What Is Known about Secondary Grades Mathematical Modelling --A Review <s> Modelling Process/sub-activities <s> This study analyzed the processes used by students when engaged in modeling activities and examined how students' abilities to solve modeling problems changed over time. Two student populations, one experimental and one control group, participated in the study. To examine students' modeling processes, the experimental group participated in an intervention program consisting of a sequence of six modeling activities. To examine students' modeling abilities, the experimental and control groups completed a modeling abilities test on three occasions. Results showed that students' models improved as they worked through the sequence of problem activities and also revealed a number of factors, such as students' grade, experiences with modeling activities, and modeling abilities that influenced their modeling processes. The study proposes a three-dimensional theoretical model for examining students' modeling behavior, with ubsequent implications for the teaching and learning of mathematical problem solving. <s> BIB001 </s> What Is Known about Secondary Grades Mathematical Modelling --A Review <s> Modelling Process/sub-activities <s> This study reports on an experimental teaching program to foster students’ thinking to promote modelling which consisted of nine lessons for Japanese 9 th grade students. In this program, the following three teaching principles were emphasized;(TP1) Conflicting Situations: The teacher presents meaningful conflicting situations arising from particular modelling problem so that students can derive key ideas from these situations, (TP2) Repeated Connections: he teacher makes repeated connections between students’ thinking that promotes modelling and (TP3) Spiral Reflections: The teacher encourages students to reflect on their thinking throughout the series of nine lessons. As a pre- and post-test, the (PISA) Heartbeat problem and a general question on modelling were used before and after the teaching program to examine what transfigurations or shifts in students’ knowledge of modelling can be observed. This general question had the following sub-questions: What processes are required to build up a functional model? What ideas are important for developing an effective functional model? A graduated coding analysis was applied to assess students’ responses to the Specific (Heartbeat) question and to the General question. A graduated coding analysis was applied to assess students’ responses to the Specific (Heartbeat) question and to the General question. Significant gains in students` post-test codes/scores on both questions were obtained. This and the resulting discussion provide strong evidence that a teaching program based on the above three teaching principles is substantially effective in fostering students’ thinking to promote modelling. <s> BIB002 </s> What Is Known about Secondary Grades Mathematical Modelling --A Review <s> Modelling Process/sub-activities <s> With the adoption of the Common Core State Standards for Mathematics (CCSSM), the process of mathematical modeling has been given increased attention in mathematics education. This article reports on a study intended to inform the implementation of modeling in classroom contexts by examining students’ interactions with the process of creating mathematical models and analyzing the types of models so generated. Results indicate students’ tendencies to oversimplify or overcomplicate the modeling process. Implications of the study are discussed, especially for understanding which aspects of the modeling cycle might be most helpful for teachers to focus on in order to develop students’ modeling abilities. <s> BIB003
Overall, across twenty-one studies with different grade levels and in different countries it was found that students are able to work through iterations of the modelling process in order to solve mathematical modelling problems (e.g.  BIB001 . There were two main modelling processes that were used or adapted in the studies: modelling process with description by Borromeo Ferri (2006) and  four step modelling process of description, manipulation, prediction, and verification. Some studies looked at just parts of the modelling process including mathematizing (e.g. and communication (e.g. . The studies also demonstrated that as students gain more experience with mathematical modelling their effectiveness of using the modelling process can improve. MaaB and Mischo (2011) conducted a study of 865 students in Germany with average age of 11.55 years with 45% of the students low SES. The researchers used both an open-ended modelling task and multiple choice questions and found that students scored an average of 1.99 on the modelling steps of the open question and 3.31 on the multiple choice questions with a range of 0 to 5 points. However, before this assessment students had little experience with applications and modelling. In a study with one class of 7 th and one class of 9 th graders in the U.S. BIB003 found that high achieving mathematics students struggled with identifying the most important variables and making assumptions with a problem on deciding the best gas station to buy gas from. In this study students were inexperienced with mathematical modelling. Also, groups could have shared their solution strategies with the rest of the class and been given more support in understanding the real world context. These studies show that mathematical modelling is something that is difficult to be proficient at with little experience and the structure of how activities are implemented is important. Studies have shown that with more experience students can improve in mathematical modelling. BIB002 had thirty-four 9 th graders who selected mathematics as an elective subject complete four modelling tasks over three months time. The researchers found that using a pre and post questionnaire to assess modelling processes that there was a statistically significant difference for setting assumptions, validating and modifying the assumptions, what process is required to solve modelling problems, and what makes a model good.