The study of mathematics is often described as the science of patterns (Resnik 1981), and the cognitive tasks involving the search, recognition, and assessment of patterns are fundamental to learning mathematics. Patterning activities lead students to a better understanding of dependent relations among representations, create a transparent way for…

Every student has mathematical strengths beyond knowing basic facts, solving problems quickly, or showing work clearly. In this article, the author presents Smiles as an "on-ramp" task that supports students working together by unveiling and leveraging mathematical strengths. Nielsen describes on-ramp mathematics tasks as scaffolds that…

Generalizing patterns is an important feature of algebraic reasoning that is accessible to students across grade-levels because it connects their numerical reasoning to algebraic reasoning. In this article, the authors describe how teachers can use the game Crack the Code to introduce generalizing to their students or can extend students'…

As we move further into the digital age, the acquisition of digital literacy (DL) and computational thinking (CT) skills is emerging internationally as an essential goal for students in contemporary school curricula. As the world becomes more uncertain and volatile due to impacts of artificial intelligence (AI), international unrest, climate…

Computational thinking can provide a basis for problem solving, for making evidence-based decisions, and for learning to code or create programs. Therefore, it is critical that all students across the K-12 continuum--including students in the early grades--have opportunities to begin developing problem solving and computational thinking skills.…

The importance of developing reasoning and justification has been highlighted in "Principles and Standards for School Mathematics" (NCTM 2000). The Common Core State Standards for Mathematics (CCSSI 2010) further reiterates the importance of reasoning and proof in several standards for mathematical practice. Students of all grades are…

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…

Virtually all mathematics is based on pattern and structure. A mathematical "pattern" is any predictable regularity, usually involving numbers or space. In every pattern, the various elements are organised in some regular fashion. The way a pattern is organised is called its "structure," which may be numerical or spatial. In…

Visual intelligence is a key element in the thought processes of the most capable and creative among individuals, and this intelligence is closely related to analogical thinking, a learner's ability to make connections between prior knowledge and newly presented information. This article describes an approach to teaching scientific inquiry at…

Richard Nisbett's "The Geography of Thought" is one of several recent works that have highlighted purported differences in thinking patterns between East Asians and Westerners on the basis of empirical research. This has implications for teaching and for other issues such as cultural integration. Based on a framework consisting of three distinct…

Magic squares have been of interest as a source of recreation for over 4,500 years. A magic square consists of a square array of n[squared] positive and distinct integers arranged so that the sum of any column, row, or main diagonal is the same. In particular, an array of consecutive integers from 1 to n[squared] forming an nxn magic square is…

Investigates the display of expert behavior by seven outstanding video game-playing children ages 10 and 11. Analyzes observation and debriefing transcripts for evidence of self-monitoring, pattern recognition, principled decision making, qualitative thinking, and superior memory, and discusses implications for educators regarding the development…

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…

The purpose of this article is to identify the perceptual skills of expert teachers and offer suggestions for teachers to learn to see like an expert. Being able to perceptively read the critical cues in a learning environment allows teachers to recognize present problems, anticipate potential problems, link immediate problems with previously…