renees's blog
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All Things Common Core is the home of the "Geared Up for Common Core" blogs and other Common Core resources. en"Core" Ideas to Follow
http://allthingscommoncore.com/content/core-ideas-follow
<div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even" property="content:encoded"> <p>When looking for math activities, information, or new ideas I have a few "core" people I follow.</p>
<p>Here is the short list:</p>
<p>Bill McCallum: <a href="http://commoncoretools.me/author/wgmccallum/">http://commoncoretools.me/author/wgmccallum/</a></p>
<p>Donna Boucher: <a href="http://mathcoachscorner.blogspot.com/">http://mathcoachscorner.blogspot.com/</a></p>
<p>Dan Meyer: <a href="http://blog.mrmeyer.com/"> http://blog.mrmeyer.com/</a></p>
<p>Marilyn Burns: <a href="http://mathsolutions.com/">Math Solutions</a></p>
<p>Jennifer Bay Williams: <a href="http://www.pearsonschool.com/index.cfm?locator=PS27P4">Pearson</a></p>
<p> </p>
<p>The "core" publications I turn to are:</p>
<p>Carpenter's Work: <a href="http://www.amazon.com/Childrens-Mathematics-Cognitively-Guided-Instruction/dp/0325001375/ref=sr_1_1?ie=UTF8&qid=1403543078&sr=8-1&keywords=children%27s+mathematics+cognitively+guided+instruction">Children's Mathematics: Cognitively Guided Instruction</a></p>
<p> <a href="http://www.amazon.com/Thinking-Mathematically-Integrating-Arithmetic-Elementary/dp/0325005656/ref=sr_1_2?s=books&ie=UTF8&qid=1403543177&sr=1-2&keywords=thinking+mathematically">Thinking Mathematically: Integrating Arithmetic and Algebra in the Elementary School</a></p>
<p>Levi & Empson: <a href="http://www.amazon.com/Thinking-Mathematically-Integrating-Arithmetic-Elementary/dp/0325005656/ref=sr_1_2?s=books&ie=UTF8&qid=1403543177&sr=1-2&keywords=thinking+mathematically">Extending Children's Mathematics:Fractions and Decimals:Innovations in CGI</a></p>
<p>Van de Walle Series: <a href="http://www.amazon.com/Elementary-Middle-School-Mathematics-Developmentally/dp/0133006468/ref=sr_1_1?s=books&ie=UTF8&qid=1403543424&sr=1-1&keywords=Elementary+and+Middle+School+Mathematics%3A+Teaching+Developmentally%3A+The+Professional+Development+Edition+for+Mathematics+Coaches+and+Other+Teacher+Leaders">Elementary and Middle School Mathematics: Teaching Developmentally</a></p>
<p> <a href="http://www.amazon.com/Teaching-Student-Centered-Mathematics-Developmentally-Appropriate/dp/0132824825/ref=sr_1_1?ie=UTF8&qid=1403543490&sr=8-1&keywords=Teaching+Student-Centered+Mathematics%3A+Developmentally+Appropriate+Instruction+for+Grades+3-5+%28Volume+II%29+%282nd+Edition%29+%28New+2013+Curriculum+%26+Instruction+Titles%29+Teaching+Student-Centered+Mathematics%3A+Developmentally+Appropriate+Instruction+for+Grades+3-5+%28Volume+II%29+%282nd+Edition%29+%28New+2013+Curriculum+%26+Instruction+Titles%29">Teaching Student Centered Mathematics: Developmentally Apporpriate Instruction for Pre-K-2</a></p>
<p> <a href="http://www.amazon.com/Teaching-Student-Centered-Mathematics-Developmentally-Appropriate/dp/0132824876/ref=sr_1_2?ie=UTF8&qid=1403543490&sr=8-2&keywords=Teaching+Student-Centered+Mathematics%3A+Developmentally+Appropriate+Instruction+for+Grades+3-5+%28Volume+II%29+%282nd+Edition%29+%28New+2013+Curriculum+%26+Instruction+Titles%29+Teaching+Student-Centered+Mathematics%3A+Developmentally+Appropriate+Instruction+for+Grades+3-5+%28Volume+II%29+%282nd+Edition%29+%28New+2013+Curriculum+%26+Instruction+Titles%29">Teaching Student Centered Mathematics: Developmentally Apporpriate Instruction for Grades 3-5,</a></p>
<p> <a href="http://www.amazon.com/Teaching-Student-Centered-Mathematics-Developmentally-Appropriate/dp/0132824868/ref=sr_1_3?ie=UTF8&qid=1403543490&sr=8-3&keywords=Teaching+Student-Centered+Mathematics%3A+Developmentally+Appropriate+Instruction+for+Grades+3-5+%28Volume+II%29+%282nd+Edition%29+%28New+2013+Curriculum+%26+Instruction+Titles%29+Teaching+Student-Centered+Mathematics%3A+Developmentally+Appropriate+Instruction+for+Grades+3-5+%28Volume+II%29+%282nd+Edition%29+%28New+2013+Curriculum+%26+Instruction+Titles%29">Teaching Student Centered Mathematics: Developmentally Apporpriate Instruction for Grades 6-8</a></p>
<p>Parrish: <a href="http://www.amazon.com/Number-Talks-Computation-Strategies-Connections/dp/1935099655/ref=sr_1_fkmr1_1?ie=UTF8&qid=1403543953&sr=8-1-fkmr1&keywords=Teaching+Student-Centered+Mathem+Number+Talks%3A+Helping+Children+Build+Mental+Math+and+Computation+Strategies%2C+Grades+K+5%2C+Updated+with+Common+Core+Connections+Number+Talks%3A+Helping+Children+Build+Mental+Math+and+Computation+Strategies%2C+Grades+K+5%2C+Updated+with+Common+Core+Connections+By+Sherry+Parrishatics%3A+Developmentally+Appropriate+Instruction+for+Grades+3-5+%28Volume+II%29+%282nd+Edition%29+%28New+2013+Curriculum+%26+Instruction+Titles%29+Teaching+Student-Centered+Mathematics%3A+Developmentally+Appropriate+Instruction+for+Grades+3-5+%28Volume+II%29+%282nd+Edition%29+%28New+2013+Curriculum+%26+Instruction+Titles%29">Number Talks: Helping Children Build Mental Math and Computation Strategies</a></p>
<p>NCTM's Series: <a href="http://www.amazon.com/gp/search/ref=sr_gnr_fkmr0?rh=i%3Aaps%2Ck%3Adeveloping+essential+understanding&keywords=developing+essential+understanding&ie=UTF8&qid=1403544095">Developing Essential Understandings (all grades)</a></p>
<p> </p>
<p>The "Core" Sites and Resources I commonly refer to are:</p>
<p><a href="http://ime.math.arizona.edu/progressions/">Arizona Progressions</a></p>
<p><a href="http://www.katm.org/baker/pages/common-core-resources.php">K-8 Flipbooks</a></p>
<p><a href="https://www.georgiastandards.org/Common-Core/Pages/Math-K-5.aspx">Georgia Frameworks K-5</a></p>
<p><a href="https://www.georgiastandards.org/Common-Core/Pages/Math-6-8.aspx">Georgia Frameworks 6-8</a></p>
<p><a href="https://www.illustrativemathematics.org/">Illustrative Mathematics</a></p>
<p><a href="http://mathsolutions.com/">Math Solutions</a></p>
<p> </p>
<p>This list is by no means exhaustive but if you are looking for quality math materials aligned to the "Core", it is a good place to start.</p>
<p>
</p><p> </p>
<p> </p>
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Mon, 23 Jun 2014 16:53:34 +0000renees6431 at http://allthingscommoncore.comhttp://allthingscommoncore.com/content/core-ideas-follow#commentsWrite? That's Right!
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<div class="field field-name-field-image field-type-image field-label-hidden"><div class="field-items"><div class="field-item even"><img typeof="foaf:Image" src="http://allthingscommoncore.com/sites/allthingscommoncore.com/files/styles/medium/public/images.jpg" width="146" height="220" alt="" /></div></div></div><div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even" property="content:encoded"> <p>Most of you know me as the math girl and that is absolutely true, but....before I was the math girl, I was the word girl. I like to joke that I am a word"smith" but it isn't a joke. I really am. I often introduce myself to new teachers by telling them that my plans for life included becoming a noted children's book author but (as I point upward) someone up there had a sense of humor and made me a math teacher instead. I usually do that to let them know that even if we don't start out believing math is our favorite subject, we can get better at it and, in my case, come to find it is our favorite thing to teach. </p>
<p>So, a funny thing happened on the way to the Common Core; math and writing collided. One of those darn Standards for Mathematical Practice insists I help children learn to construct viable arguments, to justify their thinking, and critique the reasoning of others. Suddenly, I find myself cast in the role of the communications teacher as well as math teacher. So how can this be accomplished? </p>
<p>First and foremost, students have to be immersed in rich problem solving activities (M.P. 1) and we, the adults, have to back off and let them think on their own instead of telling them how to solve. If problems are rigorous enough, children begin to pay attention to the structure of the problem (M.P. 7) and use strategies to solve that might include tools (M.P. 5), or representations that were not part of our math experiences. A student may use a different method to solve than his neighbor which provides him something to justify or construct argument about (M.P. 3). It also gives them the opportunity for higher level thinking as we compare and contrast strategies together in the whole group setting. </p>
<p>After orally communicating their thinking, students should transfer that thinking to writing. A math journal can serve as a portfolio of a student's thinking about problem solving. Students of every age should be encouraged to capture this thinking in print. For our earliest learners this might mean transferring what they did with a tool into a pictorial representation. It might include the algorithm for solving as soon as they are ready for this more abstract concept. Eventually, students start writing about their thinking. At first teachers may suggest a format for this. They might provide sentence starters to help students with sequencing their thinking but eventually students should be able to do this on their own. In classrooms where this is being done regularly, students are able to communicate their thinking very proficiently by the middle of second grade. </p>
<p>Students need regular feedback during this process which is why teachers I have been working with are using a rubric we aligned to the Common Core Standards for Mathematical Practice to assess student thinking in problem solving. They are able to capture notes about areas in which students excel and areas in which students need additional help. </p>
<p>So for all the sceptics out there that say, "Writing in a math classroom?", my response would be, "Right, or should I say, 'Write' on!"</p>
</div></div></div><div class="field field-name-field-tags field-type-taxonomy-term-reference field-label-above"><div class="field-label">Tags: </div><div class="field-items"><div class="field-item even"><a href="/tags/ccss" typeof="skos:Concept" property="rdfs:label skos:prefLabel">CCSS</a></div><div class="field-item odd"><a href="/tags/math" typeof="skos:Concept" property="rdfs:label skos:prefLabel">Math</a></div><div class="field-item even"><a href="/tags/journaling" typeof="skos:Concept" property="rdfs:label skos:prefLabel">Journaling</a></div><div class="field-item odd"><a href="/tags/8-mathematical-practices" typeof="skos:Concept" property="rdfs:label skos:prefLabel">8 mathematical practices</a></div><div class="field-item even"><a href="/tags/rubrics" typeof="skos:Concept" property="rdfs:label skos:prefLabel">Rubrics</a></div></div></div><div class="field field-name-file field-type-file field-label-above"><div class="field-label">Files: </div><div class="field-items"><div class="field-item even"><span class="file"><img class="file-icon" alt="" title="application/pdf" src="/modules/file/icons/application-pdf.png" /> <a href="http://allthingscommoncore.com/sites/allthingscommoncore.com/files/Rubric%20for%20Math%20Journaling%20tied%20to%208%20M.P.%20copy.pdf" type="application/pdf; length=58309">Rubric for Math Journaling tied to 8 M.P. copy.pdf</a></span></div></div></div>
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Wed, 07 May 2014 22:15:56 +0000renees6295 at http://allthingscommoncore.comhttp://allthingscommoncore.com/content/write-thats-right#commentsIs Faster Really Better?
