www.nyctecenter.org Sample Excerpts from the Common Core State Standards Curriculum Matrix – New York Ellen Palazzo [email protected] Successful Practices Network 3 4 5 6 New York Curriculum Matrix Summary Introduction The Curriculum Matrix data in this resource kit is provided as a guide to help educators in planning curriculum and instruction. All interpretations of state standards, Common Core State Standards, and state assessment program data that were needed to construct the correlations in this Matrix were conducted by content area specialists in each discipline and reviewed by research managers. Where and if necessary, interpretations of the learning statements used in the correlations were verified by third-party reviewers and/or officials of the state’s department of education. Every effort has been made to ensure the accuracy of the crosswalk and summary data. However, some learning outcome statements are, by their nature, subject to interpretation and determination of intent by content area specialists. Educators should always exercise their own best judgment in determining how to apply the data. Care was taken to ensure that all data used in the analyses was current at the time of publication, but all standards and assessment data remain subject to updates as states revise or update their state standards or assessment programs. The International Center welcomes your feedback, advice, and suggestions about the data provided. The Center also eagerly encourages users to help us keep the data current for all educators in their state by advising us of any such updates. Please address all comments to: International Center for Leadership in Education, 1587 Route 146, Rexford, NY 12148 or [email protected]. New York Assessment The New York State Testing Program (NYSTP) administers tests in English language arts (ELA) and mathematics in grades 3-8 and science in grades 4 and 8. High school students are required to take the Regents Comprehensive Examination in ELA, mathematics, and science. English Language Arts The New York English Language Arts Core Curriculum includes learning standards and performance indicators assessed by the NYSTP in grades 3-8, as well as through the Regents Examination for Comprehensive English Language Arts in high school, which tests learning standards and performance indicators for grades 9-11. Testing Priority Designation Information necessary to make priority designations relative to assessments was obtained from the New York State Department of Education website. Test specifications for each assessment are available at this site and were used to determine testing priority designations. Each test specification reveals the number of test items for each test-eligible standard. Priority designations were determined by averaging the number of ELA test items per test-eligible standard for each grade level. Standard deviations (STD) were calculated for each grade level and subtracted from the mean. This number established the cut-off point between Medium (M) priority designations and High (H) priority designations. Please note that the NYSTP reveals that each test item is aligned to one content performance indicator and to one or more process performance indicators. The assessment of process indicators is subsumed in the content indicator testing process and process indicator test results are not reported. Therefore, each process performance indicator has been assigned a Low (L) priority designation. The NYSTP and the Regents Examination for Comprehensive English Language Arts priority designation results can be found in Table 1. 2011 International Center for Leadership in Education 7 Table 1. New York English Language Arts Priority Designation Data Grade 3 Grade 4 Grade 5 Grade 6 Grade 7 Grade 8 High School * Mean STD 17.00 19.67 17.00 19.00 19.00 19.00 1.58* 5.62 6.12 4.68 5.92 4.57 4.57 0.66 Mean – STD 11.38 13.55 13.32 13.08 14.43 14.43 0.92 Designations M = Medium 1-11 1-14 1-12 1-13 1-14 1-14 1 L = Low 0 0 0 0 0 0 0 H = High >11 >14 >12 >13 >14 >14 >1 Outliers were not used in this calculation. New York English language arts test designations are presented in Table 2. Table 2. New York English Language Arts Assessment Data Summary English Language Arts Performance Grade/ Standards Indicators Course 115 4 3 116 4 4 101 4 5 121 4 6 113 4 7 94 4 8 102 4 9 4 90 10 4 74 11 926 36 Totals NY State Assessment H M L 71 77 64 77 67 72 52 51 37 568 30 26 20 28 25 0 10 10 10 159 14 13 17 16 21 22 40 29 27 199 H 1-19 57 64 55 57 67 58 60 51 43 512 NESSi M 20-38 49 46 40 57 37 31 33 32 27 352 L 39-50 9 6 6 7 9 5 9 7 4 62 Mathematics The New York Mathematics Core Curriculum includes learning standards and performance indicators assessed by the NYSTP in grades 3-8, as well as through the Regents Examinations for Integrated Algebra, Geometry, and Algebra 2/Trigonometry. Testing Priority Designation Information necessary to make priority designations relative to assessments was obtained from the New York State Department of Education website. Test specifications for each assessment are available at