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After the publication of Hiebert’s edited book (1986), Mathematical knowledge had been recognized mostly in the form of conceptual and procedural knowledge (Putnam, 1986). Conceptual knowledge is connected web of knowledge and rich in relationships; procedural knowledge is composed of both the knowledge of mathematical symbols and the knowledge of algorithms or procedures that “step-by-step instructions that prescribe how to complete tasks” (Putnam, 1986). A bulk of research and theory in cognitive science supports the notions that deep understanding depends on how well a learner represents and connects bits of knowledge (Kilparick, Swafford & Findell, 2001). Success in mathematics, furthermore, relies mostly on how learners internalize the meaning related to a procedure they are learning or a concept that is being taught and connections made between them (Gulcin & Meral, 2015).
Several research studies have pointed out that most of the teachers prefer to introduce concepts of measurement via formulae instead of using students’ conceptions of space and measurement (Smith, 2007; Thompson, Philipp, Thompson & Boyd, 1994). According to Gulcin & Meral’s study (2015), the findings of the current study clearly Indicated that the students could not be able to make sense of the foundational principle behind volume measurement which requires more complex reasoning about the structure of space than measuring two- or one-dimensional regions. In addition, lack of spatial visualization and of meaningful enumeration of arrays of cubes as well as poor understanding in length and area measurement might be the reasons behind the several errors of the students in volume measurement (Gulcin & Meral, 2015). It is particularly significant in learning compound cube surface area. Accordingly, it is essential to build a bridge which connected concepts of measurement and procedure of measurement. Besides it, this bridge play multiple roles such as scaffolding for spatial visualization and procedure meaning of measurement, and assistance of Inquiry Learning. Further, traditional schoolbooks do not represent the source of actual knowledge whereas creation of electronic manuals often becomes a “wrapping “ of old content in a new form (Sergey, Fedor, Pavel, & Pavel, 2015) . Manipulating physical cubes or blocks is considered as the best way for students on learning spatial concepts due to children's development stages, but sometimes it appeared to form influence in comprehending relationship between lines and surfaces because of the real-object physical property. For example, the activity regarding partitioning the compound-body to regular ones may be a loading task for students and it would result in miscounting on following work regarding measuring the length of relative lines. Augmented reality (abbreviated AR) is between real and virtual environment closer to real. It could not only provide students the visualization and interactivity of real-objects by virtual objects, but also the convenient access in anytime and anywhere. It could assist students in reducing the above-mentioned loading or miscounting. Besides, ARis a technology that augments or superimposes a real time image of the real world with either two (2D) or three-dimension (3D) Computer Generated (CG) object, allowing users to interact with them (Azuma et all., 2001). Moreover, AR is used more widely now not only because new AR applications are supported by computers and mobile devices (smartphone, tablet PC, etc.) (Wu, Lee, Chang, & Liang, 2013), but also mobile devices with improved hardware properties are available at lower prices as well as so the use of AR technology use not as difficult as it once was (Gervautz & Schmalstieg, 2012; Squire & Klopfer, 2007).