The focus in this article is on the usefulness of spatial sequencing as a tactic for interpreting a map and organizing our memory of it. This skill is useful whenever some condition varies in a systematic way with distance. When students are asked whether they see a pattern on a map of a topic like wildfires or terrorist activity, some students…

In the field of communication studies, an understanding of the relationship between form and genre is essential for mastering both practical skills and theoretical concepts in core courses such as public speaking, communication theory, and rhetorical criticism. Building on scholarship on the visual politics of presidential portraiture, this…

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…

Duncan Symons and Derek Holton discuss the different types of mathematical reasoning and what each of these might look like in the classroom. By suggesting language that can be used to describe the different methods of reasoning, they hope to provide teachers with the tools they need to better recognise and assess student reasoning.

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…

Learning to debug is a difficult, yet essential, aspect of learning to program. Students in this multi-institutional study report that finding bugs is harder than fixing them. They use a wide variety of debugging strategies, some of them unexpected. Time spent on understanding the problem can be effective. Pattern matching, particularly at the…

In an activity sequence that took place over several days, the class learned about sound and how people hear sounds. Following each activity, students engaged in whole-group sharing sessions and individual journal-writing sessions that were designed to help them see the patterns that emerged from their explorations. The activities were carefully…

Most future teachers are familiar with number patterns that represent an arithmetic sequence, and most are able to determine the general representation of the "n"th number in the pattern. However, when they are given a visual representation instead of the numbers in the pattern, it is not always easy for them to make the connection between the…

This paper describes three spreadsheet exercises demonstrating the nature and frequency of type I errors using random number generation. The exercises are designed specifically to address issues related to testing multiple relations using correlation (Demonstration I), t tests varying in sample size (Demonstration II) and multiple comparisons…

What is the role of patterns in developing algebraic reasoning? This important question deserves thoughtful attention. In response, this article examines some differing views of algebraic reasoning, discusses a controversy regarding patterns, and describes how three types of patterns--in contextual problems, in growing geometric figures, and in…

Twelve-year-old Susan took a course designed to improve her reading skills. She read short stories and the teacher would give her and her fellow students a written test every other week measuring vocabulary and reading comprehension. A few days later, Susan's instructor graded the paper and returned her exam. The test showed that she did well on…

"Making Sense of Decoding and Spelling: An Adult Reading Course of Study" is an evidence-based course of study designed to teach adult learners to decode and spell words more accurately and fluently. It is designed to be used as one component of a comprehensive adult reading course. The target population for the course is adult basic education…

Much controversy surrounds the consequences of adolescent paid work, with researchers coming to diverse conclusions about work's impact on youth. This article summarizes findings from the Youth Development Study (YDS), a long-term, ongoing longitudinal study that has followed youth from middle adolescence through early adulthood. The YDS findings…

We are just at the beginning stages of applying neuroscientific findings to music teaching. A simple model of the learning cycle based on neuroscience is Sense [right arrow] Integrate [right arrow] Act (sometimes modified as Act [right arrow] Sense [right arrow] Integrate). Additional components can be added to the model, including such concepts…