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…

In Calculus, students are often both presented problems with and taught to use three interconnected types of representations: symbolic, graphic, and numeric. However, students often fail to notice the relationship between mathematical objects (and even the same object) that are presented using different types of representations. Using the APOS…

Interactive problem solving environments, such as intelligent tutoring systems and educational video games, produce large amounts of transactional data which make it a challenge for both researchers and educators to understand how students work within the environment. Researchers have modeled the student-tutor interactions using complex network…

In an educational environment, instructors would always think of ways to provide students with motivational learning materials and efficient learning strategies. Hence, many researchers have proposed that students' problem-solving ability enhances their learning. Problem-solving ability plays an important role for users in dealing with problems…

Whilst deficit discourses in classrooms and staff rooms are pervasive and dominant, there is some research which supports teachers disrupting deficit thinking and reconnecting with student "funds of knowledge". Processes for disrupting deficit knowledges tend to assume individual teacher construction of deficit views in conversation with…

Action research is a systematic approach to investigation that enables people to find effective solutions to problems they confront in their everyday lives. A significant feature is that action research lays claim to the professional development in education. Action research as any systematic inquiry conducted by teachers, administrators, and…