1. Overview of Step 3: Conceptual Unit Design and Step: 5 Common Formative Assessments April 6, 2012 - Steve Vaerst & Kathleen Wilson

2. Questions On a post it, please answer… What questions do you have about the FES, in general? What questions do you have about steps 3 & 5, specifically? On a post it, please answer… What questions do you have about the FES, in general? What questions do you have about steps 3 & 5, specifically?

3. Rationale “If students don’t understand the concepts, then it’s likely that they’re going to forget, and the teachers are going to have to go back and review and review.” Source: James Hiebert, “Taped Lessons Offer Insights into Teaching.” Education Week, (22)29, (April 2, 2003), p. 24. “If students don’t understand the concepts, then it’s likely that they’re going to forget, and the teachers are going to have to go back and review and review.” Source: James Hiebert, “Taped Lessons Offer Insights into Teaching.” Education Week, (22)29, (April 2, 2003), p. 24.

4. Conceptual Understanding Definition “Conceptual knowledge of mathematics consists of logical relationships constructed internally and existing in the mind as a network of ideas… By its very nature, conceptual knowledge is knowledge that is understood.” Source: John Van De Walle, Elementary and Middle School Mathematics (Pearson, 2004), p. 27. “Conceptual knowledge of mathematics consists of logical relationships constructed internally and existing in the mind as a network of ideas… By its very nature, conceptual knowledge is knowledge that is understood.” Source: John Van De Walle, Elementary and Middle School Mathematics (Pearson, 2004), p. 27.

5. Procedural Understanding Definition “Procedural knowledge of mathematics is knowledge of the rules and the procedures that one uses in carrying out routine mathematical tasks and also the symbolism that is used to represent mathematics.” Source: John Van De Walle, Elementary and Middle School Mathematics (Pearson, 2004), p. 27. “Procedural knowledge of mathematics is knowledge of the rules and the procedures that one uses in carrying out routine mathematical tasks and also the symbolism that is used to represent mathematics.” Source: John Van De Walle, Elementary and Middle School Mathematics (Pearson, 2004), p. 27.

6. Do students need both? Which should come first? Students need procedural and conceptual knowledge to be successful in mathematics. Conceptual understanding should come first and then be labeled with procedural knowledge. Students need procedural and conceptual knowledge to be successful in mathematics. Conceptual understanding should come first and then be labeled with procedural knowledge.

7. Steps in Creating a Conceptual Unit Identify Important Mathematical Concepts Find and “Unwrap” the Matching Math Standards Determine the Big Ideas Write the Essential Questions Plan End-of-Unit Assessment and Scoring Guide Align Math Review Categories & Mental Math Themes Align Problem Solving Tasks Determine Key Vocabulary Identify Important Mathematical Concepts Find and “Unwrap” the Matching Math Standards Determine the Big Ideas Write the Essential Questions Plan End-of-Unit Assessment and Scoring Guide Align Math Review Categories & Mental Math Themes Align Problem Solving Tasks Determine Key Vocabulary

8. Both STEP 3 & 5 begin with Prioritizing the standards and vertically aligning across grades/courses Unwrapping the standards into concepts, skills, and Blooms Essential questions and big ideas defines what we are teaching Everything we choose to do instructionally must be filtered through the big ideas and essential questions because this is where we are trying to take students. Prioritizing the standards and vertically aligning across grades/courses Unwrapping the standards into concepts, skills, and Blooms Essential questions and big ideas defines what we are teaching Everything we choose to do instructionally must be filtered through the big ideas and essential questions because this is where we are trying to take students.

9. NEXT part of STEP 3 Defining instructional unit based on standards not based on book chapters Create "Knowledge Package" or graphic organizer to map unit design Create guiding questions or objectives or learning goals to scaffold to big ideas Align the curriculum to the "knowledge package" and guiding questions; what sections do you need to teach Choose Math Review categories to support unit Choose Mental Math theme to support unit Create Problem Solving tasks - 2 specific tasks for unit Choose key vocab & assess vocab on test Defining instructional unit based on standards not based on book chapters Create "Knowledge Package" or graphic organizer to map unit design Create guiding questions or objectives or learning goals to scaffold to big ideas Align the curriculum to the "knowledge package" and guiding questions; what sections do you need to teach Choose Math Review categories to support unit Choose Mental Math theme to support unit Create Problem Solving tasks - 2 specific tasks for unit Choose key vocab & assess vocab on test

10. NEXT part of STEP 5 Outline the pre/post test for the unit Good assessments have a variety of item types (selected response, constructed response, etc Write pre & post-assessments. Consider having the pre-test contain about 50% prerequisite content and 50% new content Create scoring guide for unit assessment Create formative assessments to monitor learning along the way linked to learning goals Administer common pre & post-assessment Outline the pre/post test for the unit Good assessments have a variety of item types (selected response, constructed response, etc Write pre & post-assessments. Consider having the pre-test contain about 50% prerequisite content and 50% new content Create scoring guide for unit assessment Create formative assessments to monitor learning along the way linked to learning goals Administer common pre & post-assessment

11. Sample Template for Step 3

12. Learning from Introduction on 2/23/12 Intermediate Algebra 1 – Ch. 7 Unwrapping document Original test New test Data from assessment Intermediate Algebra 1 – Ch. 7 Unwrapping document Original test New test Data from assessment

13. Secondary Math PD & Upcoming Trainings May 15 & May 24 review and revise prioritized standards & vertically align June 12 intensive training on Step 3 & 5 June 13-15 curriculum writing to create units based on Step 3 & 5 (must attend 6/12/12) July 16-19 curriculum writing to create units based on Step 3 & 5 (must attend 6/12/12) August 15-17 training on Step 3 & 5 curriculum writing to create units based on Step 3 & 5 May 15 & May 24 review and revise prioritized standards & vertically align June 12 intensive training on Step 3 & 5 June 13-15 curriculum writing to create units based on Step 3 & 5 (must attend 6/12/12) July 16-19 curriculum writing to create units based on Step 3 & 5 (must attend 6/12/12) August 15-17 training on Step 3 & 5 curriculum writing to create units based on Step 3 & 5