Teach Mathematics Embedded in Career/Technical Classes: An Eight-Step Process

1. 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. Session Objectives • Overview of “Math-in-CTE” integration model SC 2007 Embedding Math

3. 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. SC 2007 Embedding Math

4. 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? SC 2007 Embedding Math

5. 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. SC 2007 Embedding Math

6. 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. SC 2007 Embedding Math

7. 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 SC 2007 Embedding Math

8. 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. SC 2007 Embedding Math

9. 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. SC 2007 Embedding Math

10. 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. SC 2007 Embedding Math

11. Eight Steps for Creating an Authentic Integrated Project Unit • 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. SC 2007 Embedding Math

12. 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 SC 2007 Embedding Math

13. 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. SC 2007 Embedding Math

14. 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. SC 2007 Embedding Math

15. Eight Steps for Creating an Authentic Integrated Project Unit 2. Identify the embedded mathematics standards that can be taught through the project. SC 2007 Embedding Math

16. 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 SC 2007 Embedding Math

17. Example of Math Concept Alignment SC 2007 Embedding Math

18. Eight Steps for Creating an Authentic Integrated Project Unit • 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. SC 2007 Embedding Math

19. 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 SC 2007 Embedding Math

20. 15 Literacy Strategies Any Teacher Admit slips Exit slips Double entry or two-column notes ReQuest Interactive CLOZE Cubing Open-response questions – A KEY Source: HSTW Literacy Guide SC 2007 Embedding Math

21. KWL charts Metaphorical thinking Jigsaw reading Paired reading Graphic organizers GIST WordSplash/Capsule vocabulary RAFT SC 2007 Embedding Math

22. 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 SC 2007 Embedding Math

23. 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. SC 2007 Embedding Math

24. Getting to Mastery at the Proficient/Grade Levelis 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. SC 2007 Embedding Math

25. 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 SC 2007 Embedding Math

26. What does varying levels mean? Basic – Below grade level Proficient – At grade level Advanced – Above grade level SC 2007 Embedding Math

27. Where can we find good examplesof assessment items? • Released NAEP items http://nces.ed.gov/nationsreportcard/nde http://nces.ed.gov/nationsreportcard/itmrls/startsearch.asp • State accountability tests-released items • SkillsUSA test items http://skillsusa.org/compete/math.shtml • Textbooks (enrichment sections) SC 2007 Embedding Math

28. Team Prepares Assessment • Examine resources for pre-assessment • Select items suitable for the planned unit. SC 2007 Embedding Math

29. Eight Steps for Creating an Authentic Integrated Project Unit • 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. SC 2007 Embedding Math

30. Two emphases in this step: • Bridging the gap between the language of the pathway field as it relates to the language of mathematics. • Identifying engaging instructional strategies that aim toward college- and career-readiness. SC 2007 Embedding Math

31. Emphasis #1: Bridging the gap between language of the pathway and the language of the mathematics Determining how students will be introduced to the language of mathematics while learning the language of the pathway. SC 2007 Embedding Math

32. 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 Emphasis #2: Engaging Instructional Strategies SC 2007 Embedding Math

33. 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. SC 2007 Embedding Math

34. 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: • When the mathematics and CT teacher share the same students. • When the mathematics teacher might have some of the CT students. • When the mathematics teacher has no CT students in their classroom. SC 2007 Embedding Math

35. Communities of Practice Planning Time Consider ways the mathematics teacher will teach the mathematics embedded in the project. SC 2007 Embedding Math

36. Eight Steps for Creating an Authentic Integrated Project Unit • 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. SC 2007 Embedding Math

37. 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 SC 2007 Embedding Math

38. Communities of Practice Planning Time With your community, design reteach strategies for students failing to demonstrate understanding of mathematics competencies. SC 2007 Embedding Math

39. Eight Steps for Creating an Authentic Integrated Project Unit • Develop a summative unit exam to assess students’ understanding of mathematics concepts, skills and procedures used in the project. SC 2007 Embedding Math

40. Create summative paper and pencil assessment exams. • Released NAEP items • Assess learning through performance-based assessments ANDusing test items found in college placement exams and state level accountability tests SC 2007 Embedding Math

41. Seven Elements for Teaching Mathematics Lessons for AIP • Introduce the CTE lesson (CT teacher) • Assess students’ math awareness(CT teacher) • Work through embedded example(CT teacher) • Work through traditional math examples (math teacher) • Work through related, contextual examples (CT/math teacher) • Students demonstrate understanding(CT /math) • Formal assessment (CT/math) SC 2007 Embedding Math

42. Element 1:Introduce the CT Lesson • Explain the CT lesson • Identify, discuss, point out and pull out the mathematics embedded in the CT lesson. SC 2007 Embedding Math

43. 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. SC 2007 Embedding Math

44. 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. SC 2007 Embedding Math

45. 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. SC 2007 Embedding Math

46. Element 5: Work through TraditionalMath 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. SC 2007 Embedding Math

47. 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. SC 2007 Embedding Math

48. Element 7:Formal Assessment • Include mathematics questions in formal assessments. For example, • CT unit exams. • CT project assessments. SC 2007 Embedding Math

49. Core Principles for Math-in-CT • Develop and sustain a community of practice • Begin with the CT curriculum and not with the math curriculum • Understand math as essential workplace skill • Maximize the math in CT curricula • CT teachers are teachers of “math-in-CT” NOT math teachers SC 2007 Embedding Math

50. Core Principles for Math-in-CT • A powerful, evidence based strategy for improving math skills of students; • A way but notTHE 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 SC 2007 Embedding Math