This study concerns the cognitive process of mathematical problem posing, conceptualized in three stages: understanding the task, constructing the problem, and expressing the problem. We used the eye tracker and think-aloud methods to deeply explore students' behavior in these three stages of problem posing, especially focusing on investigating…

This study aims to describe the cognitive process of autism spectrum disorder (ASD) students in solving mathematical problems in order to provide recommendations towards ensuring an appropriate learning process. It was conducted qualitatively using three ASD students in senior high school in Indonesia with high, moderate, and low intelligence. The…

This study was conducted to reveal potential sources of students' difficulty and misconceptions about geometrical concepts with the help of eye tracking. In this study, the students' geometrical misconceptions were explored by answering the questions on the geometry test prepared based on the literature and test-taking processes and represented…

This study investigates sixth-grade students' explorations of tessellations with Scratch through the mathematical aesthetics. For this purpose, the study analyzed the students' explorations by considering the roles of mathematical aesthetics identified by Sinclair (2004): generative, evaluative, and motivational role. Six middle-school students…

We describe a formative assessment approach called whole-class think alouds, which foster evidence-based instructional practices and promote the goal of assessment to promote learning. They allow students to collaborate and orally communicate their problem solving.

Students' success in learning is inseparable from their high level of fighting power or the Adversity Quotient (AQ) they have. This study examines whether there was an Adversity Quotient (AQ) difference between Boarding Schools (BS) and NonBoarding Schools (NBS) students through the application of metacognitive learning Think-aloud cooperative…

It is essential for items in assessments of mathematics' teacher knowledge to evoke the desired response processes -- to be interpreted and responded to by teachers as intended by item developers. In this study, we sought to unpack evidence that middle school mathematics teachers were not consistently interacting as intended with constructed…

To explain children's difficulties learning fraction arithmetic, Braithwaite et al. (2017) proposed FARRA, a theory of fraction arithmetic implemented as a computational model. The present study tested predictions of the theory in a new domain, decimal arithmetic, and investigated children's use of conceptual knowledge in that domain. Sixth and…

While school performance suggests students with learning disabilities require intervention to demonstrate mathematics proficiency, little is known about how they approach problem solving in secondary geometry. Think aloud protocols highlight the higher order thinking skills underlying complex academic tasks. We conducted an exploratory descriptive…

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…

This article documents differences between novice and experienced undergraduate students' processes of reading mathematical proofs as revealed by moment-by-moment, think-aloud protocols. We found three key reading behaviors that describe how novices' reading differed from that of their experienced peers: alternative task models, accrual of…

Disciplinary literacy strategies in mathematics lessons are essential and may be embedded in three necessary parts of the lesson: before reading, during reading, and after reading. In this article, we highlight disciplinary literacy strategies that middle school mathematics teachers might implement to guide students to increased mathematical…

Solving reality-based tasks is an important goal in mathematics instruction and is anchored in education standards determined by mathematical modeling skills. These tasks demand a serious examination of the real-world as well as text comprehension to successfully solve them. Therefore, this study empirically reconstructed the comprehension process…

Self-regulated learning (SRL) is a critical component of mathematics problem-solving. Students skilled in SRL are more likely to effectively set goals, search for information, and direct their attention and cognitive process so that they align their efforts with their objectives. An influential framework for SRL, the SMART model (Winne, 2017),…

The Philippines has undergone a fundamental overhaul of its educational system to highlight basic education and overcome its deficiencies. The educational reform prompts prospective teachers to connect the concepts taught to instill a more profound understanding. As such, the researchers explored the mathematical connections made by prospective…