Most research has focused solely on understanding high school or college students' mathematical creative thinking abilities while understanding younger students' creative thinking in mathematics was ignored. These studies of older students have focused mainly on students' creative products rather than creative processes. The authors of the present…

Teachers are increasingly encouraged to creatively integrate technology into their classroom instruction as designers of technology-enhanced learning (TEL). However, they are often not competent in designing TEL due to their lack of experience as participatory designers as well as the ill-structure nature of TEL design problem. Design thinking, as…

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…

In this digital ITEMS module, Dr. Jacqueline Leighton and Dr. Blair Lehman review differences between think-aloud interviews to measure problem-solving processes and cognitive labs to measure comprehension processes. Learners are introduced to historical, theoretical, and procedural differences between these methods and how to use and analyze…

Background: Developing self-directed learning (SDL) skills in engineering students is critical to support life-long learning. This research was conducted at Iron Range Engineering (IRE), an innovative, problem-based learning (PBL) engineering program, which has suffused the concept of metacognition throughout its curriculum. Purpose/Hypotheses:…

A quantitative literacy course titled "Computational Geology" has been taught at the University of South Florida for over 20 years at the undergraduate level, largely by the same professor. Due to the extended course tenure, a unique opportunity presented itself to qualitatively study what the perceived broader impacts of the course were…

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…

Teachers spend a lot of time talking about students: They talk about how students learn, how to best plan lessons for them, and how to understand their written work using different protocols. Instead of hypothesizing about what a student might do on a task or why a student made a certain mistake, why aren't teachers just asking the student?…

This article illustrates and differentiates the unique role cognitive interviews and think-aloud interviews play in developing and validating assessments. Specifically, we describe the use of (a) cognitive interviews to gather empirical evidence to support claims about the intended construct being measured and (b) think-aloud interviews to gather…

Models of physical systems are used to explain and predict experimental results and observations. The Modeling Framework for Experimental Physics describes the process by which physicists revise their models to account for the newly acquired observations, or change their apparatus to better represent their models when they encounter discrepancies…

Most studies on fairness behavior in preschool focus on fair resource allocation and on children's behavior when faced with fairness dilemmas. The purpose of this study is to understand preschoolers' point of view: what do they think when presented with various scenarios that call for fairness behavior? We interviewed 66 children aged 3.5-6 years,…

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…

This study has identified factors stimulating creative ideas, transforming creative ideas to products, and continuing creative performance in the field of architecture based on interviews with 10 creative and successful architects. Having a penchant for liberal arts and reading books on a broad range of topics on arts, humanities, social sciences,…

How do you prepare your students for a future that you can't see? And how do you do it without exhausting yourself? Teachers need a framework that allows them to keep pace with our rapidly changing world without having to overhaul everything they do. "Learning That Transfers" empowers teachers and curriculum designers alike to harness…