The aim of this study is to explore the possibility of introducing the general notions of function and inverse function through a mathematical activity on linear functions, focusing on the quantitative meaning associated to the connection between a relation and its inverse. We present a genetic decomposition, that is, a viable cognitive path for…

Children's word problem competence is a major determinant of their career prospects. Abstract word (AW) comprehension and equal sign knowledge (ESK) are considered the foundation of discourse comprehension and pre-algebra skills, respectively. However, the link between AW and ESK in relation to the meaningful agent representative information…

The importance of mathematical problem posing has been acknowledged by many researchers. In this theoretical paper, we want to capture different meanings and aspects of problem posing by approaching it from three different levels: (1) by comparing definitions, (2) by relating it to other constructs, and (3) by referring to research and teaching…

Word problems are frequently used in school mathematics to offer students the opportunity to explore mathematical relationships and structure. However, previous studies have reported that word problems are misused or abused in ways that overlook the original intent of exploring mathematical structure and relationship. This study aims to share a…

To analyze the impact of illustrations on solving mathematical word problems for primary school students, in this study we investigated systematically the functions of illustrations in terms of various presentations of texts and illustrations, and the difficulties associated with various learning materials. The characteristics of eye movement were…

In this study, it was aimed to examine the probability problems which were posed based on continuous sample space and discrete sample space. Participants of the study consisted of 48 university students selected by using the convenience sampling method. Eight tasks related to continuous and discrete variables were designed by the researcher. Eight…

Drawing bar diagrams has been shown to improve performance on mathematical word problems wherein the relational keyword is consistent with the required arithmetic operation. This study extends this by testing the effectiveness of bar diagram drawing for word problems with an inconsistent keyword-arithmetic operation mapping. Seventy-five fifth…

In this article, the authors define numberless math stories and highlight three strategies for supporting equitable problem solving: (1) The Turn-and-Tell Strategy; (2) Storyboard and Story Mat; and (3) The Act-It-Out Strategy. These three strategies open up problem solving and give every student access to a challenging mathematics curriculum…

The nature of the development of arithmetic performance has long been intensively studied, and available scientific evidence can be evaluated and synthesized in light of Nelson and Narens' model of metacognition. According to the Nelson-Narens model, human cognition can be split into two or more interrelated levels. Obviously, in the case of more…

This study forms part of a classroom teaching experiment on the development of a group of 25 9-10 years old students' algebraic thinking. More specifically, it explored their reasoning while solving word problems built around functional relationships to determine how they generalized through questions posed using natural language, drawn figures or…

We conducted a randomized control trial assessing the effects of two variants of word-problem intervention with third graders (n = 304) experiencing mathematics difficulty. Students were assigned to a business-as-usual condition (BaU) or one of two variants of word-problem intervention. One variant included a pre-algebraic reasoning component…

According to expectancy-value models, two important motivational constructs are task value and self-efficacy expectations. As students work intensively on mathematical problems in the classroom, teachers need the competence to judge whether students value solving the problem and how confident they are that they will succeed. However, not much is…

The hundreds chart is a valuable tool for teachers in elementary mathematics classrooms. The present study investigated the effects of spatial configurations of virtual hundreds charts on children's knowledge of base-ten concepts. Kindergarten and first-grade students were assigned to three instructional conditions in which they worked with a…

Increasingly, students must demonstrate knowledge in mathematics through mathematics writing, yet research lags in understanding how students engage in mathematics-writing tasks. Most available research on mathematics writing focuses on typically achieving students without considering students with mathematics difficulty (MD). In this study, we…

The cultural diversity of Malaysia gives a way to three types of public primary schools which vary in terms of cultural and medium of instruction. This study aimed to explore the difference between the performance of grade four primary students from the rural region of Malaysia in solving word problems involving measurement formula and higher…