> Context • In 1972, Papert emphasized that “[t]he important difference between the work of a child in an elementary mathematics class and […]a mathematician” is “not in the subject matter […]but in the fact that the mathematician is creatively engaged […]” Along with creative, Papert kept saying children should be engaged in projects rather than problems. A project is not just a large problem, but involves sustained, active engagement, like children’s play. For Papert, in 1972, computer programming suggested a flexible construction medium, ideal for a research-lab/playground tuned to mathematics for children. In 1964, without computers, Sawyer also articulated research-playgrounds for children, rooted in conventional content, in which children would learn to act and think like mathematicians. > Problem • This target article addresses the issue of designing a formal curriculum that helps children develop the mathematical habits of mind of creative tinkering, puzzling through, and perseverance. I connect the two mathematicians/educators – Papert and Sawyer – tackling three questions: How do genuine puzzles differ from school problems? What is useful about children creating puzzles? How might puzzles, problem-posing and programming-centric playgrounds enhance mathematical learning? > Method • This analysis is based on forty years of curriculum analysis, comparison and construction, and on research with children. > Results • In physical playgrounds most children choose challenge. Papert’s ideas tapped that try-something-new and puzzle-it-out-for-yourself spirit, the drive for challenge. Children can learn a lot in such an environment, but what (and how much) they learn is left to chance. Formal educational systems set standards and structures to ensure some common learning and some equity across students. For a curriculum to tap curiosity and the drive for challenge, it needs both the playful looseness that invites exploration and the structure that organizes content. > Implications • My aim is to provide support for mathematics teachers and curriculum designers to design or teach in accord with their constructivist thinking. > Constructivist content • This article enriches Papert’s constructionism with curricular ideas from Sawyer and from the work that I and my colleagues have done
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Learning from Our Study Organisms about Sexual Selection: Lessons from the Ocellated Wrasse
Sexual selection is a powerful force shaping not only the details but also the breadth of what we see in nature. Yet so much unexplained variation remains. Organisms often solve the “problem” of how to pass on their genes in ways that do not fit our current expectations. I argue here that integrating empirical surprises will push our understanding of sexual selection forward. Such “nonmodel” organisms (i.e., species that do not do what we think they should do) challenge us to think deeply, integrate puzzling results, question our assumptions, and consider the new (and arguably better) questions these unexpected patterns pose. In this article, I share how puzzling observations from my long-term research on the ocellated wrasse (Symphodus ocellatus) have shaped my understanding of sexual selection and suggested new questions about the interplay among sexual selection, plasticity, and social interactions. My general premise, however, is not that others should study these questions. Instead, I argue for a change in the culture of our field—to consider unexpected results a welcome opportunity to generate new questions and learn new things about sexual selection. Those of us in positions of power (e.g., as editors, reviewers, and authors) need to lead the way.
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- Award ID(s):
- 1655297
- PAR ID:
- 10474075
- Publisher / Repository:
- University of Chicago Press
- Date Published:
- Journal Name:
- The American Naturalist
- Volume:
- 201
- Issue:
- 3
- ISSN:
- 0003-0147
- Page Range / eLocation ID:
- 418 to 428
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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