Representations play a key role in mathematical thinking: They offer "a medium" to express mathematical knowledge or organize mathematical information and to discern mathematical relationships (e.g., relative household expenditures on a pie chart) using text, symbols, or graphics. They also furnish "tools" for mathematical processes (e.g., use of…

Because fractions and percentages can be difficult for children to grasp, connecting them whenever possible is beneficial. Linking them can foster representational fluency as children simultaneously see the part-whole relationship expressed numerically (as a fraction and as a percentage) and visually (as a pie chart). NCTM advocates these…

Recognizing and interpreting variability in data lies at the heart of statistical reasoning. Since graphical displays should facilitate communication about data, statistical literacy should include an understanding of how variability in data can be gleaned from a graph. This paper identifies several types of graphs that students typically…

The abundance of qualitative data in today's society and the need to easily scrutinize, digest, and share this information calls for effective visualization and analysis tools. Yet, no existing qualitative tools have the analytic power, visual effectiveness, and universality of familiar quantitative instruments like bar charts, scatter-plots, and…

Multiple representations are a valuable tool to help students learn and understand physics concepts. Furthermore, representations help students learn how to think and act like real scientists. These representations include: pictures, free-body diagrams, energy bar charts, electrical circuits, and, more recently, computer simulations and…

Proportional reasoning has been recognised as a crucial focus of mathematics in the middle years and also as a frequent source of difficulty for students (Lamon, 2007). Proportional reasoning concerns the equivalence of pairs of quantities that are related multiplicatively; that is, equivalent ratios including those expressed as fractions and…

Data from a cough challenge study are displayed with dot charts to demonstrate the importance of graphs in understanding data, principles of graph construction and visual perception. The data are available for use in the classroom.

This study examined a random stratified sample (n = 62) of prospective teachers' work across eight institutions on three tasks that utilized dynamic statistical software. The authors considered how teachers utilized their statistical knowledge and technological statistical knowledge to engage in cycles of investigation. This paper characterizes…

The economy's need for workers originates in the demand for the goods and services that these workers provide. So, to project employment, BLS starts by estimating the components of gross domestic product (GDP) for 2020. GDP is the value of the final goods produced and services provided in the United States. Then, BLS estimates the size--in…

Methods of statistical process control were briefly investigated in the field of educational measurement as early as 1999. However, only the use of a cumulative sum chart was explored. In this article other methods of statistical quality control are introduced and explored. In particular, methods in the form of Shewhart mean and standard deviation…

The Community Science Workshops (CSWs)--with funding from the S.D. Bechtel, Jr. Foundation, and the Gordon and Betty Moore Foundation--created a network among the CSW sites in California. The goals of the CSW Network project have been to improve programs, build capacity throughout the Network, and establish new sites. Inverness Research has been…

This thesis work is mainly focused on two problems related to improving accessibility of information graphics for visually impaired users. The first problem is automated analysis of information graphics for information extraction and the second problem is multi-modal representations for accessibility. Information graphics are graphical…

When choosing a career, jobseekers often want to know which occupations offer the best prospects. Generally, occupations that have rapid job growth, many new jobs, or many job openings--and good wages--promise better opportunities. This paper shows how employment in particular occupations is projected to change from 2010 to 2020. It presents…

The purpose of this document is to summarize evidence-based, positive, proactive, and responsive classroom behavior intervention and support strategies for teachers. These strategies should be used classroom-wide, intensified for support small-group instruction, or amplified further for individual students. These strategies can help teachers…

The report presents patterns and trends in data on students and staff at UK higher education institutions covering a 10-year period that has seen a transition to new higher education funding systems across a large part of the UK. Patterns in income and expenditure of UK higher education institutions in 2015-16 are considered. For the first time…