The many studies with coin-tossing tasks in literature show that the concept of randomness is challenging for adults as well as children. Systematic errors observed in coin-tossing tasks are often related to the representativeness heuristic, which refers to a mental shortcut that is used to judge randomness by evaluating how well a set of random…

Transform mathematics instruction with the comprehensive mathematical competencies (CMC) framework--a research-based model that integrates seven essential competencies: conceptual and procedural integration, problem solving, logical reasoning, communication, tool use, pattern recognition, and student engagement. Through practical classroom…

Mathematical and computational thinking (CT) are closely interrelated, yet CT integration into mathematics instruction remains limited. This study aims to analyze the effectiveness of the teaching process for straight-line equations in enhancing students' CT skills and to propose improvements based on the findings. A qualitative case study…

Mathematically gifted students have a potential for understanding and connecting mathematics concept. Pattern generalization as a part of functional thinking becomes one of the benchmarks for gifted students in mathematics. The mathematics curriculum in Indonesia that has not accommodated the functional thinking ability of elementary school…

Learning progressions (LPs) describe the development of domain-specific knowledge, skills, and understanding. Each level of an LP characterizes a phase of student thinking en route to a target performance. The rationale behind LP development is to provide road maps that can be used to guide student thinking from one level to the next. The validity…

The habit of looking for patterns, the skills to find them, and the expectation that patterns have explanations is an essential mathematical habit of mind for young children (Goldenberg, Shteingold, & Feurzeig 2003, 23). Work with patterns leads to the ability to form generalizations, the bedrock of algebraic thinking, and teachers must nurture…

The books in this series provide an essential ingredient in the transition from concrete mathematical experience to the symbolic reasoning used in algebra. They aim to guide the student in building and extending manipulative patterns, collecting numerical data, and analyzing the results. The main objective of the activities in this book is for the…

The books in this series provide an essential ingredient in the transition from concrete mathematical experience to the symbolic reasoning used in algebra. They aim to guide the student in building and extending manipulative patterns, collecting numerical data, and analyzing the results. The main objective of the activities in this book is for the…

Pattern work is now undertaken as early as kindergarten, and both researchers and teachers have discovered that children engage in pattern work with great enthusiasm and innate ability. Having some flexibility in pattern perception and selecting mathematically useful patterns require some training, although there is nothing particularly algebraic…

Presents a problem suggested for students in grades one through six concerning the concepts of grouping, reasoning, and pattern finding. Discusses the student problem-solving process. (ASK)

Presents an activity involving the use of students' birth dates. Activity includes a classic binary representation of numerical values. In the Green Machine, Sorting Cards, and Window Cards, students observe, describe, and analyze patterns. (PVD)

This article describes a way in which the computer can be used by students in exploring patterns and solving problems associated with number theory. BASIC programs are described, along with classroom questions and procedures that aid in implementation. (Author/KR)