Presentation on theme: "Common Core State Standards"— Presentation transcript:
1 Common Core State Standards March 3, 2011Welcome. My name is Tom Adams and I am the Director of the Standards, Curriculum Frameworks and Instructional Resources Division at the California Department of Education.I am happy to have been asked to spend some time with you today, looking more closely at the content of the new Common Core State Standards.I am going to spend a few minutes providing you with an overview of the Common Core and the development of the standards.My intention is that you will leave this session with a clearer understanding of the content of the Common Core State Standards and what their adoption means for California’s students.Let’s get started.English Language Arts and Literacy in History/Social Studies, Science, and Technical SubjectsMathematicsProvided by the California Teachers Association and Tom Adams from the California Department of EducationCLAB: Developed by SCFIRD with support from ELCS, SPALD, and AADOverview Presentation CTA - CLAB: Developed by SCFIRD with support from ELCSD, SCALD, and AAD
2 The Common Core Standards Rigorous, research-based standards for English-language arts and mathematics for grades K-12Designed to prepare the nation’s students with the knowledge and skills needed for success in college and the workforceInternationally benchmarked to ensure that students will be globally competitiveA clear and consistent educational frameworkA collaborative effort that builds on the best of current state standardsOn August 2, 2010, the California State Board of Education (SBE) voted unanimously to adopt new standards for both mathematics and English-language arts.The last time California adopted new standards was 1997, so the new standards represent a timely update.The new standards are rigorous, research-based, and designed to prepare every student for success in college and the workforce.The standards are internationally benchmarked to ensure that our students are able to compete with students around the world.The standards are focused and clear, allowing students, parents and teachers to understand what is expected of them.The standards represent an ambitious collaborative effort. Let’s take a look at how they were developed, and who was involved.
3 College and Career Readiness Standards In 2009, the Council of Chief State School Officers (CCSSO) and the National Governors Association Center for Best Practices (NGA Center) committed to developing a set of standards that would help prepare students for success in college and career.In September 2009, College and Career Readiness standards were released.This work became the foundation for the Common Core.In 2009, Governors and state commissioners of education from 48 states, 2 territories and the District of Columbia, committed to developing a set of standards that would help prepare students with the knowledge and skills needed to succeed in education and training after high school.The first step in this process was the development of the College and Career Readiness standards.These became the foundation for the Common Core State Standards (CCSS).
4 The Common Core State Standards Initiative A voluntary state-led effort coordinated by the CCSSO and NGAIncludes parents, educators, content experts, researchers, national organizations and community groups from 48 states, 2 territories and the District of ColumbiaThe Common Core State Standards Initiative is a voluntary, state-led effort coordinated by the CCSSO and NGA to establish clear and consistent education standards.Parents, educators, content experts, researchers, national organizations and community groups from forty-eight states, two territories, and the District of Columbia all participated in the development of the standards. Feedback and review processes were integral to the shaping of the Common Core.Feedback teams included K-12 teachers, postsecondary faculty, curriculum and assessment experts and researchers.
5 The Common Core State Standards Feedback and review from national organizations, including:American Council on Education (ACE)American Federation of Teachers (AFT)Campaign for High School Equity (CHSE)Conference Board of the Mathematical Sciences (CBMS)Modern Language Association (MLA)National Council of Teachers of English (NCTE)National Council of Teachers of Mathematics (NCTM)National Education Association (NEA)A number of national organizations also continuously reviewed the standards and contributed feedback.
6 California and the Common Core State Standards Senate Bill 1 from the Fifth Extraordinary Session (SB X5 1):established an Academic Content Standards Commission (ACSC) to develop standards in mathematics and English–language artsstated that 85 percent of the standards were to consist of the CCSS with up to 15 percent additional materialdirected the State Board of Education (SBE) to adopt or reject recommendations of the ACSCSenate Bill 1 from the Fifth Extraordinary Session (SB X5 1) established the Academic Content Standards Commission (ACSC) to develop academic content standards in language arts and mathematics.At least 85% of the standards were to consist of the CCSS with up to 15 percent additional material as recommended by the commission.At the same time, SB X5 1 directed the SBE to accept or reject the recommendations of the ACSC by August 2, 2010.The ACSC convened during the summer of 2010 to evaluate the CCSS for rigor and alignment to California standards.They inserted words, phrases, and select California standards in their entirety to maintain California’s high expectations for students.On July 15, 2010, the commission recommended that the SBE adopt the CCSS as amended.The SBE voted unanimously to adopt the recommendations of the ACSC on August 2, 2010.
