This article is the third in a series which draws on findings from Nunes, Watson and Bryant (2009): "Key understandings in school mathematics: a report to the Nuffield Foundation". In this article the author focuses on what learners have to understand and learn in order to do secondary mathematics well in general terms. She is assuming a…

Newman (1977, 1983) defined five specific literacy and numeracy skills as crucial to performance on mathematical word problems: reading, comprehension, transformation, process skills, and encoding. Newman's Error Analysis (NEA) provided a framework for considering the reasons that underlay the difficulties students experienced with mathematical…

In American popular culture, the word "rural" invokes images of sunny farms and little red school-houses--while "urban" means drugs, poverty, and crime. But rural schools face many of the same challenges as their urban counterparts. The problems of rural schools are often invisible to the public and policy makers. The solutions…

A case is described of the development of a lesson plan for 10th grade (age range 15-16) chemistry classes on the chemistry of shower gels. The lesson plan follows a socio-critical and problem-oriented approach to chemistry teaching. This means that, aside from learning about the basic chemistry of the components making up modern shower gels in…

A problem-solving template enables a methodology of instruction that integrates aspects of both sequencing and conceptual learning. It is designed to enhance critical-thinking skills when used within the framework of a learner-centered approach to teaching, where regular, thorough assessments of student learning are key components of the…

Important tools that schools need to support a 21st century approach to teaching and learning include the usual suspects: the Internet, pen and paper, cell phones, educational games, tests and quizzes, good teachers, caring communities, educational funding, and loving parents. All of these items and more contribute to a 21st century education, but…

Action Potential Science Experience (APSE) is a five-day summer camp offering science opportunities for K-8 students. The focus of the APSE curriculum is to teach science concepts and methods while challenging the participants to solve an overarching problem from the popular-culture context. The participants in the APSE entitled Burger 'N Fries…

This article traces the experiences of several outstanding teachers while explicating both the specific character of their teaching and how they were formed as teachers. These teachers' beliefs and the characteristics of their teaching style are examined in connection with the distinguishing features of the Russian schools in which they worked. In…

The mathematics that students see in their textbooks is highly polished. The steps required to solve a problem are all clearly laid out. Thus, students are denied what could be a valuable learning experience. Often when students meet a problem that differs only slightly from the ones in the book, they are unable to proceed and afraid to "play…

The fourth graders were ready to learn long division; however, their teachers were hesitant to begin the unit--just as they are every year. In a grade-level meeting with the school's math consultant, the teachers voiced their typical concerns. The math consultant was a university mathematics education professor spending a semester of sabbatical…

Cooperation between English as a second or other language (ESOL) and content-area teachers, often difficult to achieve, is hard to assess linguistically in a revealing way. This article employs register analysis (which is different from, but complementary to, genre analysis) in a Systemic Functional Linguistic perspective to show how an ESOL…

With the 2010 Winter Olympic Games prominent in the media, children were exposed to images of athletes skiing down snow-covered slopes, coasting furiously on bobsleds, and skating gracefully across the ice. Therefore, the authors capitalized on their children's natural curiosity about the world around them by exploring the concept of motion in a…

To focus on mathematical reasoning and what makes a good argument, the authors developed an assignment that requires college students to submit a book of mathematical reasoning as an assessment during the semester. To begin, the authors looked for questions and tasks that lend themselves to developing mathematical arguments and justifications and…

Problem solving, introduced in every grade and practiced throughout elementary school, is an essential foundation on which students build their understanding of mathematical ideas, operations, and relationships. This article discusses 1-2-3 Time, an instructional mode that promotes multimodal math learning in ways that engage and sustain students'…

The purpose of this article is to discuss curriculum-based measurement (CBM) as it is currently utilized in research and practice and to propose a new approach for developing measures to monitor the academic progress of students longitudinally. To accomplish this, we first describe CBM and provide several exemplars of CBM in reading and…