Building Mathematical Comprehension: Chapter 8: Synthesizing Information 2013

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Building Mathematical Comprehension: Chapter 8: Synthesizing Information 2013

Post by Admin on Sun Sep 15, 2013 2:44 am

2013 2013 2013 <div style="text-align: center;"><img src="http://i1134.photobucket.com/albums/m605/primaryinspired/9bcea6c1-e4bb-4cd5-9b02-8e175843492e.jpg" /></div><div style="text-align: center;"><br /></div><div style="text-align: center;"><div style="text-align: left;"><span style="font-family: Verdana, sans-serif;">This book is really making me THINK! &nbsp;</span></div><div style="text-align: left;"><span style="font-family: Verdana, sans-serif;">Chapter 8 is all about Synthesizing Information. &nbsp;This is one of those strategies that I have always had a tough time explaining to the kiddos. &nbsp;</span></div><div style="text-align: left;"><span style="font-family: Verdana, sans-serif;">According to Keene and Zimmerman (1997) compare synthesis, the process of sifting through a multitude of details, focusing on the most relevant and then organizing those ideas, to the&nbsp;meticulous&nbsp;creation&nbsp;of a "mosaic of meaning, a beauty, greater than the sum of each shiny piece." &nbsp;The author states: "The process of synthesizing information may be the most complex of the comprehension strategies." (I'll say!)</span></div></div><div style="text-align: center;"><span style="font-family: Verdana, sans-serif;"><br /></span><span style="font-family: Verdana, sans-serif;">So! &nbsp;How does this apply to teaching mathematics?&nbsp;</span></div><div style="text-align: center;"><span style="font-family: Verdana, sans-serif;"><br /></span></div><div style="text-align: center;"><span style="font-family: Verdana, sans-serif;">She goes on to describe five strands or components of mathematical proficiency:</span></div><div style="text-align: center;"><span style="font-family: Verdana, sans-serif;"><br /></span></div><div style="text-align: center;"><span style="font-family: Verdana, sans-serif;">Conceptual Understanding</span></div><div style="text-align: center;"><span style="font-family: Verdana, sans-serif;">Procedural fluency&nbsp;</span></div><div style="text-align: center;"><span style="font-family: Verdana, sans-serif;">Strategic competence</span></div><div style="text-align: center;"><span style="font-family: Verdana, sans-serif;">Productive disposition</span></div><div style="text-align: center;"><span style="font-family: Verdana, sans-serif;">Adaptive reasoning</span></div><div style="text-align: center;"><span style="font-family: Verdana, sans-serif;"><br /></span></div><div style="text-align: center;"><span style="font-family: Verdana, sans-serif;">and says that they need to be interwoven and work together to solve problems (essentially&nbsp;synthesizing).</span><br /><span style="font-family: Verdana, sans-serif;"><br /></span><span style="font-family: Verdana, sans-serif;">So, What do students need to know about synthesizing? &nbsp;According to Laney Sammons kiddos need to understand that:</span><br /><br /><ol><li style="text-align: left;"><span style="font-family: Verdana, sans-serif;">Mathematicians are aware of changes in mathematical thinking through additional mathematical experiences.</span></li><li style="text-align: left;"><span style="font-family: Verdana, sans-serif;">Mathematicians synthesize ideas when they consider their new mathematical experiences in light of the existing mathematcial knowledge to construct new meaning.</span></li><li style="text-align: left;"><span style="font-family: Verdana, sans-serif;">Mathematicians understand that syntheseis is the sum of information from new math experiences and existing mathtematical knowledge that leads to new ideas or understanding.</span></li><li style="text-align: left;"><span style="font-family: Verdana, sans-serif;">Mathematicians know their knowledge of math continues to evolve as new information or ideas are encountered.</span></li><li style="text-align: left;"><span style="font-family: Verdana, sans-serif;">Mathematicians can explain how using synthesis helps them to better understand mathematics.