7 California’s Criteria for the Additional 15% Substantively enhanceAddress a perceived gapBe defensible to classroom practitionersKeep the original standard intactEnsure the rigor of California’s existing standards is maintainedStates could add up to 15% to the common core state standards developed by the State Standards Initiative consortium.California added to the common core state standards based on the following criteria:Substantively enhanceAddress a perceived gapBe defensible to classroom practitionersKeep the original standard intactEnsure the rigor of California’s existing standards is maintainedIn order to identify what was added, the Commission presented a draft to the Board with California’s Additional 15% indicated in bold and underlined font.The architects of the Common Core combined the best work of states, and in fact, California’s standards played a large part in developing the foundation for the Common Core. Because of this, California did not necessarily add the full 15% that was allowed. In terms of word count – for ELA California added approximately 8%.
8 Intentional Design Limitations Note what the Standards DO and DO NOT coverThe Standards DO…The Standards DO NOT…set grade-level standardsdefine the intervention methods or materialsallow for the widest possible range of students to participate fully permitting appropriate accommodationsdefine the full range of supports appropriate for English learners and students with special needsdefine general, cross-disciplinary literacy expectationsdefine the whole of college and career readinessThe Introduction of the Common Core State Standards, also describes what is NOT covered by the standards, the Intentional Design Limitations.The Standards do…set grade-level standards; they do not define the intervention methods or materialsallow for the widest possible range of students to participate fully permitting appropriate accommodations; they do not define the full range of supports appropriate for English learners and students with special needsdefine general, cross-disciplinary literacy expectations; they do not define the whole of college and career readiness
9 Intentional Design Limitations Note what the Standards DO and DO NOT coverThe Standards DO…The Standards DO NOT…define what all students are expected to know and be able to dodefine how teachers should teachfocus on what is most essentialdescribe all that can or should be taughtestablish a baseline for advanced learnersdefine the nature of advanced workThe Intentional Design Limitations continue with the following:The Standards do…define what all students are expected to know and be able to do; they do not define how teachers should teachfocus on what is most essential; they do not describe all that can or should be taughtestablish a baseline for advanced learners; they do not define the nature of advanced work
10 Next Steps Frameworks and Instructional Materials Milestone MathematicsReading/ELASuspension liftedFrameworkMay 2013May 2014MaterialsNovember 2014November 2016No legislative actionMay 2015May 2017November 2017November 2019It will take several years to implement curriculum, instructional materials, professional development, and assessments based on the new standards.The activities of the Curriculum Commission, which include developing curriculum frameworks and adopting new materials, were halted in the summer of 2009 by AB X4 2.Without any legislative action, work on frameworks is suspended until July 2013 and work on adoptions is suspended until November 2015.Here are two possible timelines for development of new curriculum frameworks and adoption of instructional materials.The first assumes urgency legislation, the second assumes no legislative action.Overview Presentation CTA - CLAB: Developed by SCFIRD with support from ELCSD, SCALD, and AAD
11 California Common Core Standards English Language Arts Literacy in History-Social Studies, Sciences, and Technical Subjects
12 California Common Core Standards English Language Arts Literacy in History-Social Studies, Sciences, and Technical Subjects
13 Common Core Standards for English Language Arts & Literacy in History/Social Studies, Science, and Technical SubjectsThe Common Core Standards for English Language Arts & Literacy in History/Social Studies, Science, and Technical Subjects are organized around the College and Career Readiness (CCR) Standards for Reading, Writing, Speaking and Listening, and Language.Each strand is headed by a set of CCR anchor standards that is identical across all grades and content areas.The Common Core Standards for English-language arts also set requirements for reading and writing in the social and natural sciences.Now, let’s take a closer look at the content and structure of the Common Core standards for English-language arts. The standards are arranged into four strands: Reading, Writing, Speaking and Listening, and Language.The College and Career Readiness anchor standards are the backbone of the Common Core standards for English- language arts.Each strand is headed by a set of CCR standards. These standards are identical across the grades. Kindergarteners, fourth graders, eighth graders and high school students are all working toward the same College and Career Readiness anchor standards.Developed by SCFIRD
14 Similar Organization Current CA Standards DOMAINS Common Core Standards for CASTRANDSReadingWritingListening and SpeakingWritten and Oral English Language ConventionsSpeaking and ListeningLanguageNow, we’ll take a look at some of the similarities between California’s current standards and the newly adopted Common Core Standards for California.California’s current standards are organized into four large categories called domains. The domains are:ReadingWritingListening and SpeakingWritten and Oral English Language ConventionsThe Common Core Standards for California are similarly organized into four groups called strands. The strands are:Speaking and ListeningLanguageLet’s take a closer look at some of the standards and note their similar content.
