The purpose of this paper is to review the utility of think alouds in writing instruction and highlight the function of think-aloud modeling in the development of cognitive and metacognitive strategies that support learners' independence. For these purposes, modeling with coping is also explained. Coping models, in which teachers encounter…

Students in secondary school often struggle with symbol sense, that is, the general ability to deal with symbols and to recognize the structure of algebraic formulas. Fostering symbol sense is an educational challenge. In graphing formulas by hand, defined as graphing using recognition and reasoning without technology, many aspects of symbol sense…

The goal of this paper is twofold. First, the paper clarifies and elaborates on an important theoretical construct called orientation with respect to understanding in mathematics, which denotes the degree to which students exhibit an inclination towards and demonstrate an earnest concern for understanding in mathematical learning. Second, the…

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…

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, proposes that…

This study was carried out to examine proportional reasoning problem solving processes of seventh grade students. This study was conducted with the explanatory sequential mixed method design. In this respect, firstly, quantitative data from 56 students were collected and analyzed. Then, qualitative data of the study was collected from six students…

The purpose of this study was to describe students' thinking processes in relating quantities to the problem of covariation in the process of solving mathematical problems. This study used a descriptive exploratory approach within the scope of qualitative research involving 87 students as prospective subjects from three different high schools. The…

Background: Engineering students inconsistently apply equilibrium when solving problems in statics, but few studies have explored why. Visual cognition studies suggest that features of the visual representations we use to teach students influence what domain knowledge they use to solve problems. However, few studies have explored how visual…

This work is focused on upper-secondary school students' ability to use the periodic table of elements to solve problem tasks. Eye-tracking and retrospective think-aloud methods were used to evaluate the reasoning behind the students' (N = 8) performance, i.e., to map the strategies they used and problems they faced when solving the tasks. The…

In this paper, we extend our previous work on challenges teachers face when engaging with proportional reasoning contexts to investigate two contexts that included four problems for middle grades teachers to solve as well as eight student solutions. Analysis included coding for correct solving of the problem as well as making sense of and…

An understanding of acid-base reactions is necessary for success in chemistry courses and relevant to careers outside of chemistry, yet research has demonstrated that students often struggle with learning acid-base reaction mechanisms in organic chemistry. One response to this challenge is the development of educational applications to support…

Background: Problem exploration includes identifying, framing, and defining design problems and bounding problem spaces. Intentional and unintentional changes in problem understanding naturally occur as designers explore design problems to create solutions. Through problem exploration, new perspectives on the problem can emerge along with new and…

To foster students' learning of critical-thinking skills, I previously introduced ill-structured problems to provide students opportunities to apply content knowledge and thinking skills. However, I noted that my third-year, life sciences students were not solving such problems effectively. Therefore, I used a grounded approach and conducted…

Previous studies have explored students' understanding of the relationship between definite integrals and areas under curves, but not their metacognitive experiences and skills while solving such problems. This paper explores students' mathematical performance, metacognitive experiences and metacognitive skills when solving integral-area tasks by…

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…