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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.Mathematical problems also can serve as sources of meaning and understanding if the problems stimulate students' thinking.Teaching and learning are complex activities that depend upon evolving and rarely articulated interrelationships among teachers, students, materials, and ideas.
Integration of academic and vocational education, he argues, can serve the dual goals of "grounding academic standards in the realistic context of workplace requirements and introducing a broader view of the potential usefulness of academic skills even for entry level workers." Noting the importance and utility of mathematics for jobs in science, health, and business, Jean Taylor argues for continued emphasis in high school of topics such as algebra, estimation, and trigonometry.
She suggests that workplace and everyday problems can be useful ways of teaching these ideas for students.
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.
His essay opens with a dialogue among employees of a company that intends to expand its business into Japan, and then goes on to point out many of the uses of mathematics, data collection, analysis, and non-mathematical judgment that are required in making such business decisions.
In his essay, Thomas Bailey suggests that vocational and academic education both might benefit from integration, and cites several trends to support this suggestion: change and uncertainty in the workplace, an increased need for workers to understand the conceptual foundations of key academic subjects, and a trend in pedagogy toward collaborative, open-ended projects.There are too many different kinds of workplaces to represent even most of them in the classrooms.Furthermore, solving mathematics problems from some workplace contexts requires more contextual knowledge than is reasonable when the goal is to learn mathematics.The question, then, is how to exploit opportunities for connections between high school mathematics and the workplace and everyday life.Rol Fessenden shows by example the importance of mathematics in business, specifically in making marketing decisions.In the opening essay, Dale Parnell argues that traditional teaching has been missing opportunities for connections: between subject-matter and context, between academic and vocational education, between school and life, between knowledge and application, and between subject-matter disciplines.He suggests that teaching must change if more students are to learn mathematics.This volume may be beneficially seen as a rearticulation and elaboration of a principle put forward in Students need to experience mathematical ideas in the context in which they naturally arise—from simple counting and measurement to applications in business and science.Calculators and computers make it possible now to introduce realistic applications throughout the curriculum.Contexts from within mathematics also can be powerful sites for the development of mathematical understanding, as professional and amateur mathematicians will attest.There are many good sources of compelling problems from within mathematics, and a broad mathematics education will include experience with problems from contexts both within and outside mathematics.