1. Southern Regional Education Board HSTW Teach Embedded Mathematics Teach Mathematics Embedded in Career/Technical Classes: An Eight-Step Process Gene Bottoms Senior Vice President Southern Regional Education Board gene.bottoms@sreb.org

2. Southern Regional Education Board HSTW Teach Embedded Mathematics SC 2007 Embedding Math2 Session Objectives Overview of “Math-in-CTE” integration model

3. Southern Regional Education Board HSTW Teach Embedded Mathematics SC 2007 Embedding Math3 To turn knowledge into practice, the message is clear. If school leaders and CT teachers do not lead to develop a plan for teaching the embedded math in CT courses in high school, it will not happen.

4. Southern Regional Education Board HSTW Teach Embedded Mathematics SC 2007 Embedding Math4 What specific actions will you take to plan an authentic integrated project every 12 weeks in CT courses with embedded mathematics lessons aligned to state mathematics standards working collaboratively with one or more teachers of mathematics?

5. Southern Regional Education Board HSTW Teach Embedded Mathematics SC 2007 Embedding Math5 School and teacher leaders who lead to act on research evidence that many students learn best through challenging, real-world assignments create integrated assignments that become places where students use mathematics to address adult-like problems, projects and tasks.

6. Southern Regional Education Board HSTW Teach Embedded Mathematics SC 2007 Embedding Math6 Why We Need a Mathematics- CTE Connection Rigorous CTE classes require students to use mathematics Students do not like mathematics because they do not see the use for it. CTE courses fill that need. Mathematics is one of the “new basic skills” for industry. Mathematical literacy is required of anyone entering a workplace or seeking advancement in a career.

7. Southern Regional Education Board HSTW Teach Embedded Mathematics SC 2007 Embedding Math7 Selecting Authentic Projects with a Mathematics Emphasis Full implementation will require much deeper study with on-going professional development Professional development includes teams of CTE and math teachers with strong support from leaders

8. Southern Regional Education Board HSTW Teach Embedded Mathematics SC 2007 Embedding Math8 PROCESS: Develop Math-enhanced Authentic Integrated Projects CTE/math teacher teams develop math lessons following a common lesson plan template and rubric. Teachers share, demonstrate, and discuss these lessons with other teams.

9. Southern Regional Education Board HSTW Teach Embedded Mathematics SC 2007 Embedding Math9 PROCESS: Provide On-going Math Support CTE/math teacher teams meet before each lesson. Community of practice meets several times throughout the year to discuss lessons and challenges. Community of practice meets at the end of the year to celebrate success.

10. Southern Regional Education Board HSTW Teach Embedded Mathematics SC 2007 Embedding Math10 Before Lesson Development Prior to developing lessons, math teachers and CTE teachers will work together to “align” concepts. This process involves taking math concepts that are integral to the lessons in an authentic project.

11. Southern Regional Education Board HSTW Teach Embedded Mathematics SC 2007 Embedding Math11 Eight Steps for Creating an Authentic Integrated Project Unit 1.Identify a major project that is rich with embedded mathematics content that career/technical faculty will have students complete during each 12 weeks of school.

12. Southern Regional Education Board HSTW Teach Embedded Mathematics SC 2007 Embedding Math12 Criteria for Authentic Integrated Project Large enough to cause students to acquire the major technical, academic and personal skills implied in course goals Require completion of learning activities that result in work that would be done in a real workplace Help students understand and experience major technology used in the field Require students to organize information, consider alternatives and use higher-order thinking skills

13. Southern Regional Education Board HSTW Teach Embedded Mathematics SC 2007 Embedding Math13 More Criteria for projects… Present problems and open-ended situations. Require students to apply mathematics skills that are most needed to advance in the career field. Require students to learn from the teacher, other teachers and experts outside the school. Involve both individual effort and teamwork.

