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START! Known to New

START! Known to New. College/Career Anchors and Math Performance. Agenda. What are College/Career Anchors? What are Math Performance Standards? Why are they Important? Leading Change = Making Priorities Broadest Impact Plan for Success. Reading. Inference Evidence Analyze Summarize

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START! Known to New

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  1. START! Known to New College/Career Anchors and Math Performance

  2. Agenda What are College/Career Anchors? What are Math Performance Standards? Why are they Important? Leading Change = Making Priorities Broadest Impact Plan for Success

  3. Reading Inference Evidence Analyze Summarize Interpret Integrate Evaluate Delineate

  4. Math Mathematically proficient students can… Explain meaning Conjecture Reason abstractly Critique Reasoning

  5. A Shift in Perspective The CCSS for Mathematics compel a change in the culture of traditional mathematics classroom. • In the typical mathematics classroom students are “too busy covering content” to be engaged with mathematics.

  6. The CCSS attempt to tell teachers when to slow down and emphasize student understanding of significant mathematical ideas.

  7. What Needs to Change? http://www.ted.com/talks/dan_meyer_math_curriculum_makeover.html

  8. Cognitive Targets – CCSS Requires Focus on Rigorous Elements NAEP 2009 PISA 2009 Locating / Recalling Integrating / Interpreting Critiquing / Evaluating Accessing and retrieving Integrating and interpreting Reflecting and evaluating

  9. What is Changing? Textbook? Core Curriculum? State Tests? RtI / ELL Math EOCs?

  10. CHANGE TODAY Common Core State Standards The First and Most Fundamental Change is Depth and Rigor

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  13. The Foundation

  14. Questions for Implementation What can I affect? What is most important? What will be most difficult, and therefore take the most time to change?

  15. But what does “higher standards” mean? • More topics? • No. The U.S. curriculum is already cluttered with too many topics • Teaching topics in earlier grades? • No. Analyses of the standards of high-performing countries suggest otherwise. • In Singapore, division of fractions is a 6th grade expectation; in the U.S. it is typically a 4th or 5th grade expectation. • In Japan, probability is introduced in the 7th grade; in the U.S., it can be found anywhere throughout grades 3-6, depending on the state.

  16. A Shift in Perspective Current U.S. curricula (“mile wide, inch deep”) coupled with high-stakes testing pressures teachers to • “cover” at “pace” • turn the page regardless of student needs However, the study of mathematics should not be reduced to merely “a list of topics to cover” Singapore preaches, “Teach less, learn more”

  17. Agenda What are College/Career Anchors? What are Math Performance Standards? Why are they Important? Leading Change = Making Priorities Broadest Impact Plan for Success

  18. Broad Impact The College / Career Readiness Anchors & Math Performance Standards have the Broadest Impact Across All School Personnel

  19. Define Learning Targets They Define Learning Targets Which Identify Student Skills and Skill Types

  20. Criteria for Learning Target Statements • Specific and Measureable • Order a group fractions and label them on a number line • Contain a performance verb that describes what students will do to demonstrate achievement • Order, Label • State the specific context in which the student will apply that performance • e.g. written, oral, short answer, presentation

  21. Learning Progression Standard: Identify the relative position of simple positive fractions, positive mixed numbers, and positive decimals and be able to evaluate the values based on their position on a number line. Compare fractions, decimals and mixed numbers by identifying their relative position on a number line Identify and locate the approximate location of decimals in hundredths on a number line Indicate the approximate location of thirds, fourths, and fifths on a number line Locate tenths in decimal form on a number line Place halves in fraction form on a number line Locate simple whole numbers on a number line Draw a basic number line from 0 to 10

  22. Classifying Targets Knowledge Mastery of substantive subject content where mastery includes both knowing and understanding it. Reasoning The ability to use knowledge and understanding to figure things out and solve problems. Performance The development of proficiency in doing something where it is the process that is important such as playing a musical instrument, reading aloud, speaking in a second language or using psychomotor skills. Products The ability to create tangible products, such as term papers, science fair projects, and art sculptures that meet certain standards of quality and present concrete evidence of academic proficiency.

