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:…

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…

This study describes the problem solving behaviour of bilingual (German - Turkish) primary school students, their approaches and preferences while solving the word problems. Four different types of mathematical word problems (combinations, movement, subtraction and addiction) were given successively to four pupils (one girl and three boys) and…

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…

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…

Intuitive conceptions in mathematics guide the interpretation of mathematical concepts. We investigated if they bias teachers' conceptions of student arithmetic word problem solving strategies, which should be part of their pedagogical content knowledge (PCK). In individual interviews, teachers and non-teaching adults were asked to describe…

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…

In this paper, I share the results of a study of teachers' ideas about student decision-making at entry into a professional development program to integrate engineering into their instruction. The framework for the Engineering Design Process (EDP) was based on a Challenge-Based Learning (CBL) model. The EDP embedded within the CBL model suggests…

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…