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  • New Common Core standards are due to roll out in 45 states and 3 territories by 2014. They're designed to get students ready for college and careers by requiring them to think, write and explain their reasoning. They also de-emphasize multiple-choice test questions in favor of written responses.—Toppo, 2012
  • English and Language Arts (ELA) pilot programs will take place this school year with full implementation of all standards in the 2013-2014 school year.
  • Common core is what we are going to teach. Student readiness is why we teach, and TEAM is how we teach.
  • 78% of students in Tennessee taking the ACT indicate that they want to go to college, but only 15% are ready. Of all Tennessee students that enter college, 60% have to be remediated.
  • The Common Core State Standards are a set of standards for math and English Language Arts that were developed by state leaders to ensure that every student graduates high school prepared for college or the workforce.  The standards are designed to set clear expectations of what students should know in each grade and subject.  They reflect rigorous learning benchmarks when compared to countries whose students currently outperform American students on international assessments.
  • The common core state standards offer a narrower and deeper approach to teaching and learning.
  • Have participants read slide to themselves.SAY: Discuss why this is different than what is currently practiced.
  • Say: CCSS has simplified the way teachers and administrators will read Grade Level Standards. The Domains are larger groups of related standards and Clusters are smaller groups of related standards.
  • Common Core standards will allow teachers more creativity and flexibility in their teaching while requiring a significant shift in instructional practice. Although there is some alignment between Tennessee’s standards and the Common Core, the Common Core requires a deeper engagement with a smaller number of standards than what the state currently requires. These standards will require new approaches to teaching, and students should expect enhanced rigor in their courses. Specifically, students will be required to master more critical thinking and problem-solving skills.
  • The October PBA is an assessment as learning. The February PBA is an assessment for learning, and the May PBA is an assessment of learning.
  • The transition to the Common Core will also include the adoption of new assessments that will measure what students have learned under the new standards. Starting in the 2014-15 school year, these assessments will replace the current Tennessee Comprehensive Assessment Program (TCAP) tests in math and English Language Arts for grades 3-11. These assessments will be administered online and include a summative assessment comprised of a Performance Based Assessment (PBA) and an End-of-Year Assessment (EOY). Tennessee is working with a number of other states in the Partnership for Assessment of Readiness for College and Careers (PARCC) Consortium to design these new assessments
  • Read the slide
  • Directions:(SAY) The Tennessee Department of Education has focused the work on two clusters per grade level. Each cluster will include specific standards that
  • A NOTE TO THE FACILITATOR: Hand out the Participant Packets.Directions:(SAY) Solve each task. Then compare and contrast the task.
  • In what way does the prompt for the identified item elicit a student response that will demonstrate what s/he knows about specific content within the standard?5.NF.4, 5.NF.7, 5.NF.7bWhat is it about the prompt for the identified item that will require students to use mathematical practices? Make sense of problems and persevere in solving them.Reason abstractly and quantitatively. (When students write equations and then re-contextualize the numbers telling us about the meaning of the amounts in the context of the problem, then we know they have demonstrated this standard.)Construct viable arguments and critique the reasoning of others. (Students must determine if Jessica and Samuel can both have their fraction of the gumdrops and then if they can or can’t, they must explain why.)Model with mathematics. (Students must use a diagram and write an equation to explain how they know the students can or cannot have their share of the gumdrops.)Use appropriate tools strategically. Attend to precision. Look for and make use of structure. (We will know if students understand what it means to take a fraction of a set of 48 gumdrops. We will know if students understand the meaning of the denominator and the numerator.)
  • Directions:(SAY) Determine the content standards related to the task.Refer to the notes pages for each task for the standards that relate to each task.
