Mathematics & Career Readiness in Policy and

PracticeHawaii P-20 Mathematics Summit

November 12, 2015

Agenda

• Defining Career Pathways/Programs of Study

• Integrating CTE and Mathematics Through Policy

• Integrating CTE and Mathematics Through Practice

The Not-so-Good News: There is no single “career readiness” target

The Good News: There are many ways to integrate math and CTE/career education

The Great News: You make integration happen

Career Pathways & Programs of Study

Definitions

– Career Cluster– organizer of knowledge and skills needed by a broad industry

– Career Pathway – organizer of knowledge and skills statements shared by professions

• Hawai’i: Six Career Pathways (Clusters)

– Program of Study – sequence of instruction that prepares individuals for careers of their choice

Programs of Study

• A coordinated, non-duplicative progression of courses that align secondary education with postsecondary education and include challenging academic and CTE content to adequately prepare students to succeed in postsecondary education,

• Offer the opportunity, where appropriate, for secondary students to acquire postsecondary credits, and 

• Lead to an industry-recognized credential or certificate at the postsecondary level, or an associate or baccalaureate degree.

Programs of Study in Hawai’i

• Spans a minimum of two years at the secondary level and extends to postsecondary education

• Students completing a high school Program of Study would have mastered all specific Career Pathway Core, Cluster, and academic course standards

• Dual Credit Articulated Program of Study

• CTE Honors Diploma

• 20+ organizations created common definition of career readiness

• Career Readiness requires adaptability and a commitment to lifelong learning, along with mastery of key knowledge, skills and dispositions that vary from one career to another and change over time as a person progresses along a developmental continuum.

• These include:

– Academic Knowledge and Skills,

– Technical Knowledge and Skills, and

– Employability Knowledge, Skills and Dispositions, which are inter-dependent and mutually reinforcing

Math Across Occupations

• 955 occupations (O*NET)

• Of all jobs, 437 (46%) place a level of importance of using mathematics to solve problems

• 875 (92%) place a level of importance of being able to identify complex problems and develop and evaluate solutions

• 955 occupations (O*NET) – 60% of which require less than 4-year degree

• Of those, 175 (31%) place a level of importance of using mathematics to solve problems

• 497 (87%) place a level of importance of being able to identify complex problems and develop and evaluate solutions

Integrating CTE and Mathematics Through Policy

Policy Approaches

• College/career planning (student learning plans)

• Credit equivalency/double dipping

• Contextualized mathematics courses / Augmented CTE courses

• Competency-based pathways

• Teacher certification (dual certification, integrated courses)

Tennessee Programs of Study

Career Cluster

Program of Study Level 1 Level 2 Level 3 Level 4 Level 5 Level 6

Finance AccountingIntro to

Business & Marketing

Accounting I

Accounting II AP StatisticsRemainder of

Postsecondary Requirements

Advanced Manufacturing

Mechatronics

Principles of Manufacturin

g

Principles of

Engineering

Mechatronics I

Capstone/ Internship

Remainder of Postsecondary Requirements

Greater Flexibility for Schools/DistrictsGeneral Education Courses Work-Based Learning OpportunitiesEarly Postsecondary Opportunities (Statewide/Local Dual Credit, Dual Enrollment, AP, etc)

Arizona

Students who complete following CTE pathways earn 4th credit of required mathematics:

1. Accounting and Related Services

2. Architectural Drafting 3. Automotive Technologies 4. Business Management

and Administrative Services

5. Construction Technologies6. Engineering Sciences 7. Mechanical Drafting 8. Software Development9. Welding Technologies

Arizona

• Local governing boards submit programs for approval to State Board of Education

• Programs must:

– Undergo evidence-based curriculum development/review process

– Meet all elements of approved CTE programs

• Extensive crosswalks, model lesson plans

California: UC Curriculum Integration Institute

• Statewide postsecondary admissions requirements (A-G)

• Statewide submission process with clear criteria/ approval processes

– Joint CA Dept of Ed / UC System effort

– 12,000+ approved CTE courses meet A-G admissions requirements, % also meet academic course requirement

• University of California Curriculum Integration

– Institutes & Teacher Exchange

Integrating CTE and Mathematics Through Practice

www.achieve.org/Skills-CCSS

Deeper Learning Standards

“Harness the deeper learning skills of critical thinking, problem solving, effective communication, collaboration, and learning how to

learn to help students develop a strong foundation in traditional academic subjects.”

