In this cross-national study, we explore the different ways of reasoning-and-proving (RP) presented in three 8th grade textbooks, one from each country: Turkey, Norway, and Slovakia. While the analysis revealed that all three textbooks contain similar numbers of problems involving some form of RP, differences exist in terms of the dominating ways…

A group of eighth-graders was presented with a two-day lab exploring graph theory as an enrichment experience. With the school's winter break looming, students were weary of solving linear equations, and this topic was intended to inject some new life into the classroom. In addition to learning about a completely new topic, they would be exposed…

This study aims to produce a jumping task in the form of a student worksheet which is valid and practical. Design research in the form of development studies was chosen in this study which consist of preliminary stage and prototyping stage. Data were collected by walk through, test, questionnaire, and interview. Data were analyzed descriptively.…

The purpose of the present study is to provide empirical evidence on the adaptation of the mathematics-related beliefs questionnaire (MRBQ) supplemented by info-communication technology-related items. Besides, we also investigate the relationship between their beliefs about mathematics and their ability in problem-solving mathematics. 234 grade…

A prior study developed the Computational Thinking Scale (CTS) for assessing individuals' computational thinking dispositions in five dimensions: decomposition, abstraction, algorithmic thinking, evaluation, and generalization. This study proposed the Developmental Model of Computational Thinking through validating the structural relationships…

Providing adequate proof is one essential mathematical method, but it is a difficult task for many school-age students. While previous studies have revealed the cognitive factors of proving the proof, the function of affective factors and learning engagement has been largely unexplored. This study examined the effects and processes associated with…

In this action study, instructional environments were enriched with activities related to the history of mathematics in order to deepen students' beliefs about mathematics and reveal for them fun, interesting, and useful activities. The study enrolled twenty-four 8th-grade students. Data were collected by using multiple data collection tools. The…

This study explored how approximating the practice of mathematicians by communally negotiating the standards for proof mediates middle grade students' abilities to collaboratively construct mathematical arguments. Forty-seven eighth-grade students engaged in an instructional sequence wherein they, along with the instructors, negotiated communal…

The Modeling Self-Efficacy Scale was developed to measure students' confidence in understanding and solving modeling tasks. The scale was administered to 225 eighth- and ninth-grade students. Participants read modeling tasks adapted from Programme for International Student Assessment's 2003 problem-solving assessment and rated their confidence on…

The purpose of this study was to examine the effectiveness of video-based mathematics instruction for seven middle school students with specific learning disability (SLD), using an augmented reality-based training package. The dependent variable was the percentage of steps students performed correctly to solve each type of mathematics problem. The…

Higher order thinking skills have been embedded into state teaching standards, including Standard 9 of the New Jersey Core Curriculum Content Standards (NJCCCS) for 21st Century Life and Careers. These standards aim to encourage problem solving, critical thinking, reasoning, and real-world application in order to prepare students for the workplace…

It has become gradually accepted that proof and proving are essential at all grades of mathematical learning. Among the various aspects of proof and proving, this study addresses proofs and refutations described by Lakatos, in particular a part of increasing content by deductive guessing, to introduce an authentic process into mathematics…

We report on a long-term study which was executed in a German secondary school with 128 eights graders (ages 14 to 15) in four different classes. Two of these classes served as control groups. The mathematics lessons of the other two classes (treatment groups) were frequently enriched by distinguished phases in which structured argumentation and…

The relationship between mathematical creativity (MC) and mathematical problem-solving performance (MP) has often been studied but the causal relation between these two constructs has yet to be clearly reported. The main purpose of this study was to define the causal relationship between MC and MP. Data from a representative sample of 480…

Amongst important and under-researched questions are how introductory lessons can be designed for teaching initial proofs to junior high school students, and how such lessons enrich students' understanding of proofs. With a view to improving the learning situation in the classroom, in this paper we report on the various functions of introductory…