this site and were used to determine testing priority designations. Each test specification reveals the number of test items for each test-eligible standard. Priority designations were determined by averaging the number of mathematics test items per test-eligible standard for each grade level. Standard deviations (STD) were calculated for each grade level and subtracted from the mean. This number established the cut-off point between Medium (M) priority designations and High (H) priority designations. Please note that the NYSTP reveals that each test item is aligned to one content performance indicator and to one or more process performance indicators. The assessment of process indicators is subsumed in the content indicator testing process and process indicator test results are not reported. Therefore, each process performance indicator has been assigned a Low (L) priority designation. The NYSTP and Regents Examination for Comprehensive Mathematics priority designation results can be found in Table 3. 2011 International Center for Leadership in Education 8 Table 3. New York Mathematics Priority Designation Data Mean Grade/Course 3 4 5 6 7 8 Integrated Algebra Geometry Algebra 2/Trigonometry * 5.00* 7.84* 5.33* 9.80 10.00 17.25 8.75 4.20* 3.67* STD Mean – STD 0.00 1.66 0.47 4.21 4.10 9.98 6.78 2.56 2.03 5.00 7.84 4.86 5.58 5.90 7.27 1.97 1.64 1.61 L = Low 0 0 0 0 0 0 0 0 0 Designations M = Medium 1-5 1-8 1-5 1-6 1-6 1-7 1-2 1-2 1-2 H = High >5 >8 >5 >6 >6 >7 >2 >2 >2 Outliers were not used in this calculation. New York mathematics test designations are presented in Table 4. Table 4. New York Mathematics Assessment Data Summary NY State Assessment Mathematics Grade /Course 3 4 5 6 7 8 Integrated Algebra Geometry Algebra 2/ Trigonometry Totals Strands 10 10 10 10 10 10 Performance Indicators Process Content Totals 114 62 52 119 63 56 127 60 67 125 61 64 120 56 64 104 56 48 NESS1 62 63 60 61 56 56 H 1-16 75 94 100 96 86 73 M 17-42 36 25 24 29 33 19 L 43-70 3 0 3 0 1 12 H M L 27 48 46 55 54 47 25 8 21 9 10 1 10 51 89 140 86 3 51 81 42 17 7 47 74 121 67 7 47 99 14 8 10 51 105 156 103 2 51 73 53 30 87 507 619 1126 533 86 507 777 275 74 Science The New York Science Core Curriculum includes learning standards and performance indicators assessed by the NYSTP in grades 4 and 8, as well as through the Regents Examinations for Earth Science, Living Environment, Chemistry, and Physics. Testing Priority Designation Information necessary to make priority designations relative to assessments was obtained from the New York State Department of Education website. Test specifications for each assessment are available at this site and were used to determine testing priority designations. Each test specification reveals the number of test items for each test-eligible standard. Priority designations were determined by averaging the number of science test items per test-eligible standard for each grade level. Standard deviations (STD) were calculated for each grade level and subtracted from the mean. This number established the cut-off point between Medium (M) priority designations and High (H) priority designations. Performance indicators not tested were assigned a Low (L) priority designation. The NYSTP and Regents Examination for Comprehensive Science priority designation results can be found in Table 5. 2011 International Center for Leadership in Education 9 Table 5. New York Science Priority Designation Data Mean 9.17 Grade 4 12.62 Grade 8 3.61* Earth Science 8.40* Living Environment 3.33* Chemistry 33.20 Physics * Outliers were not used in this calculation. STD Mean – STD 7.58 8.96 2.85 3.58 2.00 27.10 1.59 3.66 0.76 4.18 1.33 6.12 Designations M = Medium 1-2 1-4 1 1-4 1 1-6 L = Low 0 0 0 0 0 0 H = High >2 >4 >1 >4 >1 >6 New York science test designations are presented in Table 6. Table 6. New York Science Assessment Data Summary Science Performance Standards Grade Indicators 5 94 4 5 112 8 5 58 Earth Science 2 30 Living Environment 5 56 Chemistry 5 48 Physics 398 27 Totals NY State Assessment H M L 23 34 37 28 28 21 171 9 27 18 2 6 3 65 62 51 3 0 22 24 162 H 1-32 92 86 43 26 50 38 335 NESS1 L M 33-50 51-85 0 2 17 9 8 7 4 0 3 3 6 4 25 38 Totals for English Language Arts, Mathematics, and Science Table 7 presents the number of state assessed performance indicators compared to the number of state assessed performance indicators tested. Using this data, the percentage of state assessed performance indicators tested was calculated. Table 7. Totals and Percentages for English Language Arts, Mathematics, and Science % Performance # Performance # Performance Indicators Tested Indicators Tested Indicators 926 727 78.51 English Language Arts 1,126 619 54.98 Mathematics 398 236 59.30 Science 64.58 1,582 2,450 Totals Common Core State Standards (CCSS) to Performance Indicators Alignment Data International Center content area specialists have crosswalked English language arts and mathematics CCSS to the New York English language arts and mathematics New York learning standards and performance indicators. The purpose of this study was to determine