  23. Knowledge Target Examples • Identify sight words • Identify similes and metaphors • List defining characteristics of various literary genres • Count and group concrete manipulatives by ones, tens, and hundreds to 1,000

  24. Reasoning Target Examples • Make a prediction based on evidence • Distinguish between fact and opinion • Evaluate information from a variety of resources • Classify and compare triangles by sides and angles

  25. Performance Target Examples • Read aloud with fluency and expression • Demonstrate the use of self-correction strategies • Find and justify the laws of exponents with numeric bases using inductive reasoning • Model, identify and describe square, prime and composite numbers

  26. Product Target Examples • Produce a grammatically correct sentence • Develop a proper paragraph form in a written composition • Compose a written composition using the five-step writing process • Create a design with more than one line of symmetry

  27. Types of Target = Level of Thinking • Begin by analyzing the level of thinking required by the standard • Assess the degree of depth or complexity of knowledge reflected in the content standards and assessments • Determine how deeply a student needs to understand the content for a given response/assessment

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  29. How to Start?

  30. Learning Goals What is Cognitive Demand? What are the SKILLs involved? How do I teach it / change my teaching? What does it look it? Assess?

  31. A Shift in Perspective • Too often, students view mathematics as a trivial exercise because they are rarely given the opportunity to grapple with and come to appreciate the intrinsic complexity of the mathematics. • Despite our instincts and best intentions, we need to stop “GPS-ing” our students to death. Source: Shannon, A. (2010). Common Core: Two Perspectives on Tasks and Assessments. Presentation at the Urban Mathematics Leadership Network Retreat, June 2010.

  32. The Standards for Mathematical Practice “The Standards for Mathematical Practice describe varieties of expertise that mathematics educators at all levels should seek to develop in their students. These practices rest on important processes and proficiencies with longstanding importance in mathematics education.” (CCSS, 2010)

  33. The Standards for Mathematical Practice Source: Briars, D. & Mitchell, S. (2010). Getting Started with the Common Core State Standards. A National Council of Supervisors of Mathematics webinar. November 2010.

  34. The Standards for Mathematical Practice Conceptual Understanding Strategic Competence Productive Disposition Adaptive Reasoning Procedural Fluency Source: Briars, D. & Mitchell, S. (2010). Getting Started with the Common Core State Standards. A National Council of Supervisors of Mathematics webinar. November 2010.

  35. The Standards for Mathematical Practice “Encouraging these practices in students of all ages should be as much a goal of the mathematics curriculum as the learning of specific content” (CCSS, 2010). • 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 reasoning.

  36. The Standards for Mathematical Practice The description of each Mathematical Practice begins with the same first three words: Mathematically proficient students … Source: Briars, D. & Mitchell, S. (2010). Getting Started with the Common Core State Standards. A National Council of Supervisors of Mathematics webinar. November 2010.

  37. The Standards for Mathematical Practice The Mathematical Practices “describe the thinking processes, habits of mind and dispositions that students need to develop a deep, flexible, and enduring understanding of mathematics; in this sense they are also a means to an end.” Source: Briars, D. & Mitchell, S. (2010). Getting Started with the Common Core State Standards. A National Council of Supervisors of Mathematics webinar. November 2010.

  38. The Standards for Mathematical Practice MP #1: Make sense of problems and persevere in solving them. • Mathematically proficient students … • analyze givens, constraints, relationships • and goals … they monitor and evaluate • their progress and change course if • necessary … and continually ask • themselves, “Does this make sense?” Source: Briars, D. & Mitchell, S. (2010). Getting Started with the Common Core State Standards. A National Council of Supervisors of Mathematics webinar. November 2010.

  39. Points of Intersection: Content and Practices MP #3: Construct viable arguments and critique the reasoning of others Consider the following subtraction algorithm: • How could I demonstrate the idea that the algorithm always works? 400 – 139  399 – 138 43 – 17  46 – 20

  40. Points of Intersection: Content and Practices MP #7: Look for and make use of structure Partitioning • 8 x 7 • 33 + 58

  41. Points of Intersection: Content and Practices MP #7: Look for and make use of structure Example: Understanding and interpreting the equation of a line expressed in “Point-Slope Form” • y – y1 = m(x – x1)

  42. Target : Embed

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  44. First Things First If I cannot teach in a manner which engages at the higher levels of cognitive demand, content standards do not matter.

  45. First Things First The Change in Depth is Primary Essential Foundational Immediate

  46. To Dos Training = Awareness Direct Instruction Daily Planning Curriculum Tagging Resource ID & Sharing

  47. Lesson Modification c

  48. Resources standardstoolkit.k12.hi.us Chairman @CurriculumInstitute.Org

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