This article describes the results of a three-day professional development workshop for newer teachers (with less than six years of experience) and more experienced teachers trained in design of skills-based, year-long themes with rich interdisciplinary connections at Charles River School (Massachusetts). For the three days, the school was buzzing…

The order of problems presented to students is an important variable that affects learning effectiveness. Previous studies have shown that solving problems in a blocked order, in which all problems of one type are completed before the student is switched to the next problem type, results in less effective performance than does solving the problems…

This article reviews recent research in math problem solving for students with learning disabilities. Two recently published syntheses of research on mathematics by the Institute of Education Sciences (IES) are used as frameworks for interpreting this body of work. A significant amount of the work in special education over the last decade is…

The article articulates an educational motto--expressed in the title--found in a "prototypical narrative" of social youth work carried out by activists in Copenhagen in the 1990s. This way of modeling pedagogical practice is first outlined as different from the standardizing approach dominant in science. As a prototypical narrative, the…

Teaching advanced programming can be a challenge, especially when the students are pursuing different majors with diverse analytical and problem-solving capabilities. The purpose of this paper is to explore the efficacy of using a particular problem as a vehicle for imparting a broad set of programming concepts and problem-solving techniques. We…

Our research programme, a part of which is presented in this paper, looked at four year old children's ability to use manipulatives in the construction of cube models. We looked at how pre-school children managed the creation of cube nets as a mathematical problem and whether graphical representations of solutions could become a useful tool in a…

Field placements serve as the traditional "clinical" experience for prospective mathematics teachers to immerse themselves in the mathematical challenges of students. This article reports data from a different type of learning experience, that of a clinical simulation with a standardized individual. We begin with a brief background on…

Our students will continue to be confronted with many environment and sustainability issues during their lifetimes because they are unpredictable, serious and complex by nature. These issues challenge not just our technologies but our universities and educational institutions, values and way of living and interaction. Competency-based education…

In this paper, we frame mathematics classrooms as heterogeneous spaces wherein students draw on multiple storylines based on different notions of schooling and school mathematics to both communicate mathematical ideas and position themselves and one another. We focus on a fourth grade (age range 9.4-10.8 years) mathematics classroom discussion in…

The skillset that students acquire during college is not always well-aligned and/or well-developed relative to the skills needed to be successful in the business world. Employers have complained for many years that graduating students often lack adequate critical thinking and communication skills, in particular. In the marketing field (and other…

FOIL is a well-known mnemonic that is used to find the product of two binomials. We conduct a large sample (n = 252) observational study of first-year college students and show that while the FOIL procedure leads to the accurate expansion of the product of two binomials for most students who apply it, only half of these students exhibit conceptual…

Problem-based learning has been applied over the last three decades to a diverse range of learning environments. In this educational approach, different problems are posed to the learners so that they can develop different solutions while learning about the problem domain. When applied to conceptual modelling, and particularly to Qualitative…

New strategies can ignite teachers' imagination to create new lessons or adapt lessons created by others. In this article, the authors present the experience of an algebra teacher and his students solving linear and literal equations and explain how the use of ideas found in past NCTM journals helped bring this lesson to life. The…

Miscommunications appear to offer powerful L2 learning opportunities. In particular, they often arouse emotions that facilitate event recall, and may motivate learners by providing implicit evidence of the communicative importance and personal relevance of underlying language features. This article reports on a pedagogical approach to utilizing…

The authors teach a problem-solving course for preservice middle-grades education majors that includes concepts dealing with absolute-value computations, equations, and inequalities. Many of these students like mathematics and plan to teach it, so they are adept at symbolic manipulations. Getting them to think differently about a concept that they…