This paper introduces a revised model for the development of basic computation skills. The model draws on four key phases, which have proven to be important for the development of calculation strategies and stresses the use of gestures and the verbalisation of concrete and mental images. This seems to be of crucial importance for children with…

Reports and surveys by the U.S. government and international organizations have repeatedly acknowledged the achievement problem in math in K-12 regardless of various efforts (e.g., by the U.S. Department of Education) to diminish it. To address the problem in math achievement in K-12, teachers, scholars, and the U.S. government have developed…

Indonesia's involvement in the Programme for International Student Assessment (PISA) is one attempt to see how far the development of educational programs in our country compared to other countries in the world. PISA results show that Indonesia is still at the lower level. This means that the ability of Indonesian students in solving problems that…

Research shows that the greatest gains in student learning in mathematics classrooms occur in classrooms in which there is sustained use of high cognitive demanding tasks throughout instruction (Boston and Smith 2009). High cognitive demanding tasks, which this article will refer to as rich tasks, are mathematics problems that are complex, less…

This article shows how to modify classroom evaluation items to avoid four potential difficulties that limit a teacher's insight into students' mathematical understanding by addressing these issues: (1) poor choice of numbers; (2) implausible or inappropriate contexts; (3) inclusion of graphics that do not help make learning visible; and…

The purpose of this study is to contribute insights into how collaborative activity can help promote students' mathematical understanding. A group of six high school students (15- to 16-year olds) worked together on a challenging probability task as part of a larger, after-school, longitudinal study on students' development of mathematical ideas…

This experimental study evaluated the effectiveness of a research-based intervention, schema-based instruction (SBI), on students' proportional problem solving. SBI emphasizes the underlying mathematical structure of problems, uses schematic diagrams to represent information in the problem text, provides explicit problem-solving and metacognitive…

This experimental study evaluated the effectiveness of a research-based intervention, schema-based instruction (SBI), on students' proportional problem solving. SBI emphasizes the underlying mathematical structure of problems, uses schematic diagrams to represent information in the problem text, provides explicit problem solving and metacognitive…

The paper deals with searching for synthetic solution supported by the means of dynamic geometry. It consists of two parts. The first one describes how software influences searching for synthetic solutions of geometric problems. The second one describes a small pilot experiment in which students of Faculty of Education solved two more difficult…

The purpose of this study was to examine the efficacy of the Children's School Success (CSS) curriculum for 4-year-old children enrolled in preschool programs designed to prepare them for success in their early public school grades. The study took place in preschool classes located in five regionally distributed states, all of which were inclusive…

Gestures are associated with powerful forms of understanding; however, their causative role in mathematics reasoning is less clear. We inhibit college students' gestures by restraining their hands, and examine the impact on language, recall, intuition, and mathematical justifications of geometric conjectures. We test four mutually exclusive…

Learning analytic models are built upon traces students leave in technology-enhanced learning platforms as the digital footprints of their learning processes. Learning analytics uses these traces of learning engagement to predict performance and provide learning feedback to students and teachers when these predictions signal the risk of failing a…

One of the greatest challenges facing students new to calculus is the ability to persevere in the face of failure. Whether the student is choosing an integration technique or a series test, calculus is often the first course in mathematics where the path to the solution is not prescribed in an algorithmic way. At Jacksonville University we…

In a multi-institutional study, the authors examine elementary preservice teachers' (PSTs') noticing skills before and after their engagement in a mathematics methods course. In particular, the authors examine their use of "Cognitively Guided Instruction" (CGI) as a means of supporting the development of PSTs' "professional noticing…

Self-assessment and task-selection skills are crucial in self-regulated learning situations in which students can choose their own tasks. Prior research suggested that training with video modeling examples, in which another person (the model) demonstrates and explains the cyclical process of problem-solving task performance, self-assessment, and…