Mathematics & Career
Readiness in Policy and Practice
Hawaii 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
Finance
Accounting
Intro to
Business &
Marketing
Accounting
I
Accounting II
AP Statistics
Remainder of
Postsecondary
Requirements
Mechatronics
Principles of
Manufacturing
Principles of
Engineering
Mechatronics
I
Capstone/
Internship
Remainder of
Postsecondary
Requirements
Advanced
Manufacturing
Greater Flexibility for Schools/Districts
General Education Courses
Work-Based Learning Opportunities
Early Postsecondary Opportunities (Statewide/Local Dual Credit, Dual Enrollment, AP, etc)
Level 5
Level 6
Arizona
Students who complete following CTE pathways earn
4th credit of required mathematics:
1.
2.
3.
4.
Accounting and Related
Services
Architectural Drafting
Automotive Technologies
Business Management and
Administrative Services
5.
6.
7.
8.
9.
Construction Technologies
Engineering Sciences
Mechanical Drafting
Software Development
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, interorganizational 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:
Standards for Mathematical Practice
Content Standards
1.
Make sense of problems and
persevere in solving them
• F-BF Build a function that models a relationship
between two quantities.
2.
Reason abstractly and
quantitatively
• G-MG Apply geometric concepts in modeling situations.
3.
Construct viable arguments and
critique the reasoning of others
• S-CP Understand independence and conditional
probability and use them to interpret data.
• S-IC Understand and evaluate random processes
underlying statistical experiments.
4.
Model with mathematics
5.
Use appropriate tools
strategically
6.
Attend to precision
• S-ID Summarize, represent, and interpret data on a
single count or measurement variable.
7.
Look for and make use of
structure
• S-ID Summarize, represent, and interpret data on two
categorical and quantitative variables.
8.
Look for and express regularity
in repeated reasoning
• S-ID Interpret linear models.
• S-IC Make inferences and justify conclusions from
sample surveys, experiments, and observational studies.
• S-MD Use probability to evaluate outcomes of decisions.
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
equation𝑷 𝒕 = 𝟏𝟎𝟎/(𝟏 + 𝒆(𝟑−𝒕) ) 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 Blosveren
Associate 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-classroomtasks