the number and percent of the CCSS that are aligned/non-aligned to the learning standards and core curriculum. The same process was also used to determine the number and percent of the learning standards and core curriculum that are aligned/non-aligned to the CCSS. The results that follow provide New York teachers, curriculum planners, and administrators with information relevant to the status of the New York learning standards and performance indicators compared to the CCSS. Considerations the New York Department of Education will make include whether to adjust the current 2011 International Center for Leadership in Education 10 New York Curriculum Matrix for English Language Arts New York English Language Arts Learning Standards/ Performance Indicators Grade 10 Common Core English Language Arts Standards Strands/CCRS/CCSS Grades 9-10 National Essential Skills Study (NESS) National Rankings Rank NESS NY Regents Exam Priority H H H H H H Reading • Locate and use school and public library resources for information and research - set purpose for reading by asking questions about what they need to know for their research • Use specialized reference sources, such as glossaries, directories, and abstracts Writing Standards Research to Build and Present Knowledge 7. Conduct short as well as more sustained research projects to answer a question (including a self-generated question) or solve a problem; narrow or broaden the inquiry when appropriate; synthesize multiple sources on the subject, demonstrating understanding of the subject under investigation. Language Standards Vocabulary Acquisition and Use 4. Determine or clarify the meaning of unknown and multiple-meaning words and phrases based on grades 9–10 reading and content, choosing flexibly from a range of strategies. c. Consult general and specialized reference materials (e.g., dictionaries, glossaries, thesauruses), both print and digital, to find the pronunciation of a word or determine or clarify its precise meaning, its part of speech, or its etymology. E7 E15 E4 E15 Research information from a variety of sources and draft a well-organized, accurate, and informative report or essay that engages an audience and addresses its needs. Demonstrate ability to select and use appropriate technology or media for presenting information to the target audience for the specific purpose. Use resources (dictionary, grammar books, thesaurus, online references, etc.) as needed to edit. Demonstrate ability to select and use appropriate technology or media for presenting information to the target audience for the specific purpose. © 2011 International Center for Leadership in Education 11 New York English Language Arts Learning Standards/ Performance Indicators Grade 10 Common Core English Language Arts Standards Strands/CCRS/CCSS Grades 9-10 National Essential Skills Study (NESS) National Rankings Rank NESS NY Regents Exam Priority E6 Collect and focus thoughts about the writing activity (brainstorming, listing, drafting, etc.). H H H E13 Assess the validity, reliability, authenticity, quality, and accuracy of an informational or literary text. H H H H H H Writing Standard 1: Students will read, write, listen, and speak for information and understanding. • Select and limit topics for informational writing • Analyze data, facts, and ideas to communicate information • Take notes and organize information from written and oral texts, such as lectures and interviews Writing Standards Text Types and Purposes 2. Write informative/explanatory texts to examine and convey complex ideas, concepts, and information clearly and accurately through the effective selection, organization, and analysis of content. Writing Standards Text Types and Purposes 2. Write informative/explanatory texts to examine and convey complex ideas, concepts, and information clearly and accurately through the effective selection, organization, and analysis of content. Writing Standards Research to Build and Present Knowledge 8. Gather relevant information from multiple authoritative print and digital sources, using advanced searches effectively; assess the usefulness of each source in answering the research question; integrate information into the text selectively to maintain the flow of ideas, avoiding plagiarism and following a standard format for citation. E6 E16 Collect and focus thoughts about the writing activity (brainstorming, listing, drafting, etc.). Locate and gather information such as data, facts, ideas, concepts, and generalizations from oral sources. © 2011 International Center for Leadership in Education 12 New York Mathematics Strands/Bands/ Performance Indicators Integrated Algebra Common Core Mathematics Domains/Clusters High School National Essential Skills Study (NESS) National Rankings Rank NESS NY Regents Exam Priority H H H Problem Solving Strand Students will new mathematical knowledge through problem solving. A.PS.1 Use a variety of problem solving strategies to understand new mathematical content Number & Quantity: Quantities Reason quantitatively and use units to solve problems. 