For example, with a curriculum that emphasizes modeling and applications, high school students at the North Carolina School of Science and Mathematics have repeatedly submitted winning papers in the annual college competition, Mathematical Contest in Modeling (Cronin, 1988; Miller, 1995).
The relationships among teachers, students, curricular materials, and pedagogical approaches are complex.
The power of using workplace and everyday problems to teach mathematics lies not so much in motivation, however, for no con- text by itself will motivate all students.
The real power is in connecting to students' thinking.
Mathematical problems also can serve as sources of meaning and understanding if the problems stimulate students' thinking.
Of course, a mathematical task that is meaningful to a student will provide more motivation than a task that does not make sense.Public understanding and engagement with science, and citizen participation including through the popularization of science are essential to equip citizens to make informed personal and professional choices.Governments need to make decisions based on quality scientific information on issues such as health and agriculture, and parliaments need to legislate on societal issues which necessitate the latest scientific knowledge. For nations, it provides knowledge to compete in a technological community. In envisioning a future in which all students will be afforded such opportunities, the MSEB acknowledges the crucial role played by formulae and algorithms, and suggests that algorithmic skills are more flexible, powerful, and enduring when they come from a place of meaning and understanding. The essays in this report provide some rationale for this premise and discuss some of the issues and questions that follow.Contexts from within mathematics also can be powerful sites for the development of mathematical understanding, as professional and amateur mathematicians will attest.This finding was further verified through task-based interviews.Studies that show superior performance of students in problem-centered classrooms are not limited to high schools.Wood and Sellers (1996), for example, found similar results with second and third graders.Research with adult learners seems to indicate that "variation of contexts (as well as the whole task approach) tends to encourage the development of general understanding in a way which concentrating on repeated routine applications of algorithms does not and cannot" (Strässer, Barr, Evans, & Wolf, 1991, p. This conclusion is consistent with the notion that using a variety of contexts can increase the chance that students can show what they know.Calculators and computers make it possible now to introduce realistic applications throughout the curriculum.The significant criterion for the suitability of an application is whether it has the potential to engage students' interests and stimulate their mathematical thinking. 38) Mathematical problems can serve as a source of motivation for students if the problems engage students' interests and aspirations.