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	<title>
	Comments on: [LOA] Abstracting Abstraction	</title>
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	<description>less helpful</description>
	<lastBuildDate>Thu, 14 Feb 2013 02:02:34 +0000</lastBuildDate>
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		<title>
		By: Student Thinking About Abstracting &#171; Shifting Phases		</title>
		<link>/2012/loa-abstracting-abstraction/#comment-719868</link>

		<dc:creator><![CDATA[Student Thinking About Abstracting &#171; Shifting Phases]]></dc:creator>
		<pubDate>Thu, 14 Feb 2013 02:02:34 +0000</pubDate>
		<guid isPermaLink="false">/?p=14619#comment-719868</guid>

					<description><![CDATA[[...] My students have recently discovered the convention of describing silicon diodes as having a forward voltage of 0.7 V.Â  They know that this is not always true &#8212; or even usually true, in their experience.Â  The way they reconciled the difference made for an interesting conversation about abstraction &#8212; the verb, not the noun. [...]]]></description>
			<content:encoded><![CDATA[<p>[&#8230;] My students have recently discovered the convention of describing silicon diodes as having a forward voltage of 0.7 V.Â  They know that this is not always true &#8212; or even usually true, in their experience.Â  The way they reconciled the difference made for an interesting conversation about abstraction &#8212; the verb, not the noun. [&#8230;]</p>
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		<title>
		By: Abstraction in Language and in Math &#171; Let&#039;s Play Math!		</title>
		<link>/2012/loa-abstracting-abstraction/#comment-594437</link>

		<dc:creator><![CDATA[Abstraction in Language and in Math &#171; Let&#039;s Play Math!]]></dc:creator>
		<pubDate>Fri, 30 Nov 2012 20:09:37 +0000</pubDate>
		<guid isPermaLink="false">/?p=14619#comment-594437</guid>

					<description><![CDATA[[...] [LOA] Abstracting Abstraction [...]]]></description>
			<content:encoded><![CDATA[<p>[&#8230;] [LOA] Abstracting Abstraction [&#8230;]</p>
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		<title>
		By: dy/dan &#187; Blog Archive &#187; [LOA] London Underground Maps		</title>
		<link>/2012/loa-abstracting-abstraction/#comment-580657</link>

		<dc:creator><![CDATA[dy/dan &#187; Blog Archive &#187; [LOA] London Underground Maps]]></dc:creator>
		<pubDate>Mon, 19 Nov 2012 20:54:37 +0000</pubDate>
		<guid isPermaLink="false">/?p=14619#comment-580657</guid>

					<description><![CDATA[[...] stipulated earlier that the act of abstraction requires a context (some raw material) and a question (a purpose for [...]]]></description>
			<content:encoded><![CDATA[<p>[&#8230;] stipulated earlier that the act of abstraction requires a context (some raw material) and a question (a purpose for [&#8230;]</p>
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		<title>
		By: Detective Work &#171; make math		</title>
		<link>/2012/loa-abstracting-abstraction/#comment-497474</link>

		<dc:creator><![CDATA[Detective Work &#171; make math]]></dc:creator>
		<pubDate>Tue, 28 Aug 2012 01:33:15 +0000</pubDate>
		<guid isPermaLink="false">/?p=14619#comment-497474</guid>

					<description><![CDATA[[...] mostly triangles and quadrilaterals &#8211; in a way that is harder. Harder in a good way. Â Whole ladder of abstraction [...]]]></description>
			<content:encoded><![CDATA[<p>[&#8230;] mostly triangles and quadrilaterals &#8211; in a way that is harder. Harder in a good way. Â Whole ladder of abstraction [&#8230;]</p>
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		<title>
		By: Steve Thomas		</title>
		<link>/2012/loa-abstracting-abstraction/#comment-478263</link>

		<dc:creator><![CDATA[Steve Thomas]]></dc:creator>
		<pubDate>Wed, 25 Jul 2012 23:09:07 +0000</pubDate>
		<guid isPermaLink="false">/?p=14619#comment-478263</guid>

					<description><![CDATA[An Alternative definition: &quot;Abstraction reduces information and detail to facilitate focus on relevant concepts.&quot;

In there they also list learning objectives (See some below):
Learning Objective 5: The student can describe the combination of abstractions used to represent data.

Learning Objective 7: The student can develop an abstraction.

Learning Objective 8: The student can use multiple levels of abstraction in
computation.

