tag:blogger.com,1999:blog-5779271385256625533.post2605668299503877759..comments2017-10-10T06:38:46.205-07:00Comments on cheesemonkey wonders: Scaffolding Proof to Cultivate Intellectual Need in Geometrycheesemonkeysfhttp://www.blogger.com/profile/09311170815422010013noreply@blogger.comBlogger6125tag:blogger.com,1999:blog-5779271385256625533.post-80609959190291592012017-01-01T21:01:37.350-08:002017-01-01T21:01:37.350-08:00Hello! This post was recommended for The Best of t...Hello! This post was recommended for The Best of the Math Teacher Blogs 2016: a collection of people's favorite blog posts of the year. We would like to publish an edited volume of the posts at the end of the year and use the money raised toward a scholarship for TMC. Please let us know by responding via http://goo.gl/forms/LLURZ4GOsQ whether or not you grant us permission to include your post. Thank you, Tina and Lani.Sue VanHattumhttps://www.blogger.com/profile/10237941346154683902noreply@blogger.comtag: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 Goldenberghttps://www.blogger.com/profile/04939966966192318775noreply@blogger.com