With the discussions on the nature of mathematics, mathematics is regarded as a value laden area. That it contains a wide range of values has led to consideration of new approaches in classroom practices. The modelling approach which also includes traditional problem solving is consistent with different values of mathematics. With the recognition of mathematics that has different values with the traditional values, mathematics teacher training programs need to be addressed again. It has been intended to contribute the implementation of the program by examining the profiles of prospective mathematics teachers in the current state and the views for modelling. The profiles and modelling levels of 136 prospective mathematics teachers who study in mathematics teacher training programme at Abant Izzet Baysal University in 2008-2009 and 2009-2010 academic years have been analyzed. When the participants' levels of having positivist values and levels of having constructivist values were compared, a significant difference was determined in favor of constructivist values. When the values were analyzed in terms of gender variable, the female participants' levels of having constructivist and positivist values showed a significant difference in favor of constructivist values. Modelling levels were examined in different dimensions, and it was determined significant differences between sub-dimensions. In terms of gender variable, when sub-dimensions of each modelling levels were analyzed, there was no significant difference between female and male prospective mathematics teachers. Also, there was a positive correlation between values and modelling levels among prospective mathematics teachers.
Values in Mathematics, Constructivist Value, Positivist Value, Modelling, Prospective Mathematics Teachers.
Although mathematics and mathematics teaching are different study fields, the nature of mathematics and application of mathematics to mathematics teaching are inseparable complements. Mathematics just like many other fields interacts with social sciences such as psychology, sociology, and philosophy (Bishop, 2000). In addition, there are many examples of these interactions in the history of mathematics (Davis & Hersh, 2002). This new perspective on the nature of mathematics requires us to reconsider teaching mathematics (Ernest, 2007). In this context, two points are raised as the starting point of this study: Values in mathematics and modelling approach. Whereas values are about what is attached importance to in teaching mathematics, modelling is about how to approach teaching mathematics.
Values in Mathematics Education
While beliefs are mostly about true/false kinds of views and judgments, values correspond to significant/ insignificant kinds of views and judgments (Chin & Lin, 2001; Jorgensen & Ryan, 2004; Seah, Bishop, FitzSimons, & Clarkson, 2001). Values directly affect learning (Gedik, 2010). Hence, values should be taken into consideration in mathematics (Matthews, 2001). Indisputability of corollaries in mathematics is related to assumptions (axiom and series of theorems based on it) which are made during the process. This leads to the acceptance of them in terms of values (in an unquestionable way). However, when the values such as accuracy and fallibilism are investigated in the context of mathematics, it can be concluded that it is similar to the results in social sciences (Bishop & Clarkson, 1998; Bishop & Seah, 2002; Ernest, 1998, 2004; Glas, 1998). The accuracy of mathematical knowledge together with fallibilism calls forth questioning common knowledge in mathematics. Thus, the research on the nature of mathematics is directed towards this subject (Baki, 2008; Bishop, 2000; Brown, 1999; Chin & Lin, 2001; Dede, 2010; Ernest, 1998, 2004; FitzSimons, Bishop, Seah, & Clarkson, 1999; Glas, 1998; Seah, Bishop, FitzSimons, & Clarkson, 2001). …