A series of experiments based on problem-solving and collaborative-learning pedagogies are described that encourage students to interpret results and draw conclusions from data. Different approaches including parallel library synthesis, solvent variation, and leaving group variation are used to study a nucleophilic aromatic substitution of…

The goal of this article is to contribute fragments of concrete understanding to the on-going search for meaning in ideas associated with the learning sciences (Sawyer, 2006b) by adding to the repertoire of domain specific studies pertaining to this relatively new field. The learning sciences are first characterized as a system of learning…

Many students and adults feel that algebra is merely the shuffling of symbols. The three interrelated concepts of variable, expression, and equation are central to beginning algebra, and in recent years, helping students understand the idea of a variable has been emphasized. Although graphing calculators help students solve equations, it is also…

The material presented here was used for a semester-long capstone project for a first semester freshman course entitled Mathematical Modeling and Introduction to Calculus. The goals for the students in this work were twofold: first, enable the students to gain insight into an actual problem that affects millions of people in the United States and…

The majority of the literature on universal screening in education is devoted to academic screeners. However, research clearly indicates that other aspects of student functioning are closely associated with outcomes inside and outside of school. As a result, there are gaps in the current literature that call for additional research extending…

Healthy lifestyles are increasingly emphasized these days. This month the authors begin a series of mathematical problems that also address physical activity. They hope that these problems offer opportunities to investigate mathematics and also reinforce the desire to lead a healthy life. In their first problem of the academic year, students…

There has been much recent discussion among educators on the topic of implementing a response to intervention (RTI) framework to identify special education needs for students with specific learning disabilities. There is good reason for such discussion, as all students benefit from RTI when implemented with integrity and fidelity. The result of…

Using a nonroutine problem can be an effective way to encourage students to draw on prior knowledge, work together, and reach important conclusions about the mathematics they are learning. This article discusses a problem on the mathematical preparation of chocolate milk which was adapted from an old book of puzzles (Linn 1969) and has been used…

How do mathematics teachers introduce the concepts of slope, rate of change, and steepness in their classrooms? Do students understand these concepts as interchangeable or regard them as three different ideas? In this article, the authors report the results of a study of high school Advanced Placement (AP) Calculus students who displayed…

There is clear and widespread agreement among the public and educators that all students need to be proficient technology users. Technology literacy is among the attributes that appear in nearly every set of "21st Century Skills." However, while districts spend a great deal of money on technology, there seems to be only a vague notion of what…

The purpose of this article is to present Convergent Evidence Scaling (CES) as an emergent method for combining data from multiple assessment indicators. The CES method combines single-case assessment data by converging data gathered across multiple persons, settings, or measures, thereby providing an overall criterion-referenced outcome on which…

During the past 6 years, the authors have worked and interacted with twice-exceptional middle school students as well as with their parents at an annual residential summer camp. Through surveys and interviews with the parents and their children, the difficulties that twice-exceptional students encounter at school emerged. Furthermore, parents'…

This paper enlarges the reservoir of solved tutor problems in non-holonomic mechanics at the undergraduate level of physics education. Unlike other, rather artificial, solved problems typically used, the streetboard-rider locomotion problem presented here represents an appealing contemporary real-world problem with interesting applications in a…

This paper reports one aspect of a larger study which looked at the strategies used by a selection of grade 6 students to solve six non-routine mathematical problems. The data revealed that the students exhibited many of the behaviours identified in the literature as being associated with novice and expert problem solvers. However, the categories…

The solution of a system of linear, inhomogeneous differential equations is discussed. The particular class considered is where the coefficient matrix is skew-symmetric and orthogonal, and where the forcing terms are sinusoidal. More general matrices are also considered.