  • In what way does the prompt for the identified item elicit a student response that will demonstrate what s/he knows about specific content within the standard?5.NF.4, 5.NF.7, 5.NF.7b
  • Directions: Show the list of mathematical practices. Ask participants which of these mathematical practices students will have an opportunity to use when solving the task. (See reference to the practices on the notes pages of each of the tasks.)Probing questions and possible student responses (in italics): What does it mean to look for and make use of structure? Refer to one of the tasks to help us make sense of what this practice means. (Consider the 48 Gumdrops Task. If students must determine if the two students can each have their share of the 48 gumdrops, this means that the student must demonstrate that s/he understands that the denominator tells the number of equal groups that 48 will be partitioned into and the top number tells how many of the equal groups that s/he will get.)What does it mean to reason abstractly and quantitatively? Refer to one of the tasks to help us make sense of what this practice means. Which problems require students to use this practice? Which do not require students to use this practice and why? (The 48 Gumdrops Task permits us to assess this practice because the students have to pull out the quantities, manipulate them and then re-contextualize them explaining what the amounts mean in the context of this problem.)A fraction of a set in the 48 Gumdrops Task. We also get an opportunity to determine if students can write equations. Attend to precision means more than just getting the correct answer. What else does it mean?Why might we want students to have opportunities to use repeated reasoning? How does it help to support learners?
  • Directions:(SAY) Referring to your mathematical practice handout, discuss with your group which practice standards are being addressed by the assessment item.
  • What is it about the prompt for the identified item that will require students to use mathematical practices? Make sense of problems and persevere in solving them.Reason abstractly and quantitatively. (When students write equations and then re-contextualize the numbers telling us about the meaning of the amounts in the context of the problem, then we know they have demonstrated this standard.)Construct viable arguments and critique the reasoning of others. (Students must determine if Jessica and Samuel can both have their fraction of the gumdrops and then if they can or can’t, they must explain why.)Model with mathematics. (Students must use a diagram and write an equation to explain how they know the students can or cannot have their share of the gumdrops.)Use appropriate tools strategically. Attend to precision. Look for and make use of structure. (We will know if students understand what it means to take a fraction of a set of 48 gumdrops. We will know if students understand the meaning of the denominator and the numerator.)
  • Directions:(Say) When a high-level task is selected, it does not always remain high level as it is implemented in the classroom. Research from the QUASAR Project indicates that one of four things can occur during implementation:Maintenance of high-level demands: The cognitive demands of the task are maintained and students have a chance to think and reason about mathematics. Decline into procedures without connection to meaning: What began as a high-level task becomes a procedural task. Rather than students thinking and reasoning about mathematics, they end up applying a rule or procedure without understanding why or how it works. This can happen when students become frustrated with the challenges, and pressure the teacher to tell them how to solve the problem or to give them the answer. It can also happen when the teacher breaks down the high-level task into procedural steps.- Decline into unsystematic exploration: Although the high-level task is not proceduralized, students do not make progress toward the mathematical goal of the lesson. They may be working on mathematics, but it does not move them further toward the goal. For example, if the goal of a lesson was to explore the dimensions of a rectangle that would maximize the area for a fixed perimeter of a rectangle, students might spend the entire period building rectangles and measuring but never focusing on maximizing the area.- Decline into NO mathematical activity: The focus of the lesson is no longer on mathematics. For example, consider a lesson in which students present graphs they have made based on a collection of data on favorite ice cream. Instead of discussing the scale, what the graph tells us in terms of student preference, etc., the focus becomes the color that was used, why they liked chocolate ice cream best, etc.
  • Directions:Give participants a moment to read the slide before you ask the probing questions on this slide. If you have the time, have participants Turn and Talk with a partner before beginning the questions.Possible responses to first question about tasks (in italics): The tasks would have to give students opportunities to use the mathematical practices.The tasks should start with different representations, like the assessment tasks do, and ask for different representations to be used.The tasks would need to access multiple content standards, like the assessment tasks do.Students would need to write about the concept explored by the task in some way.In fact, the tasks probably would need to look a lot like the assessment tasks do.Possible responses to second question about teaching and learning (in italics): Teachers will need to engage students in a way that permits them to regularly use the mathematical practices when solving problems. Well-designed tasks will help that. Students will need the opportunity to learn to justify themselves orally so they can write about their justifications on the tasks and assessments.Since the tasks need to begin from different representations so that students are comfortable using tables, graphs, equations, etc., students need to be encouraged to make connections among these representations in class.So, teachers will need to consider how to arrange the sequence of instructional tasks so all these things happen!

