tag:blogger.com,1999:blog-5779271385256625533.post2605668299503877759..comments2024-03-06T22:39:11.472-08:00Comments on cheesemonkey wonders: Scaffolding Proof to Cultivate Intellectual Need in Geometrycheesemonkeysfhttp://www.blogger.com/profile/09311170815422010013noreply@blogger.comBlogger5125tag:blogger.com,1999:blog-5779271385256625533.post-11796066807873974672016-10-27T21:44:31.097-07:002016-10-27T21:44:31.097-07:00Gotcha gotcha gotcha. This makes sense to me now:
...Gotcha gotcha gotcha. This makes sense to me now:<br /><br />"Now students are starting to understand why congruent triangles are so useful and how they enable us to make use of their corresponding parts!"Dan Meyerhttps://www.blogger.com/profile/11323257310042023350noreply@blogger.comtag:blogger.com,1999:blog-5779271385256625533.post-46363128179429504902016-10-27T13:40:47.461-07:002016-10-27T13:40:47.461-07:00Hi Dan, That's a reasonable question, but it&...Hi Dan, That's a reasonable question, but it's a bit more meta than we are working with right now. We're operating in a state of 'suspended disbelief' around the need for proof itself. My students here accept the a priori need for argumentation or proof. But they have trouble sometimes seeing why you would need a particular new theorem (for example). So the essential question might be, what would enable you to make a connection between congruent triangles, say, and parallel lines?<br /><br />We are working at a more modest, micro-level than justifying proof itself!<br /><br />- Elizabeth (@cheesemonkeysf)cheesemonkeysfhttps://www.blogger.com/profile/09311170815422010013noreply@blogger.comtag:blogger.com,1999:blog-5779271385256625533.post-51175928719915848322016-10-27T12:53:08.713-07:002016-10-27T12:53:08.713-07:00Heya Cheese, this seems like really useful scaffol...Heya Cheese, this seems like really useful scaffolding for proof but I don't see the need angle. Based on this treatment, how do you hope students would respond to the question, "What's the point of proof?"Dan Meyerhttps://www.blogger.com/profile/11323257310042023350noreply@blogger.comtag:blogger.com,1999:blog-5779271385256625533.post-40009963342482253002016-10-19T21:52:30.878-07:002016-10-19T21:52:30.878-07:00Michael, I confess that I haven't read it, and...Michael, I confess that I haven't read it, and so I am curious to hear what you value about it and why. I have read a bit about it and done some investigation of this kind of approach to geometric inquiry, but I've run into a few of problems so far. The first one is that my school is so far from 1-1 with the needed technologies it has been difficult to explore. The second is that I have two blind students (plus some visually impaired) who would be completely unable to access GSP given the state of available tactile display technology (though we are cheering on the U of Michigan and their effort to come up with a full-page refreshable tactile display!). Finally, there seems to be a difference between understanding the geometry interactively (as through GSP or Geogebra) and affirmatively constructing the written argument/proof that takes advantage of that interactive understanding.<br /><br />Can you say a little more about your thoughts and/or experience with the de Villiers book/method?<br /><br />- Elizabeth (@cheesemonkeysf)cheesemonkeysfhttps://www.blogger.com/profile/09311170815422010013noreply@blogger.comtag:blogger.com,1999:blog-5779271385256625533.post-65604678914615611632016-10-19T21:22:51.040-07:002016-10-19T21:22:51.040-07:00Have you read RETHINKING PROOF WITH GEOMETER'S...Have you read RETHINKING PROOF WITH GEOMETER'S SKETCHPAD by Michael de Villiers? Michael Paul Goldenberghttps://www.blogger.com/profile/04939966966192318775noreply@blogger.com