The reforms in mathematics education require teachers to teach in ways that many of them did not experience when learning mathematics in school or learning how to teach mathematics during their teacher preparation programs. The reform methods for teaching mathematics emphasize teaching mathematics for understanding rather than having students memorize rules or just use given procedures to solve tasks. Additionally, these instructional methods stress the use of open-ended tasks and real life situations, problem solving, and encouraging collaboration through small and whole group discussions (Boaler, 2002; Boaler, 2008; Common Core State Standards Initiative, 2010; National Council of Teachers of Mathematics., 2000). These reform approaches
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Pedagogical content knowledge is the knowledge of “representing and formulating the subject matter to make it comprehensible to others” (Shulman, 1986, p. 9). In other words, PCK comprises knowing the subject matter and how to teach it. Shulman described PCK to include the representation of ideas and the use of metaphors, analogies, and strategies that teachers draw on to make learning accessible to students (1986, 1987). Additionally, the PCK component is being able to anticipate the errors, conceptions, and misconceptions that students could have in the learning process (Shulman, 1986). Dewey (1902) used the term “psychologizing” the curriculum or transforming it to suit the child’s level. That is, transforming the subject matter in a way that is familiar and appealing to the students (Dewey, …show more content…
The studies done on OTL to teach mathematics cross-nationally use the MT21 and TEDS-M data. The studies mainly focused on time spent in teacher preparation, topics covered, practical experiences, and instructional time. Schmidt and colleagues (2011) reported the different foci taken by teacher preparation programs across contexts. In particular, they found that teacher preparation programs in the United States had a wide variation in course taking patterns within and between institutions, with a particular emphasis on general pedagogy and fewer formal mathematics courses. Further, the higher achieving countries such as Taiwan took more formal mathematics courses. The previous studies on OTL from the TEDS-M data showed a course-taking pattern that differed by country contexts, program type, and content area. That is, specialist programs covered more tertiary mathematics topics (see Tatto et al., 2012; Blömeke & Kaiser, 2014). Additionally, the topical area most PSTs focused on was Numbers, while Calculus was the least studied. Additionally, studying of school mathematics and tertiary mathematics varied across the countries, but teaching methods was found to be common (Blömeke & Kaiser, 2014). In sum, the foci of the OTL documented are on course taking patterns of various levels of mathematics and mathematics methods. Missing from these studies is the extent of OTL mathematics teaching for conceptual understanding; an important component for
Pedagogical content knowledge is the knowledge of “representing and formulating the subject matter to make it comprehensible to others” (Shulman, 1986, p. 9). In other words, PCK comprises knowing the subject matter and how to teach it. Shulman described PCK to include the representation of ideas and the use of metaphors, analogies, and strategies that teachers draw on to make learning accessible to students (1986, 1987). Additionally, the PCK component is being able to anticipate the errors, conceptions, and misconceptions that students could have in the learning process (Shulman, 1986). Dewey (1902) used the term “psychologizing” the curriculum or transforming it to suit the child’s level. That is, transforming the subject matter in a way that is familiar and appealing to the students (Dewey, …show more content…
The studies done on OTL to teach mathematics cross-nationally use the MT21 and TEDS-M data. The studies mainly focused on time spent in teacher preparation, topics covered, practical experiences, and instructional time. Schmidt and colleagues (2011) reported the different foci taken by teacher preparation programs across contexts. In particular, they found that teacher preparation programs in the United States had a wide variation in course taking patterns within and between institutions, with a particular emphasis on general pedagogy and fewer formal mathematics courses. Further, the higher achieving countries such as Taiwan took more formal mathematics courses. The previous studies on OTL from the TEDS-M data showed a course-taking pattern that differed by country contexts, program type, and content area. That is, specialist programs covered more tertiary mathematics topics (see Tatto et al., 2012; Blömeke & Kaiser, 2014). Additionally, the topical area most PSTs focused on was Numbers, while Calculus was the least studied. Additionally, studying of school mathematics and tertiary mathematics varied across the countries, but teaching methods was found to be common (Blömeke & Kaiser, 2014). In sum, the foci of the OTL documented are on course taking patterns of various levels of mathematics and mathematics methods. Missing from these studies is the extent of OTL mathematics teaching for conceptual understanding; an important component for