The meaning of “circle”

This is my contribution to the week of code.

One of the things I remember from reading Papert (Mindstorms I think) was his explanation of different ways of understanding. He claimed that computation offered a different way of understanding. One example which I think was from the same source concerned the understanding of circle. The demo goes something like this.

Most of probably remember the definition of circle – a closed plane figure consisting of all points equidistant from a point. The ability to produce this definition does not really mean we understand it. He proposed the following demonstration (I hope I am remembering the source appropriately). You can turn this definition into a program (logo).

blockly

 

This demo was generated in Blockly. If you follow the code, you should be see how the code expresses the definition.

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Mastery learning

 

The theory and application of mastery learning has long been a professional interest. The origins go back to the 60s and some crude variants to even earlier models of instruction/learning. I have also presented some of these ideas in my educ psychology classes for years as an alternative way to understand learner aptitude (time to learn). In recent years I have added a component focused on the Kahn Academy. My students find Keller and Bloom to be what they call “theoretical” (even though there were clearly applications of each), but they are intrigued by Kahn. One student wanted the link today because he wanted to try the modules on biochemistry.

I have watched with interest the evolution of the Kahn Academy. By evolution, I mean the earliest version did not promote the flipped classroom (a different use of class time) and mastery learning (very similar in my thinking to Keller’s PSI). I wonder about this evolution. Is what we see now closer to the original “grand plan” or have those developing this system found that what was being developed were great ways to implement existing “big ideas”?

I do discover something new each time I prep for my presentations and visit the site to review the features. This time I discovered the separate content on programming. Educators (e.g., Maker movement) have been rediscovering programming and the Academy offers an interactive experience based in Javascript.

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Should students be encouraged to control a turtle or grow radishes?

I struggle with the concept of a new “maker culture”? I really like the concept as suggesting new educational options, but I struggle with the assumption that makers are “technology-based”. There are lots of ways to make things that do not include programming or robots or a soldering gun. Nothing wrong with programming or construction of technology devices, but we learn by making other things as well. We make something when we write. Writing and programming share the use of a symbol system to create a product. Writing, which also benefits from the use of technology, is not among those processes included by those who claim to belong to the culture of makers. One concern that I have with the popularized version of being a maker is that the examples given will not be of interest to all students or all students. I would prefer all students have the opportunity to pursue a self-identified passion.

How educators are encouraged to apply technology is somewhat schizophrenic. Educators seem caught between two platitudes. On hand they are encouraged to recognize that “it is not about the technology, it is about the learning” (a common educator twitter admonition). Of course, makers seem to argue the opposite position. Are we back to teaching a version of computer literacy or the concern that we must program or be programmed?

Perhaps students should be offered options. I mean options beyond electives such as art, music and athletics. As I have encouraged expanding the allowable electives, I have proposed developing and studying school gardens or habitats. Many may be surprised that there are such things as school gardens, but these activities are more common than many might think and have a very similar literature. One of the realities of involving all students in any supplemental activity is that students seldom accomplish more (note the plural students) than develop an awareness of the content area. I do not think this is what is intended. It makes more sense to me to find ways to allow those students with a real passion for such topics to explore in depth rather than provide all a superficial exposure.

I would encourage close reading of the following two reviews (the first is an analysis of logo programming and the second of school garden projects). These are reasonable reviews of the benefits of teaching programming (logo) and gardening. Just what kind of transfer has resulted from such learning experiences?

Salomon, G. & Perkins, D. (1989). Rocky road to transfer: Rethinking mechanisms of a neglected phenomenon. Educational Psychologist, 24(2), 113-142.

Williams, D.R. & Dixon, P. S. (2013). Impact of a garden-based learning on academic outcomes in schools: Synthesis of research between 1990  and 2010. Review of Educational Research, 83, 211-235.

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