http://allthingscommoncore.com/content/faster-really-better
<div class="field field-name-field-image field-type-image field-label-hidden"><div class="field-items"><div class="field-item even"><img typeof="foaf:Image" src="http://allthingscommoncore.com/sites/allthingscommoncore.com/files/styles/medium/public/7644044.jpg" width="220" height="160" alt="" /></div></div></div><div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even" property="content:encoded"> <p>"It's not complicated, faster is better!" If you believe the AT&T commercials faster is always better and for years we have taught math using that same theory! We taught procedures and gave daily timed math facts tests to ensure students would become faster and faster at "doing" math. We celebrated two things; the correct answer and arriving at it quickly or automatically. Through our efforts a small segment of our population was congratulated and made to believe they were our best and brightest. They were true mathematicians! But for a much larger group of people we proved just the opposite. The message was sent; you either were a mathematician or you weren't. </p>
<p>The Common Core State Standards want to change that perception for our teachers, our students, and our population as a whole. Mathematics can be learned by all. Speed is not the end-all, be-all. The standards for mathematics stress two components: conceptual understanding and fluency. The standards emphasize the need for fluency, <strong>which is not to be misinterpreted as speed</strong>, a great deal. Fluency, in the standards, is described as an understanding of the meaning of operations and their relationships to each other, the knowledge of number relationships, and a thorough understanding of the base ten number system. There are standards that call specifically for fluency with addition and multiplication facts and with standard algorithms, but this fluency is to come <strong>after</strong> adequate groundwork involving work with strategies and algorithms based on place value and the properties of operations has occurred. </p>
<p>According to William McCallum, author of the common core for math, "...being fluent in math refers to knowing how to do a calculation, whereas to know from memory means being able to produce the answer when prompted without having to do the calculation" (blog 9/4/12). On the topic of timed tests for basic facts, Marilyn Burns writes in <em>About Teaching Mathematics</em>, "...timed tests do not measure children's understanding...It doesn't ensure that students will be able to use the facts in problem-solving situations. Furthermore, it conveys to children that memorizing is the way to mathematical power, rather than learning to think and reason to figure out answers" (2000, p. 157). Accordingly, John A. Van de Walle states (2006), speed (using timed tests) "is effective only for students who are goal oriented and who can perform in pressure situations. The pressure of speed can be debilitating and provides no positive benefits." He continues with the comment, "these timed tests should generally be avoided as they do not promote reasoned approaches to fact mastery. If there is any defensible purpose for a timed test of basic facts it may be for diagnosis - to determine which combinations are mastered and which remain to be learned. Even for diagnostic purposes there is little reason for a timed test more than once every couple of months" (pp. 95-96). </p>
<p>For this reason, the common core recommends that students master strategies for efficient fact retrieval prior to practicing the facts for fluency (accuracy and speed). In the end, fluency and automaticity are important. As students explore the conceptual understandings of more rigorous concepts, they need efficient methods for determining basic facts. However, fluency and speed should not be "the goal", but one ingredient that leads to students' success in meeting their year end math goals. </p>
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Mon, 27 Jan 2014 15:29:17 +0000renees6003 at http://allthingscommoncore.comhttp://allthingscommoncore.com/content/faster-really-better#commentsCGI and the Common Core: How Do They Connect?
http://allthingscommoncore.com/content/cgi-and-common-core-how-do-they-connect
<div class="field field-name-field-image field-type-image field-label-hidden"><div class="field-items"><div class="field-item even"><img typeof="foaf:Image" src="http://allthingscommoncore.com/sites/allthingscommoncore.com/files/styles/medium/public/-1.jpeg" width="220" height="155" alt="" /></div></div></div><div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even" property="content:encoded"> <p>Recently I attended the Kansas Association of Teachers of Mathematics Conference. While at KATM, I presented Cognitively Guided Instruction and the Common Core: How do they Connect? I began the discussion with background information on CGI. Cognitively Guided Instruction is a research-based instructional strategy developed by Thomas Carpenter, Elizabeth Fennema, Linda Levi and others in the late 1980s. It was funded by the National Science Foundation and the work occurred at the University of Wisconsin at Madison. <br />The premise of CGI is to find out exactly what children can do on their own when immersed in problem solving. The research found that children intuitively solve word problems by modeling the action and relations described in them. In the training, teachers learn how basic concepts of addition, subtraction, multiplication, and division develop in children and how they can construct concepts of place value and multi digit computational procedures based on their intuitive mathematical knowledge. Teachers also gain knowledge of math problem types and children's solution strategies.<br />So why is CGI, an instructional strategy developed in the 80's, so relevant today? <br />By looking at the 8 Mathematical Practice Standards from CCSS we can see the intersection between CGI and Common Core.<br />Mathematical Practice #1: Students will make sense of problems and persevere in solving them. The connection here is obvious….that is the premise of CGI.<br />Mathematical Practice #2: Students will reason abstractly and quantitatively. When students are involved in problem solving they are seeing numbers in context and they are required to attend to the meaning of quantities. <br />Mathematical Practice #3: Students will construct viable arguments and critique the reasoning of others. This occurs on a daily basis in a CGI classroom as students share their solution strategies and their answers to problems. If disagreements occur, student are encouraged to engage in discourse with their classmates.<br />Mathematical Practice #4: Modeling with Mathematics. In CGI classrooms, students are encouraged to represent their mathematical thinking with different representations. This varies from using tools, to drawing pictures but eventually leads to equations. <br />Mathematical Practice #5: Using Appropriate Tools Strategically. CGI students will do this naturally. When presented a word problem, CGI students choose any method and tool that makes sense to them. <br />Mathematical Practice #6: Attend to Precision. CGI students are required to communicate their mathematical reasoning precisely. They are asked to attend to units and labels and use vocabulary and symbols accurately.<br />Mathematical Practice #7: Look for and make use of structure. CGI students naturally pay attention to the structure of a problem. They follow the sequence of the word problem and by using tools that make sense to them, they are able to solve complex problems. Many of these problem types are ones teachers might not believe young children are capable of understanding. <br />Mathematical Practice #8: Look for and express regularity in repeated reasoning. Students in these classrooms look for patterns, and through discussion teachers can encourage all the known solution methods and help students look for shortcuts. Children are also encouraged to continually check for reasonableness. <br />Final thoughts that I shared at the KATM session were, although there might be a few concepts in elementary mathematics that do not lend themselves to word problems, most concepts do. This is why CGI is a natural fit with the Common Core State Standards. </p>
<p>For more information about CGI: <a href="http://ncisla.wceruw.org/publications/reports/RR00-3.PDF">http://ncisla.wceruw.org/publications/reports/RR00-3.PDF</a></p>
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Thu, 07 Nov 2013 17:24:58 +0000renees5484 at http://allthingscommoncore.comhttp://allthingscommoncore.com/content/cgi-and-common-core-how-do-they-connect#commentsCalculators or No Calculators: That Is the Question
http://allthingscommoncore.com/content/calculators-or-no-calculators-question
<div class="field field-name-field-image field-type-image field-label-hidden"><div class="field-items"><div class="field-item even"><img typeof="foaf:Image" src="http://allthingscommoncore.com/sites/allthingscommoncore.com/files/styles/medium/public/39174948.jpg" width="145" height="220" alt="" /></div></div></div><div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even" property="content:encoded"> <p>I was recently contacted by an instructional coach from a school district where I work regularly. She and her teachers were working on math units aligned to common core. They were trying to determine whether students should be allowed to use calculators during instruction and whether they would be allowed to use them on the new state assessments. </p>
<p>Her question was a valid one in light of Common Core Mathematical Practice Standard#5: Using Appropriate Tools Strategically. As math educators we want students to determine when they need a tool to solve math problems and which tool is best suited to the task. If the focus of instruction is computation or basic level fact knowledge, then a calculator would not be warrented but when students are engaged in higher level thinking and problem solving, where the goal is not about assessing computation, then a calculator might be an appropriate tool. </p>
<p>Shortly after this coach's inquiry, I received an update from Education Weekly on this very subject. The two consortia involved in writing the next generation of math assessments, PARCC and SBAC, released their policies on calculator usage. "Policies emerging from the two state consortia developing common-core assessments would prohibit most students from using calculators on the grades 3-5 tests, for example. At grades 6 and above, they call for calculator "on" and "off" sections and set restrictions on what functionality is allowed. (Both consortia will provide online calculators for the computer-based tests.) Those rules, especially in today's high-stakes-testing environment, are sure to influence regular classroom use of calculators, from the elementary ban to the ways increasingly sophisticated calculator use is assumed at the secondary level, many experts say."</p>
