The National Council of Teachers of Mathematics's "Principles to Actions" (NCTM, 2014) cites posing purposeful questions and eliciting and using evidence of student thinking as effective mathematics teaching practices. Interviewing students creates opportunities for teachers to develop these practices. Through interviewing, they can try…

This paper describes our work to determine the naturalistic images that first-time second-semester university calculus students possess for series convergence. We found that the students we interviewed most frequently determined whether a series converged by imagining a process of appending summands into a running total and examining whether this…

While extensive quantitative research has shed light on the cognitive mechanisms of dyslexia, few mixed-methods studies have been conducted to examine the perceptions of and attitudes towards learning in children with dyslexia, especially in Hong Kong, a bilingual context. In addition, the validity of the metaphor elicitation technique, which was…

Contributing to a growing body of research on undergraduate students' quantitative reasoning, the study reported in this article used task-based interviews to investigate business calculus students' quantitative reasoning when solving two optimization tasks situated in the context of revenue and profit maximization. Analysis of verbal responses…

Although the ELT (English Language Teaching) materials development literature points to the influence of classroom experience on materials design, the literature is less specific about "how" such experience affects skilled textbook writing. Drawing primarily upon concurrent verbalization and pre- and post-concurrent verbalization…

This paper aimed to investigate secondary school students' representations for solving geometric word problems in different clinical interviewing processes. More specifically, the focus was to understand the changes/developments in students' representations through think-aloud interviews (TAIs) and open-ended prompting interviews (OEPIs). Three…

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…

Originating from interviews with mathematics colleagues, written accounts of mathematicians engaging with mathematics, and Wes's reflections on his own mathematical work, we describe a process that we call mathematical foresight: the imagining of a resolution to a mathematical situation and a path to that resolution. In a sense, mathematical…

In order to help students develop their critical thinking skills, teachers need to model the critical thinking skills and dispositions in front of their students. Unfortunately, very rare studies investigating prospective teachers' readiness in critical thinking dispositions are available in the field of mathematics education. This study was…

This study contributes a methodological tool to reconstruct the cognitive processes and mathematical activities carried out by mathematical modelers. Represented as Modeling Transition Diagrams (MTDs), individual modeling routes were constructed for four engineering undergraduate students. Findings stress the importance and limitations of using…

Proportional reasoning is important to the field of mathematics education because it lies at the crossroads of additive reasoning in the elementary school and multiplicative reasoning needed for more advanced mathematics. This research reports on the representations used by pre-service teachers (PSTs) as they responded to tasks involving…

In the Australian mathematics curriculum, Year 12 students (aged 16-17) are asked to solve conditional probability problems that involve the representation of the problem situation with two-way tables or three-dimensional diagrams and consider sampling procedures that result in different correct answers. In a small exploratory study, we…

This study aims to reveal the improvement of the students' learning activities, responses, and mathematical creative thinking skills (MCTS) through open-inquiry approach (OIA). Other relevant studies in mathematics learning tend to focus on guided inquiry, and especially in Indonesia, OIA is still less applied. This study is conducted at State…

Video games offer an exciting opportunity for learners to engage in computational thinking in informal contexts. This paper describes a genre of learning environments called constructionist video games that are especially well suited for developing learners' computational thinking skills. These games blend features of conventional video games with…

The purpose of this study is to identify primary school students' thinking processes within the mathematical modeling process and the challenges they encounter, if any. This is a basic qualitative research study conducted in a primary school in the city of Kütahya in the academic year of 2015-2016. The study group of the research was composed of…