Discusses how a single problem can be utilized to discuss mathematical skills and concepts at several different levels. Presents a problem involving fractions examined at the following four levels according to the abilities of the students: (1) finding solutions; (2) identifying methods for finding solutions; (3) exploring similar examples; and…

Discussed is the process of translating situations involving changing quantities into mathematical relationships. This process, called dynamical modeling, allows students to learn new mathematics while sharpening their algebraic skills. A description of dynamical systems, problem-solving methods, a graphical analysis, and available classroom…

Suggests that defining critical thinking as assessing authenticity, accuracy, and worth of knowledge claims and arguments also describes the historian's role. Recommends teaching students history in such a way as to necessitate higher level thinking skills. Argues that the writing process helps because it requires evaluation of existing data and…

Explores the role that symbolic-graphical calculators can play in the current calls for reform in the mathematics curriculum. Discusses symbolic calculators and graphing calculators in relation to problem solving, computational skills, and mathematics instruction. (MDH)

Examples from related case studies illustrate possible consequences of a social constructivist approach to learning and teaching mathematics. Discusses student tasks that promote flexibility in mathematizing subject matter; constructive versus Euclidean geometry approaches; working with real-life mathematics problems; and product versus process…

Discusses how children's books can engage students in communicating mathematical ideas. Describes situations in which teachers use literature as a stimulus for thinking, listening, writing, speaking, and reading about mathematics. (12 references) (MDH)

A unit in a college course on technology and human values involves the students' questioning of traditional Western values as they relate to technological rationalism, calling dominant ideology into question. The approach is based on Paulo Freire's problem-posing pedagogy, and incorporates analysis of selected paintings from the Futurist movement.…

Describes a teaching activity consisting of a problem-solving story about a company in a small town that is burying hazardous material which may create future problems for the community. The activity challenges students to address ethical issues relative to responsibility and accountability for protection of the water supply. (PR)

Explains how teachers applied the case method approach in a college pedagogy class, describing the case and context, noting how problem solving evolved within student groups and presenting results from follow-up surveys. Numbers of students in class and time devoted to problem solving were critical to the approach. (SM)

Describes a research project that takes a problem-solving approach to teaching about social stratification. Students identify a local issue related to stratification (homeless, welfare reform, etc.). They break into small groups and design a research plan, conduct a literature search, perform the fieldwork, and arrive at a synthesis. (MJP)

Explains that authentic teaching and assessment enable students to utilize their prior knowledge, recent learning, and critical thinking and problem-solving skills in real-world contexts. Describes examples of authentic teaching and assessment that use the "Voluntary National Content Standards in Economics" as a framework for economics…

Problem-based learning (PBL) is a pedagogical approach in which students encounter a problem and systematically set about finding ways to understand the problem through dialogue and research. PBL is an active process where students take responsibility for their learning by asking their own questions about the problem and in this paper we explore…

This article explains how to teach long division using hands-on materials (skittles, base ten blocks, colored counters, numeral cards) and investigates reviewing division word problems with middle school students (N=27) with learning disabilities in mathematics by this approach compared to spending the same amount of time on the typical practices…

Academic assessment for students with challenging behavior is often overlooked. Confronted with a curriculum that is above or below their instructional needs, students may engage in a range of inappropriate behaviors (e.g., acting-out, withdrawal, social avoidance). In that behavioral and learning problems are reciprocal, academically related…

This paper deals with Nurture Groups, which are a specialist form of provision for pupils with social, emotional and learning difficulties. The paper outlines the theoretical underpinnings of the NG approach and describes the practical arrangements and operations features of this form of provision. Evidence from research studies exploring the…