The mostly reported students’ mista

The mostly reported students’ mistakes while learning linear measurement are as follows: (a) starting from 1 rather than 0 (e.g. Ellis & Siegler, 1995; Lehrer, Jacobson, Thoyre, Kemeny, Strom, Horvath, Gance et al., 1998a), (b) iterating units by leaving gaps or overlapping units (e.g. Lehrer, Jacobson, Kemeny & Strom, 1999; Hiebert, 1981), (c) incorrect alignment with a ruler (e.g. Stephan & Clements, 2003; Bragg & Outhred, 2000), (d) counting hash marks or numbers on a ruler/scale instead of LENGTH MEASUREMENT IN THE TURKISH MATHEMATICS CURRICULUM intervals (e.g. Stephan & Clements, 2003; Bragg & Outhred, 2000; Boulton-Lewis, Wilss & Mutch, 1996), (e) focusing on end point while measuring with a ruler (e.g. Lehrer, 2003; Bragg & Outhred, 2000), (f) mixing units of length with other units of measurement (e.g. Szilagyi, 2007), and (g) confusing the concept of perimeter with area (Kidman and Cooper, 1997; Tan-Sisman & Aksu, 2009). Furthermore, Smith, Tan-Sisman, Figueras, Lee, Dietiker & Lehrer (2008a) and Smith, Tan-Sisman, Dietiker, Figueras, Males, Lee, Mosier et al. (2008b) identified the six factors associated with the students’ weak learning of measurement as given in Figure 2. All of these factors either directly or interactively affect students’ learning of spatial measurement. Considering the fact that a written curriculum includes at least three answers for the questions of “what should be taught, how it should be taught, how it should be evaluated?,” there is a close and clear relationship between what students learn and how a curriculum organized in terms of learning objectives, content, implementation, and assessment process. Emphasizing on the relationship between students’ learning and a mathematics curriculum, the National Council of Teachers of Mathematics’ (NCTM) document entitled Principles and Standards for School Mathematics (2000) states that “A school mathematics curriculum is a strong determinant of what students have an opportunity to learn and what they do learn.” (p. 15). In this respect, a well-developed curriculum may improve students’ mathematical understanding. For instance, Lehrer et al. (1998a) and Lehrer, Jenkins & Osana (1998b) conducted teaching experiments to investigate elementary students’ understanding of geometry and space. The results indicated that in a well-designed learning environment, students went beyond procedural competence to understand the underpinnings of measurement.