</span></li></ol><div style="text-align: left;"><span style="font-family: Verdana, sans-serif;">That brings up the question (at least to me) : How in the world do I teach this to children? &nbsp;Of course you will be using modeling and think alouds (these are the only type of modeling jobs I will ever have Smile ). &nbsp;I also believe strongly in using something concrete to lead children to abstract ideas. &nbsp;I don't know if you have ever read Tammy McGregor's book:&nbsp;</span><a href="http://www.amazon.com/Comprehension-Connections-Bridges-Strategic-Reading/dp/0325008876/ref=as_li_tf_mfw?&amp;linkCode=wey&amp;tag=mrsgarsweb-20"><img alt="Product Details" src="http://ecx.images-amazon.com/images/I/51ljufeArSL._SL160_PIsitb-sticker-arrow-dp,TopRight,12,-18_SH30_OU01_AA160_.jpg" style="text-align: center;" /></a><span style="font-family: Verdana, sans-serif;">but it has a lot of ideas for using concrete objects to teach comprehension strategies! &nbsp;(You can click on the cover to get your own copy! &nbsp;I would highly recommend this book!) &nbsp;</span></div><div style="text-align: left;"><span style="font-family: Verdana, sans-serif;">Anway, Tammy uses nesting dolls to teach synthesis! &nbsp;What a great idea! &nbsp;Another good way to show all of the individual pieces making a whole is by baking a cake (yum)! &nbsp;I found these adorable nesting robots! &nbsp;</span><a href="http://www.amazon.com/Matryoshka-Madness-13009-Robot/dp/B003F1KETI/ref=as_li_tf_mfw?&amp;linkCode=wey&amp;tag=mrsgarsweb-20"><img alt="Product Details" src="http://ecx.images-amazon.com/images/I/41oRx9gCiWL._AA160_.jpg" style="text-align: center;" /></a>&nbsp;<span style="font-family: Verdana, sans-serif;">They had many different styles on Amazon! &nbsp;Click the picture to check them out!</span></div><div style="text-align: left;"><span style="font-family: Verdana, sans-serif;"><br /></span></div><div style="text-align: left;"><span style="font-family: Verdana, sans-serif;"><br /></span></div><div style="text-align: left;"><span style="font-family: Verdana, sans-serif;">We all know that Problem Solving is a great way to teach math! &nbsp;She also discusses Making Conjectures. &nbsp;The NCTM (2000) Reasoning and Proof standard states that all students should be able to "make and investigate mathematical conjectures". &nbsp;The CCSS for Mathematical Practice specifies that students "make conjectures and build a logical progression of statements to explore the truth of their conjectures". (National Governors Association for Best Practices and Council of Chief State School officers 2010). &nbsp;A conjecture according to our author is: "informed guesses and predictions based on observed patterns and relationships that appear to be true but have not yet been tested." -Sammons 2013.</span><span style="font-family: Verdana, sans-serif;">&nbsp;</span></div><div style="text-align: left;"><span style="font-family: Verdana, sans-serif;"><br /></span></div><div style="text-align: left;"><span style="font-family: Verdana, sans-serif;">So, to synthesis this chapter: &nbsp;Children need to solve problems using their current and new mathematical knowledge. &nbsp;Synthesizing strengths mathematical understanding by connecting new and old knowledge about mathematical concepts and procedures. &nbsp;Using concrete examples such as nesting dolls or making a cake can help make this abstract concept a little more concrete!&nbsp;</span></div><div style="text-align: left;"><span style="font-family: Verdana, sans-serif;"><br /></span></div><div style="text-align: left;"><span style="font-family: Verdana, sans-serif;">What are you thinking about this chapter? &nbsp;I would love to know! &nbsp;<a href="http://pgruzyn.blogspot.com/">Pam's Place</a> is also hosting this chapter on her site, check it out!</span></div><div style="text-align: left;"><span style="font-family: Verdana, sans-serif;"><br /></span></div><div style="text-align: left;"><span style="font-family: Verdana, sans-serif;"><br /></span></div></div><div style="text-align: center;"><span style="font-family: Verdana, sans-serif;"><br /></span></div><div style="text-align: center;"><span style="font-family: Verdana, sans-serif;"><br /></span></div><div style="text-align: center;">"<!-- start InLinkz script --><script javascript="" text="" type=""> document.write('<script type=""text/javascript"" src=http://www.inlinkz.com/cs.php?id=279759&' + new Date().getTime() + '""><\/script>');</script><!