15 Common Core Standards for English Language Arts & Literacy in History/Social Studies, Science, and Technical SubjectsThe Standards comprise three main sections:a comprehensive K–5 sectionincludes standards for foundational skillstwo content area-specific sections for grades 6–12one for English-language artsone for literacy in history/social studies, science and technical subjects.The English-language arts standards are organized into three sections.The first is a section for grades K-5 which includes both English-language arts standards and standards for literacy in history/social studies, science and technical subjects.The K-5 section also includes standards for foundational skills for reading.Next, there’s a section for grades 6-12 English- language arts.Finally, there’s a section for grades 6-12 literacy in history/social studies, science and technical subjects. It includes standards in the reading and writing strands.The representation of literature and informational texts is balanced throughout the standards.At every grade level, students are expected to read, write and discuss literature, narratives and expository texts.Developed by SCFIRD
16 Source: Sacramento County Office of Education at http://www.scoe.net Common Core Standards for English Language Arts & Literacy in History/Social Studies, Science, and Technical SubjectsHere is a page from the standards document.You can see that there are ten standards for reading informational text for both grade spans.Because the ELA standards are built upon CCR anchor standards, each grade level has ten standards for reading informational text.There are many similarities between the CCSS and the 1997 California standards, but there are a few organizational differences.For instance, in the CCSS, the standards are organized into strands. In the 1997 CA content standards, the standards are organized into domains.Some standards have been moved. For example, vocabulary standards are found in the Reading domain in the 1997 CA standards, but they are included in the Language strand of the CCSS.Please note that the CA additions are denoted by underlined, bolded text.Source: Sacramento County Office of Education at
17 Correlating Standards Use knowledge of antonyms, synonyms, homophones, and homographs to determine the meaning of words. (3.WA.1.4)Demonstrate knowledge of levels of specificity among grade-appropriate words and explain the importance of these relations (e.g., dog/ mammal/ animal/ living things). (3.WA.1.5)Students read and understand grade-level-appropriate material. They draw upon a variety of comprehension strategies as needed (e.g., generating and responding to essential questions, making predictions, comparing information from several sources). … (3.RC.2.0)1997 CA StandardsDetermine the meaning of general academic and domain-specific words and phrases in a text relevant to a grade 3 topic or subject area. (3.RI.4)2010 CCCSSBefore we take a look at the standards, I need to provide you with a disclaimer about the art of standards correlation.While it is tempting to think that there exists a definitive crosswalk that provides a comprehensive comparison of the 1997 CA standards to the CCSS, I am here to tell you that there is no such crosswalk.Here’s an example. On the right is a CCSS for reading informational text for third grade students.On the left, in blue, is a 1997 CA standard that has been correlated to the CCSS. It’s a perfectly justifiable correlation.However, a different standards analysis suggested that standard 1.5 be joined by two additional reading standards, 1.4 and 2.0 (click twice). This is also a justifiable correlation.Which is better? Which one do we use? There is value in both correlations.Ultimately, the process of correlating standards is an exercise in judgment. It is possible to learn a lot during the process, but in the long run, where we are headed is more important than where we have been.That being said, let’s take a closer look at the standards.
18 Reading Literature Cite several pieces of textual evidence to support analysis of what the text says explicitly as well as inferences drawn from the text. (7.RL.1)Compare and contrast a written story, drama, or poem to its audio, filmed, staged, or multimedia version, analyzing the effects of techniques unique to each medium (e.g., lighting, sound, color, or camera focus and angles in a film). (7.RL.7)There are many similarities between the 1997 California Content Standards and the new CCSS.The 1997 standards and CCCS standards for literature analysis both set the expectation that students will understand the structural features of texts.Both sets of standards call for students to analyze narratives for point of view, theme, and other literary elements.The CCSS expand upon the 1997 standards by setting the expectation that students will evaluate content in diverse media and support their statements with evidence from the text.The two standards on this slide exemplify these enhancements.
19 Reading Informational Text Describe the relationship between a series of historical events, scientific ideas or concepts, or steps in technical procedures in a text, using language that pertains to time, sequence, and cause/effect. (3.RI.3)Determine the meaning of general academic and domain-specific words and phrases in a text relevant to a grade 3 topic or subject area. (3.RI.4)Here are two CCS standards for reading informational text.Both the 1997 and new standards expect students to determine main ideas and summarize texts, to make inferences and draw conclusions, and to understand the structural features of informational text.The CCSS go further by providing a set of standards specifically for reading in history/social studies, science and technical subjects.The new standards also focus on academic and technical vocabulary.