<p>Unfortunately, some teachers may see this as a ban on calculators entirely because we have been conditioned to "teach to the test" and if calculators won't be used on the assessment, then they won't be used at all. "It's absolutely true that kids need to be able to compute without calculators, ... but that's only part of what they need," said Cathy Seeley, a senior fellow emeritus at the Charles A. Dana Center at the University of Texas at Austin. "To prohibit them [on the exams] in grades 3-5 even when there are very useful ways students would use them to get to higher-level thinking" is a mistake. "It constrains the depth of the [test] problems you provide."</p>
<p>I believe the thing to keep in mind goes back to that 5th Mathematical Practice Standard. For students who are still working to build competency with number sense and fluency with facts, calculators are not an appropriate tool. These students do not have the underlying skills that would inform them as to reasonableness of answers when using a calculator. However, when these skills are intact and teachers choose to involve students in deeper levels of problem solving and critical thinking, calculators might be a logical choice.</p>
<p>Use the following link to view the entire article from Education Weekly: <a href="http://www.edweek.org/ew/articles/2013/08/21/01calculators_ep.h33.html?tkn=YMTFfsuP2uaE9zB4rBpj3w12TMRHJpNKRuVa&cmp=ENL-EU-NEWS1">http://www.edweek.org/ew/articles/2013/08/21/01calculators_ep.h33.html?tkn=YMTFfsuP2uaE9zB4rBpj3w12TMRHJpNKRuVa&cmp=ENL-EU-NEWS1</a></p>
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Wed, 28 Aug 2013 03:30:19 +0000renees4733 at http://allthingscommoncore.comhttp://allthingscommoncore.com/content/calculators-or-no-calculators-question#commentsCommon Core Math: How "Deep" Do We Go
http://allthingscommoncore.com/content/common-core-math-how-deep-do-we-go
<div class="field field-name-field-image field-type-image field-label-hidden"><div class="field-items"><div class="field-item even"><img typeof="foaf:Image" src="http://allthingscommoncore.com/sites/allthingscommoncore.com/files/styles/medium/public/Canyons_wallpapers_14.jpg" width="220" height="165" alt="" /></div></div></div><div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even" property="content:encoded"> <p>Rigor is a word receiving alot of attention in regards to the common core state standards. So what does it mean in terms of teaching and learning? The 8 mathematical practices and the college and career readiness standards give us a look at what rigor refers to. </p>
<p>Students should be challenged to solve rich, relevant problems that require effort and persistence. Problems should have multiple entry points and multiple solution paths and strategies.(M.P.1) Students should be encouraged to reason, explain, and make sense of their learning. (M.P.2)(M.P.3) Students will demonstrate independence and take responsibility for their own learning.</p>
<p>Teachers will need to consider rigor when planning their units and lessons. Concepts should be introduced in contexts that are interesting and motivating to students and students will explore and discover solutions in their own ways. Tasks will build off prior knowledge and will not focus on just one correct solution path. Teachers will encourage productive struggle and will facilitate learning through effective open-ended questioning. Rigorous formative assessment will need to be used during a unit to inform the next steps in instruction. </p>
<p>As always, teachers should consider where lessons and tasks fall on Bloom's Revised Taxonomy and Webb's Depth of Knowledge Levels. Most teachers have studied Bloom's, which defines the type of thinking needed to complete a task, but may not be as familiar with DOK Levels. Webb's refers to complexity and defines how deeply one must understand content to interact with it.</p>
<p>The following video gives a brief overiew of Webb's DOK Levels. <a href="http://vimeo.com/42788913">http://vimeo.com/42788913</a></p>
<p>The following documents give content specific examples as they align to Webb's and Bloom's.</p>
<p>Math Matrix: <a href="http://www.rcoe.k12.ca.us/edServices/assessment/20121019/DOK%20Math.pdf">http://www.rcoe.k12.ca.us/edServices/assessment/20121019/DOK%20Math.pdf</a></p>
<p>Science Matrix: <a href="http://education.ky.gov/curriculum/docs/Documents/CCA_DOK_SUPPORT_808_Science.pdf">http://education.ky.gov/curriculum/docs/Documents/CCA_DOK_SUPPORT_808_Science.pdf</a></p>
<p>ELA Matrix:<a href="http://static.pdesas.org/content/documents/M1-Slide_22_DOK_Hess_Cognitive_Rigor.pdf"> http://static.pdesas.org/content/documents/M1-Slide_22_DOK_Hess_Cognitive_Rigor.pdf</a></p>
<p>Social Studies Matrix: <a href="http://www.cde.state.co.us/EducatorEffectiveness/downloads/Implementation%20Resources/DOK-Social-Studies.pdf">http://www.cde.state.co.us/EducatorEffectiveness/downloads/Implementation%20Resources/DOK-Social-Studies.pdf</a></p>
<p>Other D.O.K. Information: <a href="http://www.stancoe.org/SCOE/iss/common_core/overview/overview_depth_of_knowledge.htm">http://www.stancoe.org/SCOE/iss/common_core/overview/overview_depth_of_knowledge.htm</a></p>
<p>Teachers will need to "dig deep" into rigor to ensure the success of their students in the common core. </p>
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Mon, 20 May 2013 21:55:01 +0000renees2292 at http://allthingscommoncore.comhttp://allthingscommoncore.com/content/common-core-math-how-deep-do-we-go#commentsThese Are a Few of My Favorite Things: Common Core Math Resources
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<div class="field field-name-field-image field-type-image field-label-hidden"><div class="field-items"><div class="field-item even"><img typeof="foaf:Image" src="http://allthingscommoncore.com/sites/allthingscommoncore.com/files/styles/medium/public/26813145.thb_.jpg" width="146" height="220" alt="" /></div></div></div><div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even" property="content:encoded"> <p>It's a Friday evening and I have just drifted off into the loveliest dream. I am the young and beautiful Julie Andrews falling for the dashing Christopher Plummer on the movie set of my favorite musical, "The Sound of Music". Things are progressing right on cue. I have sung the opening theme song, met the Captain with his "ridiculous" whistle, set on the infamous pinecone, cut up the curtains to make playclothes, and then "Up in the nursery, an absurd little bird, is calling out to say <em>"You're"</em> cuckoo, cuckoo...."</p>
<p>And we're back! I'm Renee' Smith again and I have a blogpost due in three hours. With the remnants of the dream still clinging to my consciousness, I decide to share "<strong><em>a few of my favorite things</em></strong>" for common core math.</p>
<p><strong>Resources that I recommend for teacher training for common core:</strong></p>
<p>Children's Mathematics: Cognitively Guided Instruction - Carpenter, Fennema, Franke, Levi, and Empson</p>
<p>Extending Children's Mathematics Fractions and Decimals: Innovations in Cognitively Guided Instruction - Empson and Levi</p>
<p>Elementary and Middle School Mathematics: Teaching Developmentally - John A. Van de Walle</p>
<p>Thinking Mathematically: Integrating Arithmetic and Algebra in Elementary School - Carpenter, Franke, and Levi</p>
<p>Virtually anything published by Math Solutions - Marilyn Burns</p>
<p><strong>Resources that contain activities that support common core. </strong></p>
<p>Teaching Student Centered Mathematics: Professional Mathematics Series K-3, 3-5, 5-8 - Van de Walle and Lovin</p>
<p>Investigations, Tasks, and Rubrics to Teach and Assess Math, Grades 1–6 - Lilburn and Ciurak</p>
<p><strong>Websites/Blogs:</strong></p>
<p><a href="http://allthingscommoncore.com/content/resources">allthings common core.com math resources</a></p>
<p><a href="https://docs.google.com/a/essdack.org/spreadsheet/ccc?key=0AjIqyKM9d7ZYdEhtR3BJMmdBWnM2YWxWYVM1UWowTEE#gid=0">blog.mrmeyer.com - three act math</a></p>
<p>I'm sure there are other resources that address the common core but for now, these are my favorites. I feel my eyes beginning to sag and I'm starting to drift back to...."Girls in white dresses with blue satin sashes, snowflakes that stay on my nose and eyelashes, silver white winters that melt into springs, these are a few of my favorite things."</p>
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Sat, 12 Jan 2013 04:45:06 +0000renees1707 at http://allthingscommoncore.comhttp://allthingscommoncore.com/content/these-are-few-my-favorite-things-common-core-math-resources#comments10 Things Jordyn's Math Teacher Needs to Know About CCSS
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<div class="field field-name-field-image field-type-image field-label-hidden"><div class="field-items"><div class="field-item even"><img typeof="foaf:Image" src="http://allthingscommoncore.com/sites/allthingscommoncore.com/files/styles/medium/public/DSC00135.JPG" width="220" height="165" alt="" /></div></div></div><div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even" property="content:encoded"> <p>Two months ago, Jordyn Marie was born. Nothing can match the joy of having a child, unless it is the birth of a grandchild. If you ask me, she is pretty darn perfect, and as a devoted Nee'Nee' (my name for grandma) I would like to keep her that way. I would like to make her life, most especially her school career, as smooth as possible. Therefore, I have compiled a list for the future math teachers who will be tasked with ensuring Jordyn's math understanding. Here are the top 10 things that her teachers need to make sure they are doing by 2018: </p>
<p>1. <strong>Problem Solving, Problem Solving, Problem Solving!!!</strong>-Children need to be daily problem solvers! Their ability to do just that will be measured in our assessment system and is an essential life skill. As a math consultant I believe nearly every math concept can be taught through problem solving with some "just-in-time" direct instruction. Teachers need to be trained to facilitate learning through constructivist methods, schema based instruction (such as CGI), or inquiry based instruction (Dan Meyer model). If Jordyn is to be prepared to live and work in the world beyond her formal education, she will need to be able to solve problems and apply mathematics. </p>
