Algebra progress monitoring is a research-based practice that extends a long history of research in curriculum-based measurement (CBM). This article describes the theoretical foundations and research evidence for algebra progress monitoring, along with critical features of the practice. A detailed description of one practitioner's implementation…

The inquiry-based approach to learning has gained popularity in recent times. Those who promote this approach maintain that mathematical investigation should be used to engage students. The National Council of Teachers of Mathematics (NCTM) recommends that problem solving be the center of mathematics teaching in promoting student learning through…

This paper addresses the difficulties experienced by first-grade students studying rigid body motion at Sofia University. Most quantities describing the rigid body are in relations that the students find hard to visualize and understand. They also lose the notion of cause-result relations between vector quantities, such as the relation between…

Connecting stories to qualitative coordinate graphs has been suggested as an effective instructional strategy. Even students who are able to "create" bar graphs may struggle to correctly "interpret" them. Giving children opportunities to work with qualitative graphs can help them develop the skills to interpret, describe, and compare information…

This study considers the evolving influence of variation and expectation on the development of school students' appreciation of distribution as displayed in their construction of graphical representations of data sets. Three interview protocols are employed, presenting different contexts within which 109 students, ranging in age from 6 to 15…

Most mathematical functions can be represented in numerous ways. The main representations typically addressed in school, often referred to as "the big three," are graphical, algebraic, and numerical representations, but there are others as well (e.g., diagrams, words, simulations). These different types of representations "often illuminate…

The number "e" is one of those fascinating numbers whose properties are of special interest to mathematicians. In this article, the author aims to provide a method of introducing a visual concept of the number "e". These ideas are suitable for secondary school and undergraduate tertiary students. The main concept involves areas…

Individuals with Prader-Willi syndrome (PWS) are at risk for excessive daytime sleepiness (EDS) and disruptive behavior. This pilot study explores temporal characteristics of EDS and severe disruptive behavior across time of day and day of week in seven individuals with PWS (aged between 33 and 49 years) of whom five were matched to controls.…

This article presents a designed learning environment intended to engage students in learning about the relationships among multiple representations as they work together on a shared task. Over the course of several extended problem-solving sessions, groups developed several successive alignments of participants and representations as they learned…

The purpose of this study was to determine the effects of self-graphing on the writing of 3 fourth grade students with high-incidence disabilities. Measures of written expression included total number of words written and number of correct word sequences. During intervention, students self-graphed their total number of words written in response to…

A graphical method is presented for assessing the state of identifiability of the parameters in a linear structural equation model based on the associated directed graph. We do not restrict attention to recursive models. In the recent literature, methods based on graphical models have been presented as a useful tool for assessing the state of…

This dissertation concerns kindergarteners' and second graders' invented representations of motion, their interactions with conventional representations of motion built from the child's movement in front of a motion detector and using real-time graphing tools, and any changes in the invented representations that this interaction brings about. We…

In the social studies of science, visuals and graphical representations are theorized by means of the concept of inscription, a term that denotes all representations other than text inscribed in some medium including graphs, tables, photographs, and equations. Inscriptions constitute an intrinsic and integral part of scientific practice; their…

The National Office for Research on Measurement and Evaluation Systems (NORMES) at the University of Arkansas developed a web-based interactive system to provide information on state, district, and school level achievement gaps between white students and black students, socioeconomically disadvantaged students and non-disadvantaged students, male…

As a college biology instructor, I often see graphs in lab reports that do not meet my expectations. I also observe that many college students do not always adequately differentiate between good and poor (or misleading) graphs. The activity described in this paper is the result of my work with students to improve their graphing literacy. The…