-- end InLinkz script -->" <a href="http://www.inlinkz.com/script.php?id=279759&amp;nojump=1&amp;key=IL38NjsO.L9gA">get the InLinkz code</a></div><img src="http://i1064.photobucket.com/albums/u378/designbychristi/space/sig2_zpsa8c1af6f.png" /><br> 2013 2013 2013 <br><div style="text-align: center;"><img src="http://i1134.photobucket.com/albums/m605/primaryinspired/9bcea6c1-e4bb-4cd5-9b02-8e175843492e.jpg" /></div><div style="text-align: center;"><br /></div><div style="text-align: center;"><div style="text-align: left;"><span style="font-family: Verdana, sans-serif;">This book is really making me THINK! &nbsp;</span></div><div style="text-align: left;"><span style="font-family: Verdana, sans-serif;">Chapter 8 is all about Synthesizing Information. &nbsp;This is one of those strategies that I have always had a tough time explaining to the kiddos. &nbsp;</span></div><div style="text-align: left;"><span style="font-family: Verdana, sans-serif;">According to Keene and Zimmerman (1997) compare synthesis, the process of sifting through a multitude of details, focusing on the most relevant and then organizing those ideas, to the&nbsp;meticulous&nbsp;creation&nbsp;of a "mosaic of meaning, a beauty, greater than the sum of each shiny piece." &nbsp;The author states: "The process of synthesizing information may be the most complex of the comprehension strategies." (I'll say!)</span></div></div><div style="text-align: center;"><span style="font-family: Verdana, sans-serif;"><br /></span><span style="font-family: Verdana, sans-serif;">So! &nbsp;How does this apply to teaching mathematics?&nbsp;</span></div><div style="text-align: center;"><span style="font-family: Verdana, sans-serif;"><br /></span></div><div style="text-align: center;"><span style="font-family: Verdana, sans-serif;">She goes on to describe five strands or components of mathematical proficiency:</span></div><div style="text-align: center;"><span style="font-family: Verdana, sans-serif;"><br /></span></div><div style="text-align: center;"><span style="font-family: Verdana, sans-serif;">Conceptual Understanding</span></div><div style="text-align: center;"><span style="font-family: Verdana, sans-serif;">Procedural fluency&nbsp;</span></div><div style="text-align: center;"><span style="font-family: Verdana, sans-serif;">Strategic competence</span></div><div style="text-align: center;"><span style="font-family: Verdana, sans-serif;">Productive disposition</span></div><div style="text-align: center;"><span style="font-family: Verdana, sans-serif;">Adaptive reasoning</span></div><div style="text-align: center;"><span style="font-family: Verdana, sans-serif;"><br /></span></div><div style="text-align: center;"><span style="font-family: Verdana, sans-serif;">and says that they need to be interwoven and work together to solve problems (essentially&nbsp;synthesizing).</span><br /><span style="font-family: Verdana, sans-serif;"><br /></span><span style="font-family: Verdana, sans-serif;">So, What do students need to know about synthesizing? &nbsp;According to Laney Sammons kiddos need to understand that:</span><br /><br /><ol><li style="text-align: left;"><span style="font-family: Verdana, sans-serif;">Mathematicians are aware of changes in mathematical thinking through additional mathematical experiences.</span></li><li style="text-align: left;"><span style="font-family: Verdana, sans-serif;">Mathematicians synthesize ideas when they consider their new mathematical experiences in light of the existing mathematcial knowledge to construct new meaning.</span></li><li style="text-align: left;"><span style="font-family: Verdana, sans-serif;">Mathematicians understand that syntheseis is the sum of information from new math experiences and existing mathtematical knowledge that leads to new ideas or understanding.</span></li><li style="text-align: left;"><span style="font-family: Verdana, sans-serif;">Mathematicians know their knowledge of math continues to evolve as new information or ideas are encountered.</span></li><li style="text-align: left;"><span style="font-family: Verdana, sans-serif;">Mathematicians can explain how using synthesis helps them to better understand mathematics.</span></li></ol><div style="text-align: left;"><span style="font-family: Verdana, sans-serif;">That brings up the question (at least to me) : How in the world do I teach this to children? &nbsp;Of course you will be using modeling and think alouds (these are the only type of modeling jobs I will ever have Smile ). &nbsp;I also believe strongly in using something concrete to lead children to abstract ideas. &nbsp;I don't know if you have ever read Tammy McGregor's book:&nbsp;</span><a href="http://www.amazon.com/Comprehension-Connections-Bridges-Strategic-Reading/dp/0325008876/ref=as_li_tf_mfw?