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Math Course Design

Content, Delivery, Rationale. Math Course Design. Development Timeline. January 16-17, 2012 – Full Math Team Meeting Brainstormed content, practices, and habits to be included in Transition Course Discussions with Dr. Jason Zimba and Dr. Bill McCallum, CCSS Writers

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Math Course Design

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  1. Content, Delivery, Rationale Math Course Design

  2. Development Timeline • January 16-17, 2012 – Full Math Team Meeting • Brainstormed content, practices, and habits to be included in Transition Course • Discussions with Dr. Jason Zimba and Dr. Bill McCallum, CCSS Writers • Determined criteria for Lead Writers

  3. High School: A Major Disconnect

  4. Emphases in High School • Many students in two-year and four-year colleges need remediation in math • Remedial classes lower the odds of finishing the degree or program • Need to set the agenda in high school math to prepare more students for postsecondary education and training

  5. Postsecondary instructors want deeper mastery of fewer things

  6. Just-released survey of over 1,800 postsecondary instructors Instructors rated each of the CCSSM content standards in high school as to applicability and importance for college-level work Range of courses and institutions Conley et al., validity study of CCSS

  7. Not all content areas are equally important Heuristic Importance Rating of Source: Derived from Conley (2011) data

  8. Timeline • February 13-14, 2012 – Lead Writers Meeting • Clustered content into modules for course development • Determined module components • Assigned modules to Lead Writers

  9. Standards Module Order Numbers and Operations (AR) Solving Equations (TN) Measurement (KY) Linear (GA) Systems (KY) Quadratic (NC) Exponentials (AR) Optional: Statistics (TN)

  10. The Standards for Mathematical Practice 1. Make sense of problems and persevere in solving them. 2. Reason abstractly and quantitatively. 3. Construct viable arguments and critique the reasoning of others. 4. Model with mathematics. 5. Use appropriate tools strategically. 6. Attend to precision. 7. Look for and make use of structure. 8. Look for and express regularity in repeated reasoning.

  11. The Cycle of Learning in a Class Period

  12. Timeline • March 12, 2012 – Skeletal Projects Due • CCSS (Content and Mathematical Practices) • Essential Questions • Hook and Learning Progressions • Assessment (Formative and Summative) • March 20, 2012 – Lead Writers Webinar • Focus (Gaps? Overlaps?) • Cohesiveness (Module Elements Matrix) • Rigor (Conceptual, Procedural, and Application Balance)

  13. Timeline • March 20-April 9, 2012 – SREB Feedback • Calls between Lead Writers and Adam Spiegler (Transition Course “Architect”) • April 9, 2012 – Skeletal Project Revisions Due • April 17, 2012 – Full Math Team Webinar • Select State Review Facilitators • Review Rubric & Timeline

  14. Review Rubric: • Adapted from SREB’s Planning for Improved Student Achievement: Ten Steps for Planning and Writing Standards-Based Units • Will be used for Skeletal Module Review and Fully Developed Module Review

  15. Selecting State Review Facilitators: • Each member of the State Team will review all 8 Skeletal Projects using the Review Rubric • Each State Review Facilitator will compile his/her State Team member reviews into one document and submit to SREB • SREB will compile State reviews and provide feedback to Lead Writers

  16. Standards Timeline • State Team Member Reviews to State Review Facilitators – May 8th • State Review Facilitator Compilation Review to SREB – May 15th • Lead Writer Webinar, May 15th – 2:00 EST • Fully Developed Module Template • Summative Assessments • Multi-State Compilation of Reviews by SREB to Lead Writers – May 22nd • Face-to-Face Meeting: May 31-June 1, 2012

  17. Sample Task

  18. How many cubes are needed to build this tower? (Show your calculations) • How many cubes are needed to build a tower like this, but 12 cubes high? (Explain how you figure out your answer) • How would you calculate the number of cubes needed for a tower n cubes high?

  19. Formative Assessment Lesson Forming Quadratics map.mathshell.org Time for a little “productive struggle”

  20. Pre-Lesson Assessment Task See: Page S-1 in Forming Quadratics

  21. Whole Class Introduction What makes your two graphs different? What are the common features of your graphs? How many turning points does each of your graphs have? Is this turning point a maximum or minimum? Can the curve of a quadratic function have more than one turning point/no turning points? How many roots does each of your graphs have? Where are these roots on your curve? Does anyone have a graph with a different number of roots? How many roots can a quadratic have?

  22. Collaborative Activity:Matching Dominos • Take turns at matching pairs of dominos that you think belong together. • Each time you do this, explain your thinking clearly and carefully to your partner. • It is important that you both understand the matches. If you don't agree or understand, ask your partner to explain their reasoning. You are both responsible for each other’s learning. • On some cards an equation or part of an equation is missing. Do not worry about this, as you can carry out this task without this information.

  23. Sharing Work • One student from each group is to visit another group's poster. • If you are staying at your desk, be ready to explain the reasons for your group's matches. • If you are visiting another group: • Write your card matches on a piece of paper. • Go to another group's desk and check to see which matches are different from your own. • If there are differences, ask for an explanation. If you still don't agree, explain your own thinking. • When you return to your own desk, you need to consider as a pair whether to make any changes to your own work.

  24. Sample Questions Plenary Whole Class Discussion Ella, where did you place this card? How did you decide? Ben, can you put that into your own words? What are the missing equations for this graph? How did you work them out? Did anyone use a different method?

  25. Standards Timeline • Individual Reviews of Fully Developed Modules to State Review Facilitator: August 3, 2012 • State Review Facilitator sends compiled reviews to SREB: August 10, 2012 • Compiled Review sent to Lead Writers and Conference Calls Scheduled w/ SREB: week of August 13-17, 2012 • Summative Assessments due September 7, 2012

  26. Planning the Post-Assessment How will you know if students understand and can apply the content taught during the module? How will you communicate expectations to your students at the beginning of the unit? How will the post-assessment test and task determine students’ mastery of the content and skills embedded in the standard and their ability to demonstrate and apply standards in a concrete format? These crucial decisions must be addressed early in the planning process to guide unit development and students assessment.

  27. Planning the Post-Assessment In standards-based unit development, the post-assessment includes two parts: Part one of the post-assessment is an appropriately written, high-quality paper-and-pencil test that determines the knowledge students have mastered and can apply. Part two of the post-assessment is a product-, performance- or problem-based assessment. It evaluates student progress in achieving each of the targeted standards and demonstrates mastery – specifically at or above grade level – of the standards on which the essential questions are based.

  28. Q & A • Curriculum or Assessment Questions? • Delivery Questions?

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