2010 Alabama Course of Study: MathematicsCollege- and Career-Ready Standards Professional Development: K-8 Phase I Regional Inservice Center Summer 2011
Topics for Today • Components of the Course of Study • High School Course Progressions/Pathways • Standards for Mathematical Practice • Literacy Standards for Grades 6-12 • History/Social Studies, Science, and Technical Subjects • The Big Picture • Domains of Study and Conceptual Categories • Learning Progressions/Trajectories • Vertical Alignment of Content • Addressing Content Shifts • Early Entry Algebra I • Considerations/Consequences
Components of the Course of Study Goal Conceptual Categories Domains of Study Position Statements Standards for Mathematical Practice
Components of the Course of Study • Preface • Acknowledgments • General Introduction • Conceptual Framework • Position Statements • Equity • Curriculum • Teaching • Learning • Assessment • Technology • Standards for Mathematical Practice
Components of the Course of Study • Directions for Interpreting the Minimum Required Content GRADE 4 Students will: Domain Cluster Content Standard Identifiers Content Standards
Components of the Course of Study ALGEBRA II WITH TRIGONOMETRY Students will: FUNCTIONS Conceptual Category Domain ContentStandard Identifiers Cluster Content Standards
Components of the Course of Study • Standards for High School Mathematics • Conceptual Categories for High School Mathematics • Number and Quantity • Algebra • Functions • Modeling • Geometry • Statistics and Probability • Additional Coding • (+) STEM Standards • (*) Modeling Standards • ( ) Alabama Added Content
Components of the Course of Study • (+) STEM Standards Geometry 22. Derive the formula A = (1/2)absin(C) for the area of a triangle by drawing an auxiliary line from a vertex perpendicular to the opposite side. [G-SRT9] (+)
Components of the Course of Study • (*) Modeling Standards Algebra I 28. Relate the domain of a function to itsgraph and, where applicable, to the quantitative relationship it describes. [F-IF5] *
Components of the Course of Study • Added Content Specific to Alabama Geometry 35. Determine areas and perimeters of regular polygons, including inscribed or circumscribed polygons, given the coordinates of vertices or other characteristics.
Components of the Course of Study • Description of Standards • Relation to K-8 Content • Content Progression in 9-12
Components of the Course of Study • Narrative • Domains and Clusters • Standards for Mathematical Practice
Components of the Course of Study • Appendices A-E • Appendix A • Table 1: Common Addition and Subtraction Situations • Table 2: Common Multiplication and Division Situations • Table 3: Properties of Operations • Table 4: Properties of Equality • Table 5: Properties of Inequality • Appendix B • Possible Course Progressions in Grades 9-12 • Possible Course Pathways • Appendix C • Literacy Standards For Grades 6-12 History/Social Studies, Science, and Technical Subjects • Appendix D • Alabama High School Graduation Requirements • Appendix E • Guidelines and Suggestions for Local Time Requirements and Homework • Bibliography • Glossary
High School Course Progressions • Required for All Students • Algebra I • Geometry • Algebra II with Trigonometry or Algebra II • Courses Must Increase in Rigor • New Courses • Discrete Mathematics • Mathematical Investigations • Analytical Mathematics
2010 Alabama Course of Study: MathematicsCollege- and Career-Ready Standards The Standards for Mathematical Practice
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)
Underlying Frameworks National Council of Teachers of Mathematics 5 PROCESSStandards • Problem Solving • Reasoning and Proof • Communication • Connections • Representations NCTM (2000M). Principles and Standards for School Mathematics. Reston, VA: Author.
Underlying Frameworks National Research Council Strands of Mathematical Proficiency • Conceptual Understanding • Procedural Fluency • Strategic Competence • Adaptive Reasoning • Productive Disposition NRC (2001). Adding It Up. Washington, D.C.: National Academies Press.
The Standards for Mathematical Practice Mathematically proficient students: Standard 1: Make sense of problems and persevere in solving them. Standard 2: Reason abstractly and quantitatively. Standard 3: Construct viable arguments and critique the reasoning of others. Standard 4: Model with mathematics. Standard 5: Use appropriate tools strategically. Standard 6: Attend to precision. Standard 7: Look for and make use of structure. Standard 8: Look for and express regularity in repeated reasoning.