14. Southern Regional Education Board HSTW Teach Embedded Mathematics SC 2007 Embedding Math14 More Criteria for Projects… Engage students in interacting about ways to address a problem and about lessons learned. Allow students to present results to an audience of educators, students and representatives from the career field. Require students to work with authentic tools and materials. Have clearly-defined standards that students can use to evaluate their work and take corrective action.

15. Southern Regional Education Board HSTW Teach Embedded Mathematics SC 2007 Embedding Math15 Eight Steps for Creating an Authentic Integrated Project Unit 2. Identify the embedded mathematics standards that can be taught through the project.

16. Southern Regional Education Board HSTW Teach Embedded Mathematics SC 2007 Embedding Math16 CT teachers explain project objectives so that mathematics teachers can help discover the embedded mathematics. Tools to help with this process: School/district mathematics pacing guides State math standards

17. Southern Regional Education Board HSTW Teach Embedded Mathematics SC 2007 Embedding Math17 CT PROGRAMCT ProjectCT CONCEPTS MATH CONCEPTS HEALTH OCCUPATIONS Human Structure and Function Compare cell, tissue, organ and body systems relationships Solve linear equations Read and interpret graphs and charts Problem solving involving statistical data Ratio and Proportion Example of Math Concept Alignment

18. Southern Regional Education Board HSTW Teach Embedded Mathematics SC 2007 Embedding Math18 Eight Steps for Creating an Authentic Integrated Project Unit 3.Identify the literacy strategies, study skills and habits of success that students will be expected to apply in advancing their mastery of mathematics content and skills.

19. Southern Regional Education Board HSTW Teach Embedded Mathematics SC 2007 Embedding Math19 Literacy practices associated with high achievement: Often used word-processing to complete an assignment Often revised written work to improve their quality Often wrote in-depth explanations about a class project Read and interpreted technical books or manuals at least weekly to complete assignments in CT class

20. Southern Regional Education Board HSTW Teach Embedded Mathematics SC 2007 Embedding Math20 15 Literacy Strategies Any Teacher 1.Admit slips 2.Exit slips 3.Double entry or two-column notes 4.ReQuest 5.Interactive CLOZE 6.Cubing 7.Open-response questions – A KEY Source: HSTW Literacy Guide

21. Southern Regional Education Board HSTW Teach Embedded Mathematics SC 2007 Embedding Math21 8.KWL charts 9.Metaphorical thinking 10.Jigsaw reading 11.Paired reading 12.Graphic organizers 13.GIST 14.WordSplash/Capsule vocabulary 15.RAFT

22. Southern Regional Education Board HSTW Teach Embedded Mathematics SC 2007 Embedding Math22 Select Habits of Success to: 1.Create relationships 2.Study, manage time, organize 3.Improve reading/writing skills 4.Improve mathematics skills 5.Set goals/plan 6.Access resources

23. Southern Regional Education Board HSTW Teach Embedded Mathematics SC 2007 Embedding Math23 Eight Steps for Creating an Authentic Integrated Project Unit 4.Assess students’ current knowledge and skills pertinent to the mathematics standards/concepts embedded in the project.

24. Southern Regional Education Board HSTW Teach Embedded Mathematics SC 2007 Embedding Math24 Getting to Mastery at the Proficient/Grade Level is the key! Identify what students must know and be able to do for each new skill or concept. Identify any prerequisite skills students need in order to be successful.

25. Southern Regional Education Board HSTW Teach Embedded Mathematics SC 2007 Embedding Math25 20 item pre-assessment, including: At least ten reading problems Procedural mathematics problems Assess various vocabulary, skills and understanding of mathematics content Varying levels of the mathematics problem Source: See HSTW Classroom Assessment Guide

26. Southern Regional Education Board HSTW Teach Embedded Mathematics SC 2007 Embedding Math26 Basic – Below grade level Proficient – At grade level Advanced – Above grade level What does varying levels mean?