<p>2. <strong>Insist on precision.</strong> Not only should Jordyn be required to supply the correct answer to problems, but she should also be required to know what the number represents. Of course this requires problem solving, problem solving, problem solving. (see above) No one knows what "37" represents in a "naked number" probem but we do know it represents "37 cookies" when it is framed in the context of someone eating 13 of the 50 cookies in a package. Another area where precision is required in mathematics is in its vocabulary. Teachers and students alike need to know the precise meaning of mathematical terms and use them correctly. Don't baby her along. I know she is a little kid, but little kids love big words, and when taught in context even little kids can learn them. </p>
<p>3. <strong>Multiple Strategies and Representations (CRA): </strong>Do you know there are 28 ways to teach subtraction and the USA is the only country that has taught only 1 of those methods? I want "Jordyn's Method" of representing a problem to be acceptable in your classroom. As she solves problems in your classroom you should be questioning her as to how she arrived at her solution, not dictating the method. She should also have the opportunity to represent her solution with a <strong>C</strong>oncrete tool, a pictorial <strong>R</strong>epresentation or with an <strong>A</strong>bstract algorithm if it makes sense to her and she can explain her thinking. <strong><br /></strong></p>
<p>4. <strong>Tools, Tools, Tools! </strong>Unifix cubes, color tiles, base-ten blocks, pattern blocks, number lines, clocks, 100's and 200's charts, tens frames, double tens frames, dice, dominoes, playing cards, play money, counters of any kind (beans, buttons, chips, etc...), two-colored counters, hands-on equations, measuring devices, calculators, etc....she should have access to all of these and have the right to choose the ones she wants to use to solve problems. Your classroom may be a little messier than it used to be.<strong><br /></strong></p>
<p>5. <strong>Critical Thinking/Argumentation/Cooperative Learning: </strong>These three are all life skills and they all go together. Kids need to be critical thinkers. They need to hear thinking modeled aloud and they need to have opportunities to practice this in a safe environment. They need to learn to communicate their thoughts to others in the same way. Kids have to be allowed to work and talk together about mathematics. Your classroom may be a little noiser than it used to be.<strong> <br /></strong></p>
<p>6. <strong>Differentiate: </strong>Not all children are ready for the same problem type at the same time. Listen to your students, notice the ones that finish quickly and do have true understanding of their answers. Some take longer to solve and need more questioning to help them reach true understanding. Know which type of child Jordyn is. If she needs time, let her take it. If she needs to be pushed, extend her with a more difficult problem. <strong><br /></strong></p>
<p>7. <strong>Create an environment where students "Embrace the Struggle"-don't enable her!</strong> I know you went into teaching because you love students and you never want to see them struggle or fail but the definition of "problem" is that it is something that cannot be solved immediately. Teach your students that fast isn't always best and that being incorrect isn't a failure; it is merely another opportunity to try. Teach her to persevere.</p>
<p>8. <strong>Throw away the worksheets and most of the timed tests: </strong>There are so many instructional strategies that will allow you to assess what Jordyn knows and give her repeated practice on skills other than worksheets. Save a tree and quit using worksheets and workbook pages. Save another tree and keep timed tests to a minimum. Math facts are important but timed math facts tests should only be used as a formative assessment so see which facts kids know and to drive your instruction on the ones they don't. Use them sparingly and help lessen the math anxiety in children. </p>
<p>9. <strong>Help her generalize but not overgeneralize:</strong> I want Jordyn to discover the properties of math (zero, identity, commutative, associative, distributive, etc...) but I don't want her to develop misconceptions that can be avoided. Too many repititions of problems like 4 + 3 = ___ could lead Jordyn to misconstue the meaning of the equal sign. I don't want her to believe the equal sign means "put an answer here". I want her to discover early on that the two sides of an equation must be balanced. Problems like __ = 4 + 3 and 8 + 4 = ____ + 5 will help with that. I don't want her to believe that all plane shapes are regular. Help her classify triangles that aren't equilateral, octagons that aren't shaped like stop signs and pentagons that don't look like a building in Washington D.C.</p>
<p>10. Make it<strong> FUN; </strong>help her<strong> LOVE Math; </strong>and always remember<strong>: Nee'Nee' will be watching!</strong> </p>
</div></div></div><div class="field field-name-field-tags field-type-taxonomy-term-reference field-label-above"><div class="field-label">Tags: </div><div class="field-items"><div class="field-item even"><a href="/tags/math" typeof="skos:Concept" property="rdfs:label skos:prefLabel">Math</a></div><div class="field-item odd"><a href="/tags/ccss" typeof="skos:Concept" property="rdfs:label skos:prefLabel">CCSS</a></div><div class="field-item even"><a href="/tags/cgi" typeof="skos:Concept" property="rdfs:label skos:prefLabel">CGI</a></div><div class="field-item odd"><a href="/tags/dan-meyer" typeof="skos:Concept" property="rdfs:label skos:prefLabel">Dan Meyer</a></div></div></div>
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Wed, 07 Nov 2012 01:28:31 +0000renees1538 at http://allthingscommoncore.comhttp://allthingscommoncore.com/content/10-things-jordyns-math-teacher-needs-know-about-ccss#commentsM4: Midwest Mathematics Meeting of the Minds
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<div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even" property="content:encoded"> <p>I recently attended the M4 Conference in Kansas City, where math leaders from Kansas, Missouri, Nebraska, and Iowa met to discuss the Common Core Standards for Mathematics. I was privileged to hear from Matt Larson the keynote speaker from Lincoln, Nebraska. After humerously acknowledging that his state was one of the four who had, as of yet, not adopted the common core standards, Larson got right to work convincing us that the Common Core State Standards may be our last opportunity to get math education right!</p>
<p>Larson began his keynote address by looking back at the ten year cycle of math education beginning in the 1950's. He cited a 2011 article entitled, <em>Slouching Toward a National Curriculum</em>, when he said, that despite these previous reforms, instruction has remained largely the same. Larson then posed the question, "Will the CCSS Matter Ten Years From Now?". He answered this question by first addressing what we know from research. </p>
<p>Larson pointed to three major factors that can make a difference in student achievement. </p>
<p>1. The quality of the teacher and teaching. When it comes to the quality of teaching, Larson reminded us that instruction matters; teaching has six to ten times as much impact on achievement as all other factors combined. He also referenced the book, <em>Embedded Formative Assessment,</em> when he said, "In the U.S., the classroom effect appears to be at least four times the size of the school effect...it doesn't matter very much which school you go to, but it matters very much which classrooms you're in." Important components of instruction are emphasized in the practice standards of the common core and Larson emphasized the need for conceptual engagement, productive struggle, and mathematical discourse. He even went so far as to say, that the United States has an instructional gap rather than an achievement gap. </p>
<p>2. Access to challenging curriculum. When Larson adderessed content expectations, he said the consequences are clear - less opprotunity to learn challenging mathematics corresponds to lower achievement. Curriculum needs to be at a higher level of cognitive demand and <strong>all</strong> students must have the opportunity to learn and circumstances to engage in and spend time on quality academic tasks. </p>
<p>3. Access to organized classes where student's are well known and supported. Students must receive early interventions when necessary and more time, rather than less demanding tasks, if we are to lessen the gaps between high and low perfoming students as well as the gaps between different ethnic and socio economic groups. </p>
<p>Larson concluded his speech with the statement that the common core <strong>will</strong> matter in ten years, if we do these four things. First, our focus must be on the Mathematical Practices, making our reform effort more about instruction and not just about content. Secondly, we put structures in place to support <strong>all</strong> students in achieving the goals of the Common Core. Next, we put structures in place to support teachers in improving their instruction by focusing their collaborative efforts on embedding the Mathematical Practices in their instuction. Finally, Larson says, we have to address the cultural resistance to change in our schools and in our culture at large. </p>
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Thu, 15 Mar 2012 14:22:56 +0000renees1286 at http://allthingscommoncore.comhttp://allthingscommoncore.com/content/m4-midwest-mathematics-meeting-minds#commentsI Couldn't Have Said It Better
http://allthingscommoncore.com/content/i-couldnt-have-said-it-better
<div class="field field-name-field-image field-type-image field-label-hidden"><div class="field-items"><div class="field-item even"><img typeof="foaf:Image" src="http://allthingscommoncore.com/sites/allthingscommoncore.com/files/styles/medium/public/26783405.thm_.jpg" width="220" height="146" alt="" /></div></div></div><div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even" property="content:encoded"> <p>Are You Prepared for the Common Core Standards? This is the question posed in the latest edition of <a href="http://blogs.edweek.org/teachers/teaching_ahead/are-you-prepared-for-the-common-core-standards/">Education Week Teacher</a>. </p>
<p>I encourage you to read how five classroom teachers from around the nation answered that question. Their responses include information on the importance of the 8 Mathematical Practices; the importance of sequence, pace, and support resources; how critical teacher collaboration will be in the implementation of the standards; and how the standards encourage us to let go of the control, thereby creating student centered classrooms and independent learners.</p>
<p>I really couldn't have said it any better!</p>
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Thu, 15 Mar 2012 14:18:51 +0000renees1285 at http://allthingscommoncore.comhttp://allthingscommoncore.com/content/i-couldnt-have-said-it-better#commentsCommon Core Math Curriculum: How Do We Know It's Aligned?