20 Emphasis on Informational Text The Standards aim to align instruction with this National Assessment of Educational Progress (NAEP) frameworkPercentages do not imply that high school ELA teachers must teach 70% informational text; they demand instead that a great deal of reading should occur in other disciplinesDistribution of Literary and Informational Passages by Grade in the 2009 NAEP Reading FrameworkGradeLiteraryInformation450%845%55%1230%70%An awareness of the emphasis on Informational Text is critical in ensuring student success.The standards aim to align with NAEP in the distribution of literary and informational text. This emphasis on informational text must begin K-3, because as you can see, by Grade 4 the distribution is 50/50.Note that literary non-fiction is included in the Literary category, and this includes essays, speeches, and biographies. Therefore, the actual weight in informational text may be even higher than what is outlined in this table.It is important to note that the high percentages of informational text in high school is a shared responsibility between ELA teachers other disciplines. This does not mean that all 70% of informational reading needs to happen in the ELA classrooms.
21 WritingGather relevant information from multiple authoritative print and digital sources, using advanced searches effectively; assess the strengths and limitations of each source in terms of the task, purpose, and audience; integrate information into the text selectively to maintain the flow of ideas, avoiding plagiarism and overreliance on any one source and following a standard format for citation including footnotes and endnotes. (11-12.W.8)Both the 1997 and CCS standards for writing expect that students will be able to use written communication to construct well-organized arguments and narratives for varied purposes.Students are expected to write both narrative and informational text, conduct research, and provide evidence for the arguments in their writing.As you can see from the standard on this slide, the CCS standards go further by accounting for the need for students to carefully evaluate the many sources of information available to them and to avoid plagiarism.The CCSS also provide specific standards for writing in history/social studies, science and technical subjects so students learn about the specific structures unique to the documents generated in these fields.Technology and use of media are integrated throughout the standards.
22 Writing Write routinely over extended time frames (time for research, reflection, and revision) and shorter time frames (a single sitting or a day or two) for a range of discipline-specific tasks, purposes, and audiences. (2-12.W.10)The new standards also call for extended writing time.As you can see here, starting in grade two and continuing through grade twelve, the CCSS expect that students will spend significant periods of time writing to diverse purposes and audiences.
23 A Progression of Writing The Standards cultivate three mutually reinforcingwriting capacities:To persuadeTo explainTo convey real or imagined experienceOne reason for this shift in the organization of writing standards is to better prepare students for college and career writing. This shift matches the NAEP (National Assessment of Educational Progress) framework.Notice the decreasing emphasis on writing to convey an experience (narrative), and the increase in writing to persuade or explain.Distribution of Communicative Purposes by Grade in the 2011 NAEP Writing FrameworkGradeTo PersuadeTo ExplainTo Convey Experience430%35%81240%20%
24 Speaking and Listening Make strategic use of digital media (e.g., textual, graphical, audio, visual, and interactive elements) in presentations to enhance understanding of findings, reasoning, and evidence and to add interest.(11-12.SL.5)Both the 1997 and CCS standards for speaking and listening focus on collaboration, analysis and evaluation of communications and expect that students will be prepared to make effective presentations.As shown in this slide, the new standards go beyond the analysis of media to set the expectation that students integrate the use of diverse media into their presentations to support their claims and findings.The Common Core standards for speaking and listening also expand upon the CA standards by defining more diverse collaborative groupings and expecting communications to be more focused on grade appropriate topics.The standards are also designed to prepare students to analyze and synthesize the large amounts of information that they encounter in their lives.Students are expected to develop communication skills through participation in rich, structured conversations.
25 Emphasis on Collaborative Conversations Speaking and Listening, Grade 51. Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with diverse partners on grade 5 topics and texts, building on others’ ideas and expressing their own clearly.Come to discussions prepared, having read or studied required material; explicitly draw on that preparation and other information known about the topic to explore ideas under discussion.Follow agreed-upon rules for discussions and carry out assigned roles.Pose and respond to specific questions by making comments that contribute to the discussion and elaborate on the remarks of others.Review the key ideas expressed and draw conclusions in light of information and knowledge gained from the discussions.California’s current standards place more of an emphasis on formal presentation. The Common Core Standards add an emphasis on collaborative conversations; a skill that one might argue is used on an everyday basis.Here is an example of a Speaking and Listening standard addressing Collaborative Conversation. Take a moment to read the standard.