1. Use units as a way to understand problems and to guide the solution of multi-step problems; choose and interpret units consistently in formulas; choose and interpret the scale and the origin in graphs and data displays. Algebra: Reasoning with Equations & Inequalities Solve equations and inequalities in one variable. 3. Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. 4. Solve quadratic equations in one variable. a. Use the method of completing the square to transform any quadratic equation in x into an equation of the form (x – p)2 = q that has the same solutions. Derive the quadratic formula from this form. b. Solve quadratic equations by inspection (e.g., for x2 = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as a ± bi for real numbers a and b. Understand and apply a systematic methodology or procedure (e.g., direct or indirect measurement, direct or indirect proof, inductive or deductive reasoning) to model and solve problems. M10 © 2011 International Center for Leadership in Education 13 New York Mathematics Strands/Bands/ Performance Indicators Integrated Algebra A.PS.1 (Continued from previous page) A.PS.8 Determine information required to solve a problem, choose methods for obtaining the information, and define parameters for acceptable solutions A.N.2 Simplify radical terms (no variable in the radicand) Common Core Mathematics Domains/Clusters High School National Essential Skills Study (NESS) National Rankings Rank (Continued from previous page) Functions: Interpreting Functions Interpret functions that arise in applications in terms of the context. 6. Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph. There is no New York Mathematics Performance Indicator–Common Core alignment. M10 Number & Quantity: The Real Number System Extend the properties of exponents to rational exponents. 2. Rewrite expressions involving radicals and rational exponents using the properties of exponents. M20 M29 M33 A.N.3 Perform the four arithmetic operations using like and unlike radical terms and express the result in simplest form Algebra: Reasoning with Equations & Inequalities Understand solving equations as a process of reasoning and explain the reasoning. 2. Solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may arise. M33 Understand and apply a systematic methodology or procedure (e.g., direct or indirect measurement, direct or indirect proof, inductive or deductive reasoning) to model and solve problems. Understand and apply the basic properties and laws of exponents and scientific notation to solve problems, including those with fractional, negative, and zero exponents. Factor a composite number into its prime components and use least common denominators or least common multiples to solve equations. Perform operations with radicals, such as addition, subtraction, and multiplication. Perform operations with radicals, such as addition, subtraction, and multiplication. NESS NY Regents Exam Priority H H H M H H M H H © 2011 International Center for Leadership in Education 14 New York Science Key Ideas/Performance Indicators Earth Science – High School 1.3 Access, select, collate, and analyze information obtained from a wide range of sources such as research data bases, foundations, organizations, national libraries, and electronic communications networks, including the Internet. National Essential Skills Study (NESS) Rankings NY Regents Exam Priority H H H H H H H H H H H H M L M H L M M L M Rank E7 E12 1.4 Receive news reports from abroad and work in groups to produce newspapers reflecting the perspectives of different countries. S12 1.5 Utilize electronic networks to share information. S12 1.6 Model solutions to a range of problems in mathematics, science, and technology using computer simulation software. NESS S15 Research information from a variety of sources and draft a well-organized, accurate, and informative report or essay that engages an audience and addresses its needs. Preview (skim) informational text to anticipate content (title, chapter headings, Internet search results, illustrations, table of contents, etc.). Explain, interpret, and classify observations and data in a logical way. Present information using scientific vocabulary, mathematical relationships, and technology. Explain, interpret, and classify observations and data in a logical way. Present information using scientific vocabulary, mathematical relationships, and technology. Plan and apply real or hypothetical models and constructions to facilitate short- and long-term investigation, learning, and solutions to practical problems, including experimental design that incorporates variables and a method for collecting fair and adequate data. Key Idea 2. Knowledge of the impacts and limitations of information systems is essential to its effective and ethical use. 2.1 Explain the impact and use and abuse of electronically generated information on individuals and families. S42 S47 2.2 Evaluate software packages relative to their suitability to a particular application and their ease of use. S4 2.3 Discuss the ethical and social issues