1 elem  ccss in-service presentation 1 elem ccss in-service presentation Presentation Transcript

  • Common Core State Standards: An Overview 0
  • Goals for Our Session • Help to calm fears concerning Common Core State Standards (CCSS) • Common Core Instructional Shifts in Education • Implementation of CCSS (what, why, how and when) • Analyzing a Performance Based Assessment • Mathematical Content vs. Mathematical Practices • The Structure of a Lesson • How the Implementation of a Task Impacts Learning • Assessing and Advancing Questions • How CCSS Ties to TEAM Evaluation 1
  • State Adoption of Common Core 2
  • Transitional Plan for 2012-2013 Six Key Instructional Shifts MATH: 1. Focus strongly where the Standards focus 2. Coherence: think across grades, and link to major topics within grades 3. Rigor: require conceptual understanding, procedural skill and fluency, and application with intensity. ELA: 1. Building knowledge through content-rich nonfiction and informational texts 2. Reading and writing grounded in evidence from text 3. Regular practice with complex text and its academic vocabulary 3
  • Shift One: Focus Strongly where the Standards focus •Significantly narrow the scope of content and deepen how time and energy is spent in the math classroom •Focus deeply only on what is emphasized in the standards, so that students gain strong foundations 4
  • It starts with Focus • The current U.S. curriculum is “a mile wide and an inch deep.” • Focus is necessary in order to achieve the rigor set forth in the standards. • Hong Kong example: more in-depth mastery of a smaller set of things pays off 5
  • The shape of math in A+ countries Mathematics topics intended at each grade by at least two-thirds of A+ countries Mathematics topics intended at each grade by at least twothirds of 21 U.S. states 1 Schmidt, Houang, & Cogan, “A Coherent Curriculum: The Case of Mathematics.” (2002). 6
  • Shift Two: Coherence Think across grades, and link to major topics within grades • Carefully connect the learning within and across grades so that students can build new understanding onto foundations built in previous years. • Begin to count on solid conceptual understanding of core content and build on it. Each standard is not a new event, but an extension of previous learning. 7
  • Shift Three: Rigor In the major work, equal intensity in conceptual understanding, procedural skill/fluency, and application •The CCSSM require a balance of: – Solid conceptual understanding – Procedural skill and fluency – Application of skills in problem solving situations •This requires equal intensity in time, activities, and resources in pursuit of all three 8
  • Implementation of Common Core State Standards Compliments other Work Underway Student readiness for postsecondary education and the workforce (WHY we teach) Common Core State Standards provide a vision of excellence for WHAT we teach TEAM provides a vision of excellence for HOW we teach 9
  • Our Transition to Common Core Standards is Central to Strengthening Tennessee’s Competitiveness Only 21% of adults in TN have a college degree TN ranks 46th in 4th grade math and 41st in 4th grade reading nationally Tennessee’s Competitiveness 54% of new jobs will require postsecondary education Only 15% of high school seniors in TN are college ready Source: “Projections of Jobs and Education Requirements Through 2018” (The Georgetown University Center on Education and the Workforce), 2011 NCES NAEP data, ACT 10
  • What are the Common Core State Standards? The Standards . . . • are aligned with college and work expectations; • are clear, understandable and consistent; • include rigorous content and application of knowledge through high-order skills; • build upon strengths and lessons of current state standards; • are informed by other top performing countries, so that all students are prepared to succeed in our global economy and society; and • are evidence-based. http://corestandards.org/about-the-standards 11
  • Common Core State Standards are narrower… # of TN Standards for 3rd Grade Math: # of Common Core Standards for 3rd Grade Math: 25 113 There are 1,119 Tennessee ELA standards not covered in the Common Core CLE CU GLE SPI Grand Total 45 501 109 464 1119 12
  • …and deeper. 3rd Grade Math 3OA.3 (Operations and Algebraic thinking): Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities, e.g., by using drawings and equations with a symbol for the unknown number to represent the problems. There were 28 cookies on a plate. Five children each ate 1 cookie. Two children each ate 3 cookies. One child ate 5 cookies. The rest of the children each ate 2 cookies. Then the plate was empty How many children ate 2 cookies? Use multiplication equations and other operations, if needed, to show how you found your answer. Jane thinks this question can be solved by dividing 28 by 2. She is wrong. Explain using equations and operations why this is not possible. Source: University of Pittsburgh, Copyrighted 13
