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…

The facilitator plays a key role in guiding students' efforts during case discussions. However, few studies have compared differences in learning outcomes for students participating in facilitated versus non-facilitated discussions. In this research, we used "problem space coverage" as a learning measure to compare outcomes between…

The procedure of a physical chemistry experiment for university students must be designed in a way that the accuracy and precision of the measurements is properly maintained. However, in many cases, that requires costly and sophisticated equipment not readily available in developing countries. A simple, low-cost experiment to determine isobaric…

There is a long-standing tradition in mathematics education to look to history to inform instruction. An historical analysis of the genesis of a mathematical idea offers insight into: (i) the contexts that give rise to a need for a mathematical construct; (ii) the ways in which available tools might shape the development of that mathematical idea;…

This study aimed to investigate how the semantic structures of problems posed by sixth-grade middle school students for the addition of fractions affect their problem-posing performance. The students were presented with symbolic operations involving the addition of fractions and asked to pose two different problems related to daily-life situations…

The status of educational technology research in a VUCA world is examined. The acronym, VUCA, stands for "Volatility" (rapidly changing contexts and conditions), "Uncertainty" (information missing that is critical to problem solving), "Complexity" (multiple factors difficult to categorize or control), and…