raised by the use and abuse of information systems S42 S47 Identify individual, cultural, and technological contributions to scientific knowledge that have had an impact on the history of human society and the quality of life worldwide. Know the history and assess the benefits and drawbacks of modern technologies (e.g., nanotechnology, biotechnology, and information technology). Make observations and accurate and precise measurements using senses, tools, and technology. Identify individual, cultural, and technological contributions to scientific knowledge that have had an impact on the history of human society and the quality of life worldwide. Know the history and assess the benefits and drawbacks of modern technologies (e.g., nanotechnology, biotechnology, and information technology). © 2011 International Center for Leadership in Education 15 New York Career and Technical Education Matrix for English Language Arts The “9” designations in the columns under each career pathway identify significant opportunities for academic standards-related instruction within the various career-technical programs. The absence of an “9” should not, however, be interpreted as offering no opportunity for interdisciplinary instruction and teachers should make decisions based on their own instructional goals, best judgments and student interests. Agribusiness Systems Power, Structural & Technical Systems Environmental Service Systems Plant Systems Natural Resource Systems Animal Systems Design/ Pre-Construction Construction Maintenance/ Operations Performing Arts Visual Arts Printing Technology Journalism & Broadcasting A/V Technology & Film Telecommunications Arts, A/V Technology & Communications Food Products & Processing Systems New York English Language Arts Learning Standards/ Performance Indicators Grade 10 Architecture & Construction NY Regents Comprehensive English Exam Agriculture, Food & Natural Resources H 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 H 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 H 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 Reading Standard 1: Students will read, write, listen, and speak for information and understanding. • Locate and use school and public library resources for information and research - set purpose for reading by asking questions about what they need to know for their research • Use specialized reference sources, such as glossaries, directories, and abstracts • Read and follow written directions and procedures to solve problems and accomplish tasks - use workplace documents Writing Standard 1: Students will read, write, listen, and speak for information and understanding. • Use both primary and secondary sources of H information for research • Select and limit topics for informational H writing • Analyze data, facts, and ideas to H communicate information • Take notes and organize information from written and oral texts, such as lectures and H interviews © 2011 International Center for Leadership in Education 16 Standard 2: Students will read, write, listen, and speak for literary response and expression. • Write original literary texts - use literary devices, such as figurative language, allegory, irony, symbolism, and stream of consciousness - create multiple levels of meaning, with assistance - use language and sentence structure creatively to elicit the reader’s emotional response • Write interpretive and responsive essays of approximately three pages to - express judgments and support them through references to the text, using direct quotations and paraphrase - explain how the author’s use of literary devices affects meaning - examine development and impact of literary elements, such as character (protagonist and antagonist), action (conflict, intrigue, suspense, and climax), and setting (locale and time period), in literary texts and performances - compare and contrast the treatment of literary elements in different genres and by more than one author - engage in a variety of prewriting experiences, such as using a variety of visual representations to express interpretations, feelings, and new insights H 9 9 H 9 9 © 2011 International Center for Leadership in Education 17 Telecommunications A/V Technology & Film Journalism & Broadcasting Printing Technology Visual Arts Arts, A/V Technology & Communications Performing Arts Maintenance/ Operations Construction Design/ Pre-Construction Architecture & Construction Animal Systems Natural Resource Systems Plant Systems Environmental Service Systems Power, Structural & Technical Systems Agribusiness Systems Food Products & Processing Systems New York English Language Arts Learning Standards/ Performance Indicators Grade 10 NY Regents Comprehensive English Exam Agriculture, Food & Natural Resources The Next Navigator While the national focus has been on the shift to the Common Core State Standards, the larger challenge will be preparing students for success on the next generation assessments. These new assessments will be fundamentally different from the current state tests in that they will be performance-based. Students