http://allthingscommoncore.com/content/common-core-math-curriculum-how-do-we-know-its-aligned
<div class="field field-name-field-image field-type-image field-label-hidden"><div class="field-items"><div class="field-item even"><img typeof="foaf:Image" src="http://allthingscommoncore.com/sites/allthingscommoncore.com/files/styles/medium/public/83949029.thm-1.jpg" width="165" height="220" alt="" /></div></div></div><div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even" property="content:encoded"> <p>As more and more teachers become familiar with the common core math standards, the question that is beginning to crop up is, "What curriculum (ie. textbook) is going to be aligned to the common core?". My standard response has been two-fold. My inclination is that most companies will <strong>SAY</strong> they are aligned to the common core; after all, they cover most of the content somewhere in the book. Of course my reaction to that is, "Buyer Beware". Like all good consumers, we will have to investigate the claims made by the textbook companies and make an informed decision. We know that not only must the content match the grade levels to which it has been assigned but we must also take into account the 8 Standards for Mathematical Practice and the College and Career Readiness Standards that play an equally important role in the effectiveness of the common core. As districts look toward adoption of textbooks, or make a decision to write their own curriculum there will be certain criteria they need to follow to align to the common core. </p>
<p>The good news is we are not alone in this process. Many groups have already begun to tackle this issue and have developed rubrics or checklists to make the search easier. One such document, that contains a set of rubrics for elementary through high school curriculum is the <a href="http://www.google.com/url?sa=t&rct=j&q=&esrc=s&source=web&cd=9&ved=0CGwQFjAI&url=http%3A%2F%2Fwww.mathedleadership.org%2Fdocs%2Fccss%2FCCSSO%2520Mathematics%2520Curriculum%2520Analysis%2520Project.Whole%2520Document.6.1.11.Final.docx&ei=14JGT7P1EsG2tweaz_WrDg&usg=AFQjCNFq24-dZEKIo_Q1V_CfHPEfGwtmeQ">Common Core State Standards Mathematics Curriculum Materials Analysis Project.</a> This work, supported by the Council of Chief State School Officers, the Brookhill Foundation, and Texas Instruments, will assist reviewers in using appropriate criteria for choosing mathematics curricula. </p>
<p>In her blog post,<a href="http://blog.tomsnyder.com/math-hub/bid/47813/Teacher-Checklist-How-to-Choose-the-Right-Textbook">Teacher Checklist: How to Choose the Right Textbook</a>, Jennifer Chintala shares a checklist she found online which could be used by districts to evaluate curriculum for the common core.</p>
<p>Al Cuoco recommends choosing curriculum attuned to the 8 Standards for Mathematical Practices and his comments can be found in this <a href="http://commoncoretools.me/2011/08/31/essay-by-al-cuoco-on-choosing-curriculum-aligned-to-the-practices/">two page essay</a>.</p>
<p>Each of these resources will be posted to the resources tab on this site and as we find more that might be helpful to schools who are in the process of textbook adoption we will continue to add them, so check back often. </p>
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Fri, 24 Feb 2012 01:48:53 +0000renees1237 at http://allthingscommoncore.comhttp://allthingscommoncore.com/content/common-core-math-curriculum-how-do-we-know-its-aligned#commentsWhen the Stars Align
http://allthingscommoncore.com/content/when-stars-align
<div class="field field-name-field-image field-type-image field-label-hidden"><div class="field-items"><div class="field-item even"><img typeof="foaf:Image" src="http://allthingscommoncore.com/sites/allthingscommoncore.com/files/styles/medium/public/profile.jpg" width="220" height="220" alt="" /></div></div></div><div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even" property="content:encoded"> <p>Yesterday, it was as though the stars aligned and things I have been working on for over twenty years converged and crystallized in my mind.</p>
<p>Years ago when my children were young, I was the public speaking leader for their 4-H club. I taught 4-Hers how to write and deliver interesting and engaging speeches. They learned how to hook the audience by peaking their curiosity, deliver the bulk of the message in the body of the speech, and end in a clever way, usually leaving the audience wanting more. </p>
<p>When I returned to the classroom, I knew the essential elements of a speech also applied to a math lesson. I had to find ways to intrigue my students, engage them in the lesson, and then sum things up at the end. However, I don't believe I have ever seen this done in a more deliberate and creative way than I did while listening to <a href="http://blog.mrmeyer.com/">Dan Meyer</a> present on real-world problem solving yesterday.</p>
<p>During our time together, Meyer led us through his version of the "Three Acts" of a math class. He equated these acts to the scenes of a movie. In "Act One" Meyer uses a visual, either picture or video, to peak the students' curiosity. He relates a short story to draw his audience in and with as few words as possible he sets the hook. He lures the students into wanting to know something mathematical. </p>
<p>According to Meyer there are several important aspects of this opening act. The first thing is allowing students to pose all sorts of questions based upon the visual presented. As all the questions are posted, the teacher should ask for a show of hands about other people who had the same question. This is one of the methods Meyer believes helps reluctant students buy-in to the process. After all questions have been posed, each question is addressed by the teacher and then eliminated until one remains. This is the problem that the class will solve. </p>
<p>Another important feature of "Act One", is having students estimate what they think the answer might be. Meyer also requires students to write down a guess they know is too low to be the correct answer and one that is too high to be the correct answer, thereby establishing a range within which a reasonable answer would be found. According to Meyer, "Everyone can hazard a guess, and it only costs you about 7 seconds of class time. This is one way to engage some of your more reluctant math students." </p>
<p>In "Act Two", the teacher asks students to help solve the problem but does not initially supply all the needed information. The participants determine what information they might need in the form of a list and then the teacher addresses each item on the list and supplies only enough information, in a visual format, so the problem can be attacked. The teacher then acts as a facilitator, or guide on the side, as students do the bulk of the work on solving the problem. At no time during "Act Two", does the teacher dictate a strategy that students must use to find their solution. The teacher merely circulates, asks questions about the work, redirects students as necessary, and takes notes on different strategies.</p>
<p>During "Act Three", Meyer believes teachers should ask students to check the reasonableness of their answer; does it fit within the range of numbers that were chosen in act one? The remainder of this act involves leading a summary discussion of the different strategies that were used by various groups of students. The teacher can also use this time to formalize the mathematics. Meyer noted another way to engage students during the summary discussion is to assign them a task at the beginning of the discussion. He asks students to think about which group was the "laziest" and used the most efficient method to solve the problem. At the end of the act, Meyer again returns to a visual method to show the correct answer. He also suggests acknowledging the student with the closest original guess, thereby letting the class know that estimating at the beginning of the lesson was not busy work. </p>
<p>I look at this "Three Act" script as a perfect opportunity for math teachers of all age groups to address most or all of the common core practice standards. It might also lead to students who are more engaged in math and see its usefulness.</p>
</div></div></div><div class="field field-name-field-tags field-type-taxonomy-term-reference field-label-above"><div class="field-label">Tags: </div><div class="field-items"><div class="field-item even"><a href="/tags/math" typeof="skos:Concept" property="rdfs:label skos:prefLabel">Math</a></div><div class="field-item odd"><a href="/tags/ccss" typeof="skos:Concept" property="rdfs:label skos:prefLabel">CCSS</a></div><div class="field-item even"><a href="/tags/dan-meyer" typeof="skos:Concept" property="rdfs:label skos:prefLabel">Dan Meyer</a></div></div></div>
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Thu, 09 Feb 2012 08:26:56 +0000renees1268 at http://allthingscommoncore.comhttp://allthingscommoncore.com/content/when-stars-align#commentsNew and Improved? Assessments
http://allthingscommoncore.com/content/new-and-improved-assessments-0
<div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even" property="content:encoded"> <p>When it comes to discussions of the common core, the conversation quickly turns to the question uppermost in teachers’ minds, “What will the new state assessment look like?” The truth of the matter is, we aren’t sure yet.</p>
<p>Initially, the word was that the new math assessment would be groundbreaking. It is supposed to include selected response, multiple mark, constructed response, computer simulation, and open-ended questions as well as performance based tasks. Both of the assessment consortiums, as outlined by Deb Haneke, in <a href="node/30">Assessments and Common Core Standards</a>, are charged with helping ensure students who graduate from high school are college and career ready. Their plans for the new assessments are similar but not identical. The Smarter Balance Assessment Consortium, of which Kansas is a governing state, is planning an adaptive assessment; one in which the computer aligns the difficulty of the questions to the student’s performance level.</p>
<p>At this point, there seems to be some backpedaling when it comes to the news about the new assessments. According to an article in Education Week, <a href="http://www.edweek.org/ew/articles/2011/04/12/28aera.h30.html?tkn=YMLFacXdHUujY0MFYtAEH40IJPJ846b%2FrlO2&cmp=clp-sb-ascd">Experts See Hurdles Ahead for Common Core Tests,</a> there are several factors that may impede the creation of a truly innovative assessment. As in most areas of education today, the lack of money rears its ugly head. Although both consortiums received Race to the Top Assessment grant funds, this does not include long-term funding for test administration or revision. With this in mind, there is pressure to get the test right the first time. The timeline for development is also a factor that may impede the amount of innovation that we see in the final product.</p>
<p>So my advice to teachers at this stage of the game is to focus on the standards themselves and leave the test, for now, to the test makers.</p>
</div></div></div><div class="field field-name-field-tags field-type-taxonomy-term-reference field-label-above"><div class="field-label">Tags: </div><div class="field-items"><div class="field-item even"><a href="/tags/ccss" typeof="skos:Concept" property="rdfs:label skos:prefLabel">CCSS</a></div><div class="field-item odd"><a href="/tags/assessments" typeof="skos:Concept" property="rdfs:label skos:prefLabel">Assessments</a></div><div class="field-item even"><a href="/tags/sbac" typeof="skos:Concept" property="rdfs:label skos:prefLabel">SBAC</a></div><div class="field-item odd"><a href="/tags/parcc" typeof="skos:Concept" property="rdfs:label skos:prefLabel">PARCC</a></div></div></div>
