Flexibility in transforming algebraic expressions is recognized as fundamental for a rich procedural knowledge. Here, flexibility in-depth is proposed as the ability to apply one strategy to a wide range of unfamiliar expressions. In this study, design experiments with four groups of students were conducted to support students' flexibility…

The purpose of this study is to enhance our understanding of how students listen and attend to multiple solutions proposed by their classmates during the activity of comparison. This study examines ten consecutive lessons in each of the two eighth-grade classrooms in Tokyo that are organized in the style of "structured problem solving".…

It is a widely known fact that gifted students have different skills compared to their peers. However, to what extent gifted students use mathematical thinking skills during probability problem solving process emerges as a significant question. Thence, the main aim of the present study is to examine 8th grade gifted students' probability…

Computational estimation is an important skill necessary for students' mathematical development. Students who can estimate well for computations rely on an understanding of many mathematical topics, including a strong number sense, which facilitates understanding the mathematical operations and contextual evidence within a problem. In turn, good…

This article reports on students' problem-solving approaches across three representations--number lines, coordinate planes, and function graphs--the axes of which conventional mathematics treats in terms of consistent geometric and numeric coordinations. I consider these representations to be a part of a "hierarchical representational…

In this article, the authors present three adolescent Latinas' perceptions of ideal mathematical competencies, their perception of their individual "abilities" in mathematics, and their work on a mathematics problem-solving task. Results indicate that these Latinas recognize flexible mathematics as the ideal mathematical competency in…

Making decisions about the production and use of chemical substances is of central importance in many fields. In this study, a research team comprising teachers and educational researchers collaborated in collecting and analyzing cognitive interviews with students from 8th grade through first-year university general chemistry in an effort to map…

In recent years, the topic of integrating history to mathematics lessons in teaching-learning processes has been frequently discussed among researchers. The main aim of this study is to present an example activity which enriched with history of mathematics and to take the views of students about teaching course in this way. In addition, to create…

Researchers and educators support the idea of providing authentic literacy experiences to students. However, a critical misconception of the locus of authenticity exists; the focus has generally been on making tasks authentic to college, careers, or researcher-determined notions of authenticity rather than making tasks authentic to students and…

Adolescents often use root word and affix knowledge to figure out unknown words. Anglin (1993) found that younger readers favor the Part-to-Whole strategy, and Tyler and Nagy (1989) confirmed the importance of root-word knowledge for middle school students. This study seeks to understand the different strategies middle school readers use so that…

Linear algebra is one of the most challenging topics to learn and teach in many countries. To facilitate the teaching and learning of linear algebra, priority should be given to epistemologically analyze the concepts that the undergraduate students have difficulty in conceptualizing and to define their ways of reasoning in linear algebra. After…

This study aims to determine how primary school eighth grade (14 years old) gifted students use knowledge types while solving problems. In the context, the data were collected through clinical interviews conducted with three gifted students. The students' voice recordings during problem solving and the solutions they wrote on the paper formed the…

The aim of this study is to explore the problems encountered while teaching force and motion unit in 8th grade science and technology course from teachers' perspectives and offer solutions to eliminate these problems. The study was conducted with 248 science and technology teachers working in 7 regions in Turkey in 2012-2013 academic year.…

Incorporating engineering concepts into middle school curriculum is seen as an effective way to improve students' problem-solving skills. A selection of findings is reported from a science, technology, engineering and mathematics (STEM)-based unit in which students in the second year (grade 8) of a three-year longitudinal study explored…

In line with continuing efforts to explain the demanding nature of multiplicative reasoning among middle-school students, this study explores the fine-grained knowledge elements that two pairs of 7th and 8th graders deployed in their attempt to coordinate the known and unknown quantities in the gear-wheel problem. Failure to conceptualize the…