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 aims to describe how subjects construct explicit warrant derived from implicit warrant when completing mathematical proof. This research was conducted on seventeen students of mathematics education study programs by providing tests on vector material in elementary linear algebra courses. The test results show that there are four…

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…

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),…

In classroom learning, students need mathematical cognitive flexibility to be able to solve mathematical problems with the various ideas they express. To solve the problems, they must be able to grasp the problem, see it from various points of view, and should not be rigid thinking with one solving method. In fact, the students still lack the…

In this study, we describe the methodology used to identify and validate a set of expert-defined fraction subtraction related attributes. These attributes are expected to be mastered by 6th grade students toward proficiency in fraction subtraction. This research argues and demonstrates that state standards guiding subject instruction plays an…

We developed an intervention based on the learning by teaching paradigm to foster self-regulatory processes and better learning outcomes during complex mathematics problem solving in a technology-rich learning environment. Seventy-eight elementary students were randomly assigned to 1 of 2 conditions: learning by preparing to teach, or learning for…

The purpose of this qualitative study was: (a) to explore the cognitive and metacognitive processes of mathematics problem-solving discourse of 10-year-old students in Russia, Spain, Hungary, and the United States; and (b) to explore the patterns of social interactions during small group work. Data were analyzed using a cognitive/metacognitive…

Although test scores from similar tests in multiple choice and constructed response formats are highly correlated, equivalence in rankings may mask differences in substantive strategy use. The author used an experimental design and participant think-alouds to explore cognitive processes in mathematical problem solving among undergraduate examinees…

Within the current test-centered educational reform movement, considerable emphasis is placed on using assessment results to make instructional decisions for individual students. Test scores are used to estimate a student's current level of skill, monitor his or her progress during instruction, and identify whether the student has gained the…

Rate of change is an important concept for students to study, and little is known about the ways in which secondary students make sense of rate of change. In this qualitative study I examined how four high school students who have not taken calculus reasoned about changing quantities when interacting with mathematical tasks involving multiple…