2010 Alabama Course of Study: Mathematics College- and Career-Ready Standards

1. 2010 Alabama Course of Study: MathematicsCollege- and Career-Ready Standards The Standards for Mathematical Practice

2. 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)

3. 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.

4. 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.

5. 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.

6. 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

7. 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

8. 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

9. 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

10. 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

11. 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

12. 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

13. 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

14. 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…

15. CONNECTION and BALANCE

18. 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

21. Analyzing the Button Task The Button Task was: Scaffolded Foreshadows linear relationships Requires critical thinking skills Did not suggest specific strategy

22. www.insidemathematics.org

23. 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

24. 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)

25. 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…

26. 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

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28. Contact Information ALSDE Office of Student Learning Curriculum and Instruction Section Cindy Freeman, Mathematics Specialist Phone: 334.353.5321 E-mail: cfreeman@alsde.edu