  • How to Read the Grade Level Standards 14
  • How will the Common Core State Standards affect Teaching in Tennessee? • Creativity and Flexibility • Deeper Engagement • Smaller Number of Standards • Critical Thinking and Problem Solving 15
  • Forms of Assessment Assessment as Learning Assessment of Learning Assessment for Learning 1 16
  • 2012-2013 Assessment Plan, Math 3-8 Student performance on the Constructed Response Assessments will not affect teacher, school, or district accountability for the next two years. October • CRA 1 (paper and online option, scored by teachers in Field Service Center region, reported by school team) February • CRA 2 (paper and online option, scored by teachers in Field Service Center region, reported by school team) May • Official Constructed Response Assessment (paper-based only, scored by state, results reported in July) 17
  • We will narrow the focus of the TCAP and expand use of Constructed Response Assessments 2011-2012 2012-2013 2013-2014 2014-2015 TCAP Constructed Response PARCC We will remove 15-25% of SPIs that are not reflected in Common Core State Standards from the TCAP NEXT year. The specific list of SPI’s will be shared on May 1. We will expand the constructed response assessment for all grades 3-8, focused on the TNCore focus standards for math. NAEP NAEP 18
  • The Common Core State Standards 19 The standards consist of:  The CCSS for Mathematical Content  The CCSS for Mathematical Practice 19
  • Overview of Activity • Analyze and discuss the CCSS for mathematical content and mathematical practices. • Analyze the PBA in order to determine the way the assessment is assessing the CCSSM. • Discuss the CCSS related to the tasks and the implications for instruction and learning. • Discuss what it means to develop and assess conceptual understanding. 2 20
  • Analyzing a Performance-Based Assessment 2 21
  • 2012 – 2013 Tennessee Focus Clusters Grade 5 • Extend understanding of fraction equivalence and ordering. • Build fractions from unit fractions by applying and extending previous understanding of operations of whole numbers. 2 22
  • Analyzing Assessment Items (Private Think Time) One assessment item has been provided:  48 Gumdrops Task • Solve the assessment item. • Make connections between the standard(s) and the assessment item. 2 23
  • 1. 48 Gumdrops Task Two children are sharing 48 gumdrops. Jessica says, “I want 2/4 of the set of 48 gumdrops.” Samuel says, “I want 2/3 of the set of 48 gumdrops.” a. Is it possible for Jessica and Samuel to each have a fraction of the gumdrops that they want? Answer: ____________________ b. If you respond yes, use diagrams and equations to explain how you know they can each receive the share of gumdrops they want. If you respond no, use diagrams and equations to explain why the children cannot receive the number of gumdrops they each want. 24
  • Discussing Content Standards (Small-Group Time) With your small group, discuss the connections between the content standard(s) and the assessment item. 2 25
  • The CCSS for Mathematical Content: Grade 5 Number and Operations – Fractions 5.NF Apply and extend previous understandings of multiplication and division to multiply and divide fractions. Apply and extend previous understandings of multiplication to 5.NF.4 multiply a fraction or whole number by a fraction. Interpret multiplication as scaling (resizing), by: 5.NF.5 Explaining why multiplying a given number by a fraction greater than 5.NF.5b 1 results in a product greater than the given number (recognizing multiplication by whole numbers greater than 1 as a familiar case); explaining why multiplying a given number by a fraction less than 1 results in a product smaller than the given number; and relating the principle of fraction equivalence a/b = (n × a)/(n × b) to the effect of multiplying a/b by 1. Solve real-world problems involving multiplication of fractions and 5.NF.6 mixed numbers, e.g., by using visual fraction models or equations to represent the problem. Apply and extend previous understandings of division to divide unit 5.NF.7 fractions by whole numbers and whole numbers by unit fractions. Common Core State Standards, NGA Center/CCSSO, 2010 26