27. Southern Regional Education Board HSTW Teach Embedded Mathematics SC 2007 Embedding Math27 Where can we find good examples of assessment items? Released NAEP items http://nces.ed.gov/nationsreportcard/nde http://nces.ed.gov/nationsreportcard/itmrls/star tsearch.asp State accountability tests-released items SkillsUSA test items http://skillsusa.org/compete/math.shtml Textbooks (enrichment sections)

28. Southern Regional Education Board HSTW Teach Embedded Mathematics SC 2007 Embedding Math28 Team Prepares Assessment Examine resources for pre- assessment Select items suitable for the planned unit.

29. Southern Regional Education Board HSTW Teach Embedded Mathematics SC 2007 Embedding Math29 Eight Steps for Creating an Authentic Integrated Project Unit 5.Have career/technical and math teachers work together to design lessons and assignments to engage students with the mathematics knowledge and skills embedded in the project to teach in CT class.

30. Southern Regional Education Board HSTW Teach Embedded Mathematics SC 2007 Embedding Math30 Two emphases in this step: 1.Bridging the gap between the language of the pathway field as it relates to the language of mathematics. 2.Identifying engaging instructional strategies that aim toward college- and career-readiness.

31. Southern Regional Education Board HSTW Teach Embedded Mathematics SC 2007 Embedding Math31 Determining how students will be introduced to the language of mathematics while learning the language of the pathway. Emphasis #1: Bridging the gap between language of the pathway and the language of the mathematics

32. Southern Regional Education Board HSTW Teach Embedded Mathematics SC 2007 Embedding Math32 Emphasis #2: Engaging Instructional Strategies Cooperative learning Project-based learning Socratic method Anticipation guides Videos Readings Teacher Demonstrations Technology integration Graphing calculators CBL’s Excel Literacy Strategies Use of manipulatives Multi-intelligences approach Practice Problems

33. Southern Regional Education Board HSTW Teach Embedded Mathematics SC 2007 Embedding Math33 Eight Steps for Creating an Authentic Integrated Project Unit 6.Have mathematics and CT teachers work together to prepare lessons to teach the mathematics knowledge and skills embedded in the project in the math class.

34. Southern Regional Education Board HSTW Teach Embedded Mathematics SC 2007 Embedding Math34 Bridging the Gap between the Language of Mathematics and the Language of the Pathway. Determine how the language of CT can be introduced into a traditional mathematics classroom: 1.When the mathematics and CT teacher share the same students. 2.When the mathematics teacher might have some of the CT students. 3.When the mathematics teacher has no CT students in their classroom.

35. Southern Regional Education Board HSTW Teach Embedded Mathematics SC 2007 Embedding Math35 Communities of Practice Planning Time Consider ways the mathematics teacher will teach the mathematics embedded in the project.

36. Southern Regional Education Board HSTW Teach Embedded Mathematics SC 2007 Embedding Math36 Eight Steps for Creating an Authentic Integrated Project Unit 7.Describe how students will demonstrate their understanding of mathematics knowledge and skills by completing the project as well as completing assignments designed to provide additional practice.

37. Southern Regional Education Board HSTW Teach Embedded Mathematics SC 2007 Embedding Math37 Most important to remember: Require students to demonstrate understanding at varying levels of difficulty (basic, proficient, advanced) Skills USA test items Include contextual problems from the pathway

38. Southern Regional Education Board HSTW Teach Embedded Mathematics SC 2007 Embedding Math38 Communities of Practice Planning Time With your community, design reteach strategies for students failing to demonstrate understanding of mathematics competencies.

39. Southern Regional Education Board HSTW Teach Embedded Mathematics SC 2007 Embedding Math39 Eight Steps for Creating an Authentic Integrated Project Unit 8.Develop a summative unit exam to assess students’ understanding of mathematics concepts, skills and procedures used in the project.

