I've wanted to have a paper that describes the ideas that get developed in a unit of inquiry - highlighting how very deep these ideas go, even if the topic we cover in 5 weeks is one that most courses cover in 1. -- This semester had some really cool ideas; a few profound, some just cute -- so I thought I could draft a paper based on those. I'm imagining this for TPT. I could also make it a chapter in a book I want to write... but that's too daunting. It already feels a bit smarmy (?) for TPT.
Wonderful Ideas about Optics:
Student Investigations into Light & the EyeWriting of her experience as a developmental psychologist, Eleanor Duckworth (1996) describes one 7-year-old boy, Kevin, arranging straws. Upon seeing the straws he has an idea of how he wants to arrange them, struggles, succeeds, and is clearly delighted by the wonderful idea he had—the idea to arrange an assortment of straws in order by length. Reflecting on Kevin’s joy, Duckworth notes, “The having of wonderful ideas is what I consider the essence of intellectual development. And I consider it the essence of pedagogy to give Kevin the occasion to have his wonderful ideas and to let him feel good about himself for having them.” (p. 1)
It’s tempting to believe that Duckworth is referring to
childhood intellectual development and
primary school pedagogy; that we cannot expect high school students or undergraduates to be delighted by the Krebs cycle or Snell’s Law in the same way that a first-grader enjoys arranging straws, or expect all introductory physics students to delight and feel good about physics (in fact, students’ emotional responses to physics are often quite the opposite). Reading this story, however, I was reminded of my first experience working in a physics lab as a summer REU student at the University of Washington. My task was tedious and rather mundane—aligning a laser with a mirror—but at some point I saw an unexpected, though easily explained, pattern of light. I tentatively approached the postdoc to show him and talk through the mechanism behind the observation and was relieved when he shared in my excitement, saying “You have to show Eric! He will get a kick out of this!” Though most of my summer research experience is lost to me, this event stands out— having and sharing a wonderful idea with a member of the physics community, witnessing his enthusiasm for it, and the sense was that this was the kind of thing that was to be celebrated and shared with the PI. It was striking not only because of the magical quality of that moment, but because of the absence of such moments from the rest of my undergraduate experience. (“Hey professor! Look at this! I’ve found the eigenvectors for the del-squared operator!” said no student ever.)
Scientific lives are bookended with the having of wonderful ideas — children delight in falling objects, and practicing scientists- as part of their job description- have and share wonderful ideas with colleagues. It is only during formal education that we find scant opportunities for students to have wonderful ideas and feel good about themselves for having them. Our exams and surveys ask students about scientifically correct ideas - that is, if they have learned and understood others’ wonderful ideas. In reform curricula, we walk students through steps by which they can re-create wonderful ideas. But opportunities for students to construct their own ideas from their own questions and to share these ideas as the raw material of curriculum, are rare. Given that this is a hallmark of scientific practice - having and sharing novel ideas - its absence is troubling for those concerned with students’ conceptual development. Given the sense of joy, wonder and esteem that having and sharing novel ideas can bring, its absence from our curricula is troubling in an ethical sense as well.
A course on scientific inquiry taught at CSU, Chico, seeks to remedy this. In this course, students examine complex phenomena and construct ideas and representations that account for these phenomena. We use neither textbook nor lab manual. Instead, students work in groups with everyday items, sharing ideas and findings with other groups as the class moves towards consensus models of phenomena. The syllabus describes the goals of the class as follows:
This is a class on Inquiry — not a class on Light & Color. (Just like a drawing class might spend time drawing flowers, but the class is not a class about flowers.) You are not assessed on how accurately your ideas mirror the ideas of scientists, but on how accurately your activities mirror the practices that scientists engage in when they study light & color— problematizing phenomena, creating careful definitions, constructing models of phenomena that are consistent with evidence, designing tests to further test those models (particularly competing models), using those models to explain and predict, reading and following the ideas of colleagues (your classmates), critiquing and improving ideas over time, and sharing work via writing.
Despite the emphasis on inquiry (rather than the products of inquiry), student ideas from this class - semester after semester - not only recapitulate major ideas from geometric optics, but they go well beyond ideas from introductory physics, asking questions, devising experiments and developing representations that address core issues in physics.
In other descriptions of the course (cite) we have described students’ understanding of the nature of science and their engagement in scientific practices, consistent with the goals of the course. Here, however, we emphasize the scientific ideas that students generated during one month during the Fall 2012 semester. The ideas are intriguing in their own right and may prove useful for conceiving of problems and investigations for instruction; more importantly, however, we wish to demonstrate the kinds of ideas that students generate, and that the call by Duckworth for pedagogy that allows students to have “wonderful ideas and to let [them] feel good about [themselves] for having them” can be consistent with the development of deeply scientific ideas - often ones that far exceed goals we might have set for an introductory-level course.
The ideas:
Using gelatin to visualize a focused image
- by J. Cerdo, N. Etchison, E. Johnson, A. Lerner
The index of refraction of a contact lens
- N. Cassel
(why do my glasses keep getting thicker and my contact lenses don't?)
The Schachar mechanism and human lenses
- E. Honeycutt, M. Gonzales
(we expect that straining our eyes would mean tightening muscles that control the lens; and we expect that tight muscles would flatten out the lens. But we strain to see up close (rounded lens) not far. Why?)
The Cardinality of Infinite Sets: Magnifying Images
- K. Mulhern
(how can we magnify an image without "gaps"?)
Depth perception and virtual images
- D. Barrett
("virtual images" suggest that a magnified image is located behind the actual object - but it doesn't look like that - looking through binoculars doesn't make objects look realllly big and reallllly far away. why?)
Limits of perception: viewing cells
- K. McAtee
(you can't see the resolution of a high def tv when you're viewing it on a low-def tv screen)