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The real power is in connecting to students' thinking.
Teaching and learning are complex activities that depend upon evolving and rarely articulated interrelationships among teachers, students, materials, and ideas.
No prescription for their improvement can be simple.
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.
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.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.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.The motivational benefits that can be provided by workplace and everyday problems are worth mentioning, for although some students are aware that certain mathematics courses are necessary in order to gain entry into particular career paths, many students are unaware of how particular topics or problem-solving approaches will have relevance in any workplace.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.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.