  • The CCSS for Mathematical Content: Grade 5 Number and Operations – Fractions 5.NF Apply and extend previous understandings of multiplication and division to multiply and divide fractions. Interpret division of a unit fraction by a non-zero whole number, and 5.NF.7a compute such quotients. For example, create a story context for (1/3) ÷ 4, and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that (1/3) ÷ 4 = 1/12 because (1/12) × 4 = 1/3. Interpret division of a whole number by a unit fraction, and compute such 5.NF.7b quotients. For example, create a story context for 4 ÷ (1/5), and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that 4 ÷ (1/5) = 20 because 20 × (1/5) = 4. Solve real-world problems involving division of unit fractions by non-zero 5.NF.7c whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. For example, how much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 1/3-cup servings are in 2 cups of raisins? Common Core State Standards, NGA Center/CCSSO, 2010 27
  • 1. 48 Gumdrops Task Two children are sharing 48 gumdrops. Jessica says, “I want 2/4 of the set of 48 gumdrops.” Samuel says, “I want 2/3 of the set of 48 gumdrops.” a. Is it possible for Jessica and Samuel to each have a fraction of the gumdrops that they want? Answer: ____________________ b. If you respond yes, use diagrams and equations to explain how you know they can each receive the share of gumdrops they want. If you respond no, use diagrams and equations to explain why the children cannot receive the number of gumdrops they each want. 28
  • Determining the Mathematical Practices Associated with the Performance-Based Assessment 29
  • The CCSS for Mathematical Practices 1. Make sense of problems and persevere in solving them. 2. Reason abstractly and quantitatively. 3. Construct viable arguments and critique the reasoning of others. 4. Model with mathematics. 5. Use appropriate tools strategically. 6. Attend to precision. 7. Look for and make use of structure. 8. Look for and express regularity in repeated reasoning. Common Core State Standards for Mathematics, 2010, NGA Center/CCSSO 30
  • Discussing Practice Standards (Small-Group Time) With your small group, discuss the connections between the practice standards and the assessment item. 3 31
  • 1. 48 Gumdrops Task Two children are sharing 48 gumdrops. Jessica says, “I want 2/4 of the set of 48 gumdrops.” Samuel says, “I want 2/3 of the set of 48 gumdrops.” a. Is it possible for Jessica and Samuel to each have a fraction of the gumdrops that they want? Answer: ____________________ b. If you respond yes, use diagrams and equations to explain how you know they can each receive the share of gumdrops they want. If you respond no, use diagrams and equations to explain why the children cannot receive the number of gumdrops they each want. 3 32
  • Mathematical Tasks: A Critical Starting Point for Instruction 33
  • The Structures and Routines of a Lesson Set Up the Task Set-Up of the Task The Explore Phase/Private Work Time Generate Solutions The Explore Phase/ Small-Group Problem Solving 1. Generate and Compare Solutions 2. Assess and Advance Student Learning MONITOR: Teacher selects examples for the Share Discuss based on: • Different solution paths to the same task • Different representations • Errors • Misconceptions SHARE: Students explain their methods, repeat others’ ideas, put ideas into their own words, add on to ideas and ask for clarification. REPEAT THE CYCLE FOR EACH SOLUTION PATH COMPARE: Students discuss Share Discuss and Analyze Phase 1. Share and Model 2. Compare Solutions 3. Focus the Discussion on Key Mathematical Ideas 4. Engage in a Quick Write similarities and differences between solution paths. FOCUS: Discuss the meaning of mathematical ideas in each representation. REFLECT: Engage students in a Quick Write or a discussion of the process. 34
  • Mathematical Tasks: A Critical Starting Point for Instruction There is no decision that teachers make that has a greater impact on students’ opportunities to learn and on their perceptions about what mathematics is than the selection or creation of the tasks with which the teacher engages students in studying mathematics. Lappan & Briars, 1995 35
  • Linking to Research/Literature: The QUASAR Project The Mathematical Tasks Framework TASKS TASKS TASKS as they appear in curricular/ instructiona l materials as set up by the teachers as implemented by students Student Learning Stein M. K., Smith, M. S., Henningsen, M. A., & Silver, E. A. (2000). Implementing standards-based mathematics instruction: A casebook for professional development, p. 16. New York: Teachers College Press. 36
  • The Enactment of the Task (Private Think Time) • Read the Vignettes • Consider the following question: What are students learning in each classroom? 37 37