Master Core Academic Content

Engage in Expanding the Structure of Knowledge

Think Critically and Solve Complex Problems

Communicate Effectively

Work Collaboratively

Learn How to Learn

Career Cluster Essential Skill Statements

“The knowledge and skills that are essential in any employment situation…They are the starting point and should be contextualized within any pathway and plan

of study.”1. ACADEMIC FOUNDATIONS: Achieve additional academic knowledge and skills required to

pursue the full range of career and postsecondary education opportunities within a career cluster.

2. COMMUNICATIONS: Use oral and written communication skills in creating, expressing and interpreting information and ideas including technical terminology and information.

3. PROBLEM-SOLVING AND CRITICAL THINKING: Solve problems using critical thinking skills (analyze, synthesize, and evaluate) independently and in teams. Solve problems using creativity and innovation.

4. INFORMATION TECHNOLOGY APPLICATIONS: Use information technology tools specific to the career cluster to access, manage, integrate, and create information. Work Collaboratively

5. SYSTEMS: Understand roles within teams, work units, departments, organizations, inter-organizational systems, and the larger environment. Identify how key organizational systems affect organizational performance and the quality of products and services. Understand global context of industries and careers.

Career Cluster Essential Skill Statements Cont.

6. SAFETY, HEALTH AND ENVIRONMENTAL: Understand the importance of health, safety, and environmental management systems in organizations and their importance to organizational performance and regulatory compliance. Follow organizational policies and procedures and contribute to continuous improvement in performance and compliance.

7. LEADERSHIP AND TEAMWORK: Use leadership and teamwork skills in collaborating with others to accomplish organizational goals and objectives.

8. ETHICS AND LEGAL RESPONSIBILITIES: Know and understand the importance of professional ethics and legal responsibilities

9. EMPLOYABILITY AND CAREER DEVELOPMENT: Know and understand the importance of employability skills. Explore, plan, and effectively manage careers. Know and understand the importance of entrepreneurship skills.

10. TECHNICAL SKILLS: Use of technical knowledge and skills required to pursue careers in all career cluster, including knowledge of design, operation, and maintenance of technological systems critical to the career cluster.

KEY FINDING 1: Skills Strongly/Largely Reflected in the CCSS

Problem solving skills (e.g., analyzing information, evaluating solutions)

Reasoning skills (e.g., critical thinking, forming arguments, using logic)

The application/extension of core content in various situations (e.g., modeling)

Use of data (e.g., evaluation, understanding structure, interpretation)

Communications skills (e.g., speaking, listening, messaging)

Teamwork/group work skills (e.g., collaboration, goal setting)

Research skills (e.g., gathering and analyzing information and sources)

Time management skills (developing goals, prioritizing tasks)

Use of technology (e.g., email, internet)

Examples of Skills Strongly/Largely Reflected in CCSS in Mathematics include:

Content Standards• F-BF Build a function that models a relationship

between two quantities.• G-MG Apply geometric concepts in modeling situations.• S-CP Understand independence and conditional

probability and use them to interpret data.• S-IC Understand and evaluate random processes

underlying statistical experiments.• S-IC Make inferences and justify conclusions from

sample surveys, experiments, and observational studies.

• S-ID Summarize, represent, and interpret data on a single count or measurement variable.

• S-ID Summarize, represent, and interpret data on two categorical and quantitative variables.

• S-ID Interpret linear models.• S-MD Use probability to evaluate outcomes of

decisions.

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

Integration in the Classroom

• Professional development

• Instructional resources

• Planning time/commitment

• Enabling policies

Practice Approaches

• Math-in-CTE (enhance CTE courses)

• Interdisciplinary projects, experiences (capstones, teacher externships)

• Professional learning communities

CCSS/CTE Instructional Tasks Pilot

• Facilitate cross-disciplinary discussions about the Common Core State Standards and CTE instruction.

