ABSTRACT:Researchers and policy makers often use the metaphor of an ever-narrowing pipeline to describe the trajectory to a science, technology, engineering or mathematics (STEM) degree or career. This study interrogates the appropriateness of the STEM pipeline as the dominant frame for understanding and making policies related to STEM career trajectories. Our review of pertinent literature and independent analysis of data from the National Educational Longitudinal Study of 1988 finds that the trajectory implied by the pipeline metaphor fails to describe the experience for nearly half of those who go on to become scientists or engineers, masks meaningful differences in trajectories by subfield, and informs policies that do little to diversify or increase the size of the STEM workforce. We suggest a pathway metaphor to better illuminate the multiple trajectories toward STEM degrees and careers and present four composite trajectories as useful categorizations of the individual paths taken by STEM graduates and career entrants.

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The vision for school mathematics described by the National Council of Teachers of Mathematics (NCTM) suggests a need for new approaches to the teaching and learning of mathematics, as well as new curriculum materials to support such change. This article discusses implications of the NCTM standards for mathematics curriculum and instruction and provides three examples of lessons from problem-based curricula for various grade levels. These examples illustrate how the teaching of important mathematics through student exploration of interesting problems might unfold, and they highlight the differences between a problem-based approach and more traditional approaches. Considerations for teaching through a problem-based approach are raised, as well as reflections on the potential impact on student learning.