A Little History 1957--- Sputnik (Space Race, We Won) 1983 --- A Nation At Risk (Perceived Shortage Of Scientists, Technicians, Engineers And Mathematicians) 1983 To Now --- A Hue And Cry For Higher Academic Standards In Math And Science Decreasing CTE (Voced) Programs In Many States, Lesser Time On Task
Voc Ed/CTE Responses 1984 --- Principles Of Technology 1987 --- Applied Communication 1987 --- Applied Mathematics 1990 --- Applied Chemistry/Biology 1990s On --- VTE/CTE Program Analysis To ID Academic Content 1990s On --- “Integration” Of Academics And Voc Ed – Many Curricular Approaches 1980s To Date - Academics UP, CTE Down Snyder Taxonomy
The “Math Myth” An Assumption That All Jobs Need Advanced Mathematics Equal To Four Year College Entry Vast Majority Of Jobs, Some 90%, Require No More Than Basic Algebra (X=AB) ACT Math Analysis In Work Keys Development And Tests
Arizona Standards State Academic Content Standards Established At Four Levels CTE Program Standards Industry Validated And Occupational Specific (Broadly Defined) Includes Measurement Criteria For Each Standard
Arizona Academic Standards Established at Four Levels (Estimation Example) Grade 7 Make estimates appropriate to a given situation.. Grade 8 Make estimates appropriate to a given situation. High School (Grade 9-10) Use estimation to determine the reasonableness of a solution. Determine which measure of center is most appropriate in a given situation and explain why.. College and Work Readiness (Grades 11 and 12) Recognize the limitations of estimations by assessing the amount of error resulting from estimation and determining whether the error is within acceptable tolerance limits.
Arizona Academic Standards Established at Four Levels (Data Analysis Example) Grade 7 Identify outliers and determine their effect on mean, median, mode, and range. Grade 8 Describe how summary statistics relate to the shape of the distribution. High School (Grade 9-10) Determine which measure of center is most appropriate in a given situation and explain why. College and Work Readiness (Grades 11 and 12) Compute and explain summary statistics for distributions of data including measures of center and spread, including variance and standard deviation. Compute and explain summary statistics for distributions of data including measures of center and spread, including variance and standard deviation.
Arizona CTE Sample Standard STANDARD 8.0 - DEMONSTRATE DESIGN DRAFTING CONCEPTS AS RELATED TO ARCHITECTURAL DESIGN USING CADD/VDCM SYSTEMS 8.1 Draft a floor plan from preliminary sketch 8.2 Draft a foundation/basement foundation plan etc
Arizona Analysis Process Concerned With Rigor NOT “What Math Do You Think Is In This CTE Program”? An Analyses Team For Each Cte Program Two Math Experts Five To Seven CTE Program Instructors Analyze Each Measurement Criteria For High School Math Required To Teach Or Perform EACH Measurement Criteria CTE Instructors Must Be Able To Convince Math Teachers That Math Is Truly Used
Sample Analysis Product CTE Automotive Tech Measurement Criteria --- Check continuity and measure resistance in electrical/electronic circuits and components using an ohmmeter; determine necessary action. Math Academic Content Applied --- Strand 1: Number and Operations, Concept 3: Estimation, High School Level PO 1: Determine rational approximations of irrational numbers. PO 2: Use estimation to determine the reasonableness of a solution. PO 3: Determine when an estimate is more appropriate than an exact answer. Strand 1: Number and Operations, Concept 1: Estimation, College Work Readiness Level PO 1 Recognize the limitations of estimations by assessing the amount of error resulting from estimation and determining whether the error is within acceptable tolerance limits.
Sample Analysis Product CTE Automotive Tech Measurement Criteria Check continuity and measure resistance in electrical/electronic circuits and components using an ohmmeter; determine necessary action. Math -- Strand 2: Data Analysis, Probability, and Discrete Mathematics, Concept 1: Data Analysis (Statistics), High School Level PO 1: Draw inferences about data sets from lists, tables, matrices, and plots. PO 2: Organize collected data into an appropriate graphical representation with or without technology. PO 3: Display data, including paired data, as lists, tables, matrices, and plots with or without technology; make predictions and observations about patterns or departures from patterns. PO 4: Make inferences by comparing data sets using one or more summary statistics. PO 6: Evaluate the reasonableness of conclusions drawn from data analysis. PO 7: Identify mis-presentations and distortions in displays of data and explain why they are misrepresentations or distortions. PO 8: Design simple experiments or investigations and collect data to answer questions. Math -- Strand 2: Data Analysis, Probability, and Discreet Mathematics, Concept 1: Data Analysis (Statistics), College Work Readiness Level PO 1: Explore different forms of complex numbers; determine if the properties of the real number system extend to complex numbers and matrices. PO 5: Identify misleading uses of data and explain why they are misleading. PO 9: Use matrices to organize and represent data.
