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…

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 presents a teaching experiment in which second-grade primary school students compared a city and a town according to population estimates. The activities were presented to them as Fermi problems and required an analysis of the reality to identify sub-problems that students could deal with. The students' products were analyzed from the…

In this study, we aim to explain choices that groups of preservice teachers made to implement modelling tasks in primary school. We found that the preservice teachers decided to facilitate everyday-inspired contexts for the tasks and that this could be explained by their reasoning that modelling is supposed to be an activity close to reality.…

Fermi problems are useful for introducing modelling in primary school classrooms, although teachers' difficulties in problem solving may hinder their successful implementation. These difficulties are associated with the modelling process, but also with the estimation and measurement skills required by Fermi problems. In this work, a specific…

This study explored how students develop meaning of functions by building on their understanding of expressions and equations. A teaching experiment using design research was conducted in a sixth-grade classroom. The data was analyzed using a grounded theory approach to provide explanations about why events occurred within this teaching episode…

Linear quantity models such as pre-tapes, tape diagrams, and number line diagrams have drawn increasing attention in mathematics education around the world. However, we still know relatively little about how teachers actually use these models in the classroom. This study explores how exemplary US and Chinese elementary teachers use linear quantity…

Mathematical modeling is an important and accessible process for elementary school students because it allows them to use mathematics to engage with the world and consider if and when to use it to help them reason about a situation. It fosters productive struggle and twenty-first-century skills that will aid them throughout their lifetime.

This study was designed to examine predictors of instructional beliefs related to problem solving that influence mathematics in-service teachers' practices in the Chilean context. A total of 713 in-service mathematics teachers from various elementary schools participated in the survey study during 2015 and 2016. Results showed that teachers'…

Mathematical relationships are crucial elements to consider for learning mathematics. However, too often students pay more attention to the calculations to be done rather than the reasons for doing them. Relying on the relational paradigm to support elementary school students, we proposed two specially designed tasks to help students recognize and…

Previous studies have repeatedly shown that children often incorrectly use an additive model for multiplicative word problems, and a multiplicative model for additive word problems. The present study aimed to investigate which model upper primary school children tend to choose in word problems that are open to "both" ways of reasoning.…

Whole number arithmetic is the foundation of higher mathematics and a core part of elementary mathematics. Awareness of pattern and underlying problem structure promote the learning of whole number arithmetic. A growing consensus has emerged on the necessity to provide students with the opportunity to engage in algebraic reasoning earlier in their…

Many teachers are using the Five Practices model to guide them in orchestrating whole-class mathematics discussions that focus on understanding: (1) anticipate an array of possible student-generated solution strategies to a mathematical task before implementing the lesson; (2) monitor students' work as they grapple with the task; (3) select a…

Tape diagrams, also known as strip diagrams, bar models, fraction strips, or length models, are linear representations that can be used to effectively model quantitative relationships during problem solving. Tape diagrams are a powerful model recommended by the Common Core, but they are relatively new to teachers and students in the United States.…