This paper presents the development of a heuristic framework that integrates three aspects of context (perspective, content and level) from a number of established theoretical approaches. In this framework, context is viewed from different perspectives (subjective and objective), it comprises different contents (physical, social and formal) and it…

Linear functions are an important part of the middle school mathematics curriculum. Students in the middle grades gain fluency by working with linear functions in a variety of representations (NCTM 2001). Presented in this article is an activity that was used with five eighth-grade classes at three different schools. The activity contains 15 cards…

This article reports on students' problem-solving approaches across three representations--number lines, coordinate planes, and function graphs--the axes of which conventional mathematics treats in terms of consistent geometric and numeric coordinations. I consider these representations to be a part of a "hierarchical representational…

The purpose of this article is to identify the order of significance of the variables that affect science and mathematics achievement in middle school students. For this aim, the study deals with the relationship between science and math in terms of different angles using the perspectives of multiple causes-single effect and of multiple…

This paper introduces a simple and intuitive graphical display for transition table based accountability models that can be used to communicate information about students' status and growth simultaneously. This graphical transition table includes the use of shading to convey year to year transitions and different sized letters for performance…

Amazon, Walmart, and other large-scale retailers owe their success partly to efficient inventory management. For such firms, holding too little inventory risks losing sales, whereas holding idle inventory wastes money. Therefore profits hinge on the inventory level chosen. In this activity, students investigate a simplified inventory-control…

Admittedly, the Fundamental Theorem of Calculus-TFA holds an important role in the Complex Analysis-CA, as well as in other mathematical branches. In this article, we bring a discussion about the TFA, the Rouché's theorem and the winding number with the intention to analyze the roots of a polynomial equation. We propose also a description for a…

Data distributions can be represented using different external representations, such as histograms and boxplots. Although the role of external representations has been extensively studied in mathematics, this is less the case in statistics. This study helps to fill this gap by systematically varying the representation that accompanies a task…

A renewed emphasis was placed on ratio and proportional reasoning in the middle grades in the Common Core State Standards for Mathematics (CCSSM). The expectation for students includes the ability to not only compute and then compare and interpret the results of computations in context but also interpret ratios and proportions as they are…

We have investigated the various approaches taken by first-year university students (n[image omitted]550) when asked to determine the direction of motion, the constancy of speed, and a numerical value of the speed of an object at a point on a numerical linear distance-time graph. We investigated the prevalence of various well-known general…

The maximum power theorem is a useful extension to work on EMF and internal resistance at school level. Furthermore, a very simple physical collision model can be used to show equivalent mathematical patterns to those found with the maximum power theorem and to emphasize fundamental links to ideas of impedance matching. (Contains 2 tables and 6…

Participants in this study were asked to report what strategies were most often used in their attempts to foster their students' problem solving abilities. Participants included 70 second through fifth-grade elementary teachers from 42 schools in a large state of the south central region in the U.S. Data analyses of the interviews revealed that…

If educators want to interest students in mathematics (and science), they must engage them in the lower forms of high school or even earlier (Fisher, 2012). So, teachers should always consider a topic's ability to interest students in the early years of instruction in high school and its topicality. Networks have come into prominence recently with…

We constantly encounter data--in the form of graphs--that convey information about weather, medicine, politics, finances, and nutrition. These graphs are intended to help us visualize data for easy interpretation; however, approximately 41% of adults in the United States have low graph literacy (Galesic and Garcia-Retamero 2011). In this article,…

This study examined how 12- and 13-year-old students' mathematics and science background knowledge affected line graph interpretations and how interpretations were affected by graph question levels. A purposive sample of 14 students engaged in think aloud interviews while completing an excerpted Test of Graphing in Science. Data were…