What Is Known about Secondary Grades Mathematical Modelling --A Review <s> Population <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> Population <s> In this study, we report on an analysis of the mathematization processes of one 6th and one 8th grade group, with emphasis on the similarities and differences between the two groups in solving a modeling problem. Results provide evidence that all students developed the necessary mathematical constructs and processes to actively solve the problem through meaningful problem solving. Eighth graders who were involved in a higher level of understanding the problem presented in the activity employed more sophisticated mathematical concepts and operations, better validated and communicated their results and reached more efficient models. Finally, a reflection on the differences in the diversity and sophistication of the constructed models and mathematization processes between the two groups raises issues regarding the design and implementation of modeling activities in elementary and lower secondary school level. <s> BIB002 </s> What Is Known about Secondary Grades Mathematical Modelling --A Review <s> Population <s> This chapter introduces a long-term modelling project that has been conducted at Goethe-Gymnasium-Germersheim with 14-/15-year-old students. The main question of this project was if (and how) it is possible to integrate real-world modelling tasks into regular math lessons in a way that demands for the application of knowledge from selected topics of a whole school year. Moreover we wanted to know if the pupils accept the intended frequency of five modelling phases as a convenient diversion or if they consider them not worthwhile (concerning the effort)? Finally, we were curious to learn to which extent we can expect pupils to learn mathematical modelling through frequent repetition. The students had to deal with five realistic modelling tasks and one final comparison task. Solutions developed by the students as well as the concept of the questionnaires used for evaluation are presented. <s> BIB003 </s> What Is Known about Secondary Grades Mathematical Modelling --A Review <s> Population <s> Modelling is a mathematical competence and a means of learning significant mathematics. Preliminary findings on the nature of competence and modelling competencies, as well as the development of mathematical modelling competencies of Grade 7 students are presented in this chapter. Twelve students solved three model-eliciting tasks in groups over a period of 12 weeks. The development of competencies is considered across the group as a whole. Analysis of the data shows that modelling competencies are activated and do develop when students take part in well-orchestrated modelling activities. <s> BIB004 </s> What Is Known about Secondary Grades Mathematical Modelling --A Review <s> Population <s> This chapter describes a classroom teaching experiment conducted in three Year 6 classes where the purpose was to induct students into the mathematising of real world tasks. The focus is on whether applications and mathematical modelling are viewed as being outside of mathematics, as an add-on, or as an integral part of mathematics, requiring students and teachers to operate in a “culture of mathematising as a practice” (Bauersfeld 1993 cited in Yackel and Cobb J Res Math Educ 27(4):459, 1996). Two tasks were used. In one task student mathematising was quite superficial. The second task, introduced with an explicit focus on modelling, resulted in more in-depth mathematising but students still stalled in the modelling process. <s> BIB005 </s> What Is Known about Secondary Grades Mathematical Modelling --A Review <s> Population <s> Nature and the constructed world in which students live have provided suitable sources of tasks for junior high school students in the past. The decreasing number of bluefin tuna was considered another appropriate context. Students were asked to provide a mathematical solution to this problem, utilising data on the number of bluefin and the catch of bluefin in the past. Three different mathematical approaches, appropriate to the educational level of the students involved, were taken to considering the decline in bluefin tuna. Year 7 students used a proportional model, Year 8 students used linear function models, and in Year 9 students used recurring formula models. Each set of models was appropriate to the mathematics in the curricula at the level. The aim of this mathematical modelling activity was to develop people with the skills to lead the way in our society. <s> BIB006
The population of the studies varied, as well as the ages of the students and the number of students. The studies represented a good mix of ages and sample sizes though. The studies were done in a number of countries. The number of studies per country is as follows: Germany (19), USA (12), Australia (11), Sweden (5), Japan (4), Cyprus (4), Singapore (4), Portugal (2), Denmark (2), South Korea (1), South Africa (1), Brazil (1), Albania (1), Canada (1), and Spain (1). Student demographics or school setting information was also provided in the studies. Twenty-two studies gave the number of male and female students. In twelve of the studies students had little experience with applications and modelling and in six of the studies students had prior experience with mathematical modelling. Thirteen of the studies involved high mathematics ability students, three studies involved mixed ability students, three studies average ability students, and four studies with low ability students. Nine studies were done in urban locations, two with low Social Economic Status (SES) students, two with medium SES students, two in a suburban location, and two in a rural location. Fewer studies used these characteristics in their analysis. There were three studies that looked at gender in their analysis BIB003 BIB005 . There was one study that compared the solutions of high and low mathematics achieving students BIB004 and one study that compared a treatment group of medium mathematics ability students with a control group of high mathematics ability students (Dunne & Galbraith, 2003) . Four studies also compared students based on different grade levels BIB001 BIB002 BIB006 .