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…

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…

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…

Most teachers feel confident espousing the benefits of using picture books in English lessons, talking about the importance of using the illustrations to enhance the text, engaging students and fostering a love and appreciation of literature. How many teachers passionately advocate the use of these same picture books in mathematics lessons? This…

This article draws out many mathematical ideas connected with a familiar game often used by middle school teachers. (Contains 5 figures and 1 table.)

The stereotypical view of English spelling as an awesome mess is no longer widely held by linguists. That view assumes that spelling should represent pronunciation directly and simply. Instead, spelling is currently understood as representing a more abstract level of language as well as reflecting etymology. Examples from a middle school spelling…