Learning Objective 9: The student can use models and simulations to raise and answer questions. [P3]

Evidence for Learning Objective 9: Student work is characterized by:
9a. Use of models and simulations to generate new understanding and knowledge.
9b. Use of different levels of abstraction to represent phenomena.
9c. Use of models and simulations to formulate, refine, and test hypotheses.
9d. Use of simulations to facilitate testing of models.

In thinking about this I am thinking of using some &quot;worked examples&quot; with the kids where I walk them up and down the ladder.  And then perhaps ask them to explain (or facilitate their explanations) of the abstractions used in video games.

This is from csprinciples.org: Learning Objectives and Evidence Statements  (found here: https://docs.google.com/file/d/0B60yN79VbSzTNTJiMTM5NDUtMDNhOS00ZjVhLWIxYWMtZWMxNjQzYzk5ZDFi/edit)]]></description>
			<content:encoded><![CDATA[<p>An Alternative definition: &#8220;Abstraction reduces information and detail to facilitate focus on relevant concepts.&#8221;</p>
<p>In there they also list learning objectives (See some below):<br />
Learning Objective 5: The student can describe the combination of abstractions used to represent data.</p>
<p>Learning Objective 7: The student can develop an abstraction.</p>
<p>Learning Objective 8: The student can use multiple levels of abstraction in<br />
computation.</p>
<p>Learning Objective 9: The student can use models and simulations to raise and answer questions. [P3]</p>
<p>Evidence for Learning Objective 9: Student work is characterized by:<br />
9a. Use of models and simulations to generate new understanding and knowledge.<br />
9b. Use of different levels of abstraction to represent phenomena.<br />
9c. Use of models and simulations to formulate, refine, and test hypotheses.<br />
9d. Use of simulations to facilitate testing of models.</p>
<p>In thinking about this I am thinking of using some &#8220;worked examples&#8221; with the kids where I walk them up and down the ladder.  And then perhaps ask them to explain (or facilitate their explanations) of the abstractions used in video games.</p>
<p>This is from csprinciples.org: Learning Objectives and Evidence Statements  (found here: <a href="https://docs.google.com/file/d/0B60yN79VbSzTNTJiMTM5NDUtMDNhOS00ZjVhLWIxYWMtZWMxNjQzYzk5ZDFi/edit" rel="nofollow ugc">https://docs.google.com/file/d/0B60yN79VbSzTNTJiMTM5NDUtMDNhOS00ZjVhLWIxYWMtZWMxNjQzYzk5ZDFi/edit</a>)</p>
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		<title>
		By: James Key		</title>
		<link>/2012/loa-abstracting-abstraction/#comment-477943</link>

		<dc:creator><![CDATA[James Key]]></dc:creator>
		<pubDate>Wed, 25 Jul 2012 13:56:39 +0000</pubDate>
		<guid isPermaLink="false">/?p=14619#comment-477943</guid>

					<description><![CDATA[Two contrasting attitudes:

non-math person: &quot;Math is so abstract.&quot;  i.e. &quot;hard to understand&quot;

math person: We abstract *in order to understand.*

Part of our job is to teach people this latter mentality.]]></description>
			<content:encoded><![CDATA[<p>Two contrasting attitudes:</p>
<p>non-math person: &#8220;Math is so abstract.&#8221;  i.e. &#8220;hard to understand&#8221;</p>
<p>math person: We abstract *in order to understand.*</p>
<p>Part of our job is to teach people this latter mentality.</p>
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		<title>
		By: MARY KIM SCHRECK		</title>
		<link>/2012/loa-abstracting-abstraction/#comment-477879</link>

		<dc:creator><![CDATA[MARY KIM SCHRECK]]></dc:creator>
		<pubDate>Wed, 25 Jul 2012 12:24:40 +0000</pubDate>
		<guid isPermaLink="false">/?p=14619#comment-477879</guid>

					<description><![CDATA[Your mind is indeed &quot;light, and deft and beautiful&quot;...this was a delight to read and consider and apply to my field of English literacy as well as to math. I am currently an educational consultant and author. I give workshops all over the country on engagement, creativity, and literacy. I always refer the math teachers I meet to your blog as well as your TED presentation. As someone who has only agonizing memories of Algebra II in high school, I find your work an oasis.]]></description>
			<content:encoded><![CDATA[<p>Your mind is indeed &#8220;light, and deft and beautiful&#8221;&#8230;this was a delight to read and consider and apply to my field of English literacy as well as to math. I am currently an educational consultant and author. I give workshops all over the country on engagement, creativity, and literacy. I always refer the math teachers I meet to your blog as well as your TED presentation. As someone who has only agonizing memories of Algebra II in high school, I find your work an oasis.</p>
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