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Tue, 10 Jan 2012 00:28:14 +0000renees1236 at http://allthingscommoncore.comhttp://allthingscommoncore.com/content/new-and-improved-assessments-0#commentsWhen Five Plus Five Equals Eight
http://allthingscommoncore.com/content/when-five-plus-five-equals-eight
<div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even" property="content:encoded"> <p>For the last several months, I have been privileged to work with hundreds of teachers as they unpack the <a href="http://www.corestandards.org/"><strong>Common Core State Standards</strong>.</a> In each session, which have been held in grade level groups, we have worked through the meanings of the 8 Standards for Mathematical Practice and each time one point becomes extremely obvious. These eight standards, or measures of student behavior, are inextricably linked. It is no surprise really, as they were developed using information from the National Council of Teachers of Mathematics (NCTM) Process Standards and the National Research Council’s (NRC) Strands of Mathematical Proficiency. The point is driven home, however, when teachers work through the process of identifying for themselves what each standard means and does not mean for their classroom.</p>
<p>NCTM’s five process standards include:</p>
<p><strong>Problem Solving</strong></p>
<ul><li>Build new mathematical knowledge through problem solving</li>
<li>Solve problems that arise in mathematics and in other contexts</li>
<li>Apply and adapt a variety of appropriate strategies to solve problems</li>
<li>Monitor and reflect on the process of mathematical problem solving</li>
</ul><p><strong>Reasoning and Proof</strong></p>
<ul><li>Recognize reasoning and proof as fundamental aspects of mathematics</li>
<li>Make and investigate mathematical conjectures</li>
<li>Develop and evaluate mathematical arguments and proofs</li>
<li>Select and use various types of reasoning and methods of proof</li>
</ul><p><strong>Communication</strong></p>
<ul><li>Organize and consolidate their mathematical thinking through communication</li>
<li>Communicate their mathematical thinking coherently and clearly to peers, teachers, and others</li>
<li>Analyze and evaluate the mathematical thinking and strategies of others;</li>
<li>Use the language of mathematics to express mathematical ideas precisely.</li>
</ul><p><strong>Connections</strong></p>
<ul><li>Recognize and use connections among mathematical ideas</li>
<li>Understand how mathematical ideas interconnect and build on one another to produce a coherent whole</li>
<li>Recognize and apply mathematics in contexts outside of mathematics</li>
</ul><p><strong>Representation</strong></p>
<ul><li>Create and use representations to organize, record, and communicate mathematical ideas</li>
<li>Select, apply, and translate among mathematical representations to solve problems</li>
<li>Use representations to model and interpret physical, social, and mathematical phenomena</li>
</ul><p>The five stands of mathematical proficiency are:</p>
<p>(1)<em><a href="http://mason.gmu.edu/%7Ejsuh4/teaching/concept.htm"> Conceptual understanding</a></em> refers to the “integrated and functional grasp of mathematical ideas”, which “enables them [students] to learn new ideas by connecting those ideas to what they already know.” A few of the benefits of building conceptual understanding are that it supports retention, and prevents common errors.</p>
<p>(2)<a href="http://mason.gmu.edu/%7Ejsuh4/teaching/procedure.htm"><em> Procedural fluency</em> </a>is defined as the skill in carrying out procedures flexibly, accurately, efficiently, and appropriately.</p>
<p>(3)<em><a href="http://mason.gmu.edu/%7Ejsuh4/teaching/strategic.htm"> Strategic competence</a></em> is the ability to formulate, represent, and solve mathematical problems.</p>
<p>(4)<a href="http://mason.gmu.edu/%7Ejsuh4/teaching/reasoning.htm"> <em>Adaptive reasoning</em></a> is the capacity for logical thought, reflection, explanation, and justification.</p>
<p>(5)<a href="http://mason.gmu.edu/%7Ejsuh4/teaching/disposition.htm"><em> Productive disposition</em> </a>is the inclination to see mathematics as sensible, useful, and worthwhile, coupled with a belief in diligence and one’s own efficacy. (NRC, 2001, p. 116)</p>
<p>When you combine the two you end up with these 8 Standards for Mathematical Practice:</p>
<p>1. Make sense of problems and persevere in solving them.</p>
<p>2. Reason abstractly and quantitatively.</p>
<p>3. Construct viable arguments and critique the reasoning of others.</p>
<p>4. Model with mathematics.</p>
<p>5. Use appropriate tools strategically.</p>
<p>6. Attend to precision.</p>
<p>7. Look for and make use of structure.</p>
<p>8. Look for and express regularity in repeated reasoning.</p>
<p>As teachers begin to discuss each of these eight standards they see how the process standards and mathematical proficiencies are interwoven throughout. Examples of what that looks like for their classrooms and their practice can be found on videos at: <a href="http://summingitallup.com/wp-admin/For%20the%20last%20several%20months,%20I%20have%20been%20privileged%20to%20work%20with%20hundreds%20of%20teachers%20as%20they%20unpack%20the%20Common%20Core%20State%20Standards.%20In%20each%20session,%20which%20have%20been%20held%20in%20grade%20level%20groups,%20we%20have%20worked%20through%20the%20meanings%20of%20the%208%20Standards%20for%20Mathematical%20Practice%20and%20each%20time%20one%20point%20becomes%20extremely%20obvious.%20%20These%20eight%20standards,%20or%20measures%20of%20student%20behavior,%20are%20inextricably%20linked.%20%20It%20is%20no%20surprise%20really,%20as%20they%20were%20developed%20using%20information%20from%20the%20National%20Council%20of%20Teachers%20of%20Mathematics%20%28NCTM%29%20Process%20Standards%20and%20the%20National%20Research%20Council%E2%80%99s%20%28NRC%29%20Strands%20of%20Mathematical%20Proficiency.%20%20%20The%20point%20is%20driven%20home,%20however,%20when%20teachers%20work%20through%20the%20process%20of%20identifying%20for%20themselves%20what%20each%20standard%20means%20and%20does%20not%20mean%20for%20their%20classroom.%20%20NCTM%E2%80%99s%20five%20process%20standards%20include:%20%20Problem%20Solving%20%20%E2%80%A2Build%20new%20mathematical%20knowledge%20through%20problem%20solving%20%E2%80%A2Solve%20problems%20that%20arise%20in%20mathematics%20and%20in%20other%20contexts%20%E2%80%A2Apply%20and%20adapt%20a%20variety%20of%20appropriate%20strategies%20to%20solve%20problems%20%E2%80%A2Monitor%20and%20reflect%20on%20the%20process%20of%20mathematical%20problem%20solving%20Reasoning%20and%20Proof%20%20%E2%80%A2Recognize%20reasoning%20and%20proof%20as%20fundamental%20aspects%20of%20mathematics%20%E2%80%A2Make%20and%20investigate%20mathematical%20conjectures%20%E2%80%A2Develop%20and%20evaluate%20mathematical%20arguments%20and%20proofs%20%E2%80%A2Select%20and%20use%20various%20types%20of%20reasoning%20and%20methods%20of%20proof%20%20Communication%20%20%E2%80%A2Organize%20and%20consolidate%20their%20mathematical%20thinking%20through%20communication%20%20%E2%80%A2Communicate%20their%20mathematical%20thinking%20coherently%20and%20clearly%20to%20peers,%20teachers,%20and%20others%20%E2%80%A2Analyze%20and%20evaluate%20the%20mathematical%20thinking%20and%20strategies%20of%20others;%20%E2%80%A2Use%20the%20language%20of%20mathematics%20to%20express%20mathematical%20ideas%20precisely.%20%20%20%20Connections%20%20%E2%80%A2Recognize%20and%20use%20connections%20among%20mathematical%20ideas%20%E2%80%A2Understand%20how%20mathematical%20ideas%20interconnect%20and%20build%20on%20one%20another%20to%20produce%20a%20coherent%20whole%20%E2%80%A2Recognize%20and%20apply%20mathematics%20in%20contexts%20outside%20of%20mathematics%20Representation%20%20%E2%80%A2Create%20and%20use%20representations%20to%20organize,%20record,%20and%20communicate%20mathematical%20ideas%20%E2%80%A2Select,%20apply,%20and%20translate%20among%20mathematical%20representations%20to%20solve%20problems%20%E2%80%A2Use%20representations%20to%20model%20and%20interpret%20physical,%20social,%20and%20mathematical%20phenomena%20%20%20%20The%20five%20stands%20of%20mathematical%20proficiency%20are:%20%281%29%20Conceptual%20understanding%20refers%20to%20the%20%E2%80%9Cintegrated%20and%20functional%20grasp%20of%20mathematical%20ideas%E2%80%9D,%20which%20%E2%80%9Cenables%20them%20%5Bstudents%5D%20to%20learn%20new%20ideas%20by%20connecting%20those%20ideas%20to%20what%20they%20already%20know.%E2%80%9D%20A%20few%20of%20the%20benefits%20of%20building%20conceptual%20understanding%20are%20that%20it%20supports%20retention,%20and%20prevents%20common%20errors.%20%20%282%29%20Procedural%20fluency%20is%20defined%20as%20the%20skill%20in%20carrying%20out%20procedures%20flexibly,%20accurately,%20efficiently,%20and%20appropriately.%20%20%283%29%20Strategic%20competence%20is%20the%20ability%20to%20formulate,%20represent,%20and%20solve%20mathematical%20problems.%20%284%29%20Adaptive%20reasoning%20is%20the%20capacity%20for%20logical%20thought,%20reflection,%20explanation,%20and%20justification.%20%285%29%20Productive%20disposition%20is%20the%20inclination%20to%20see%20mathematics%20as%20sensible,%20useful,%20and%20worthwhile,%20coupled%20with%20a%20belief%20in%20diligence%20and%20one%E2%80%99s%20own%20efficacy.%20%28NRC,%202001,%20p.%20116%29%20When%20you%20combine%20the%20two%20you%20end%20up%20with%20these%208%20Standards%20for%20Mathematical%20Practice:%201.%20Make%20sense%20of%20problems%20and%20persevere%20in%20solving%20them.%202.%20Reason%20abstractly%20and%20quantitatively.%203.%20Construct%20viable%20arguments%20and%20critique%20the%20reasoning%20of%20others.%204.%20Model%20with%20mathematics.%205.%20Use%20appropriate%20tools%20strategically.%206.%20Attend%20to%20precision.%207.%20Look%20for%20and%20make%20use%20of%20structure.%208.%20Look%20for%20and%20express%20regularity%20in%20repeated%20reasoning.%20As%20teachers%20begin%20to%20discuss%20each%20of%20these%20eight%20standards%20they%20see%20how%20the%20process%20standards%20and%20mathematical%20proficiencies%20are%20interwoven%20throughout.%20%20Examples%20of%20what%20that%20looks%20like%20for%20their%20classrooms%20and%20their%20practice%20can%20be%20found%20on%20videos%20at:%20%20http://www.insidemathematics.org/index.php/common-core-standards"><strong>http://www.insidemathematics.org/index.php/common-core-standards</strong></a></p>
</div></div></div><div class="field field-name-field-tags field-type-taxonomy-term-reference field-label-above"><div class="field-label">Tags: </div><div class="field-items"><div class="field-item even"><a href="/tags/common-core-state-state-standards" typeof="skos:Concept" property="rdfs:label skos:prefLabel">common core state state standards</a></div><div class="field-item odd"><a href="/tags/nctm" typeof="skos:Concept" property="rdfs:label skos:prefLabel">NCTM</a></div><div class="field-item even"><a href="/tags/national-research-council" typeof="skos:Concept" property="rdfs:label skos:prefLabel">National Research Council</a></div><div class="field-item odd"><a href="/tags/mathematics" typeof="skos:Concept" property="rdfs:label skos:prefLabel">Mathematics</a></div></div></div>
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Tue, 10 Jan 2012 00:17:38 +0000renees1235 at http://allthingscommoncore.comhttp://allthingscommoncore.com/content/when-five-plus-five-equals-eight#commentsPersistent Problem Solving
http://allthingscommoncore.com/content/persistent-problem-solving
<div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even" property="content:encoded"> <p>A question I have been asked frequently is, "What should the common core look like in practice?" In my opinion there is no one right answer to that question. However, the common core's eight standards for mathematical practice suggests that it should not be business as usual.</p>
