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…

The paper deals with the question of the practicability and the effectiveness of different approaches to foster students' mathematical modelling competencies. Within the modelling project ERMO (Acquirement of modelling competencies) a holistic and an atomistic approach of mathematical modelling were compared in order to find out which approach is…

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…

Empirical findings show that students have manifold difficulties when dealing with mathematical modeling problems. Accordingly, approaches for supporting students in modeling-based learning environments have to be investigated. In the research presented here, we adopted a scaffolding perspective on teaching modeling with the aim of both providing…

This study presents a content analysis of the new Iranian Grade 9 mathematics textbook and two Australian Year 9 mathematics textbooks, examining the extent to which the problems show characteristics associated in the literature with promoting mathematical literacy. The new Iranian book was produced to meet a range of needs including several well…

The chart of Indonesian student of mathematical ability development in Program for International Student Assessment (PISA) event during the last 4 periods shows an unstable movement. PISA aims to examine the ability of children aged 15 years in reading literacy, mathematics literacy, and science literacy. The concept of mathematical literacy is…

This paper describes the ideas that mathematics teachers (grades 5-9) have regarding mathematical models of real-world phenomena, and explores how teachers' ideas differ depending on their educational background. Participants were 56 United States in-service mathematics teachers. We analyzed teachers' written responses to three open-ended…

In a study with ninth-grade mathematics students on learning the concept of variance, students experienced either direct instruction (DI) or productive failure (PF), wherein they were first asked to generate a quantitative index for variance without any guidance before receiving DI on the concept. Whereas DI students relied only on the canonical…

This paper discusses the implementation of the Tri-Squared Test as an advanced statistical measure used to verify and validate the research outcomes. This type of statistical measure is ideal for teachers professional development as educators can create and validate instruments for educational settings. The initial research investigation published…

Considerable evidence indicates that student motivation and use of learning strategies are related. There is insufficient understanding, however, about their reciprocal effects--whether motivation affects strategy use, the converse, or whether the effects are bidirectional--and which components of motivation and strategies are involved. A two-wave…

In the present study, I examine a modelling strategy as employed by a teacher in the context of an algebra lesson. The actions of this teacher suggest that a modelling approach will have a greater impact on enriching student learning if we do not lose sight of the need to manage associated cognitive loads that could either aid or hinder the…