps to improve what elementary teachers learn through their program studies in East Asia. By reflecting on teacher preparation practices in the United States, it is not surprising to find very limited course requirements in mathematics for prospective elementary teachers (Li, in press). Given these facts, would it then be a possible solution in the United States to prepare elementary teachers as content specialists? Results from some recent studies suggest that there may not be a simple solution in the U.S. context (e.g., Li, Ma, & Pang, in press; Li & Smith, 2007; Schmidt, Tatto, Bankov, Blomeke, Cedillo, Cogan, et al., 2007).

In a recent study with a limited scale (Li & Smith, 2007), a group of 46 prospective middle school teachers in the United States were surveyed about their own perceptions of their preparation in mathematics and pedagogy and the extent of their knowledge on the topic of fraction division. The results revealed that participating prospective middle school teachers were confident in the preparation they received in mathematics and pedagogy for future teaching careers. For example, in answering the survey question “Considering your training and experience in both mathematics and instruction, how ready do you feel you are to teach the topic of ‘Number - Representing and explaining computations with fractions using words, numbers, or models?’ ” On a scale of three ratings (Very ready; Ready; Not ready), 60% of the participants thought they were ‘ready’, while 38% chose ‘very ready’ and 2% ‘not ready.’ However, these participating teachers seemed to have limited knowledge in mathematics and pedagogy for teaching. For example, only 59% of these prospective teachers provided a correct answer to the mathematics question, “Tell whether ⁹/₁₁ ²/₃ is greater or less than ⁹/₁₁ ³/₄ without solving. Explain your reasoning.”

The results obtained from this group of U.S. prospective middle school teachers, who were trained more as content specialists, present a different picture in comparison with what we recently learned from prospective elementary teachers sampled in Mainland China and South Korea (Li, Ma, & Pang, in press). For example, for the same survey question presented above, only 12% of 361 participating prospective teachers in China and 6% of 291 those in South Korea thought they were ‘very ready’. 44% Chinese and 70% Korean participants chose ‘ready’, while 44% Chinese and 23% Korean participants perceived ‘not ready.’ In contrast, 94% of these sampled Chinese and 95% of Korean prospective elementary teachers provided a correct answer to the above mathematics question. Thus, although the sampled prospective elementary teachers in Mainland China and South Korea did not have a high confidence in their knowledge preparation, they were actually very good on the selected school mathematics content topic that they will teach.

Because the topic of fraction division in school mathematics is important and also difficult (Li, 2008), the cross-national contrasting results led us to ponder whether the preparation of content specialists in the United States would be an automatic solution. As revealed in U.S. prospective middle school teachers' performance on the mathematics test (Li & Smith, 2007), the sampled prospective teachers had many difficulties with fraction division. With the high confidence in the preparation they received, these prospective teachers did not even realize that they have deficiencies in their mathematical preparation. As teaching mathematics requires a special set of skills (Viadero, 2004), it becomes necessary for U.S. teacher educators to identify what knowledge in mathematics and pedagogy prospective teachers need to learn through their program study, which may be even more important than simply thinking to change elementary teacher preparation program from preparing generalists to content specialists.

Efforts to provide a better preparation program for prospective mathematics teachers have also led to large-scale international collaborations recently, to investigate what prospective teachers learn as an outcome of their program studies. The project of Mathematics Teaching in the 21st Century (MT21) is such an effort to examine and pursue better teacher education in the international context (see, Schmidt et al., 2007). By focusing on middle school teacher preparation in six education systems (Chinese Taipei, South Korea, Bulgaria, Germany, Mexico and the United States), MT21 study revealed many more cross-system variations than similarities in prospective teachers' course taking, knowledge of mathematics and mathematics pedagogy, and beliefs about mathematics at the end of their program studies. Based on the study's findings, the researchers indicated that there is a preparation gap in middle school mathematics teacher preparation between the United States and two education systems in East Asia (i.e., Chinese Taipei and South Korea). In particular, the researchers pointed out that the preparation of prospective teachers in the United States lag behind in the amount of emphasis given to mathematics and mathematics pedagogy, as compared to the practices in these two Asian education systems.

Another lesson that we may learn from teacher preparation practices in East Asia (Li, in press; Li, Ma, & Pang, in press) is to align the program study for teacher preparation with what teachers will be expected to teach in schools in the future. Back into the U.S. context, it can be suggested that the preparation of elementary teachers should be aligned with what elementary teachers will be assigned to teach. Thus, a shift in mathematical preparation of elementary teachers from generalists to content specialists would ideally require the systematic changes in teachers' instruction responsibility as well in the U.S. elementary schools.

References

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