Digital game-based learning (DGBL) has emerged as an effective strategy to enhance students' learning effectiveness. Concept mapping, recognized as a valuable tool for knowledge construction, has been widely implemented in educational settings. However, research indicates challenges when integrating concept maps into games, particularly when the…

Several studies have pointed out difficulties of various types encountered by students in both secondary and high schools to acquire the exact meaning of the integral and to master the ability to invest it correctly in different domains. This contribution attempts to explore the effectiveness of some cognitive activities engaged in teaching…

In a 1-hour teaching interview, 20 children (aged 7 to 11) discovered how to tell whether objects might be made of the same material by using ratios of measures of weight and size. We examine progress in the children's reasoning about measurement and proportional relations, as well as design features of instruments, materials, and tasks crafted to…

In an experiment, secondary students from Australia and Malaysia (n = 130) were randomly assigned to one of three approaches (equation, unitary, unitary-pictorial) to learn how to solve challenging percentage-change problems. In line with the differential types of cognitive load associated with the three approaches, the unitary-approach group…

We identify and document 3 cognitive obstacles, 3 cognitive affordances, and 1 type of integer understanding that can function as either an obstacle or affordance for learners while they extend their numeric domains from whole numbers to include negative integers. In particular, we highlight 2 key subsets of integer reasoning: understanding or…

The study of functions is a critical route into teaching and learning algebra in the elementary grades, yet important questions remain regarding the nature of young children's understanding of functions. This article reports an empirically developed learning trajectory in first-grade children's (6-year-olds') thinking about generalizing functional…

A total of 136 eighth-grade math students from 2 Singapore schools learned from either productive failure (PF) or vicarious failure (VF). PF students "generated" solutions to a complex problem targeting the concept of variance that they had not learned yet before receiving instruction on the targeted concept. VF students…

Writing plays an integral role in any disciplinary course setting. In the sciences, WAC and WID initiatives primarily focus on using writing to deepen student understanding of scientific concepts. Scholars, however, have paid less attention to how writing may facilitate an understanding of the link between concepts and their quantitative…

Confidence intervals are beginning to play an increasing role in the reporting of research findings within the social and behavioral sciences and, consequently, are becoming more prevalent in beginning classes in statistics and research methods. Confidence intervals are an attractive means of conveying experimental results, as they contain a…

The National Council of Teachers of Mathematics (NCTM) has stated that mathematics programs should take full advantage of the power of calculators at all grade levels. This recommendation urges that students be provided access to calculators, and that calculator use be integrated into the core mathematics curriculum on a regular basis. This…

Presents computer approach formulated within a framework of versatile thinking designed to overcome obstacles to understanding algebra. Results from related studies comparing the computer and traditional approaches taught to 11, 12, and 13 year olds showed that the computer approach significantly improved the understanding of higher order concepts…

The estimation processes used by fifth through eighth grade students as they responded to computational estimation test items were examined. Interview-based process descriptions were cross-validated using large group test data from an open-ended test and a multiple choice test. Five question formats were used to test different estimation…

Matrix tasks designed to assess the logical properties of multiple classification and multiple seriation were administered to 105 first, third, and fifth grade children. The tasks included cross-class and double series matrices, each of which had a reproduction and a transposition instructional set, and a revised set of cross-class and double…

Recent calls for mathematics instruction reform recommend that a problem-solving inquiry-oriented (PSIO) classroom environment be established. Students, however, may view mathematics as a static, ruled-based discipline that runs counter to the PSIO approach. A study examined the student/teacher interactions as seen from the viewpoint of five…