<p>The first of those eight standards requires students to make sense of problems and persevere in solving them. For me, this suggests the need for problems that are something other than the word problems in textbooks. They need to be engaging, perplexing, and present a challenge to students. For older students a good source of this type of problem can be found in Dan Meyer's blog, <a href="http://blog.mrmeyer.com/">dy/dan</a>. His 3 Acts videos entitled Hot Coffee, Incredibly Shrinking Dollar, and Domino Skyscraper are just a few examples of this type of problem. Meyer poses non-routine problems in an engaging manner without immediately disclosing every detail necessary for students to solve the problems. Determining the important information needed to solve each problem should be a part of the students' discovery process and is a critical component of sense making. </p>
<p>We, at ESSDACK, are looking forward to meeting and learning more about "Real World Math" from Meyer on February 6, 2012. </p>
<p> </p>
</div></div></div><div class="field field-name-field-tags field-type-taxonomy-term-reference field-label-above"><div class="field-label">Tags: </div><div class="field-items"><div class="field-item even"><a href="/tags/mathematics" typeof="skos:Concept" property="rdfs:label skos:prefLabel">Mathematics</a></div><div class="field-item odd"><a href="/tags/ccss" typeof="skos:Concept" property="rdfs:label skos:prefLabel">CCSS</a></div></div></div>
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Mon, 07 Nov 2011 04:40:40 +0000renees1183 at http://allthingscommoncore.comhttp://allthingscommoncore.com/content/persistent-problem-solving#commentsAll For One and One For All
http://allthingscommoncore.com/content/all-one-and-one-all
<div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even" property="content:encoded"> <p>Seven entities with vested interest in the area of mathematics and common core state standards have agreed to lend their collective expertise to the formation of a new coalition called MC3. The organizations include the National Council of Teachers of Mathematics (NCTM), the National Council of Supervisors of Mathematics (NCSM), the Association of Mathematics Teacher Educators (AMTE), the Association of State Supervisors of Mathematics (ASSM), the Council of Chief State School Officers (CCSSO), the Smarter Balanced Assessment Consortium (SBAC), and the Partnership for the Assessment of Readiness for College and Careers (PARCC). </p>
<p>Their <a href="nctm.org/standards/mathcommoncore/">website</a>, lists the mission of the Math Common Core Coalition as striving to ensure the successful communication, interpretation, implementation, and assessment of the Common Core State Standards. They will work together to: </p>
<ul><li>Provide a means to review, research, nurture and communicate common messages throughout the implementation and assessment of the CCSSM.</li>
<li>Provide expertise and advice from the communities of mathematics education content and assessment experts for the development of the content framework of the assessment consortia for the CCSSM.</li>
<li>Collect, analyze, and disseminate information about the implementation and assessment processes of the CCSSM that will inform future revisions of the CCSSM.</li>
</ul></div></div></div><div class="field field-name-field-tags field-type-taxonomy-term-reference field-label-above"><div class="field-label">Tags: </div><div class="field-items"><div class="field-item even"><a href="/tags/nctm" typeof="skos:Concept" property="rdfs:label skos:prefLabel">NCTM</a></div><div class="field-item odd"><a href="/tags/ccss" typeof="skos:Concept" property="rdfs:label skos:prefLabel">CCSS</a></div><div class="field-item even"><a href="/tags/mathematics" typeof="skos:Concept" property="rdfs:label skos:prefLabel">Mathematics</a></div></div></div>
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Mon, 05 Sep 2011 21:15:38 +0000renees1173 at http://allthingscommoncore.comhttp://allthingscommoncore.com/content/all-one-and-one-all#commentsGood Advice From the Top
http://allthingscommoncore.com/content/good-advice-top
<div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even" property="content:encoded"> <p>I just read a blog post by the National Council of Teachers of Mathematics President, J. Michael Shaughness, about the Common Core State Standards for Mathematics. In his post,<a href="http://www.nctm.org/about/content.aspx?id=30009"> CCSSM and Curriculum and Assessment: NOT Business as Usual</a>, Shaughness shares his thoughts about how the common core movement affords our nation an opportunity to make significant changes in mathematics instruction. He includes links to assessment sites and his thoughts on curriculum and instruction. Shaughness encourages schools to begin examining current curriculum to see how it aligns to the common core but warns against states or districts writing their own curriculum. With the majority of the states adopting the common core standards, this is our first opportunity to have a nationwide collaborative community working to improve mathematics curriculum, and instructional and assessment practices. </p>
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Mon, 05 Sep 2011 16:54:18 +0000renees1172 at http://allthingscommoncore.comhttp://allthingscommoncore.com/content/good-advice-top#commentsTidbits from NCSM
http://allthingscommoncore.com/content/tidbits-ncsm-0
<div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even" property="content:encoded"> <p class="MsoNormal">A few weeks ago, I attended a meeting of the Kansas State Mathematics Leaders. A good portion of our day was spent discussing the common core state standards and what is known about the future mathematics assessment. Several of the members attended the <a href="http://ncsmonline.org/">National Council of Supervisors of Mathematics</a> national convention and reported back to the group. Here are some of the things they shared.</p>
<p class="MsoListParagraphCxSpFirst">· The new state assessment will include the opportunity to learn (OTL) component that is currently available in Kansas at the high school level. This means a 12-week testing window at the end of each school year will allow for two opportunities to take the state assessment. Schools will be allowed to re-teach and re-test students who do not reach the level of mastery expected for that grade level on the first administration.</p>
<p class="MsoListParagraphCxSpLast">· The reporting of assessment results will be in the form of a growth model, which may mean each student would have to be pre-tested or screened at the beginning of each school year.</p>
<p class="MsoListParagraph">· Concepts will not be retaught from one grade to the next. Mastery of grade level content is expected at the end of each year. Therefore, it is imperative we develop support structures for struggling students early. They will need access to the regular curriculum and additional support for content not mastered in a previous grade. RTI and MTSS will play a critical role in the common core standards process.</p>
<p class="MsoListParagraph">· The concerns about the common core for math that were enumerated at the convention included: a disregard for technology, due to political debates; the overload of material to be covered in sixth grade; concepts only being taught once; the need for vertical discussions about what and when to teach content; the need for professional development for teachers in both math content knowledge and pedagogical skills; and the fact that everyone must teach the common core state standards for their grade level or the system will break down. </p>
</div></div></div><div class="field field-name-field-tags field-type-taxonomy-term-reference field-label-above"><div class="field-label">Tags: </div><div class="field-items"><div class="field-item even"><a href="/tags/ncsm" typeof="skos:Concept" property="rdfs:label skos:prefLabel">NCSM</a></div><div class="field-item odd"><a href="/tags/mathematics" typeof="skos:Concept" property="rdfs:label skos:prefLabel">Mathematics</a></div><div class="field-item even"><a href="/tags/ccss" typeof="skos:Concept" property="rdfs:label skos:prefLabel">CCSS</a></div><div class="field-item odd"><a href="/tags/rti" typeof="skos:Concept" property="rdfs:label skos:prefLabel">RTI</a></div><div class="field-item even"><a href="/tags/mtss" typeof="skos:Concept" property="rdfs:label skos:prefLabel">MTSS</a></div></div></div>
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Tue, 24 May 2011 16:20:32 +0000renees1144 at http://allthingscommoncore.comhttp://allthingscommoncore.com/content/tidbits-ncsm-0#commentsNew... and Improved? Assessments
http://allthingscommoncore.com/content/new-and-improved-assessments
<div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even" property="content:encoded"> <p class="MsoNormal">When it comes to discussions of the common core, the conversation quickly turns to the question uppermost in teachers’ minds, “What will the new state assessment look like?” The truth of the matter is, we aren’t sure yet. </p>
<p class="MsoNormal">Initially, the word was that the new math assessment would be groundbreaking. It is supposed to include selected response, multiple mark, constructed response, computer simulation, and open-ended questions as well as performance based tasks. Both of the assessment consortiums, as outlined by Deb Haneke, in <a href="http://allthingscommoncore.com/node/30">Assessments and Common Core Standards</a>, are charged with helping ensure students who graduate from high school are college and career ready. Their plans for the new assessments are similar but not identical. The Smarter Balance Assessment Consortium, of which Kansas is a governing state, is planning an adaptive assessment; one in which the computer aligns the difficulty of the questions to the student’s performance level.</p>
<p class="MsoNormal">At this point, there seems to be some backpedaling when it comes to the news about the new assessments. According to the recent article in Education Week, <a href="http://www.edweek.org/ew/articles/2011/04/12/28aera.h30.html?tkn=YMLFacXdHUujY0MFYtAEH40IJPJ846b%2FrlO2&cmp=clp-sb-ascd">Experts See Hurdles Ahead for Common Core Tests,</a> there are several factors that may impede the creation of a truly innovative assessment. As in most areas of education today, money rears its ugly head. Although both consortiums received Race to the Top Assessment grant funds, this does not include long-term funding for test administration or revision. With this in mind, there is pressure to get the test right the first time. The timeline for development is also a factor that may impede the amount of innovation that we see in the final product. </p>
<p>So my advice to teachers at this stage of the game is to focus on the standards themselves and leave the test, for now, to the test makers. </p>
<p> </p>
</div></div></div><div class="field field-name-field-tags field-type-taxonomy-term-reference field-label-above"><div class="field-label">Tags: </div><div class="field-items"><div class="field-item even"><a href="/tags/common-core-standards" typeof="skos:Concept" property="rdfs:label skos:prefLabel">common core standards</a></div><div class="field-item odd"><a href="/tags/common-core-assessments" typeof="skos:Concept" property="rdfs:label skos:prefLabel">common core assessments</a></div><div class="field-item even"><a href="/tags/smarter-balance-assessment-consortium" typeof="skos:Concept" property="rdfs:label skos:prefLabel">smarter balance assessment consortium</a></div><div class="field-item odd"><a href="/tags/partnership-assessment-readiness-college-and-careers" typeof="skos:Concept" property="rdfs:label skos:prefLabel">Partnership for Assessment of Readiness for College and Careers</a></div></div></div>
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Tue, 10 May 2011 15:37:43 +0000renees55 at http://allthingscommoncore.comhttp://allthingscommoncore.com/content/new-and-improved-assessments#commentsWhere Do We Begin?