&amp;linkCode=wey&amp;tag=mrsgarsweb-20"><img alt="Product Details" src="http://ecx.images-amazon.com/images/I/51ljufeArSL._SL160_PIsitb-sticker-arrow-dp,TopRight,12,-18_SH30_OU01_AA160_.jpg" style="text-align: center;" /></a><span style="font-family: Verdana, sans-serif;">but it has a lot of ideas for using concrete objects to teach comprehension strategies! &nbsp;(You can click on the cover to get your own copy! &nbsp;I would highly recommend this book!) &nbsp;</span></div><div style="text-align: left;"><span style="font-family: Verdana, sans-serif;">Anway, Tammy uses nesting dolls to teach synthesis! &nbsp;What a great idea! &nbsp;Another good way to show all of the individual pieces making a whole is by baking a cake (yum)! &nbsp;I found these adorable nesting robots! &nbsp;</span><a href="http://www.amazon.com/Matryoshka-Madness-13009-Robot/dp/B003F1KETI/ref=as_li_tf_mfw?&amp;linkCode=wey&amp;tag=mrsgarsweb-20"><img alt="Product Details" src="http://ecx.images-amazon.com/images/I/41oRx9gCiWL._AA160_.jpg" style="text-align: center;" /></a>&nbsp;<span style="font-family: Verdana, sans-serif;">They had many different styles on Amazon! &nbsp;Click the picture to check them out!</span></div><div style="text-align: left;"><span style="font-family: Verdana, sans-serif;"><br /></span></div><div style="text-align: left;"><span style="font-family: Verdana, sans-serif;"><br /></span></div><div style="text-align: left;"><span style="font-family: Verdana, sans-serif;">We all know that Problem Solving is a great way to teach math! &nbsp;She also discusses Making Conjectures. &nbsp;The NCTM (2000) Reasoning and Proof standard states that all students should be able to "make and investigate mathematical conjectures". &nbsp;The CCSS for Mathematical Practice specifies that students "make conjectures and build a logical progression of statements to explore the truth of their conjectures". (National Governors Association for Best Practices and Council of Chief State School officers 2010). &nbsp;A conjecture according to our author is: "informed guesses and predictions based on observed patterns and relationships that appear to be true but have not yet been tested." -Sammons 2013.</span><span style="font-family: Verdana, sans-serif;">&nbsp;</span></div><div style="text-align: left;"><span style="font-family: Verdana, sans-serif;"><br /></span></div><div style="text-align: left;"><span style="font-family: Verdana, sans-serif;">So, to synthesis this chapter: &nbsp;Children need to solve problems using their current and new mathematical knowledge. &nbsp;Synthesizing strengths mathematical understanding by connecting new and old knowledge about mathematical concepts and procedures. &nbsp;Using concrete examples such as nesting dolls or making a cake can help make this abstract concept a little more concrete!&nbsp;</span></div><div style="text-align: left;"><span style="font-family: Verdana, sans-serif;"><br /></span></div><div style="text-align: left;"><span style="font-family: Verdana, sans-serif;">What are you thinking about this chapter? &nbsp;I would love to know! &nbsp;<a href="http://pgruzyn.blogspot.com/">Pam's Place</a> is also hosting this chapter on her site, check it out!</span></div><div style="text-align: left;"><span style="font-family: Verdana, sans-serif;"><br /></span></div><div style="text-align: left;"><span style="font-family: Verdana, sans-serif;"><br /></span></div></div><div style="text-align: center;"><span style="font-family: Verdana, sans-serif;"><br /></span></div><div style="text-align: center;"><span style="font-family: Verdana, sans-serif;"><br /></span></div><div style="text-align: center;">"<!-- start InLinkz script --><script javascript="" text="" type=""> document.write('<script type=""text/javascript"" src=http://www.inlinkz.com/cs.php?id=279759&' + new Date().getTime() + '""><\/script>');</script><!-- end InLinkz script -->" <a href="http://www.inlinkz.com/script.php?id=279759&amp;nojump=1&amp;key=IL38NjsO.L9gA">get the InLinkz code</a></div><img src="http://i1064.photobucket.com/albums/u378/designbychristi/space/sig2_zpsa8c1af6f.png" /><br>2013 2013 2013 <br> <a href="http://www.matrixar.com/" title="Matrix ">المصفوفة : أجمل الخلفيات والصور</a>

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