26 Language Use knowledge of language and its conventions when writing, speaking, reading, or listening.a. Choose words and phrases to convey ideas precisely.b. Choose punctuation for effect.c. Differentiate between contexts that call for formal English (e.g., presenting ideas) and situations where informal discourse is appropriate (e.g., small-group discussion).(4.L.3)The 1997 and CCS standards share the expectation that students will master written and oral English language conventions.Both sets of standards have a strong focus on vocabulary development.The CCSS advance the CA standards by emphasizing the acquisition of academic and domain-specific vocabulary.The new standards also emphasize an understanding of how language functions in different contexts.Mastering language conventions, and developing a broad vocabulary in the context of reading, writing, speaking and listening are the focus of the language strand.Here is an example of a language standard that focuses on using appropriate language for a given context.
27 Focus on Text Complexity By the end of the year, read and comprehend literature, including stories, dramas, and poetry, at the high end of the grades 4–5 text complexity band independently and proficiently. (5.RL.10) Initiate and participate effectively in a range of collaborative discussions (one-on one, in groups, and teacher-led) with diverse partners on grades 11–12 topics, texts, and issues, building on others’ ideas and expressing their own clearly and persuasively. (11-12.SL.1)There are a few overarching features you will notice as you become more familiar with the new standards.One is the focus on text complexity.The new standards require that students work with appropriately challenging texts as they progress through the grades.For reading, standard number ten explicitly defines the levels of complexity of the materials that students should be reading at each grade level.The importance of text complexity is carried over into the writing and speaking and listening strands.At each grade level, students are expected to write about and discuss grade-level topics, texts, and issues.
28 Vocabulary Acquisition Participate in collaborative conversations with diverse partners about grade 2 topics and texts with peers and adults in small and larger groups. (2.SL.1) Use precise language and domain-specific vocabulary to inform about or explain the topic. (7.W.2.d) Determine the meaning of word and phrase as they are used in the text, including figurative and connotative meanings; analyze the cumulative impact of specific word choices on meaning and tone (e.g., how the language evokes a sense of time and place; how it sets a formal or informal tone). (9-10.RL.4)Vocabulary acquisition and practice are also threaded throughout the four strands, reflecting current research about how students best learn new words.Both writing and collaborative conversations about grade-level topics and text provide students opportunities to practice using new vocabulary.
29 Critical Analysis and Use of Evidence Distinguish their own point of view from that of the narrator or those of the characters. (3.RL.6) Summarize the points a speaker or a media source makes and explain how each claim is supported by reason and evidence, and identify and analyze any logical fallacies. (5.SL.3) Develop claim(s) and counterclaim(s) fairly and thoroughly, supplying the most relevant evidence for each while pointing out the strengths and limitations of both in a manner that anticipates the audience’s knowledge level, concerns, values, and possible biases. (11-12.W.1.b)Across grade levels and integrated throughout the strands, the CCSS focus on critical analysis of both fiction and non-fiction.Students analyze text for the author’s perspective and purpose, compare and contrast texts, and evaluate evidence used to support the thesis of the text or the main points of a speaker.They use these skills in their own writing and speaking.These selected standards are examples of how students are to apply analysis skills across grade levels.Now, let’s turn our attention to mathematics.
30 California’s Additional 15% Examples of Additions Analysis of text features in informational text (Gr. 6-12)Career and consumer documents included in Writing (Gr. 8)“Both in isolation and in text” added to the application of phonics and word analysis skills (Gr. K-3)Penmanship added to Language (Gr. 2-4)Formal presentations included in Speaking and Listening (Gr. 1-12)Minor additions and insertions to enhance and clarify (e.g., archetypes, thesis)California’s Additional 15% includes the following:Analysis of text features in informational text (Gr. 6-12) For example – in grade 6 ”Analyze the use of text features (e.g., graphics, headers, captions) in popular media” was added to Standard 5 to add specificity.Included Career and Consumer Documents in Writing (Gr. 8) – Career and consumer documents were not specifically called out in the Common Core – so “including career development documents (e.g., simple business letters and job applications)” was added to a CCS standard in order to add specificity.Application of phonics and word analysis skills both in isolation and in text (Gr. K-3) – this was added to ensure that students were expected to apply these skills BOTH in isolation and in text.Penmanship added to Language (Gr. 2-4): CCS only included specific standards addressing Penmanship in Kinder and Grade 1Formal presentations in Speaking and Listening (Gr. 1-12): CCS placed more emphasis on collaborative conversations, formal presentations were specifically called out in the additional 15% – “Plan and deliver an informative/explanatory presentation…”Minor additions and insertions to clarify (e.g., archetypes, thesis)Obviously, this is not an exhaustive list. Remember, in order to identify what was added, the Commission presented a draft to the Board with California’s Additional 15% indicated in bold and underlined font.
