This research explores the interplay between students' understandings of proportional and functional relationships. Approximately 90 students participated in an early algebra intervention in Grades 3- 5. Before the intervention and after each year of the intervention, we evaluated their understandings of proportional and functional relationships.…

Background: The format of a mathematics problem often influences students' problem-solving performance. For example, providing diagrams in conjunction with story problems can benefit students' understanding, choice of strategy, and accuracy on story problems. However, it remains unclear whether providing diagrams in conjunction with symbolic…

The aim of the study was to determine mathematics teacher candidates' knowledge about problem solving strategies through problem posing. This qualitative research was conducted with 95 mathematics teacher candidates studying at education faculty of a public university during the first term of the 2015-2016 academic year in Turkey. Problem Posing…

In this study I examine the issue of how to support students' coordination of computer algebra systems (CAS) and paper-and-pencil in solving mathematics problems. Together with a classroom teacher I designed and conducted a collaborative teaching experiment in a ninth-grade algebra classroom to understand how to support students' coordination of…

Mastering the ability for learning to learn is the most ambitious goal of modern educators. A distinction is made between two relatively independent components of this expertise: (a) the reflective component of the learning to learn ability that allows a person comprehend what knowledge and skills he or she lacks to act in the new situation; (b)…

The purpose of this study is to investigate the impact of graphing calculator on students' problem solving success in solving linear equation problems and their attitude toward problem solving in mathematics. A quasi-experimental non-equivalent control and treatment group using the pretest post-test design was employed in this study to test the…

This study aimed to investigate differences in the mathematical problem-solving and metacognitive skills of the fifth-grade students in Oman as a function of gender and level of academic achievement. The participants were 90 grade five students randomly selected from one educational governorate in the Sultanate of Oman. They were evenly divided…

One characteristic of a person having a critical thinking disposition is engaging in the activity with reflective skepticism. Skeptical attitudes can encourage a person to reflect so as to produce a correct conclusion and make the right decision. This article aims to determine: (1) the cause of students skeptic in dealing with illlogical…

In the abstract for "Calculus for a New Century: A Pump, Not a Filter," Lynn Steen wrote: "The authors agree on the forces that are reshaping calculus, but disagree on how to respond to these forces. They agree that the current course is not satisfactory, yet disagree about new content emphases. They agree that the neglect of…

The purpose of this study was to enhance our understanding of the relationship between collaborative talk and metacognitive talk during group mathematical problem-solving. Research suggests that collaborative talk may mediate the use of metacognitive talk, which in turn is associated with improved learning outcomes. However, our understanding of…

This paper focuses on how to link and combine activities of posing and answering questions with the ones of studying pre-existing answers at university level. Our research, developed within the framework of the Anthropological Theory of the Didactic, presents the design and use of an instructional device--study and research paths (SRP)--aimed at…

Teaching teachers to participate in mathematical inquiry has the potential to both transform belief systems about mathematics and to transform teachers from consumers of mathematics to producers of mathematics. The focus of this paper is to describe the use of a problem, based on a non-traditional binary operation, to encourage and teach…

Chemical kinetics is a highly quantitative content area that involves the use of multiple mathematical representations to model processes and is a context that is under-investigated in the literature. This qualitative study explored undergraduate student integration of chemistry and mathematics during problem solving in the context of chemical…

The present study aims at answering the question of whether there is any relationship between brain hemisphericity and non-routine problem solving skills of prospective teachers. One hundred twenty-three prospective teachers participated in the study. The Brain Hemisphericity Test and Non-routine Problem Solving Test were used to evaluate…

A Number Talk is a brief activity (10-15 minutes in length) that is designed to support students' mathematical sense making and promote flexible thinking. During a Number Talk, students engage in mental computations. Number Talks help students do the following: (1) Develop number sense focused on making sense of quantity and mathematical…