Standard 1: Make sense of problems and persevere in solving them.What do mathematically proficient students do? • Analyze givens, constraints, relationships • Make conjectures • Plan solution pathways • Make meaning of the solution • Monitor and evaluate their progress • Change course if necessary • Ask themselves if what they are doing makes sense
Standard 2: Reason abstractly and quantitatively. What do mathematically proficient students do? • Make sense of quantities and relationships • Able to decontextualize • Abstract a given situation • Represent it symbolically • Manipulate the representing symbols • Able to contextualize • Pause during manipulation process • Probe the referents for symbols involved
Standard 3: Construct viable arguments and critique the reasoning of others. What do mathematically proficient students do? • Construct arguments • Analyze situations • Justify conclusions • Communicate conclusions • Reason inductively • Distinguish correct logic from flawed logic • Listen to/Read/Respond to other’s arguments and ask useful questions to clarify/improve arguments
Standard 4: Model with mathematics. What do mathematically proficient students do? • Apply mathematics to solve problems from everyday life situations • Apply what they know • Simplify a complicated situation • Identify important quantities • Map math relationships using tools • Analyze mathematical relationships to draw conclusions • Reflect on improving the model
Standard 5: Use appropriate tools strategically. What do mathematically proficient students do? • Consider and use available tools • Make sound decisions about when different tools might be helpful • Identify relevant external mathematical resources • Use technological tools to explore and deepen conceptual understandings
Standard 6: Attend to precision. What do mathematically proficient students do? • Communicate precisely to others • Use clear definitions in discussions • State meaning of symbols consistently and appropriately • Specify units of measurements • Calculate accurately & efficiently
Standard 7: Look for and make use of structure. What do mathematically proficient students do? • Discern patterns and structures • Use strategies to solve problems • Step back for an overview and can shift perspective
Standard 8: Look for and express regularity in repeated reasoning. What do mathematically proficient students do? • Notice if calculations are repeated • Look for general methods and shortcuts • Maintain oversight of the processes • Attend to details • Continually evaluates the reasonableness of their results
The Standards for [Student] Mathematical Practice SMP1: Explain and make conjectures… SMP2: Make sense of… SMP3: Understand and use… SMP4: Apply and interpret… SMP5: Consider and detect… SMP6: Communicate precisely to others… SMP7: Discern and recognize… SMP8: Note and pay attention to…
Draw Pattern 4 next to Pattern 3. See answer above. How many white buttons does Gita need for Pattern 5 and Pattern 6? Explain how you figured this out. 15 buttons and 18 buttons How many buttons in all does Gita need to make Pattern 11? Explain how you figured this out. 34 buttons Gita thinks she needs 69 buttons in all to make Pattern 24. How do you know that she is NOT correct? How many buttons does she need to make Pattern 24? 73 buttons
Analyzing the Button Task The Button Task was: Scaffolded Foreshadows linear relationships Requires critical thinking skills Did not suggest specific strategy
The Standards for [Student] Mathematical Practice “Not all tasks are created equal, and different tasks will provoke different levels and kinds of student thinking.” Stein, Smith, Henningtsen & Silver, 2000 “The level and kind of thinking in which students engage determines what they will learn.” Herbert, Carpenter, Fennema, Fuson, Wearne, Murray, Oliver, & Human, 1997
But, WHAT TEACHERS DO with the tasks matters too! The Mathematical Tasks Framework Tasks are enacted by teachers and students Tasks as they appear in curricular materials Tasks are set up by teachers Student Learning Stein, Grover, & Henningsen (1996) Smith & Stein (1998) Stein, Smith, Henningsen, & Silver (2000)
Standards for [Student] Mathematical Practice The Standards for Mathematical Practice place an emphasis on student demonstrations of learning… Equity begins with an understanding of how the selection of tasks, the assessment of tasks, and how the student learning environment create inequity in our schools…
Leading with the Mathematical Practice Standards • You can begin by implementing the 8 Standards for Mathematical Practice now • Think about the relationships among the practices and how you can move forward to implement BEST PRACTICES • Analyze instructional tasks so students engage in these practices repeatedly
2010 Alabama Course of Study: MathematicsCollege- and Career-Ready Standards Literacy Standards for Grades 6 – 12
APPENDIX CLiteracy Standards for Grades 6 – 12History/Social Studies, Science and Technical Subjects “These standards are designed to supplement students’ learning of the mathematical standards by helping them meet the challenges of reading, writing, speaking, listening, and language in the field of mathematics.”
It is essential for educators to: • select and develop resources that ensure students can connect their curriculum with the real world. • help students recognize and apply math concepts in areas outside of the mathematics classroom. • provide students with opportunities to participate in mathematical investigations. • help students develop problem-solving techniques and skills which enable them to interconnect ideas and build on existing content.
Basis of Literacy Standards The Literacy Standards for Reading and Writing are based on the College and Career Readiness (CCR) anchor standards as outlined in the English Language Arts (ELA) common core. Both of which are outlined in Appendix C.