Students who are adept in modeling with mathematics have the capability to use mathematics in situations that arise in everyday life. The German Tank problem described in this article created the expectation that student reasoning was rooted in logical deductions (NCTM 2000). By engaging in this problem, students grappled with challenging…

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.…

Word problems have been well recognised for their pedagogical value in mathematics teaching and learning. The authors of this paper examined Fijian primary mathematics teachers' mathematical knowledge by analysing 34 teachers response to three word problems. The teachers were enrolled in a primary mathematics teaching methods course at a Fijian…

Pupils' difficulties in solving word problems continue to attract attention: while researchers highlight the importance of relational reasoning and modelling, school curricula typically use short word problems to develop pupils' knowledge of arithmetic operations and calculation strategies. The Relational Paradigm attributes the leading role in…

The solving of structured multi-step word problems has been a dominant practice in schools and is seen as a way to develop students' mathematical reasoning abilities. Unfortunately, it is limited in scope and does not provide opportunities for eliciting deeper reasoning as they are neither rich enough nor anchored in authentic data that resemble…

Many current and future teachers have little experience with modeling and how to integrate it into their teaching. However, with the introduction of the Common Core State Standards for Mathematics (CCSSM) and its emphasis on mathematical modeling in all grades (CCSSI 2010), this integration has become paramount. Therefore, middle-grades teachers…

In an innovative, progressive school, students were asked to solve a fairly routine mathematical problem using real money in a "real-world" scenario. Even though the school values students' ideas, the reaction of the teacher to one student's alternative modelling of the problem suggests that he was expecting a particular answer to be…

For many students, making connections between mathematical ideas and the real world is one of the most intriguing and rewarding aspects of the study of mathematics. In the Common Core State Standards for Mathematics (CCSSI 2010), mathematical modeling is highlighted as a mathematical practice standard for all grades. To engage in mathematical…

This paper analyzes the quantitative and situational structure of algebra story problems, uses these materials to propose an interpretive framework for written problem soving protocols, and then presents an exploratory study of the episodic structure of algebra story problem solving in a sizable group of mathematically competent subjects. Analyses…

An individualized project is introduced to accompany a differential equations course with different modules ranging from standard to advanced levels with "Matlab" scripts. (Contains 1 figure.)

This document contains the fifth volume of the proceedings of the 30th Conference of the International Group for the Psychology of Mathematics Education. Conference presentations are centered around the theme "Mathematics at the Centre." This volume features 59 research reports by presenters with last names beginning between Sac and Zaz:…

This volume of the 30th annual proceedings of the International Group for the Psychology of Mathematics Education conference presents: plenary panel papers; research forum papers; short oral communication papers; and poster presentation papers from the meeting. Information relating to discussion groups and working sessions is also provided.…