http://allthingscommoncore.com/content/where-do-we-begin
<div class="field field-name-field-image field-type-image field-label-hidden"><div class="field-items"><div class="field-item even"><img typeof="foaf:Image" src="http://allthingscommoncore.com/sites/allthingscommoncore.com/files/styles/medium/public/footprints_in_the_sand_op_493x600.jpg" width="181" height="220" alt="" /></div></div></div><div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even" property="content:encoded"> <p><strong>A journey of a thousand miles begins with a single step.</strong><em> ~Lao-tzu Chinese philosopher (604 BC – 531 BC)</em></p>
<p>With every new task we undertake, there is the question of where to begin. Sometimes the first step is obvious and other times there are various options. Moving to the Common Core State Standards could be equated to the journey of a thousand miles, in that it requires new learning for the majority of teachers in the nation.</p>
<p>Obviously, one of the first steps is to acquaint oneself with the grade level and subjects one is required to teach. However, on a larger scale, it is important to be familiar with all the standards. It is important to understand what content students have already been exposed to, been expected to master, and what they will be learning in the future.</p>
<p>Another critical component to be aware of is the transition timeline we will encounter as we move from our old system of standards to the new Common Core Standards. Without careful investigation and gradual implementation of the Common Core, students will have gaps in their understandings when the new assessments are fully implemented.</p>
<p>The Kansas Department of Education has recommended that teachers of Kindergarten and First Grade begin implementing the Common Core Standards in 2011-2012. The rationale is that those students will never have to take the current state assessment and this would alleviate part of the gaps we might experience when we are fully implementing and assessing the Common Core Standards.</p>
<p>At Essdack, we are working to make teachers’ first steps into the Common Core meaningful by providing days for investigating the content at their grade level. We also recommend investigating the crosswalks between the current state standards and the Common Core. As teachers learn where the Common Core and current standards overlap and differ, they will be able to design instruction that should lessen the gaps that might occur when the new assessments are implemented.</p>
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Wed, 13 Apr 2011 19:04:12 +0000renees36 at http://allthingscommoncore.comhttp://allthingscommoncore.com/content/where-do-we-begin#commentsWhat's Behind the Common Core Math Standards?
http://allthingscommoncore.com/content/whats-behind-common-core-math-standards
<div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even" property="content:encoded"> <p>The release of the Common Core State Standards (CCSS) is a milestone in the standards movement that began more than 20 years ago when the National Council of Teachers of Mathematics (NCTM) published Curriculum and Evaluation Standards for School. NCTM, along with the National Council of Supervisors of Mathematics and other mathematics organizations, supports the goal of the CCSS to describe a coherent, focused curriculum that has realistically high expectations and supports an equitable mathematics education for all students.</p>
<p>The Standards for Mathematical Practice, which describe expertise that math educators at all levels seek to develop in students, is also a key component of the new Common Core Standards movement. These practices rest on key “processes and proficiencies” with longstanding importance in mathematics education, including the NCTM process standards and the strands of mathematical proficiency from the National Research Council’s report Adding It Up. The five process standards which run through all grade levels are problem solving, reasoning and proof, communication, representations, and connections. The strands of proficiency specified by "Adding It Up" include: adaptive reasoning, strategic competence, conceptual understanding, proceduaral fluency, and a productive disposition. </p>
<p>Other key elements in a student's success in mathematics are: • Making sense of problems and persevering in solving them. • Reasoning abstractly and quantitatively. • Modeling with mathematics. • UsIng appropriate tools strategically. • Attending to precision. • Looking for and making use of structure.</p>
<p>So, what is behind the common core standards for mathematics....RESEARCH!</p>
</div></div></div><div class="field field-name-field-tags field-type-taxonomy-term-reference field-label-above"><div class="field-label">Tags: </div><div class="field-items"><div class="field-item even"><a href="/tags/common-core-standards" typeof="skos:Concept" property="rdfs:label skos:prefLabel">common core standards</a></div><div class="field-item odd"><a href="/tags/strands-mathematical-proficiency" typeof="skos:Concept" property="rdfs:label skos:prefLabel">Strands of Mathematical Proficiency</a></div><div class="field-item even"><a href="/tags/nctm" typeof="skos:Concept" property="rdfs:label skos:prefLabel">NCTM</a></div><div class="field-item odd"><a href="/tags/principles-and-standards-school-mathematics" typeof="skos:Concept" property="rdfs:label skos:prefLabel">Principles and Standards for School Mathematics</a></div><div class="field-item even"><a href="/tags/math" typeof="skos:Concept" property="rdfs:label skos:prefLabel">Math</a></div><div class="field-item odd"><a href="/tags/mathematics" typeof="skos:Concept" property="rdfs:label skos:prefLabel">Mathematics</a></div></div></div>
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Sat, 12 Mar 2011 23:57:29 +0000renees19 at http://allthingscommoncore.comhttp://allthingscommoncore.com/content/whats-behind-common-core-math-standards#commentsFocus on Fractions
http://allthingscommoncore.com/content/focus-fractions
<div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even" property="content:encoded"> <p>The <a href="http://www.corestandards.org/the-standards/mathematics">Common Core Standards for Mathematics,</a> have focused on fractions, and for good reason. In its comprehensive report on the state of math education in America, the <a href="http://us.lrd.yahoo.com/SIG=11vhel735/**http%3A//www2.ed.gov/about/bdscomm/list/mathpanel/index.html">National Math Panel</a> said understanding fractions is "the most important foundational skill NOT developed among American students," and is key to learning Algebra. Since fractions are the gateway to Algebra and Algebra is a required class for high school graduation, elementary and middle school math teachers need to have a clear understanding of fractions and fraction instruction.</p>
<p>Today, in many middle school classrooms, students struggle with fractional concepts. In the common core standards, students will first be introduced to fractions in the third grade. They will learn that fractions are numbers, not just parts of cookies or pizzas. This transition from thinking of fractions as "parts of a shape" to numbers will make it easier for students to comprehend their use in operations. Students will be expected to work proficiently with fraction operations by the end of sixth grade and understand the relationship between fractions, decimals, and percents by the end of seventh grade. </p>
<p>With the new, and long overdue, emphasis on fractional concepts in the common core standards, it will behoove teachers to examine their own understanding of fractions. It is often true, we teach the same way we were taught and most of us weren't taught about fractions from a conceptual standpoint but rather in a very procedural manner. In response to this new focus on fractions, teachers need to look for professional development opportunities that will increase their own conceptual understanding and provide them with instructional strategies to help their students. </p>
<p> </p>
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Tue, 08 Mar 2011 03:17:16 +0000renees16 at http://allthingscommoncore.comhttp://allthingscommoncore.com/content/focus-fractions#commentsA Whole New Look
http://allthingscommoncore.com/content/whole-new-look
<div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even" property="content:encoded"> <p>For teachers who are proficient at navigating their current state standards, the Common Core Standards may have a completely different look. In the area of mathematics, the content of the document is divided into domains, clusters, and standards. <em>Domains</em> are the overarching term and refer to a large group of related standards. <em>Clusters</em> are groups of related standards. Because mathematics is a connected subject, standards from different domains and clusters may be closely related. Finally, the <em>standards</em> define what students should understand and be able to do. An example from fourth grade would be: Domain - Operations and Algebraic Thinking; Clusters - Use the four operations with whole numbers to solve problems (three separate standards), Gain familiarity with factors and multiples (one standard), and Generate and analyze patterns (one standard).</p>
<p>Within the document, each grade level does not necessarily have the same domains or number of domains as the preceding grade. However, the standards are aligned vertically from one grade to the next. Unlike some current state standards, the Common Core State Standards do not spell out every step in the instructional process and some do not have example problems. Therefore, educators are going to have to investigate the new standards thoroughly and translate them into new instructional practices. </p>
<p> </p>
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Tue, 08 Mar 2011 01:55:31 +0000renees15 at http://allthingscommoncore.comhttp://allthingscommoncore.com/content/whole-new-look#commentsDeep, Not Wide
http://allthingscommoncore.com/content/deep-not-wide
<div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even" property="content:encoded"> <p>For years, teachers have bemoaned the fact that they were forced to teach a mile wide and an inch deep. The new Common Core State Standards for Mathematics are designed to reduce the number of concepts that will be taught at each grade level, thereby allowing teachers to devote more time and depth of instruction to each standard. </p>
<p>The concepts placed at each grade level were determined based on prerequisite topics that were to have been taught in a previous grade, international comparisons and the professional judgement of educators, researchers, and mathematicians. </p>
<p>These standards do not dictate a predetermined order of instruction or a particular curriculum. As it says in the Common Core document, "These Standards are not intended to be new names for old ways of doing business. They are a call to take the next step. It is time for states to work together to build on lessons learned from two decades of standards based reforms. It is time to recognize that standards are not just promises to our children, but promises we intend to keep."</p>
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Tue, 08 Mar 2011 01:35:03 +0000renees14 at http://allthingscommoncore.comhttp://allthingscommoncore.com/content/deep-not-wide#comments