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),…

We explored the mediating role of prior knowledge on the relation between intelligence and learning proportional reasoning. What students gain from formal instruction may depend on their intelligence, as well as on prior encounters with proportional concepts. We investigated whether a basic curriculum unit on the concept of density promoted…

This paper reports on a design-based study within the context of a 3-day "digital making" (DM) summer camp attended by a group of students (aged 11-13) in grades 5 and 6. During the camp, students were presented with a set of mathematical problems to solve in a block-based programming environment, which was connected to various physical…

We investigated the effect of emphasising the realistic modelling complexity in text or in the accompanying picture on the solution of P-items, in relation to pupils' grade. 290 pupils from the 5th and 6th grade of various elementary schools in Flanders (Belgium) made a paper-and-pencil task with 7 word problems that are problematic from a…

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…

This study investigates the participation and knowledge growth of children with mathematical difficulties as they work in groups with their classmates on a year-long sequence of modelling tasks. It involves observations of a class of 23 fifth graders, 9 of whom were identified as having difficulties in mathematics. All the students worked for 8…

This article presents the Snail problem, a relatively simple challenge about motion that offers engaging extensions involving the notion of infinity. It encourages students in grades 5-9 to connect mathematics learning to logic, history, and philosophy through analyzing the problem, making sense of quantitative relationships, and modeling with…

A study conducted with 25 Year 6 primary school students investigated the potential for a short classroom intervention to begin the development of a "Modelling" conception of mathematics on the way to developing a sense of mathematics as a way of thinking about life. The study documents the developmental roots of the cognitive activity,…

The aim of this study was to investigate the use of the "dual mathematical modelling cycle framework" as one way to meet the espoused goals of the Australian Curriculum Mathematics. This study involved 23 Year 6 students from one Australian primary school who engaged in an "Oil Tank Task" that required them to develop two…

We confronted 151, 5th and 6th elementary grade pupils with a quantitative problem in a mathematics or religion class, to examine the influence of the context on pupils' understanding and solution of such problems inside and outside the mathematics class. Pupils were first asked to solve a problem about fair sharing either during a mathematics or…

The study explored the effects of a computer-assisted COnceptual Model-based Problem-Solving (COMPS) program on multiplicative word-problem-solving performance of students with learning disabilities or difficulties. The COMPS program emphasizes mathematical modeling with algebraic expressions of relations. Participants were eight fourth and fifth…

Previous research has shown that when confronted with missing-value word problems, primary school students strongly tend to use proportional solution approaches, even if these approaches are inappropriate. The authors investigated whether (besides the missing-value formulation of word problems) the numbers appearing in word problems are part of…

The authors explored the effects of teaching conceptual model-based problem-solving instruction on students' ability to solve problems in various situations. Participants were 3 4th-and 5th-grade students with or at risk for mathematics disabilities. The authors used an adapted multiple-probe across-participants design to assess the functional…

Interventions that aim to promote social competence, reduce problem behavior, and improve school climate are common at all levels of schooling. This whole-school focus, coupled with researchers' concerns about contamination or spillover effects in evaluations that randomly assign classrooms or students to conditions, as well as advances in…

To examine how conceptual knowledge about fraction magnitudes changes as students' learning progresses, 5th and 7th-grade students were asked to solve fraction magnitude problems that entailed finding a fraction between two given fractions and then to evaluate solutions for similar problems that were modeled for them. When the given fractions…