<br><br><div class="gmail_quote">On Fri, Mar 12, 2010 at 8:47 AM, Maria Droujkova <span dir="ltr"><<a href="mailto:droujkova@gmail.com">droujkova@gmail.com</a>></span> wrote:<br><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex;">
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<br><br><div class="gmail_quote"><div><div></div><div class="h5">On Fri, Mar 12, 2010 at 8:30 AM, Caroline Meeks <span dir="ltr"><<a href="mailto:caroline@solutiongrove.com" target="_blank">caroline@solutiongrove.com</a>></span> wrote:<br>
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<br><br><div class="gmail_quote"><div><div></div><div>On Fri, Mar 12, 2010 at 8:08 AM, Maria Droujkova <span dir="ltr"><<a href="mailto:droujkova@gmail.com" target="_blank">droujkova@gmail.com</a>></span> wrote:<br>
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<br><div class="gmail_quote"><div>On Fri, Mar 12, 2010 at 1:48 AM, <span dir="ltr"><<a href="mailto:forster@ozonline.com.au" target="_blank">forster@ozonline.com.au</a>></span> wrote:<br></div><div>
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The strongest argument against is that any easily administered testing is biased towards lower level skills (as defined in Bloom's taxonomy). That would be OK, depending on how the data is used. Any attempt to modify teaching in response, biases the teaching towards the lower level skills.<br>
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In the Australian case, schools will be forced to confine their teaching to lower order skills to maintain their ranking, preserve enrolments and avoid criticism and funding cuts. In the case of RTI, it risks defining student progress by a narrow subset of education skills and overly concentrating teaching on this narrow subset.<br>
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Tony<br></blockquote></div><div><br>Tony,<br><br>This is my perennial response to the existing programs of this sort. When I plan interventions, I start with meaning and significance of math in the life of the person, their family and their social networks. Then some major concepts areas that can support and advance these meanings become apparent. From there, skills and tasks within concept areas can be mapped and developed. <br>
<br>What is highly problematic is that all the existing mainstream heavy testing machinery is at the level of skills. And what I am doing on the individual basis is not currently scalable. I can't even explain many parts of this highly intuitive, expertise-based process.<br>
<br>To address this problem, I just started to work on a crowdsourced rubric that will probe personal meaning and significance of math, and later used during interventions to help people track growth of math's significance in their lives. I am now polling local parents who work with me, with some very fruitful initial brainstorming happening among them. I am also meeting with several people who have large QA sites or projects that can be used to aggregate "sparse" info for crowdsourced projects. This may not happen fast, because of my other tasks such as the math game design project, but we will see what happens. I want this tool to measure the impact of my projects, which we currently observe in a purely qualitative, case-study manner.<br>
</div></div></blockquote><div><br></div></div></div><div>Maria,</div><div><br></div><div>I am going to shift the conversation back to reading because there just isn't enough data on math yet to talk about it. But I'm making the assumption that the neurology has an analog in math. </div>
<div><br></div><div>Although I of course agree with the need for meaning and significance there is also a risk in your approach.</div><div><br></div><div>As a dyslectic let me tell you how painful this type of approach can be. When you can't read or spell or remember things the way other people can and you really are motivated, want to, understand why you should etc. Then people keep over and over again talking and working with you on motivation, understanding of meaning and significance etc. let me tell you first hand this is very hard on the child's self image. You are sending the message that if only you wanted to you could do this just like everyone else.</div>
<div><br></div><div>The science says that isn't true for all children. The fMRIs show that dyslectic children are not using their brain in the same way and that these difference continue into adulthood and continue to have effects even after the child has learned to read using different pathways.</div>
<div><br></div><div>So one approach has the risk of ignoring higher level thinking and reasoning.</div><div><br></div><div>The other approach has the risk of ignoring actual malfunctions in low level brain based thinking. And if caught at an early age, and the correct interventions are done, these issues can be mitigated significantly.</div>
<div><br></div><div>To me its clear that we need to stop arguing about which approach is better and put on our engineer hats and figure out how to efficiently do both.</div></div></blockquote></div></div><div><br>Caroline,<br>
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This is an excellent point and a great personal story to go with it. I
am going to refer to that image when talking about the issues.<br>
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Good BALANCE between three directions is crucial. The three directions for math are
meaning and significance; conceptual understanding; and procedural fluency. I believe similar directions exist for other areas, as well, though they may have different names.<br></div></div></blockquote><div><br></div><div>
<br></div><div>Yes, I think this is excellent. I've seen many things broken down into 3 sides, Prof. Elmore does that a great deal in his school reform work.</div><div><br></div><div>The model I use is of a triangle. Student achievement is the center of the triangle, you are trying to get that to move up. If you raise any one corner of the triangle you will have a little effect for a while but then it will stop. To really see a change in the middle (student achievement) you have to have all three corners move up.</div>
<div><br></div><div>This model has another interesting point. If the triangle does not start flat, for instance in your example the child has fluency and understanding but little meaning, then when you put effort into the corner that is lowest you see a huge impact on the center.</div>
<div><br></div><div>As each student, school, country may start with corners at different levels, even if their center is at the same height, what works amazing well for one student, school, country, won't show much results in another context.</div>
<div><br></div><div>But rather then throwing our hands up in the air and saying you just can't transfer what you learn in one context to another, this triangular model gives us the idea that we could measure not just the hight of the center of the triangle but where the corners are and then have a much better idea of where effort will see good effect.</div>
<div><br></div><div>Another thing this model gives you is an understanding as to why interventions stop being effective. If a corner is low and you raise it at first you will see a huge impact on the center. But once that corner is higher then the others the amount the center moves up gets slower and then stops. It doesn't mean there was anything wrong with your intervention, it just means you have to rebalance.</div>
<div><br></div><div>I'll try to do a youtube with visuals this weekend. So comments and suggestions very welcome.</div><div><br></div><div>The news media thrives on simple dichotomies, but they don't lead us to good engineering decisions. But here in our community we could try to move to a culture where when we see one of these dichotomies in the media and talk about a triangle model model for it, play with that model, and see what insights it could give us as to how to design our systems.</div>
<div><br></div><div>Thanks!</div><div>Caroline</div><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex;"><div class="gmail_quote"><div>
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For math, there are plenty of tools to measure procedural fluency AND
effects of interventions on procedural fluency. There are also some
tools for measuring conceptual understanding, though fewer, most significantly problem solving tools, project-based rubrics, and essay-type tools ("explain why..."). There are motivation
tools and anxiety tools, as well, somewhat reflecting on meaning and
significance. <br>
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I am now working on this particular meaning and significance measure tool not because I consider it more
important than other tools, but because I'd like it to exist so I can
use it together with other tools.<br>
<br>Thank you for the engineering hat reminder. I will try my best to always talk about the balance of the three directions, rather than how dangerous one is without the others. It will be more productive.<div class="im">
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Cheers,<br>
Maria Droujkova<br>
<a href="http://www.naturalmath.com" target="_blank">http://www.naturalmath.com</a><br>
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Make
math your own, to make your own math.<br>
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</blockquote></div><br><br clear="all"><br>-- <br>Caroline Meeks<br>Solution Grove<br>Caroline@SolutionGrove.com<br><br>617-500-3488 - Office<br>505-213-3268 - Fax<br>