• Provide strategies for mathematics educators to integrate real-world examples and exercises into classroom instruction that is aligned to the CCSS.

• Provide strategies for CTE educators to inject rigorous mathematics into their courses.

• Lead to the development of instructional tasks that were well aligned to the CCSS in math and state-selected CTE expectations.

• Support existing integration/alignment activities already underway in a state

• Develop a protocol any state or district leader could use to ensure the alignment and authenticity of their existing or new instructional tasks.

CCSS/CTE Instructional Tasks Protocol

• Step 1. Read the task thoroughly.

• Step 2. Compare your work with the answer key/rubric and other instructional support materials and/or with the work of colleagues.

• Step 3. Identify the content and performances required to complete the task.

• Step 4. Compare task performances to the CCSS Standards for Mathematical Practice (Rate Alignment 0-3, describe strengths/weaknesses of task with respect to each practice standard)

• Step 5. Compare task content and performances to the grade-level (grades 6-8) and high school CCSS (Rate Alignment 0-3, describe strengths/weaknesses of task with respect to each mathematics standard)

• Step 6. Compare task content and performances to the Knowledge and Skills statements that apply to the relevant Career Cluster/ Pathway. (Rate Alignment 0-3, describe strengths/weaknesses of task with respect to each knowledge/skill statement)

Sample Task from New Jersey: Spread of Disease

Disease can spread quickly in enclosed spaces, such as on an airplane. The spread of the flu is modeled by the equation where P (t) is the total number of passengers infected after t days of a trip on an airplane.

1. Estimate the initial number of people infected with the flu.

2. How fast is the flu spreading after 3 days?

3. When will the flu spread at its maximum rate? What is the maximum rate?

Adapted from http://yale.edu/ynhti/curriculum/units/2009/5/09.05.08.x.html

Sample Task from New Jersey: Spread of Disease

• How can the set up be improved?

• What exactly is it asking students to do?

• How authentic is it?

– Not a realistic prompt (who spends days on a plane?)

– Not anchored in solving a problem

– Only hit on two mathematical practices (perseverance/problem solving and mathematical modeling) when opportunity for more application

Final Task: Spread of Disease

Disease can spread quickly without the use of universal precautions. Suppose the spread of a direct contact disease in a stadium is modeled by the exponential equation P(t) = 10,000/(1 + e3-t) where P(t) is the total number of people infected after t hours. (Use the estimate for e (2.718) or the graphing calculator for e in your calculations.)

1. Estimate the initial number of people infected with the disease. Show how you found your answer.

2. Assuming the disease does not present symptoms for 24 hours, how many people will have been infected after 3 hours? Show how you found your answer.

3. What is the maximum number of people who can become infected? (Note: e(3-t) will approach 0 for very large values of t).

4. Explain why your answer for Question #3 is the maximum.

5. The stadium needs to warn its guests about a rapid disease spread if it affects over 800 people. After how many minutes should the stadium have had to inform its guests of the disease? Show how you found your answer.

6. Create a flyer/poster/pamphlet describing the chain(s) of infection for a typical contact disease, the mode(s) of prevention, and what your school can do to limit the spread of disease/pathogens. Research will be required to verify flyer information and statistics. (Materials could be shared/posted throughout school)

The Challenge

Getting on the same page

Making the time

Building trust

Questions?

Kate BlosverenAssociate Executive Director

National Association of State Directors of Career Technical Education Consortium

kblosveren@careertech.org

@KateRobynBlos

Resources

• Career Readiness Partnership Council: www.careerreadynow.org

• UC Curriculum Integration: http://ucci.ucop.edu/index.html

• Arizona’s CTE Embedded Academic Credit Project: www.azed.gov/career-technical-education/academic-standards/

• Understanding the Skills in the Common Core State Standards: www.achieve.org/Skills-CCSS

• Math-in-CTE: www.nrccte.org/professional-development/math-cte & http://www.ctemathlessons.com/

• CCSS-CTE Instructional Tasks: www.achieve.org/ccss-cte-classroom-tasks