A seminal study by Chi "et al." firmly established the paradigm that novices categorize physics problems by "surface features" (e.g., "incline," "pendulum," "projectile motion," etc.), while experts use "deep structure" (e.g., "energy conservation," "Newton 2," etc.). Yet, efforts to replicate the study frequently fail, since the ability to…

This article advocates biased spinners as an engaging context for statistics students. Calculating the probability of a biased spinner landing on a particular side makes valuable connections between probability and other areas of mathematics. (Contains 2 figures and 1 table.)

The authors examined the long-term learning effects of two different practice set assignment approaches on business students' long-term learning: a comprehensive, multiple-period practice set and a topic-specific practice set. Student learning was measured longitudinally across semesters. The authors found evidence that students using a…

This account of practice explores the concept of resistance in action learning. Resistance is conceptualized as an attempt of self-protection that is manifested in action learners' struggles with their sense of self-efficacy and their social Self. These struggles are an inherent part of the action learning process and may elicit defensive…

E-Learning brings access to a powerful but often overlooked teaching tool: random number generation. Using random number generation, a practically infinite number of quantitative problem-solution sets can be created. In addition, within the e-learning context, in the spirit of the mastery of learning, it is possible to assign online quantitative…

This study reports on the use of formative, diagnostic online assessments for the topic percentages. Two new item formats (drag-drop and slider) are described. About one-third of the school students (Years 7 to 9) could, using a slider, estimate "80% more than" a given length, in contrast with over two-thirds who could estimate "90%…

Because the relationship between computer use and achievement is still puzzling, there is a need to prepare and analyze good quality datasets on computer use and achievement. Such a dataset can be derived from TIMSS data. This paper describes how this dataset can be prepared. It also gives an example of how the dataset may be analyzed. The…

Researchers have extensively documented, and math teachers know from experience, that algebra is a "gatekeeper" to more advanced mathematical topics. Students must have a strong understanding of fundamental algebraic concepts to be successful in later mathematics courses. Unfortunately, algebraic misconceptions that students may form or…

Not only are the problems teachers pose throughout their teaching of great importance but also the ways in which they use those problems make this a critical component of teaching. A problem-posing episode includes the problem setup, the statement of the problem, and the follow-up questions. Analysis of problem-posing episodes of precalculus…

Many teachers have designed lessons for students who will be working in groups to discuss and solve a problem. After investing time in constructing an interesting problem, creating strategically designed groups, and introducing the problem carefully, teachers may be left wondering how to help students collaborate to make sense of mathematical…

Textbook style problems including detailed solutions introducing pharmaceutical topics at the level of an introductory chemical engineering course have been created. The problems illustrate and teach subjects which students would learn if they were to pursue a career in pharmaceutical engineering, including the unique terminology of the field,…

A facility with signed numbers forms the basis for effective problem solving throughout developmental mathematics. Most developmental mathematics textbooks explain signed number operations using absolute value, a method that involves considering the problem in several cases (same sign, opposite sign), and in the case of subtraction, rewriting the…

This article illustrates using carbon emissions data in an introductory statistics assignment. The carbon emissions data has desirable characteristics including: choice of measure; skewness; and outliers. These complexities allow research and public policy debate to be introduced. (Contains 4 figures and 2 tables.)

This article describes the technique of introducing a new variable in some calculus problems to help students master the skills of integration and evaluation of limits. This technique is algorithmic and easy to apply.

The achievement of deep learning by secondary students requires teaching approaches that draw students into task commitment, integrated curricula, and analytical thinking. By using real-world data sets in project based instructional units, teachers can guide students in analyzing, interpreting, and reporting quantitative data. Working with…