tag:blogger.com,1999:blog-7965571054864902078.post4905182251674306456..comments2012-10-01T23:07:40.030-07:00Comments on Blended Learning with Mrs. Delaney: Week 5 - successful and not so successful bdelaneyhttp://www.blogger.com/profile/04889862734123211152noreply@blogger.comBlogger5125tag:blogger.com,1999:blog-7965571054864902078.post-39909368233992812752012-10-01T23:07:40.030-07:002012-10-01T23:07:40.030-07:00Maybe have the kids come up with what they'd c...Maybe have the kids come up with what they'd call it?Suzannehttp://www.blogger.com/profile/15271008245885122023noreply@blogger.comtag:blogger.com,1999:blog-7965571054864902078.post-28121396424210497322012-10-01T17:31:13.496-07:002012-10-01T17:31:13.496-07:00Great explanation Suzanne. I did something similar...Great explanation Suzanne. I did something similar today with "naked math". I used the words "what do you know about" 3 x 16 and 6 x 8? It was a real eye opener to math language and thinking. I prompted them with looking for relationships, patterns and anything we use to describe numbers. All four classes took the discussion in different directions but it was powerful discussion and generated a lot of thinking. I think I have adopted a new routine for developing mathematical thinking! <br />However, I will need different words than "naked math"! :-)<br />bdelaneyhttp://www.blogger.com/profile/04889862734123211152noreply@blogger.comtag:blogger.com,1999:blog-7965571054864902078.post-4002675521049296772012-10-01T07:39:10.863-07:002012-10-01T07:39:10.863-07:00You may not want to use the phrase we've adopt...You may not want to use the phrase we've adopted but we use "Notice/Wonder" with "naked math"! So, for example, something like:<br /><br />What do you notice? What do you wonder?<br />Find (5/10) รท (5/6)<br /><br />I think it takes some time to develop thorough noticings of naked math but it might be something to work on.<br /><br />Here are some of the kinds of things we'd expect kids to get to the point of thinking about:<br />* Will the answer be a number? Whole number? Positive? Negative?<br />* What's too high?<br />* What's too low?<br />* What's a reasonable guess?<br /><br />Another question to ask with that same prompt is "How can you solve your problem? How many different ways?" <br />* Think about different strategies you could use.<br />* What did you notice or think about to help you choose a strategy?<br />* Did you get stuck? What did you notice or think about to help you get unstuck?<br />* How do you know you are right? Is your answer reasonable? Does it match your estimation?<br /><br />So, while "problem solving" might make us think of story problems or word problems or PoWs, we might also extend it to solving naked math problems!Suzannehttp://www.blogger.com/profile/15271008245885122023noreply@blogger.comtag:blogger.com,1999:blog-7965571054864902078.post-56906077585612650872012-09-30T19:39:40.381-07:002012-09-30T19:39:40.381-07:00Thanks Suzanne! What a great idea. I am going to s...Thanks Suzanne! What a great idea. I am going to see how I can adapt this into the daily practice. I have taught them "Notice/Wonder" with problem solving. Maybe it is time to just hand them a scenario only problem and get all of them thinking. <br /><br />I have been taking video of my class. It is a great reflection on my teaching. It is still too teacher centered. If I want them to learn to think, I need to let them lead with their "Noice/Wonder". More to come..............bdelaneyhttp://www.blogger.com/profile/04889862734123211152noreply@blogger.comtag:blogger.com,1999:blog-7965571054864902078.post-26175797345271081692012-09-30T18:21:25.178-07:002012-09-30T18:21:25.178-07:00Barbara, your story and what you're working on...Barbara, your story and what you're working on figuring out how to support remind me of why we developed our "Notice/Wonder" scenario-only activity for the Math Forum Problems of the Week. As you know well when the question is removed from the problem scenario, the struggling students engage and the high achieving students have no where to go except deeper into the thinking about the context.<br /><br />I wonder if some of that strategy can be applied to what you are assigning? How can homework/classwork be presented so that students are encouraged to:<br />* make sense of the problems and persevere in solving them<br />* reason abstractly and quantitatively<br />.... and all of the other Practices #3 through #8?<br /><br />Would it help to remove more of the questions? Is it the nature of the tasks that are making it difficult to support both struggling students and high achievers? Can we differentiate better when there are fewer questions to answer and more activities in which the students engage?<br /><br />I'm looking forward to reading your continuing stories -- it's so great to have a window into what you and your students are doing. Thank you so much for sharing your thoughts.<br />Suzannehttp://www.blogger.com/profile/15271008245885122023noreply@blogger.com