The following study shows how reparameterizations and constraints of the general linear model can serve to parse quantitative and qualitative aspects of predictors. We demonstrate three different approaches. The study uses data from the High School Longitudinal Study of 2009 on mathematics course-taking and achievement as an example. Results show…

According to expectancy-value models, two important motivational constructs are task value and self-efficacy expectations. As students work intensively on mathematical problems in the classroom, teachers need the competence to judge whether students value solving the problem and how confident they are that they will succeed. However, not much is…

Pedagogical strategies for nurturing group creativity in school mathematics have remained largely unexplored despite their significance. In this study, we explored the use of role playing in mathematical modeling activities for nurturing group creativity in a 9th-grade mathematics class in Korea. We described the theoretical bases and types of…

To solve mathematical modelling problems, students must translate real-world situations, which are typically presented in text form, into mathematical models. To complete the translation process, the problem-solver must first understand the real-world situation. Therefore, reading comprehension can be considered an essential part of solving…

We investigated how students' strategic knowledge about situational (pictorial) drawings and mathematical (schematic) drawings affects drawing accuracy and modeling competencies in the domain of geometry. We conducted a pre-posttest experimental study with 473 students in grade 9. Students were randomly assigned to one of three treatment…

Mathematical modeling is a challenging and creative process. If one considers only interim or final solutions to modeling problems or interviews modelers afterward, often only their "explicit" models are accessible -- those expressed in work products or evinced in verbal and written reflections. The inner world of tacit knowledge and its…

Metacognitive competencies are of great importance for developing modelling competencies. However, there are assumptions about useful metacognitive knowledge and strategies for individuals working on modelling problems as well as for whole groups, but their coherence as well as their influence on modelling processes is not evaluated…

This article describes a modeling project the author did with his algebra, geometry, and applications students in grades 9, 10, and 11 as an enrichment and exploration of an extremely relevant real-world phenomenon and introduction to the adult profession of epidemiologist. With discussion and exploration, this project consumed two periods of 88…

Posing modelling problems in class is supposed to increase students' motivation. As motivation is assumed to emerge from task value and self-efficacy expectations, the present study considered both constructs with the aims to examine (1) whether students have different values and self-efficacy expectations concerning modelling problems versus…

One hundred four students aged 8 to 16 worked on one Fermi problem involving estimating the number of people that can fit in their school playground. We present a qualitative analysis of the different mathematical models developed by the students. The analysis of the students' written productions is based on the identification of the model of…

Based on a teaching intervention with modelling activities involving experimental work in 9th grade classes, the goal of this study is to find out how students estimate the credibility a modelling task setting when it integrates a hands-on experimental approach. The theoretical background is based on the concept of authenticity and its long…

Why are math modeling problems the source of such frustration for students and teachers? The conceptual understanding that students have when engaging with a math modeling problem varies greatly. They need opportunities to make their own assumptions and design the mathematics to fit these assumptions (CCSSI 2010). Making these assumptions is part…

This mixed methods study examined an association between cognitive types of teachers' mathematical content knowledge and students' performance in lower secondary schools (grades 5 through 9). Teachers (N = 90) completed the Teacher Content Knowledge Survey (TCKS), which consisted of items measuring different cognitive types of teacher knowledge.…

This study came to characterize the features of mathematical models built by mathematics pre-service teachers for a model eliciting activity. Fourteen groups participated in building the models. We used a combination of deductive and inductive content analysis to characterize the pre-service teachers' elicited models, taking into account features…

In the subject matter of functional relationships, a student's ability to translate from one form of representation to another is seen as a central competence. In the course of the HEUREKO project (heuristic work with representations of functional relationships and the diagnosis of mathematical competencies of students), a theoretical competence…