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…

"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…

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.)

I describe how data pooling and data visualization can be employed in the first-semester general chemistry laboratory to introduce core statistical concepts such as central tendency and dispersion of a data set. The pooled data are plotted as a 1-D scatterplot, a purpose-designed number line through which statistical features of the data are…

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…

Along with the bright hues of orange, red, and yellow, the season of fall represents significant changes, such as day length and temperature. These changes provide excellent opportunities for students to use science process skills to examine how abiotic factors such as weather and temperature impact organisms. In this article, the authors describe…

Patterning is an essential skill in early mathematics learning, particularly in the development of spatial awareness, sequencing and ordering, comparison, and classification. This includes the ability to identify and describe attributes of objects and similarities and differences between them. Patterning is also integral to the development of…