  • The Enactment of the Task (Small-Group Discussion) Discuss the following question and cite evidence from the cases: What are students learning in each classroom? 38 38
  • The Enactment of the Task (Whole-Group Discussion) What opportunities did students have to think and reason in each of the classes? 39 39
  • Linking to Research/Literature: The QUASAR Project How High-Level Tasks Can Evolve During a Lesson • Maintenance of high-level demands • Decline into procedures without connection to meaning • Decline into unsystematic and nonproductive exploration • Decline into no mathematical activity 40
  • Factors Associated with the Decline and Maintenance of High-Level Cognitive Demands Decline Maintenance • Problematic aspects of the task become routinized • Scaffolds of student thinking and reasoning provided • Understanding shifts to correctness, completeness • A means by which students can monitor their own progress is provided • Insufficient time to wrestle with the demanding aspects of the task • Classroom management problems • Inappropriate task for a given group of students • Accountability for high-level products or processes not expected • High-level performance is modeled • A press for justifications, explanations through questioning and feedback • Tasks build on students’ prior knowledge • Frequent conceptual connections are made • Sufficient time to explore 41
  • Linking to Research/Literature: The QUASAR Project Task Set-Up Task Implementation A. High High B. Low Low C. High Low Student Learning High Low Moderate Stein & Lane, 1996 42
  • Assessing and Advancing Questions 43
  • Using Questioning During the Exploration Phase Imagine that you are walking around the room as your groups of students work on 48 Gumdrops Task – if it were a lesson, not an assessment. Consider what you would say to the groups who produced responses in order to assess and advance their thinking about key mathematical ideas, problem-solving strategies, or use of and connection between representations. Specifically, for each response, indicate what questions you would ask: – to determine what the student knows and understands (ASSESSING QUESTIONS) – to move the student towards the target mathematical goals (ADVANCING QUESTIONS) 44
  • Characteristics of Questions that Support Students’ Exploration Assessing Questions • Based closely on the work the student has produced. • Clarify what the student has done and what the student understands about what s/he has done. • Provide information to the teacher about what the student understands. Advancing Questions • Use what students have produced as a basis for making progress toward the target goal. • Move students beyond their current thinking by pressing students to extend what they know to a new situation. • Press students to think about something they are not currently thinking about. 45
  • 48 Gumdrops Task: Amanda's Work 46
  • Gumdrops Task •Assessing Questions: •Advancing Questions: • Tell me what you did. • Can you write an explanation for how you used the values to draw a diagram? • What does ___ represent? • Why did you … ? • How does you diagram represent the equation (or vice versa)? • How did you know how to draw your diagram? • If Amanda had 1/5 of the gumdrops and Samuel had 2/3 of the gumdrops, how many would be leftover? • Your neighbor says that they have do enough to share. How could you help them understand that this conclusion is incorrect? 47
  • Supporting Student Thinking and Learning In planning a lesson, what do you think can be gained by considering how students are likely to respond to a task and by developing questions in advance that can assess and advance their learning, depending on the solution path they choose? 48
  • Reflection What have you learned about assessing and advancing questions that you can use in your classroom? Turn and Talk 49
  • Tennessee Education Rubric Which of the indicators on the Teacher Education Rubric are related to the use of Assessing and Advancing questions? 50
  • Using the Assessment to Think About Instruction In order for students to perform well on the PBA, what are the implications for instruction? • What kinds of instructional tasks will need to be used in the classroom? • What will teaching and learning look like and sound like in the classroom? 51
  • Common Core and the TN Core 4 – Linking to the TEAM Evaluation Model This year the TEAM Evaluation will focus on the following four areas: 1. Questioning 2. Academic Feedback 3. Thinking 4. Problem Solving 52
  • Questioning 53
  • Academic Feedback 54
  • Thinking 55
  • Problem Solving 56