CCSS Instructional Practice Guides for Mathematics
PAGE 2 Consider… What do the Common Core State Standards look like in a classroom?
PAGE 3 Objectives Understand the relationship between the Instructional Shifts and the Instructional Practice Guide for Mathematics Identify teacher and student actions that are present in Common Core aligned lessons, as identified in the Instructional Practice Guide Observe and rate a lesson using the Instructional Practice Guide
PAGE 4 The CCSS Require Three Shifts in Mathematics 1.Focus: Focus strongly where the Standards focus. 2.Coherence: Think across grades, and link to major topics within grades. 3.Rigor: In major topics, pursue conceptual understanding, procedural skill and fluency, and application.
PAGE 5 What educators have to say about the Shifts
PAGE 6 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 on what is emphasized in the Standards, so that students gain strong foundations.
PAGE 7 Focus Move away from "mile wide, inch deep" curricula identified in TIMSS. Learn from international comparisons. Teach less, learn more. “Less topic coverage can be associated with higher scores on those topics covered because students have more time to master the content that is taught.” – Ginsburg et al., 2005
PAGE 8 GradeFocus Areas K–2 Addition and subtraction - concepts, skills, and problem solving and place value 3–5 Multiplication and division of whole numbers and fractions – concepts, skills, and problem solving 6 Ratios and proportional relationships; early expressions and equations 7 Ratios and proportional relationships; arithmetic of rational numbers 8 Linear algebra and linear functions Key Areas of Focus in Mathematics
PAGE 9 Focus by Grade Level Achievethecore.org/focus
PAGE 10 Progress to Algebra in Grades K-8
PAGE 11 Focus in High School The mile-wide inch-deep problem looks different in high school. In earlier grades its a matter of having too many topics. In high school its a matter of having too many separately memorized techniques, with no overall understanding of the structure to tie them altogether. So narrowing and deepening the curriculum is not so much a matter of eliminating topics, as seeing the structure that ties them together. -Prof. William McCallum, 2/18/12 commoncoretools.me/2012/02/16/the-structure-is-the-standards/#comments
PAGE 12 Widely Applicable Prerequisites Achievethecore.org/prerequisites
PAGE 13 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 on foundations built in previous years. Begin to count on conceptual understanding of core content and build on it. Each standard is not a new event, but an extension of previous learning. Coherence in K-8 standards set students up for success in high school.
PAGE 14 Coherence: Think across grades One of several staircases to Algebra designed in the OA domain.
PAGE 15 Coherence: Link to Major Topics Within Grades Example: Data Representation Standard 3.MD.B.3 Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories. Solve one- and two-step “how many more” and “how many less” problems using information presented in scaled bar graphs. For example, draw a bar graph in which each square in the bar graph might represent 5 pets.
PAGE 16 Coherence: Link to Major Topics Within Grades Example: Statistics Standard 8.SP.A.3 Use the equation of a linear model to solve problems in the context of bivariate measurement data, interpreting the slope and intercept. For example, in a linear model for a biology experiment, interpret a slope of 1.5cm/hr as meaning that an additional hour of sunlight each day is associated with an additional 1.5 cm in mature plant height.
PAGE 17 Rigor: In Major Topics, Pursue Conceptual Understanding, Procedural Skill and Fluency, and Application The CCSSM require a balance of: Conceptual understanding Procedural skill and fluency Application of skills in problem solving situations Pursuit of all three requires equal intensity in time, activities, and resources.
PAGE 18 Rigor: The three-legged stool
PAGE 19 Conceptual Understanding Teach more than “how to get the answer” and instead support students’ ability to access concepts from a number of perspectives Students are able to see math as more than a set of mnemonics or discrete procedures Conceptual understanding supports the other aspects of rigor (fluency and application)
PAGE 20
PAGE 21
PAGE 22 Fluency The Standards require speed and accuracy in calculation. Class time and/or homework time must be structured so that students can practice core functions such as single-digit multiplication Fluency allow students to better understand and work with more complex concepts
PAGE 23 Required Fluencies in K-6 GradeStandardRequired Fluency KK.OA.5Add/subtract within 5 11.OA.6Add/subtract within OA.2 2.NBT.5 Add/subtract within 20 (know single-digit sums from memory) Add/subtract within OA.7 3.NBT.2 Multiply/divide within 100 (know single-digit products from memory) Add/subtract within NBT.4Add/subtract within 1,000, NBT.5Multi-digit multiplication 66.NS.2,3 Multi-digit division Multi-digit decimal operations
PAGE 24 Application Students can use appropriate concepts and procedures for application even when not prompted to do so. Teachers provide opportunities at all grade levels for students to apply math concepts in “real world” situations, recognizing this means different things in K-5, 6-8, and HS. Teachers in content areas outside of math, particularly science, ensure that students are using grade-level-appropriate math to make meaning of and access science content. 24
PAGE 25 Instructional Practice Guide: Coaching - Design Designed to guide effective integration of the Common Core Shifts into instructional practice. Support teachers in developing their practice and help coaches or other instructional leaders in supporting them to do so. For example, through: ‒ Coaching and feedback from instructional coaches or leaders ‒ Teacher-to-teacher learning in PLCs, grade-level meetings or other collaborative structures ‒ Teacher self-reflection ‒ Lesson planning and preparation*
PAGE 26 Instructional Practice Guide: Coaching - Structure The Instructional Practice Guide: Coaching tool has 3 Core Actions teachers take when they are implementing the Common Core State Standards Each Core Action includes 3 – 6 indicators which describe what teachers are doing – and students are demonstrating – when those Core Actions are displayed
PAGE 27 Getting Started
PAGE 28 Summary of Core Actions
PAGE 29 Notes
PAGE 30 Core Actions for Mathematics 1.Ensure the work of the lesson reflects the Shifts required by the CCSS for Mathematics. 2.Employ instructional practices that allow all students to learn the content of the lesson. 3.Provide all students with opportunities to exhibit mathematical practices while engaging with the content of the lesson.
