FOIL is a well-known mnemonic that is used to find the product of two binomials. We conduct a large sample (n = 252) observational study of first-year college students and show that while the FOIL procedure leads to the accurate expansion of the product of two binomials for most students who apply it, only half of these students exhibit conceptual…

Design-based learning (DBL) is an educational approach in which students gather and apply theoretical knowledge to solve design problems. In this study, we examined how critical DBL dimensions (project characteristics, design elements, the teacher's role, assessment, and social context) are applied by teachers in the redesign of DBL projects.…

New strategies can ignite teachers' imagination to create new lessons or adapt lessons created by others. In this article, the authors present the experience of an algebra teacher and his students solving linear and literal equations and explain how the use of ideas found in past NCTM journals helped bring this lesson to life. The…

Feedback is generally considered a beneficial learning tool, and providing feedback is a recommended instructional practice. However, there are a variety of feedback types with little guidance on how to choose the most effective one. We examined individual differences in working memory capacity as a potential moderator of feedback type. Second-…

Introduction: The macroscopic perspective is one of the frameworks for research on problem solving in mathematics education. Coming from this perspective, our study addresses the stages of thought in mathematical problem solving, offering an innovative approach because we apply sequential relations and global interrelations between the different…

The present study tested the hypothesis that children's fluency with basic number facts and knowledge of computational strategies, derived from early arithmetic experience, predicts their performance on complex arithmetic problems. First-grade students from United States and Taiwan (N = 152, mean age: 7.3 years) were presented with problems that…

This paper used narrative to present the author's understanding process of "concept study" in teachers' professional learning. The understanding process was advanced by several questions emerging from the preparation of doing "concept study". Thus, the several questions and their solutions became the threads of the narrative.…

This article explores the relative importance of different socio-demographic and practice-oriented factors that are related to proficiency in problem solving in technology-rich environments (PSTREs) and by extension may be related to complex problem solving (CPS). The empirical analysis focuses on the proficiency measurements of PSTRE made…

The authors teach a problem-solving course for preservice middle-grades education majors that includes concepts dealing with absolute-value computations, equations, and inequalities. Many of these students like mathematics and plan to teach it, so they are adept at symbolic manipulations. Getting them to think differently about a concept that they…

In this experiment, we used the deferred imitation paradigm to assess 24-month-olds' ability to use conceptual similarity to solve new problems after a delay. Infants in the experimental condition participated in four sessions that were each separated by 24 h. In Session 1, the experimenter modeled three target actions using one set of stimuli and…

In this article, Sarah Currier, a math specialist at Elizabeth Hall International School in Minnesota, describes how she used origami in a deliberate manner to teach content. She shares how she uses paper folding to teach mathematical concepts, reinforce vocabulary, and as a problem-solving model. She also offers ideas for using origami in other…

Across the mathematics curriculum there is a renewed emphasis on applications of mathematics and on mathematical modeling. Providing students with modeling experiences beyond the ordinary classroom setting remains a challenge, however. In this article, we describe the 24-hour Mathematical Modeling Challenge, an extracurricular event that exposes…

Multiple studies report that Computer Science (CS) instructors face problems on how to integrate visualizations in their teaching. This problem gets compounded for instructors in technology-constrained classrooms that are common in developing countries. In these classrooms, students are not able to interact with visualization directly; instead,…

This paper presents results from three teaching experiments intended to guide students to reinvent truth-functional interpretations for mathematical disjunctions. The initial teaching experiments revealed that students' emergent strategies for assessing disjunctions did not entail or facilitate the development of a relevant partitioning of example…

In this paper we report the interview questions used in a study of middle school students' mathematical problem solving behaviors which were chosen based on Vygotsky's concept formation theory and Berger's appropriation theory. We discuss the task design/selection process along with the findings associated with the use of these tasks so to provide…