40. Southern Regional Education Board HSTW Teach Embedded Mathematics SC 2007 Embedding Math40 Create summative paper and pencil assessment exams. Released NAEP items Assess learning through performance-based assessments AND using test items found in college placement exams and state level accountability tests

41. Southern Regional Education Board HSTW Teach Embedded Mathematics SC 2007 Embedding Math41 Seven Elements for Teaching Mathematics Lessons for AIP 1.Introduce the CTE lesson (CT teacher) 2.Assess students’ math awareness (CT teacher) 3.Work through embedded example (CT teacher) 4.Work through traditional math examples (math teacher) 5.Work through related, contextual examples (CT/math teacher) 6.Students demonstrate understanding (CT /math) 7.Formal assessment (CT/math)

42. Southern Regional Education Board HSTW Teach Embedded Mathematics SC 2007 Embedding Math42 Element 1: Introduce the CT Lesson Explain the CT lesson Identify, discuss, point out and pull out the mathematics embedded in the CT lesson.

43. Southern Regional Education Board HSTW Teach Embedded Mathematics SC 2007 Embedding Math43 Element 2: Assess Students’ Math Awareness Begin “bridging” between the CT and mathematics. Introduce math vocabulary through the math embedded in the CT. Use methods and techniques to assess the whole class.

44. Southern Regional Education Board HSTW Teach Embedded Mathematics SC 2007 Embedding Math44 Element 3: Work through the Math Example Embedded in the CT Lesson Work through the steps or processes of the embedded math example. Continue to bridge the CT and math vocabulary.

45. Southern Regional Education Board HSTW Teach Embedded Mathematics SC 2007 Embedding Math45 Element 4: Work through Related Math-in-CT Examples Using the same embedded math concept: Work through similar problems in the same occupational context. Use examples of varying levels of difficulty; order from basic to advanced. Continue to bridge CT and math vocabulary. Check for understanding.

46. Southern Regional Education Board HSTW Teach Embedded Mathematics SC 2007 Embedding Math46 Element 5: Work through Traditional Math Examples Using the same embedded math concept: Work from applied to abstract problems. Work through examples as they may appear on standardized tests. Move from basic to advanced problems. Continue to bridge CT-mathematics vocabulary. Check for understanding.

47. Southern Regional Education Board HSTW Teach Embedded Mathematics SC 2007 Embedding Math47 Element 6: Students Demonstrate Understanding Provide students with opportunities to demonstrate their understanding of the math concepts embedded in the CT. Connect the math back to CT context. Conclude the lesson with CT.

48. Southern Regional Education Board HSTW Teach Embedded Mathematics SC 2007 Embedding Math48 Element 7: Formal Assessment Include mathematics questions in formal assessments. For example, CT unit exams. CT project assessments.

49. Southern Regional Education Board HSTW Teach Embedded Mathematics SC 2007 Embedding Math49 Core Principles for Math-in-CT A.Develop and sustain a community of practice B.Begin with the CT curriculum and not with the math curriculum C.Understand math as essential workplace skill D.Maximize the math in CT curricula E.CT teachers are teachers of “math-in- CT” NOT math teachers

50. Southern Regional Education Board HSTW Teach Embedded Mathematics SC 2007 Embedding Math50 Core Principles for Math-in-CT A powerful, evidence based strategy for improving math skills of students; A way but not THE way to help high school students master math Not a substitute for traditional math courses Lab (experiential venue) for mastering what many students learn but don’t understand

51. Southern Regional Education Board HSTW Teach Embedded Mathematics SC 2007 Embedding Math51 What specific actions will you take to plan an authentic integrated project every 12 weeks in at least five CT courses with embedded mathematics lessons aligned to Regents mathematics standards working collaboratively with one or more teachers of mathematics?

52. Southern Regional Education Board HSTW Teach Embedded Mathematics SC 2007 Embedding Math52 HSTW trainer can provide state, district and/or school site workshops for teaching embedded mathematics National workshops planned on March 13-14, in Atlanta Where Can I Get Help?

53. Southern Regional Education Board HSTW Teach Embedded Mathematics SC 2007 Embedding Math53 For more information, contact: Gene Bottoms or Leslie Carson gene.bottoms@sreb.org leslie.carson@sreb.org