PAGE 31 Highlight 4-7 key words in each indicator.
PAGE 32 Core Action 1: Finding Evidence IndicatorWhat shift is this related to? What information might be helpful to rate this indicator? What are some artifacts that would provide evidence of this indicator? What are examples of this indicator being met and not being met? Indicator A: The lesson focuses on the depth of grade-level cluster(s), grade- level content standard(s) or part(s) thereof.
PAGE 33 Core Action 1: Lesson Plan Review Carefully read the lesson plan. Note evidence that shows the lesson meeting or not meeting each indicator for Core Action 1. (Do not rate the indicators.) Be ready to share the evidence you found.
PAGE 34 How do I know if the lesson reflects the Shifts? Is the lesson addressing on grade-level content? What is the full intent of the standard(s) being addressed? Is the aspect of rigor required by the standard(s) the same as the aspect(s) being addressed in the lesson? How does the lesson connect to and build on students’ prior skills and knowledge? Digital Planning Tool available at achievethecore.org/lesson-planning-tool
PAGE 35 Core Action 2
PAGE 36 Core Action 2: A Closer Look
37 Don’t Leave Out the Math: Phil Daro on Teaching
PAGE 38 Core Action 2: A Closer Look
PAGE 39 Core Action 2: Finding Evidence Each small group will be assigned one indicator from Core Action 2 Highlight 4 – 7 key words in the indicator, including words from the scale Describe 2 or 3 examples that would show this indicator being met Describe 1 or 2 examples that would show this indicator not being met
PAGE 40 How do I know if the instructional practices allow all students to learn the content of the lesson? How is the mathematics of the lesson made explicit? How does the instruction go beyond just getting the answer? What opportunities do students have to work with and practice grade level problems? How is the lesson differentiated so that all students can work on grade-level content? How does the teacher check for understanding? How does the lesson change based on those checks? What student solution methods are shared to support understanding? How is the mathematics of the lesson summarized? Digital Planning Tool available at achievethecore.org/lesson-planning-tool
PAGE 41
PAGE 42 5 Some or most of the indicators should be observable in every lesson, though not all will be evident in all lessons.
PAGE 43 Standards for Mathematical Practice There is not a one-to-one correspondence between the indicators for Core Action 3 and the Standards for Mathematical Practice. These indicators and the associated illustrative student behavior collectively represent the Standards for Mathematical Practice that are most easily observable during instruction.
PAGE 44 Highlight 4 -7 key words in each indicator for Core Action 3.
PAGE 45 Core Action 3: Problems that Share Thinking Read over the problems. Identify which two problems best prompt students to share their developing thinking. Choose one of the remaining problems and revise it so that the problem will allow students to share their thinking.
PAGE 46 How do I know that all students have opportunities to exhibit mathematical practices while engaging with the content of the lesson? Are questions and problems posed that prompt students to share their developing thinking? What strategies are used to encourage collaboration among students? Do students explain their thinking? Do students talk about each other’s thinking? Do students persist in solving challenging problems? Does the teacher connect student’s informal language to precise mathematical language? Do students choose appropriate tools strategically or are tools given to students? Do students revise their work based on the teacher’s feedback? Digital Planning Tool available at achievethecore.org/lesson-planning-tool
PAGE 47 Core Action 3: Role Play Activity 47 Using your given indicator from Core Action 3, create a three minute role play that you will present to the full group that shows evidence of the indicator. Be sure you show teacher and student behaviors that demonstrate your given indicator.
PAGE ° Lesson Observation Activity 48 Now, you will have a chance to use the entire coaching tool to observe a lesson. As you observe the lesson, record evidence of the indicators in the space provided. Use that evidence to rate each indicator on the scales provided in the coaching tool. Discuss your ratings in small groups and try to come to consensus on the ratings for each indicator.
PAGE ° Lesson Observation Activity: Gallery Walk After your small group has come to consensus for each rating, write that rating and one piece of evidence for each indicator on a sticky note. Place the sticky note for the specified indicator where others can access it. 49
PAGE 50 The Instructional Practice Guide: Coaching tool can help guide us to… Ensure the work of the lesson reflects the Shifts required by the CCSS for Mathematics (Core Action 1) Employ instructional practices that allow all students to learn the content of the lesson (Core Action 2) Provide all students with opportunities to exhibit mathematical practices while engaging with the content of the lesson (Core Action 3)
PAGE 51 There is a digital version of the Instructional Practice Guide available at achievethecore.org/coaching-tool More Information on Instructional Practice Guides
PAGE 52 More Information on Instructional Practice Guides There are CCSS Instructional Practice Coaching Guides for: K-8 Math High School Math K-2 ELA/Literacy 3-5 ELA/Literacy 6-12 ELA/Literacy 6-12 Literacy in Science/Technical Subjects 6-12 Literacy in History/Social Studies All guides are available at achievethecore.org/instructional-practice.
PAGE 53 More Information on Instructional Practice Guides There are CCSS Over the Course of the Year Instructional Practice Guides as supplements for Math (K-High School) and ELA/Literacy (K-12)
PAGE 54 The Digital Instructional Practice Guide: Lesson Planning tool is available at achievethecore.org/lesson-planning-tool More Information on Instructional Practice Guides
Thank you!