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UCDMP Saturday Series 2013-14 The Vision of the Common Core: Changing Beliefs, Transforming Practice Kindergarten – 6th Grade Saturday, September 21, 2013 Agenda Introductions and Overview Problem Solving: Jim and Jesse’s Money Review of SMP’s Assessment of and for Learning Lunch Planning a Common Core Unit and Lesson Standards Analysis and Resource Evaluation Sharing and Reflections Wireless Access Go to Moobilenet Sign in information Email address: [email protected] Password: wireless Introductions The Staff Pam Hutchison, Director, UCDMP Andrea Williams, UCDMP Teacher Leader and 4th grade teacher, FSUSD Diana Zaragoza, UCDMP Teacher Leader and District Math Coach, DJUSD Renee Yeasted, UCDMP Teacher Leader and Content Area Specialist, VUSD Overview of Saturdays November 2, 2013 Assessment of and for learning Formative assessments Assessing students’ ability to Explain their reasoning, Construct viable arguments and Critique the reasoning of others. The use of games Planning for the CCSS-M Overview of Saturdays January 25, 2014 The use of mathematical tasks As an instructional tool, As an assessment tool for Problem solving Explanations Connecting to prior knowledge Developing a deep understanding Planning for the CCSS-M Overview of Saturdays March 15, 2014 Developing and using rubrics to assess understanding, communication, and problem solving General rubrics, Task specific rubrics CCSS rubrics K-2 “Construct viable arguments and critique the reasoning of others” 3-5 Using technology to learn math Planning for the CCSS-M Overview of Saturdays May 3, 2014 Summative Assessments Performance tasks Model with Mathematics K-2 Using technology to learn math 3-5 “Construct viable arguments and critique the reasoning of others” Planning for the CCSS-M Units Available for purchase Attend 3 sessions 2 quarter units Attend all 5 sessions 3 quarter units Online Course Constructive Classroom Conversations: Mastering the Language of the Common Core State Standards Standford Online October 21 – Dec 9 Andrea and Diana’s Money Andrea and Diana each had the same amount of money. Andrea spent $58 to fill the car up with gas for a roadtrip. Diana spent $37 buying snacks for the trip. Afterward, Andrea had 1/4 as much money as Diana had. How much money did each have at first? The CCSS in Mathematics have two sections: Standards for Mathematical CONTENT and Standards for Mathematical PRACTICE The Standards for Mathematical Content are what students should understand, know, and be able to apply. The Standards for Mathematical Practice are what students should do. Mathematical “Habits of Mind” 1. Make sense of problems and persevere in solving them 6. Attend to precision OVERARCHING HABITS OF MIND CCSS Mathematical Practices REASONING AND EXPLAINING 2. Reason abstractly and quantitatively 3. Construct viable arguments and critique the reasoning of others MODELING AND USING TOOLS 4. Model with mathematics 5. Use appropriate tools strategically SEEING STRUCTURE AND GENERALIZING 7. Look for and make use of structure 8. Look for and express regularity in repeated reasoning Proficiency Matrix Standards for Mathematical Practice Initial Intermediate Advanced PS, QW, GE, etc. Student engagement strategies Self-Evaluation Where are you on this matrix? What SMP’s are you already overtly fostering in students? Are you getting them to the initial, intermediate, or advanced stage? What SMP’s do you really not address at this point? Make a Plan Pick 1 to 2 SMP’s that you want to focus on in the next month or so. What are you going to do to support students in developing those standards? Where are you (as the teacher) starting from? What can you do to help “move” students to the next stage on the matrix? Share Share your plan at your table. What are your strategies and ideas? What are your concerns? Assessments What are various ways in which we assess: what students know? what students understand? Assessment and Learning “Assessment should be an integral part of teaching. It is the mechanism whereby teachers can learn how students think about mathematics as well as what students are able to accomplish.” Assessment and Learning “Assessment should allow all students to show what they know, understand and can do.” (Cockcroft Report 1982) Assessment and Learning “Assessment for learning is one of the most powerful ways of improving learning and raising standards“ (Black and Wiliam 1998) Assessment What are characteristics of “good” assessment? According to the Shell Centre, high quality assessment has: Curriculum balance Curriculum value Fitness for purpose Formative Assessments Assessment for learning Occurs continuously in classroom both within and between lessons Used to adjust teaching strategies Provides students with useful and meaningful feedback Formative Assessments Focus: To determine what learning comes next Examples: Feedback Open questioning Exit tickets Observations Discussions Ungraded classwork/homeworks Summative Assessments Assessment of learning Occur within, between, and among instructional units Used to identify strengths and gaps in curriculum and instruction Curriculum may be refined Teachers may modify instruction Summative Assessments Focus: To determine: how student groups are progressing how well program is working Examples Graded class work