will need to demonstrate their ability to function in Quadrant D by thinking in complex ways and applying their skills when confronted with perplexing, complicated problems. To bridge the gap between the current state tests and the next generation assessments, The Next Navigator will show the differences between the two and support teachers in planning instruction that prepares students for these new requirements. The Next Navigator will: • Provide teachers with an online environment for comparing their state standards with the Common Core State Standards and state assessment items with next generation assessment items. • Provide exemplary performance tasks and scoring guides that will help prepare students for the rigor of the next generation assessments. • Improve instruction by aiding teachers in developing and improving performance tasks and lessons that will prepare students for the next generation assessments. • Help teachers move instruction from Quadrant A to D. The Next Navigator includes, among other things: • A template and scoring guides used for developing and critiquing performance tasks • Knowledge Taxonomy Verb Analyzer helps move lessons to Quadrant D by replacing verbs often used in Quadrant A, B, and C lessons and replacing with Quadrant D verbs. • Real-world Relevance Wizard helps check the relevance of each lesson and suggests edits to increase the level as necessary. • Student Work Sorter helps ensure lessons require a variety of different student work types. • Stretch Moments helps differentiate instruction by offering suggestions to stretch the lesson. 18 www.nyctecenter.org First Time User? Click “First time User?” under the Log In Button. Create a Profile: Complete the required information to register to have access to the complete CTE TAC Website Please note: NickName has to be unique in the data base. “Your First Name” typically would not be a good NickName. Unless you used your first name and your street number after without a space. Be sure to check “I have read and agree with terms of use. Once your registration has been accepted, login for your first time. If you are having challenges logging in, email: [email protected] Or call 518‐723‐2137 Van Meter Secondary School: Rigor and Relevance Model Adaptation Student Driven Knowledge Taxonomy Compare and discriminate between ideas Assess values of theories, presentations Make choices on reasoned arguments Verify value of evidence / Recognize subjectivity Make judgments/choices based on criteria/standards/conditions Use creativity to make something new Generalize from given facts Predict or draw conclusion See patterns/relationships Recognize of hidden parts Take ideas/learning apart Find unique characteristics 4 Observation and recall of information Knowledge of dates, events, places Student Thinks and Works (Relationships critical!) A 3 B Acquisition Application Students gather and store bits of knowledge and information and are expected to remember or understand this acquired knowledge. Students use acquired knowledge to solve problems, design solutions, and complete work. The highest level of application is to apply appropriate knowledge to new and unpredictable situations. 2 Order, group, infer causes Interpret facts, compare/contrast Predict consequences Teacher Work Knowledge: “Information gathering” Teacher Driven (Relationships important) Solve problems using required skills and/or knowledge Make use of learning in new or concrete manner, or to solve problems Comprehension: “Confirming” Understand information Translate knowledge into new context Grasp meaning of materials learned, communicate learnings, and interpret learnings Adaptation Students have the competence that, when confronted with perplexing unknowns, they are able to use their extensive knowledge base and skills to create unique solutions and take action that further develops their skills and knowledge. Organize parts Identify components Separate into component parts Application: “Making use of knowledge” Use of information Use methods, concepts, theories in new situations Assimilation Student Think Analysis: “Taking apart” D Students extend and refine their knowledge so that they can use it automatically and routinely to analyze and solve problems and create solutions. 5 Synthesis: “Putting together” Use old ideas to create new ones Relate knowledge from several areas Reorganize parts to create new original thing, idea, concept C 6 Evaluation: “Judge the outcome” Mastery of subject matter Gain specific facts, ideas, vocabulary, etc. 1 Student Work (Relationship of little importance) (Relationships important) Application Model Rigor x Relevance x Relationships = Meaningful Learning If one of these are missing, the equation equals 0 RxRx0=0 Rx0xR=0 0xRxR=0 1 2 3 4 5 Knowledge in one discipline Apply knowledge in one discipline Apply knowledge across disciplines Apply knowledge to real world, predictable situations Apply knowledge to real world, unpredictable situations Classroom Real Life JCC July 2007
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