Programs Analyzed to Date Accounting Automotive Tech Carpentry Construction Cabinetmaking Culinary Drafting (Architectural) Drafting (Electrical) Drafting (Mechanical) Financial Services
Academic Skill Analysis Result Disappointing!! Limited Az Hs Math Credit Skills (Algebra Or Greater) Required To Learn Or Perform Standards AB=X (One Unknown) Is Generally The Most Complex Required, Ohms Law Good Example Automotive Tech Is The Exception Results Can Be Seen At AZ DOE Website http://www.ade.state.az.us/cte/CurriculumFra mework/AcademicMathCrosswalk/
AZ State Board HS Graduation Rule 4. Local school district governing boards or charter schools may grant to career and technical education and vocational education program completers a maximum of five and one-half credits to be used toward the Board English, mathematics, science, and economics credit requirements for graduation, subject to the following restrictions: a. The (Local) Board has approved the career and technical education and vocational education program for equivalent credit to be used toward the Board English, mathematics, science, and economics credit requirements for graduation. (Other possibilities exist, but do not seem to be attainable)
AZ State Board HS Graduation Rule 5. Competency requirements. a. The awarding of a credit toward the completion of high school graduation requirements shall be based on the successful completion of State Board-adopted academic standards for subject areas … b. The determination and verification of student accomplishment and performance shall be the responsibility of the subject area teacher.
NCLB – “Highly Qualified” Qualification Exam Exists For Non-majors … However, Requires BA/BS, Difficult Exam Regional Accrediting Agencies Require Teachers To Be Certified In Areas Of Instruction So, What Is To Be Done? Two Major Roadblocks
Promising Practices “Teacher of Record” Not new, but seems to hold the most promise as a method of granting math credit for multiple CTE programs with one Certified Math Instructor Kentucky Master teacher develops videos, CTE instructor shows them in class, tests are given on content Michigan Has established guidelines, see --- http://www.michigan.gov/documents/mde/Credit_in _CTE_and_Integrated_Guidelines_199363_7.pdf
Other States Activities Virginia Granting Physics credit for Principles of Technology Wyoming Not addressing the credit issue South Carolina Not addressing the credit issue now, but have legislation requiring all students to have a career major, and most CMs are related to CTE programs. This minimizes the impact of increased HS graduation requirements on CTE program numbers. Kansas Teams working on math in CTE enhancement Iowa Working on specific math lessons related to CTE content
Promising Practices Arizona We will continue Identifying academic skills as a model for local district use in establishing CTE credit Pima JTED (Joint Technical Education District) has a grant to use teams of academic and CTE teachers to develop curriculum that focuses on math content in CTE programs Pima JTED plans to use Michigan guidelines as a model for granting credit We are exploring the use of the “Teacher of Record” concept to address the “highly qualified” issue
A Possible Answer ACT WorkKeys Level 5 academics are deemed by ACT as equivalent of the ACT Mathematics Test College Readiness Standards (20-23 Range) So, analyze CTE programs using the ACT Level 5 Academic Content, or the ACT 20-23 Math standards http://www.act.org/research/policymak ers/pdf/ReadinessBrief.pdf http://www.act.org/research/policymak ers/pdf/ReadinessBrief.pdf
A Caveat As Niall Ferguson has put it, 'Those whom the gods want to destroy they first teach math.' Vanity Fair, December 2008, “Wall Street Lays Another Egg” He concluded that too many people were good at math, not history
Thank You!! For further information: CTE Web site http://www.ade.state.az.us/cte/Curricul umFramework/AcademicMathCrosswalk Charles Losh, Ph.D. Workforce Education and Development Office Arizona State University email@example.com or firstname.lastname@example.org 602.705.1309
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