31 Shared Responsibility for Teaching the Standards A single K-5 set of grade-specific standardsMost or all of the instruction students receive comes from one teacherTwo content area–specific sections for grades 6-12One set of standards for ELA teachersOne set of standards for history/social studies, science, and technical subject teachersThe literacy standards in history/social studies, science, and technical subjects are meant to complement rather than supplant content standards in those disciplinesAnother shift is a more overt emphasis on shared responsibility for students’ literacy development. This was already part of California’s ELA and subject frameworks. These standards make the shared responsibility more overt. Our current History and Science frameworks already include many of the standards – so it is not really new to teach reading and writing in the subject areas. In fact, History and Science materials were recently adopted, so many districts have instructional materials in these content areas that do a good job of teaching and incorporating reading and writing.Instructor Note: Paraphrase the following paragraphs from the Introduction p. 2.The Standards insist that instruction in reading, writing, speaking, listening,and language be a shared responsibility within the school. The K–5 standardsinclude expectations for reading, writing, speaking, listening, and languageapplicable to a range of subjects, including but not limited to ELA. The grades6–12 standards are divided into two sections, one for ELA and the other forhistory/social studies, science, and technical subjects. This division reflects theunique, time-honored place of ELA teachers in developing students’ literacyskills while at the same time recognizing that teachers in other areas must havea role in this development as well.Part of the motivation behind the interdisciplinary approach to literacypromulgated by the Standards is extensive research establishing the needfor college and career ready students to be proficient in reading complexinformational text independently in a variety of content areas. Most of therequired reading in college and workforce training programs is informationalin structure and challenging in content; postsecondary education programstypically provide students with both a higher volume of such reading than isgenerally required in K–12 schools and comparatively little scaffolding.Let’s take a look at who is responsible for which portion of the Standards.In K-5, since most of the instruction students receive comes from one teacher, there is a single set of grade-specific standards for which the classroom teacher is responsible.In grades 6-12, there is one set of standards for which ELA teachers are responsible.Another set of literacy standards for history/social studies, science, and technical subjects includes standards for which responsibility must be shared between ELA teachers and teachers in other content areas.The literacy standards in history/social studies, science, and technical subjects are meant to complement rather than supplant content standards in those disciplines; the point is that there are discipline-specific literacy skills that should be addressed in other content areas.
32 Mathematical Proficiency as defined by the California Framework (2006) ConceptualUnderstandingProceduralSkillsProblemSolvingFor many years California has promoted and supported the importance of a “balanced” mathematics instructional program.The current CA Mathematics Framework defines such a program as one in which students:Become proficient in procedural skills (computation)Develop conceptual understanding, andBecome adept at problem solvingDOINGMATH
33 Common Core Standards for Mathematics The standards for mathematics:aim for clarity and specificitystress conceptual understanding of key ideasbalance mathematical understanding and procedural skillare internationally benchmarkedNow, let’s take a look at the content and structure of the Common Core standards for mathematics.The Common Core standards for mathematics:aim for clarity and specificitystress conceptual understanding of key ideasbalance mathematical understanding and procedural skill andare internationally benchmarked
34 Common Core Standards for Mathematics Two Types of StandardsMathematical Practice (recurring throughout the grades)Mathematical Content (different at each grade level)They include two types standards:Standards for Mathematical Practice which remain constant throughout the grades andStandards for Mathematical Content which are different for each grade level.
35 Standards for Mathematical Practice Make sense of problems and persevere in solving them.Reason abstractly and quantitatively.Construct viable arguments and critique the reasoning of others.Model with mathematics.Use appropriate tools strategically.Attend to precision.Look for and make use of structure.Look for and express regularity in repeated reasoningA summary of the eight Common Core Standards for Mathematical Practice are listed here.The “Mathematical Practice” standards define how students develop mathematical understanding as they make sense of a problem, reason abstractly, construct arguments, model with mathematics, use tools strategically, attend to precision, and look for structure and repeated reasoning.
36 Develop Conceptual Understandings Solve addition and subtraction word problems, and add and subtract within 10, e.g., by using objects or drawings to represent the problem. (K.OA.2) Add and subtract within 1000, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method. Understand that in adding or subtracting three-digit numbers, one adds or subtracts hundreds and hundreds, tens and tens, ones and ones; and sometimes it is necessary to compose or decompose tens or hundreds. (2NBT.7)The CCSS focus on arithmetic and fluency with whole numbers in the early grades.The kindergarten through grade five standards provide students with a solid foundation in whole numbers arithmetic (addition, subtraction, multiplication and division), fractions, and decimals.Mastery of these skills prepares students for learning more advanced concepts and procedures in later grades.Here are two standards that explicitly call for the use of concrete models or drawings.
