What Is Known about Secondary Grades Mathematical Modelling --A Review <s> Blockages/difficulties During the Modelling Process <s> In a qualitative-orientated empirical study the effect of context on the student's approach towards real world problems is investigated. First results show that contexts given in a task can internally be reconstructed in very different ways. It is also shown that both, the student's affective proximity to the context and the student's real world knowledge can have fostering but also hindering effects on his or her performance. <s> BIB001 </s> What Is Known about Secondary Grades Mathematical Modelling --A Review <s> Blockages/difficulties During the Modelling Process <s> In this article we present, illustrate, test and refine a framework developed by Galbraith, Stillman, Brown and Edwards (2006) for identifying student blockages whilst undertaking modelling tasks during transitions in the modelling process. The framework was developed with 14~15 year old students who were engaging in their first experiences of modelling at the secondary level. <s> BIB002 </s> What Is Known about Secondary Grades Mathematical Modelling --A Review <s> Blockages/difficulties During the Modelling Process <s> The Galbraith, Stillman, Brown, and Edwards Framework (2007) for identifying blockages hindering progress in transitions in the modeling process is applied to a modeling task undertaken by 21 Year 9 students. The Framework identified where challenges occurred; but, because some blockages proved to be more robust than others, another construct “level of intensity” was added. The blockages described here occurred during the formulation phase of the modeling cycle. We infer that blockages induced by lack of reflection, or by incorrect or incomplete knowledge, are different in nature and cognitive demand from those involving the revision of mental schemas (i.e., cognitive dissonance). The nature and intensity of the blockage have consequences for teacher intervention and task implementation. <s> BIB003 </s> What Is Known about Secondary Grades Mathematical Modelling --A Review <s> Blockages/difficulties During the Modelling Process <s> This chapter presents types of mathematical knowledge application during a design-based interdisciplinary project as displayed through the work of student-group cases from grades 7 and 8 (aged 13–14) in two educational streams across three Singapore government secondary schools. It was found that the students did not apply all the expected mathematical knowledge and skills afforded by the project. They also lacked awareness of the purpose of scale and displayed limited activation of real-world knowledge for mathematical decision making. Findings presented have implications on the facilitation of quality mathematical application in contextualised tasks. <s> BIB004
Eight studies looked at difficulties that students can have during the modelling process and found that students might have difficulties at all parts of the modelling process. Galbraith, Stillman, Brown, and Edwards (2007) developed a framework that has 31 general possible blockages between the six modelling steps and was used by BIB003 in their analysis of the shot on goal problem. Using the same problem Stillman (2011) identified five metacognitive responses that students could have when faced with difficulties. Several studies found that if students lacked needed mathematics knowledge it could cause a blockage BIB002 Galbraith et al., 2007; BIB004 . Another frequent blockage was caused by understanding the real world situation BIB001 Galbraith et al., 2007; BIB004 BIB003 . If students do not understand the context and what is being asked then it can be difficult to develop an appropriate model. In addition, the more the consistency with the real world is emphasized the more difficult it can be to solve a problem  . While time may need to be spent ensuring that students have needed background knowledge on the real world context, the real world context also provides motivation for students (Busee & Kaiser, 2003) . Use of technology was found to help students continue through the modelling process (Galbraith et al., 2007) but also a cause of blockage if students are unfamiliar with how to use the technology BIB002 . Duration of the modelling problem can also lead to difficulties. Ng (2011) conducted a case study of one class of 13-14 year old students in Singapore in which the task was to design an environmentally friendly building and create a scale model. The activity lasted 15 class sessions and the researcher found that the students lost motivation and interest in the project. For longer modelling activities, others have suggested allowing students to chose a situation of their own to model. investigated four classes of students age 12 to 15 in Portugal who worked for 4 weeks on group selected projects. She found that the projects were the most frequent topics of conversation between students and their parents about what happens in mathematics class. In the eight studies, MEAs were not used. The structure of MEAs, including the self-assessment principle, and their implementation method, having groups share and discuss their ideas and then time for revision, could help to alleviate difficulties that students can have during the modelling process.