This study aimed to explore preservice elementary teachers' use of a bar model as a heuristic for conceptualising relationships between quantities in situations involving ratio and percentages. As a part of a larger project, we focused on two preservice teachers, Maia and Jane, and investigated their solution paths in ratio and percentage problems…

The mathematical modeling process is also a powerful way to teach students the meaning of data. In mathematical modeling, students are collecting data to answer a question. Data collection is the means to an end and not the end in itself. The author was looking for an engaging way to introduce his third-grade mathematics class to the skill of…

This paper contributes to accumulating the knowledge base about prospective elementary school teachers' (PTs') understanding of socio-critical modeling by exploring how PTs make connections to features of mathematical modeling and social justice while posing mathematical problems and reflecting on their problem-posing. We present a conceptual…

Previous research has highlighted the importance of social relationships in mathematical group work while working on modelling activities. This study analyses the interaction of sixth-grade students in Primary Education (11 to 12 years old) carrying out a modelling task in groups with a Fermi problem used as the modelling activity. The focus of…

When teaching fractions, teachers make instructional decisions about if, when, and how to use the many different types of fraction models and manipulatives. In this study, we sought insights into their pedagogical reasoning with fraction representations via their preferences, both for solving tasks themselves and for teaching (in general and for…

Using mathematical modelling to solve problems appears in all year levels in the Australian Curriculum: Mathematics (v. 9), and is probably the most authentic way of teaching mathematics in context. However, the term mathematical modelling, even if familiar to teachers, may not be well understood or enacted confidently by teachers in their…

The revised Australian curriculum presents a new emphasis in primary schools on the process of Mathematical Modelling. A modelling focus brings close attention to confidence and capability with a potentially new problem-solving process, associated language, and pedagogical processes. This paper presents a Year 4 classroom modelling experience that…

Studies have found that some teacher professional development programs that are based on Cognitively Guided Instruction (CGI) can increase student mathematics achievement. The mechanism through which those effects are realized has been theorized, but more empirical study is needed. In service of this need, we designed a novel measure of…

This study aims to reveal how model eliciting principles are used in the process of designing, applying, and evaluating teacher candidates' model-eliciting activities. This study was conducted in three stages in a multi-tiered teaching experiment. Firstly, 15 teacher candidates designed activities for Grade 7 students after they were trained on…

This study examined whether learning with heuristic worked examples can improve students' competency in solving reality-based tasks in mathematics (mathematical modeling competency). We randomly assigned 134 students in Grade 5 and 180 students in Grade 7 to one of three conditions: control condition (students worked on reality-based tasks),…

This research was performed as a single group pretest-posttest experimental design to determine the effect of mathematical modeling instruction on pre-service primary school teachers' (PPSTs) problem-solving skills and attitudes towards mathematics. Based on an online intervention due to the pandemic, the study involved 12 PPSTs who participated…

Connections among the mathematics, science, and engineering disciplines have been recognized and affirmed in national standards. For example, the application of mathematical ideas and skills within science has been highlighted in national science standards for over 20 years. More recently, the Next Generation Science Standards (NGSS; NGSS Lead…

This study aimed to examine the collective mathematical creativity of gifted middle school students within a group through model-eliciting activities. The current study employed the case study design. The participating four gifted students were selected through the purposive sampling technique. To examine the collective creativity of the students…

In this paper the results of a questionnaire about mathematics teachers' inclusion in their teaching of mathematical modelling and problem posing are presented. To make teachers able to choose a coherent teaching method for a mathematical topic, teachers' knowledge of valuable methods for the teaching of mathematics should be fostered. In this…

Engagement in complex, challenging and multifaceted model-eliciting activities is considered helpful for preparing learners for everyday life. The current study seeks to trace the evolution of modelling routines during two model-eliciting activities. To identify how these routines emerged and evolved, we video-recorded a group of five prospective…