or homework Quizzes End of unit tests Midterms District benchmarks Large Scale Assessments Assessment of learning Frequently high stakes Examine trends over time Used to develop long-term evaluation of curriculum and programs Used to monitor school site, district and state progress Large Scale Assessments Focus: To determine how schools, districts and states are progressing over time Examples: End of course exams CST NAEP SAT/ACT Exams AP Exams Assessment Think of how and when you assess your students. Which ones are assessments for learning? Which ones are assessments of learning? Assessment “What a difference a word makes” Read the article Record 1 thing with which you agree 1 thing with which you might argue 1 thing to which you aspire 1 Aha! Sharing Go around the group and share one of the following: the thing with which you agree the thing with which you might argue the thing to which you aspire your Aha! Pick one thing from your group to share with the whole group Large Scale Assessment WYTIWYG! Large Scale Assessment What you test is what you get! Goals of Assessment “We must ensure that tests measure what is of value, not just what is easy to test. If we want students to investigate, explore, and discover, assessment must not measure just mimicry mathematics.” Everybody Counts PARCC States PARCC States CCSS-M SMARTER Claims Claim #1: Concepts and Procedures “Students can explain and apply mathematical concepts and interpret and carry out mathematical procedures with precision and fluency.” CCSS-M SMARTER Claims Claim #2: Problem Solving “Students can solve a range of complex well-posed problems in pure and applied mathematics, making productive use of knowledge and problem solving strategies.” CCSS-M SMARTER Claims Claim #3: Communicating Reasoning “Students can clearly and precisely construct viable arguments to support their own reasoning and to critique the reasoning of others.” CCSS-M SMARTER Claims Claim #4: Modeling and Data Analysis “Students can analyze complex, realworld scenarios and can construct and use mathematical models to interpret and solve problems.” Score Reporting-Individual “Total Mathematics” score The composite mathematics score will need to have scaling properties that allow for the valid determination of student growth over time. This score will be a weighted composite from the four claims Claim #1: 40% Claims #2-4: about 20% each. Smarter Balanced Assessment Consortium Problem Types SR – selected-response item CR – constructed-response item ER – extended-response item TE – technology-enhanced item PT – performance task CCSS-M SMARTER Claims Claim #1: Concepts and Procedures “Students can explain and apply mathematical concepts and interpret and carry out mathematical procedures with precision and fluency.” Claim 1 Selected Response Typical Multiple Choice Selected Response Constructed Response Extended Response Technology Enhanced Assessment Items Group 1 Claim 1 – Selected Response Typical Multiple Choice Answer the problems. Assessment Items Group 1 Claim 1 – Selected Response Typical Multiple Choice How are these problems similar and/or different from the typical CST questions? Assessment Items Group 2 Claim 1 – Selected Response Selected Response Answer the problems. Assessment Items Group 2 Claim 1 – Selected Response How are these problems different from the typical CST questions? What do students have to know and/or understand to do these problems that they don’t have know/understand to do a typical multiple choice question. th 5 Grade Multiplication Models Smarter Balanced Assessment Consortium Problem Types SR – selected-response item CR – constructed-response item ER – extended-response item TE – technology-enhanced item PT – performance task rd 3 Grade – CR th 4 Grade – CR th 5 Grade – CR th 6 Grade – CR Rubric Scoring rd 3 Grade – ER th 5 Grade – ER th 4 Grade – TE th 6 Grade – TE th 6 Grade – TE, cont. Claim 1 “Students can explain and apply mathematical concepts and interpret and carry out mathematical procedures with precision and fluency.” So what are the classroom implications if we are assessing students in these ways? Multiple Representations Look at the standards for your grade level. Which standards clearly imply that students need to be familiar with a variety of models, representations, and/or strategies? Unit Planning Unit Planning Unit Planning Template Unit Planning Questions 2nd Grade Unit Planning Questions Topic: What is the big idea that you will be addressing in this unit? Unit Planning Questions Content Standards: Which common core standards (or parts of standards) will be addressed in this unit? Use place value understanding and properties of operations to add and subtract. 5. Fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction. 6. Add up to four two-digit numbers using strategies based on place value and properties of operations. 7. 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. 7.1 Use estimation strategies to make reasonable estimates in problem solving. CA 8. Mentally add 10 or 100 to a given number 100–900, and mentally subtract 10 or 100 from a given number 100–900. 9. Explain why addition and subtraction strategies work, using place value and the properties of operations.3 Explanations may be supported by drawings or objects. 