37 Emphasis on FluencyFluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g. knowing that 8 x 5 = 40, one knows 40 ÷ 5 = 8) or properties of operations. By the end of grade 3, know from memory all products of two one-digit numbers. (3.OA.7) Fluently multiply multi-digit whole numbers using the standard algorithm. (5.NBT.5)Here are selected standards for grades 3 and 5.By the time students exit grade 5, they should be using algorithms to manipulate numbers fluently.The CCSS build upon practices of countries with high achievement in mathematics.
38 Grade Shifts: Examples Concept1997 StandardsCCSSCompose simple shapes to form larger shapes (e.g., 2 triangles to form a rectangle)Grade2KIntroduction to Probability37Introduction of fractions as numbersAdd and subtract simple fractions4Although the CCSS maintain the current focus on operations with whole numbers, fractions and decimals at the early grades, with full implementation of the CCSS, some topics will be taught at different grades.Here are some examples of topics moving both up and down one or more grade levels.Notice that the introduction to probability moves from grade 3 in the 1997 standards to grade 7 in the CCSS.The introduction of fractions as numbers moves from grade two to grade three. Although introduced later, the CCSS addresses the development of fractions in a very focused and coherent manner.Overview Presentation CTA - CLAB: Developed by SCFIRD with support from ELCSD, SCALD, and AAD
39 A Focus on FractionsRepresent a fraction 1/b on a number line diagram by defining the interval from 0 to 1 as the whole and partitioning it into b equal parts. Recognize that each part has size 1/b and that the endpoint of the part based at 0 locates the number 1/b on the number line. (3.NF.2.a) Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g. by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5+ 1/2 = 3/7, by observing that 3/7 < 1/2. (5.NF.2)Student mastery of the conceptual and procedural knowledge about fractions is essential to success in algebra.In grade three, students begin to develop an understanding of fractions as numbers and represent fractions on a number line diagram.Addition and subtraction of fractions are introduced in grade four, and multiplication and division in grade five.
40 Grade 8 MathematicsThe CCSS prepare students for Algebra 1 in grade 8.The CCSS also include a set of challenging grade 8 standards to prepare students for success in higher math, including Algebra 1.The CCSS are consistent with the goal that all students succeed in Algebra 1.Students who master the content and skills through grade seven will be well-prepared for algebra in grade eight.Recognizing that all students must continue their study of mathematics, the CCSS move students forward with a set of grade eight standards that prepare them for higher mathematics, including Algebra 1.
41 High School Mathematics The high school standards are listed in conceptual categories:Number and QuantityAlgebraFunctionsModeling (*)GeometryStatistics and ProbabilityModeling standards are indicated by a (*) symbol.Standards necessary to prepare for advanced courses in mathematics are indicated by a (+) symbol.The Common Core high school standards are listed in conceptual categories:Number and QuantityAlgebraFunctionsModelingGeometryStatistics and ProbabilityModeling standards are indicated by a star symbol.Standards necessary to prepare for advanced courses in mathematics are indicated by a plus symbol.
42 High School Mathematics Build a function that models a relationship between two quantities1. Write a function that describes a relationship between two quantities. *a. Determine an explicit expression, a recursive process, or steps for calculation from a context.b. Combine standard function types using arithmetic operations. For example, build a function that models the temperature of a cooling body by adding a constant function to a decaying exponential, and relate these functions to the model.c. (+) Compose functions. For example, if T(y) is the temperature in the atmosphere as a function of height, and h(t) is the height of a weather balloon as a function of time, then T(h(t)) is the temperature at the location of the weather balloon as a function of time.Here’s an example from the high school standards for functions.The entire standard is a modeling standard, as indicated by the star symbol.All students are expected to master standards 1a and 1b.Standard 1c reflects mathematics that students pursuing advanced courses in mathematics should study, as indicated by the (+) symbol.
43 High School Mathematics This slide shows two possible pathways for high school mathematics.Detailed information about designing high school mathematics courses based on the CCSS is included in Appendix A of the CCSS for mathematics which is available on the CCSS Web page at:Source: Appendix A of the CCSS for Mathematics at
44 Timeline for Assessment Development STAR sunsets inNew Common Core Assessments projected toPilot TestingField TestingImplementation inCA has joined the Partnership for Assessment of Readiness for College & Careers (PARCC)On March 9, 2011, CA could change their consortium membership as both consortia will be presenting to the SBE.For more information on each assessment consortium:PARCC:Smarter Balanced Assessment:
45 Assessment Component Advantages Through-course approach will focus instruction throughout the year and nearer to the assessmentThe sum of the components address the full range of the common coreAllows for multiple measures across the full range of performanceAllows for in-depth assessment of writing and mathematics problem-solvingBoth through-course and end-of-year components provide data that teachers can use to adjust instruction
46 Assessment System Design: Distributed Summative Assessment Through-Course 2End-Of-YearSTART OF SCHOOL YEARENDOFSCHOOL YEAR25%50%75%90%Through-Course 1Through-Course 3Through-Course 4Key components:Three through-course components distributed throughout the year in ELA and mathematics, grades 3-11.One Speaking/Listening assessment administered after students complete the third through course component in ELA; required but not part of summative score – could be used for course grades.One end-of-year assessmentSlide source: PARCCSource: Graphic adapted from a representation prepared by the Center for K-12 Assessment & Performance Management (www.k12center.org)
47 Assessment System Design: Distributed Summative Assessment Through-Course 2START OF SCHOOL YEARENDOFSCHOOL YEAR25%50%Through-Course 1Through-Course 1 and 2:ELA-1 and ELA-2: One or two tasks involving reading texts, drawing conclusions, and presenting analysis in writing.Math-1 and Math-2: One to three tasks that assess one or two essential topics in mathematics (standards or clusters of standards).Slide source: PARCCSource: Graphic adapted from a representation prepared by the Center for K-12 Assessment & Performance Management (www.k12center.org)
48 Assessment System Design: Distributed Summative Assessment Through-Course 2START OF SCHOOL YEARENDOFSCHOOL YEAR25%50%75%Through-Course 1Through-Course 3Through-Course 4Through-Course 3 and Through-Course 4 (ELA only):ELA-3: Performance task(s) that require evaluating information from within a set of digital resources, evaluating their quality, selecting sources, and composing an essay or research paper.ELA-4 (speaking and listening): Students will present their work from ELA-3 to classmates and respond to questions. Teachers will score, using a standardized rubric, and can use results in determining students’ class grades.Math-3: Performance task(s) that require conceptual understanding, procedural fluency, and application of mathematical tools and reasoning.Slide source: PARCCSource: Graphic adapted from a representation prepared by the Center for K-12 Assessment & Performance Management (www.k12center.org)
49 Assessment System Design: Distributed Summative Assessment Through-Course 2End-Of-YearSTART OF SCHOOL YEARENDOFSCHOOL YEAR25%50%75%90%Through-Course 1Through-Course 3Through-Course 4End-of-Year:EOY: Comprehensive, computer-scored assessment that includes a range of item types, including innovative, technology-enhanced items. Enables quick turnaround of student scores.A student’s summative score—used for accountability purposes—will include his/her performance on Through-Courses 1, 2, and 3 as well as the End-of-Year assessment.Slide source: PARCCSource: Graphic adapted from a representation prepared by the Center for K-12 Assessment & Performance Management (www.k12center.org)
50 Assessment System Design: Distributed Summative Assessment Administration and Scoring:Overall assessment system will include a mix of constructed response items, performance tasks, and computer-enhanced, computer-scored items.Assessments for grades 6-12 will be administered via computer while 3-5 will be administered via paper and pencil (in the short term).Combination of artificial intelligence (AI) and human scoring will be employed; states will individually determine the extent to which teachers will be involved in scoring.Slide source: PARCC
51 Many helpful resources related to the Common Core are available on the CDE Common Core State Standards Resources Web page.Here you can find frequently asked questions, informational flyers, and links to additional resources, including the standards themselves.
52 Source: http://www.cde.ca.gov/re/mm/it/ CDE on iTunes UAll the Common Core materials on the Web page, as well as some additional videos, are also available on CDE on iTunes U. The CDE recently launched this site which includes a wealth of presentations (in a variety of different formats) on a wide variety of topics, provided by individuals, county offices, and other organizations.Source:
53 Resources http://www.cde.ca.gov/ci/cc For more information, visit the California Department of Education’s Common Core State Standards Web page at:The standardsFrequently asked questionsInformational flyersAdditional resourcesFor additional information, contact:Standards, Curriculum Frameworks andInstructional Resources DivisionCurriculum, Learning and Accountability BranchCalifornia Department of Education1430 N Street, Sacramento, CA 95814I hope you have found today’s presentation useful and that you leave here with the information you need as we move forward with the Common Core Standards.Remember, for more information, including frequently asked questions, informational flyers, and links to additional resources, visit the California Department of Education’s Common Core State Standards Web page at:
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