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Hi

I'm a CS and Sociology senior. I'm graduating this summer. I'm going into the peace corps next year. Eventually I'd like to teach elementary school; probably 3rd or 4th grade.

contact:

cmagill@gmail.com

Assignments

Assignment 13
Assignment 12
Assignment 10
Assignment 9
Assignment 8
Assignment 6
Assignment 5
Assignment 4
Assignment 3
Assignment 2
Assignment 1

Independent Research

The following are books I read this semester which relate to topics we've seen in the Design, Learning, and Collaboration class. The last 2 are most directly related to learning by doing, the topic of our group's research:

  • The Hidden Connections, Fritjof Capra
This book continues the exploration of the science of living systems which Capra began in The Web of Life and extends the discussion to the social implications of this science. Part of the book deals with the Santiago Theory of Cognition, of which Capra says this: "The central insight of the Santiago Theory is the identification of cognition, the process of knowing, with the process of life. Cognition, according to Maturana and Varela, is the activity involved in the sef-generation and self-perpetuation of living networks." "The Santiago Theory is the first scientific theory that overcomes the Cartesian division of mind and [brain], and will thus have far-reaching implications. Mind and matter no longer appear to belong to two separate categories, but can be seen as representing two complementary aspects of the phenomenon of life–process and structure." Among other things, this theory provides a theoretical basis for critiques of instructivist theories of learning based on a computational model of the mind.

I took the independent research portion of this class as an opportunity to read this book in part because I had read The Web of Life for another class which Hal was involved in, along with Ernie Arias. The Hidden Connections turned out to be less relevant to the topic of learning than Capra's earlier book, which was disappointing. You can read a longer summary and review of The Web of Life by downloading the document you'll find at the other end of this link: http://grackle.colorado.edu:4242/envd4363/uploads/44/

  • Amusing Ourselves to Death, Niel Postman
Postman argues that all information media have their own epistemological biases; each medium is best suited to carrying particular types of information. He contrasts the currently-dominant medum, television, with its predecessor, print. Television is best able to carry visually stimulating material in short, unrelated chunks, but doesn't easily accomodate lengthy exposition, or the degree of subtlety and complexity of argument, rationality, and intellectual distance which are characteristic of the contents of print media. Postman argues that the shift from print to television as our main information-sharing technology has dangerously reduced the quality of public discourse in our society. This book was short and fun to read–I recommend it to anyone in our class who is interested in the relationship between technology and culture.

Also see this speech by Postman, Informing Ourselves to Death

  • The Roots of Literacy, David Hawkins
Hawkins was a former CU professor of philosophy who died not long ago. This is a book which I first read several years ago and which I keep coming back to. It's a collection of essays covering topics related to literacy in a broad sense, to education, and to the teaching of science and mathematics. The essays I've been thinking about most in relation to this class are The Union of Number and Form: Mathematics for Childhood and Beyond; Reconstruction in Education: A Perspective on Dewey's Development; and Critical Barriers to Science Learning. The last of those, Critical Barriers, provided the seed for a design for an educational game which I think would be a good fit for the STRONG framework. The game would teach geometric concepts surronding a basic principle of geometric optics and an example of a critical barrier: angle of reflection equals the angle of incidence. I've described the idea for the game below.

  • Logic in Action, Frances Pockman Hawkins
The subtitle of this book is "from a teachers notebook." It is a day by day account of a teacher's work with a group of profoundly deaf 4 and 5 year-olds. Hawkins' detailed and intimate descriptions of the daily events in that classroom provide a concrete example of learning by doing thrown into high relief by the unusual situation of a nearly language-free classroom. As you progress through its chapters and through the weeks the children spent with Mrs. Hawkins, the children's growth becomes a convincing argument for the appropriateness of hands-on activities, particularly in classrooms of young children. Interwoven with the descriptions of the children's activities are Hawkins' articulation of and reflections on her own process as a teacher designing and creating a classroom environment to support learning. I can't recommend this book highly enough. It's out of print, so the CU library is probably the only place you can find a copy.

game

The idea for this game was motivated by one of the examples of Critical Barriers to science learning from David Hawkins' essay. Most people (85% in Hawkins' informal experiments) cannot correctly answer a question which asks them to predict where a certain object will appear in a mirror. The intention of this game is that it lead students into developing a robust understanding of one elementary concept (angle of incidence equals angle of reflection) while introducing a number of other geometrical terms and concepts.

Two children play the game in front of one computer; they cooperate to solve certain problems, and compete to solve others. The game proceeds through a series of activities with earlier activities aimed at exposing students' misconceptions about mirror vision and supplying a simple, correct explanation, and later activities aimed at helping students generalize from the the correct explanation and connect it to other geometric concepts/terms they may know. Each activity proceeds through a repeating sequence of sub-activities, with each subactivity characterized by particular visual elements and a distinct POV (which would be easier to draw than to describe, if only I could draw).

The game will be implemented in flash, in the familiar mock-3d style, except for the abstract-math POV, which will be simple rendered 3-d movies.

The very first subactivity might show students their two avatars (player-icons) from the rear, standing on a line parallel to and facing a wall, and require the students to place a mirror on the wall so that the avatars would be able to see each other in it. The students successfully complete this subactivity when they place the mirror at the midpoint between the two avatars. When that happens the POV changes to a first-person view from each avatar in turn, looking into the mirror and at the other's face, this POV gives the student a visual verification that their solution is correct. The third POV is an abstract-math-view in which students see their avatars in a 3-d cartesian space which rotates to a direct overhead view and draws in the angles formed by the avatars and mirror, highlighting for the first time the basic fact the game is trying to teach: angle of incidence equals angle of reflection. Finally, the POV returns to 3rd-person rear and the students repeat a different version of the first problem.

All the activities follow the same pattern of four subactivities–first a 3rd-person view for playing a game or solving a problem, then 2nd-person view for checking the solution, then an abstract view for illustrating the underlying concept, and finally back to the playing-a-game view. Each activity after the first builds a little more complexity into the problems and explanations. For example, the second activity might give students a room with a fixed mirror and ask them to take turns moving their avatars left to right until they can see each other–in this case the mirror will still end up directly in the middle, but now the first student's choice influences her teammate's choice (and depending on where the first student places her avatar the point on the line where its reflection is visible might not even be on the screen, if that happens the "verification" point of view should make that clear). A third activity would allow the students to place their avatars anywhere on the plane of the floor to find each other in a fixed (or movable) mirror; freedom in the depth dimension will mean that the mirror will no longer generally be at the midpoint of the horizontal interval the avatars delimit; the abstract-math section for this activity should emphasize that it is the equality of the angles, rather than the horizontal distance, that remains constant. The abstract math POV is also an opportunity for the game to model the use of geometric ideas such as parallel and perpendicular lines, complementary angles, midpoint, and the cartesian plane. Subsequent activities can continue to explore the concept of reflection and build the students grasp of the associated geometry by modifying one element at a time in each new activity: adding a third dimension of freedom (height), adding a second mirror, facing players in different directions, adding obstacles, round mirrors...?

Each activity should go pretty fast and present an interesting puzzle.

Course project


link to the STRONG swiki

see in particular the assessment pages, which were my contribution to the implementation.

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