Decimals are alternative representations of rational numbers where each rational number can be written as a decimal. The importance of decimals in the mathematics curriculum is emphasized while using calculators and understanding metric measures (Thipkong & Davis, 1991). Besides, decimals are widely used in daily life and are critical for students’ pre-algebraic readiness for learning further mathematic skills (NCTM, 2000). In Turkish national middle school mathematics curriculum (MoNE, 2013), decimals have an important place through different grade levels. While students are expected to learn to order decimals, place decimals on number line and perform operations (addition and subtraction) with decimals in the 5^th grade, they are expected to decompose decimals and perform operations (multiplication and division) in 6^th grade.

While curricula put significant emphasis on decimals, research studies showed that students have difficulties with decimals based on their overgeneralization of whole number properties (Brown, 1981; Roche & Clarke, 2004; Wearne & Kouba, 2000). Misconceptions and difficulties with decimals are not only observed in students, but also in samples of prospective teachers (Widjaja, Stacey, Steinle, 2008). The research studies present that prospective teachers have difficulties with decimal numeration (Putt, 1995; Stacey, Helme, Steinle, Baturo, Irwin, & Bana, 2001; Thipkong & Davis, 1991), in identifying decimals between two decimals (Widjaja, Stacey & Steinle, 2008), with operations in decimals word problems (Graeber & Tirosh, 1988). However, there were limited number of studies that focus on prospective teachers’ solution strategies while working with decimal. Investigation of solution strategies would give valuable information on prospective teachers’ understanding on decimals and highlight the points that they have difficulty with.

Considering this importance, we focused on the subject matter knowledge (SMK) of prospective middle school mathematics teachers in the domain of multiplication with decimals. SMK is the knowledge that involves categories related with content knowledge that is vital in teachers’ mathematical knowledge for teaching (Hill, Ball & Schilling, 2008; Shulman, 1986). The category that is specific to teaching task is named as specialized content knowledge (SCK) and SCK includes “providing explanation for mathematical explanations for common rues and explanations” (Hill et al., 2008, p. 378). That is, teachers’ SCK shows their profound and connected understanding of school mathematics. We considered the mathematical knowledge for teaching framework (Hill et al., 2008) while performing the items in a written test of decimals and analyzing the outcome. Specifically, it was decided to investigate prospective teachers’ strategies of placing the decimal point and characteristics of their strategies about the placing the decimal point.  In this regard, the following research questions were determined:

What are the prospective middle school mathematics teachers’ strategies of placing the decimal point in the multiplication of two decimals?

What are the characteristics of prospective middle school mathematics teachers’ strategies of placing the decimal point in the multiplication of two decimals?

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