3 Unit Planning Questions Practice Standards: What standards for mathematical practice (1-2) do I want to focus on and promote during this unit? Unit Planning Questions What should students already know? What have students learned in previous grades? How does what they should already know connect to what they are going to learn? Where does this unit fall on the continuum of “Concrete – Representational – Abstract” Unit Planning Questions What will students learn and how will I know what they have learned? What should students understand by the end of the unit? What are some ideas for assessing student understanding? Unit Planning Questions What will students learn and how will I know what they have learned? What should students know and be able to do by the end of the unit? What are some ideas for assessing procedural skills? Unit Planning Questions What will students learn and how will I know what they have learned? How should students be able to demonstrate their ability to apply what they have learned by the end of the unit? What are some possible assessment ideas and/or tasks? Unit Planning Questions What will students learn and how will I know what they have learned? Key Vocabulary Unit Planning Questions What tools, models, and materials are necessary to fully address the standards for this unit? Unit Planning Questions Anticipated Number of Days Approximately how many days do I anticipate needing for this unit (including all assessments)? How many days are needed for lessons related to: Conceptual understanding Procedures and skills Applications and problem solving Unit Planning Questions Sketch of Unit by Days (Overview) Brief description of big ideas for each day Lesson Planning Questions Topic: What is the topic of the lesson? Lesson Day: Where is this lesson in the overall plan of the unit? Lesson Planning Questions OVERVIEW Content Standard(s): What part of the standard(s) is being addressed today? This should be a brief statement or goal. Practice Standard(s): What practice standard will I be focusing on today? Lesson Planning Questions Type of Lesson: Concept Lesson Procedure or Skill Lesson Application or Problem Solving Lesson Review Lesson Key Vocabulary: What vocabulary needs to be introduced or reviewed today? How and when will that take place? Lesson Planning Questions Materials Needed: What materials are needed for this lesson? Materials include (but are not limited to): textbook resources, supplemental student activity pages or worksheets, manipulatives, rulers, protractors, strategies, models, technology,… Lesson Planning Questions How and when will I support students in connecting to prior knowledge? What prior knowledge does this lesson build on and extend? It could be from the prior day or earlier in the year or the previous year. How and when will I deal with homework? Lesson Planning Questions Opening prompt or problem: Leads in and connects to the topic of the day Lesson Planning Questions Lesson Part 1, 2, 3,…: Description of what happens in each part of the lesson. What am I doing? What are students doing? What specific problems or activities are involved? What are some key questions that I want to ask? What materials are needed for this part? Lesson Planning Questions Closure: What prompt can I use to help students review what they have learned? How will I know what they have learned? Collaboration Lesson planning is easier and more efficient when done with teams of teachers Share strategies Share workload (if need to create, copy or collect materials) Share struggles and successes Reflect and revise Resources Illustrative Mathematics Website http://illustrativemathematics.org A work in progress Designed to provide examples that help to clarify what each CCSS means Resources Inside Mathematics Website http://www.insidemathematics.org Resources on SMP’s, including: Classroom video examples illustrating the math practice standards, including commentary Videos of exemplary lessons integrating multiple math practices Resources Inside Mathematics Website New resources on SMC’s, including: Common Core-aligned tasks, searchable either by grade level or by Common Core content area, such as “Operations and Algebraic Thinking,” or “Geometry Congruence.” Resources Inside Mathematics Website Additional classroom videos of Number Talks Four new classroom videos of “Number Talks” showing students engaged in mental math exercises and conversations about math, including one from a bilingual Spanish-English classroom. Resources NCTM Illuminations Website http://illuminations.nctm.org/ National Council of Teachers of Mathematics Contains activities, lessons and links related to the CCSS Resources Common Core Flip Books http://katm.org/wp/wp-content/uploads/ flipbooks Grade level books with additional examples, strategies and ideas for teaching the CCSS-M Resources SBAC Website Sample Items http://www.smarterbalanced.org/smarterbalanced-assessments/ Scroll down to “Mathematics” Find “Mathematics 3-5” (ZIP) or “Mathematics 6-8” (ZIP) Folder of currently released sample assessment items for the 4 claims Resources SBAC Website Practice Tests https://sbacpt.tds.airast.org/student/ Resources California Department of Education Common Core State Standards – M http://www.cde.ca.gov/be/st/ss/documen ts/ccssmathstandardaug2013.pdf Mathematics Framework (DRAFT) http://www.cde.ca.gov/ci/ma/cf/draft2ma thfwchapters.asp Break-Out Groups K-2: 3-5: