Even mentioning data analysis puts many educators on edge; they fear that in data discussions, their performance will be judged. And, the authors note, it's a human trait to look for the source of a problem in the behavior of people involved rather than the system surrounding those people--what some call the Fundamental Attribution Error. When…

This task asks readers to figure out why when you stir a cup of hot liquid and tap on the side of the cup with a spoon, the pitch of sound starts low and ends up high. The solution to last month's tasks relating to the circumference of the Earth and how many stars are in the (visible) sky is also presented.

Separation of variables can be a powerful technique for solving many of the partial differential equations that arise in physics contexts. Upper-division physics students encounter this technique in multiple topical areas including electrostatics and quantum mechanics. To better understand the difficulties students encounter when utilizing the…

The purpose of this article is to contribute to the growing body of research that focuses on active learning techniques. Active learning techniques require students to consider a given set of information, analyze, process, and prepare to restate what has been learned--all strategies are confirmed to improve higher order thinking skills. Active…

We investigate teachers' practices in a whole-class context when they scaffold students' learning in situations where students use technologies that facilitate group learning to solve mathematical problems in small groups. We describe teachers' practices in order to evaluate their contribution to "Whole-Class Scaffolding" in the context…

Many introductions to algebra in high school begin with teaching students to generalise linear numerical patterns. This article argues that this approach needs to be changed so that students encounter variables in the context of modelling visual patterns so that the variables have a meaning. The article presents sample classroom activities,…

The Applied and Industrial Mathematics program partners applied mathematics students with businesses, governments, laboratories, and agencies to solve real problems. We will discuss the logistics of the program and give advice on starting and running similar programs. We also give a detailed example of a specific project, namely our work with the…

Earlier institution-sponsored research revealed that about 20% of students in community college basic math and pre-algebra programs lacked a sense of part-whole relationships with whole numbers. Using the same tool with a group of 86 workforce students, about 75% placed five whole numbers on an empty number line in a way that indicated lack of…

The purpose of this study is to enhance our understanding of how students listen and attend to multiple solutions proposed by their classmates during the activity of comparison. This study examines ten consecutive lessons in each of the two eighth-grade classrooms in Tokyo that are organized in the style of "structured problem solving".…

We examined the relation of parental socioeconomic status (SES) to the neural bases of subtraction in school-age children (9- to 12-year-olds). We independently localized brain regions subserving verbal versus visuo-spatial representations to determine whether the parental SES-related differences in children's reliance on these neural…

Reflection is a critical factor in solving design problems. Using good methods to observe designers' reflection is essential to inform the design of the learning environments that support the development of design problem-solving skills. In this study, we have developed and validated a novel self-reporting questionnaire as an efficient instrument…

How can activities in which collaborative skills of an individual are measured be standardized? In order to understand how students perform on collaborative problem solving (CPS) computer-based assessment, it is necessary to examine empirically the multi-faceted performance that may be distributed across collaboration methods. The aim of this…

Continuing pressures are being placed on undergraduate business education to alter curriculum content and delivery. The anticipated product of these changes is a graduate that is capable of performing the higher order thinking skills needed to navigate a constantly changing, global business environment. This article describes the implementation of…

A picture is worth more than a thousand words--in mathematics too. Many students fail in learning mathematics because, in some cases, teachers do not offer the necessary visualization. Nowadays technology overcomes this problem: computer aided instruction is one of the most efficients methods in teaching mathematics. In this article we try to…

Seventy-three children between 6 and 7 years of age were presented with a problem having ambiguous subgoal ordering. Performance in this task showed reliable fingerprints: (a) a non-monotonic dependence of performance as a function of the distance between the beginning and the end-states of the problem, (b) very high levels of performance when the…