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)

To build understanding of, and the ability to use, first-year science and engineering calculus, students were introduced to differential equations and asked to carry out research on differential equation modeling projects. Describes a model for the research paper; appendices provide a copy of the student handout and five examples of student…

The problem-of-the-week (POW) and problem-solving class openers are exemplified as methods for the integration of course-relevant problem solving into a first-year algebra classroom without sacrificing time spent on developing skills and learning concepts. Illustrated examples, as well as problem sources, are included. (JJK)

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…

College teachers have done an excellent job over the years of teaching technical concepts, but they may not have done as good a job of teaching their adult students to be a good problem-solvers. Nine representatives from the technical industry and academia were interviewed in this study for their expert opinions on the subject of teaching…

The purpose of this study was to determine the influence of three college courses on attitude change toward older adults. To measure attitude change the Kogan Attitudes Toward Old People Scale (1961) was administered to 221 college students at the beginning and end of the semester. Participants were enrolled in one of three college courses: Child…

Many students doubt that statistical distributions are of practical value. Simulation makes it possible for students to tackle challenging, understandable projects that illustrate how distributions can be used to answer "what-if" questions of the type often posed by analysts. Course materials that have been developed over two years of classroom…