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The relationships among teachers, students, curricular materials, and pedagogical approaches are complex.
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.
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.
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 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.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 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.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.By increasing the number of potential links to the diverse knowledge and experience of the students, more students have opportunities to excel, which is to say that the above premise can promote equity in mathematics education.There is also evidence that learning mathematics through applications can lead to exceptional achievement.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).