tag:blogger.com,1999:blog-1907702537884089718.post5329044576256761411..comments2019-09-27T11:04:09.875-07:00Comments on Exit 10A: The D WordJoe Schwartzhttp://www.blogger.com/profile/02304083254248927187noreply@blogger.comBlogger7125tag:blogger.com,1999:blog-1907702537884089718.post-22012018257807676382018-11-27T17:31:57.733-08:002018-11-27T17:31:57.733-08:00Great question! The fact remains that, differenti...Great question! The fact remains that, differentiation or no differentiation, students are accountable for grade level standards, whether they're ready for them or not. So in the example above, if the standard is solving multi-step multiplication number stories, and there are students who that day elect not to solve any problems involving multi-step multiplication, it wouldn't absolve the teacher of teaching the standard or holding students accountable for it. What I described above is an alternative differentiation model and not a replacement for a specific lesson. The student-generated problems could be left up for days for kids to work on as the teacher meets with small, very targeted groups that are still working on specific content standards. Joe Schwartzhttps://www.blogger.com/profile/02304083254248927187noreply@blogger.comtag:blogger.com,1999:blog-1907702537884089718.post-54251553683858152872018-11-27T07:53:33.285-08:002018-11-27T07:53:33.285-08:00This work is so important! Thank you for posting,...This work is so important! Thank you for posting, Joe. I hope this opens the doors for the students to have access to quality tasks instead of quality text book writing. Better to have scaffolding "as needed" rather than "just in case it is needed."<br /><br />A question for you though: How might you respond to someone that argues this approach may not land on a standard that a specific lesson was targeting?Ericahttps://www.blogger.com/profile/17361437929693867462noreply@blogger.comtag:blogger.com,1999:blog-1907702537884089718.post-48255295541703448392018-10-17T02:58:56.764-07:002018-10-17T02:58:56.764-07:00Thanks for the comment Dan. For me, this goes to ...Thanks for the comment Dan. For me, this goes to the very heart of what it means to do mathematics. In the school setting, it is very defined and rarely taken to mean things like noticing and wondering, creating new questions, etc. (This is actually a subject that Edmund Harriss and I are having a very robust e-mail exchange about.) This is due to many factors, but one big one is the nature of standardized testing. Until the quality of the questions you ask is valued more than the accuracy of the ones you answer, then teachers and students will continue to be measured by that very narrow definition. And the differentiation and remediation will continue to be more of the same, only slower and louder. Who's responsible? Joe Schwartzhttps://www.blogger.com/profile/11524614672307520366noreply@blogger.comtag:blogger.com,1999:blog-1907702537884089718.post-68816336253002882422018-10-14T16:21:29.700-07:002018-10-14T16:21:29.700-07:00Your post has me thinking about a transformation i...Your post has me thinking about a transformation in content knowledge I've been making way too slowly over my entire life.<br /><br />My content knowledge transforms when I realize how many different ways there are to understand any given area of mathematics. Many more than just "the formal operations in that area," which was my impression for a long time. Instead, you can eg. notice & wonder mathematically, make reasonable predictions, select an appropriate representation for a question, create <em>new</em> questions about the math, understand connections between that area and others, etc.<br /><br />That content knowledge transformation increases our options for remediation and differentiation.<br /><br />If math is just formal operations, then the best and really the only way to remediate is to show students enough examples of those operations until they can repeat them. If math is just operations, then the only way to differentiate is to move students to the next set of formal operations.<br /><br />As my field of vision on mathematics increases so too does my imagination for ways I can help students, for ways I can enrich a task beyond its formal operations.Dan Meyerhttp://blog.mrmeyer.com/noreply@blogger.comtag:blogger.com,1999:blog-1907702537884089718.post-74110545319974878242018-09-27T02:48:36.930-07:002018-09-27T02:48:36.930-07:00Thanks Simon. As always, you express what I mean ...Thanks Simon. As always, you express what I mean to say much better than I'm able to. That "losing awareness of any line" is really important to me. I'm not sure we can completely eliminate it, but it's nice to forget that it's there, if even for a time.Joe Schwartzhttps://www.blogger.com/profile/02304083254248927187noreply@blogger.comtag:blogger.com,1999:blog-1907702537884089718.post-65205983232407997572018-09-26T12:13:27.728-07:002018-09-26T12:13:27.728-07:00This challenges the idea that there's one dime...This challenges the idea that there's one dimension, a road that we're either way ahead on, or way back on. That there are high kids and low kids. That they can't be involved in conversation with each other.<br /><br />I've found that the kids who have the interesting questions aren't necessarily the same as those with most experience handling numbers. Same with the ones who like to explore. Or who want to explain things. Or the ones who watch what's happening. We force it all into some grotesque beauty contest when we narrow down what we're asking of our students.<br /><br />I love how your scissors work takes away the lining-up-in-order of lowness that is so common. Instantly there are more dimensions, we lose awareness of any line.Simon Gregghttps://www.blogger.com/profile/07751362728185120933noreply@blogger.comtag:blogger.com,1999:blog-1907702537884089718.post-1961519654090659392018-09-24T14:14:25.553-07:002018-09-24T14:14:25.553-07:00Love it, Joe. By cutting it down to the situation,...Love it, Joe. By cutting it down to the situation, everyone's mathematizing is valuable, and there's more to see than just this question which I think I can or can't answer. Plus, how much richer is the discussion going to be?John Goldenhttps://www.blogger.com/profile/18212162438307044259noreply@blogger.com