Get Real Integrating RealWorld, HighLevel Academic Content into Career Classes

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Get Real! Integrating Real-World, High-Level
Academic Content into Career Classes

• Ivy C. Alford
• SREB/High Schools That Work

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Objectives of Session

• Review current strategies to integrate academic
  content into CT classes
• Introduce an 8 step process for integrating
  mathematics
• Review current structures and procedures to
  assist teachers with integration efforts

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Why change?
For more information www.astd.org
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Students can do basics
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347 453
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But Students Cannot Solve Problems
Mrs. Smiths class has read 174 books and
Mr. Jones class has read 90 books. How
many more books do they need to read to reach
the goal of reading 575 books?
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The Importance of Workplace Everyday Mathematics

• Estimation
• Trigonometry
• Spreadsheets
• Algebra
• Teaching math via workplace everyday problems
  can make math more meaningful for all students.

Source www.nap.edu/readingroom/books/hs_math/ch4.
html
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A Call for Results

• No Child Left Behind
• New Carl D. Perkins Requirements
• ACADEMIC VALUE ADDED
• HIGH-WAGE, HIGH-DEMAND CAREERS

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Percent of Students Stating that their CT
teachers emphasized
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Additional data points

• 47 percent stated that they NEVER completed a
  joint project that used CTE and math skills.
• 23 percent reported that they use mathematics to
  complete challenging assignments in CTE classes
  weekly.

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How do CTE students score?
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Percentage of Students Scoring at Various
Proficiency Levels
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The Challenges

• High-level mathematics needed
• Low-level mathematics assigned
• Limited Use of Literacy in Classrooms
• Different terminology than mathematics classes
• Limited opportunities for teachers to work
  together

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Technical Numeracy

• Numeracy is to math as literacy is to language
• A means of communicating
• A gatekeeper to many desirable work roles
• The ability to apply mathematical knowledge,
  skills and reasoning to a career field

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How Do We Start?

• Brainstorm all math concepts that are associated
  with your class
• Brainstorm how YOU use mathematics in your
  everyday life?

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What are the state math standards?

• Algebra
• Indicator 1 Use procedures to transform
  algebraic expressions.
• Indicator 2 Use a variety of algebraic concepts
  and methods to solve equations and inequalities.
• Indicator 3 Interpret and develop mathematical
  models.
• Indicator 4 Describe and use properties and
  behaviors of relations, functions, and inverses.

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What are the state math standards?

• Geometry
• Indicator 1 Use deductive and inductive
  reasoning to recognize and apply properties of
  geometric figures.
• Indicator 2 Use properties of geometric figures
  to solve problems from a variety of perspectives.

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What are the state math standards?

• Measurement
• Indicator 1 Apply measurement concepts in
  practical applications.

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What are the state math standards?

• Number Sense
• Indicator 1 Analyze the structural
  characteristics of the real number system and its
  various subsystems. Analyze the concept of value,
  magnitude, and relative magnitude of real
  numbers.
• Indicator 2 Apply operations within the set of
  real numbers.
• Indicator 3 Develop conjectures, predictions, or
  estimations to solve problems and verify or
  justify the results.

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What are the state math standards?

• Statistics and Probability
• Indicator 1 Use statistical models to gather,
  analyze, and display data to draw conclusions.
• Indicator 2 Apply the concepts of probability to
  predict events/outcomes and solve problems.

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Parabola Instruction Problem

• Vertex (-b/2a, f(-b/2a))
• The parabola opens downward if a is negative,
  giving the maximum value.
• The parabola opens upward if a is positive,
  giving the minimum value.
• Calculate the vertex and graph the following
  function f(x) -4x2 400x

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Parabola Solution

• f(x) -4x2 400x
• x (-400)/(2 -4)
• x (-400)/(-8)
• x 50
• f(x) -4(50)2 400(50)
• f(x) -10,000 20,000
• f(x) 10,000

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Parabola Graph
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Parabola Business

• The number of hours spent on advertising directly
  relates to the amount of revenue. A company
  advertising computer printers has found that when
  the advertising is p hours, the revenue R (in
  dollars) is r(p) -4p2 400p
• Calculate and graph the maximum revenue using the
  vertex of a parabola method.

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Parabola Manufacturing

• A manufacturer of suitcases has found that demand
  for the product varies directly with the price.
  When the unit price is p dollars, the demand d
  is d(p) -4p2 400p
• Calculate and graph the maximum demand using the
  vertex of a parabola method.

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Parabola Health

• A hospital monitoring contractions for women in
  labor has found that the intensity of
  contractions varies directly with the duration.
  When the duration is d seconds, the contraction
  level is c(d) -d2 64d
• Calculate and graph the maximum contraction level
  using the vertex of a parabola method.

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Parabola Agriculture

• A farmer with 2000 meters of fencing wants to
  enclose a rectangular lot that borders on a
  river. If the farmer does not fence the side
  along the river, what is the largest area that
  can be enclosed?

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Parabola Construction

• A Norman window has the shape of a rectangle
  surmounted by a semicircle of diameter equal to
  the width of the rectangle. If the perimeter of
  the window is 20 feet, what dimensions will admit
  the most light (maximize the area)?

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• What standards can you emphasize in your classes?

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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.

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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

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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.

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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.

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Eight Steps for Creating an Authentic Integrated
Project Unit

• 2. Identify the embedded mathematics standards
  that can be taught through the project.

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• CT teachers explain project objectives so that
  mathematics teachers can help discover the
  embedded mathematics.
• Tools to help with this processSchool/district
  mathematics pacing guides
• State math standards

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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.

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• 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

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15 Literacy Strategies Any Teacher Can Use

• Admit slips
• Exit slips
• Double entry or two-column notes
• ReQuest
• Interactive CLOZE
• Cubing
• Open-response questions A KEY

Source HSTW Literacy Guide
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• KWL charts
• Metaphorical thinking
• Jigsaw reading
• Paired reading
• Graphic organizers
• GIST
• WordSplash/Capsule vocabulary
• RAFT

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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

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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.

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• 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.

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• 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
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What does varying levels mean?

• Basic Below grade level
• Proficient At grade level
• Advanced Above grade level
• Use your SD mathematics resources

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Where can we find good examplesof assessment
items?

• Released NAEP items
• http//nces.ed.gov/nationsreportcard/nde
• http//nces.ed.gov/nationsreportcard/itmrls/start
  search.asp
• State accountability tests-released items
• SkillsUSA test items
• http//skillsusa.org/compete/math.shtml
• Textbooks (enrichment sections)

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Team Prepares Assessment

• Examine resources for pre-assessment
• Select items suitable for the planned unit.

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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.

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• Two targets 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.

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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.

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Business Math

• Order of precedence
• Chart
• Spreadsheet
• Formula
• Pie chart
• Cell
• - multiplication
• Points (desktop publishing)
• Grids in a spreadsheet

• Order of operations
• Graph
• Table (chart of values)
• Equation
• Circle graph
• XY coordinate
• Dot multiplication
• Inch
• Array

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Emphasis 2 Engaging Instructional Strategies

• Cooperative learning
• Project-based learning
• Socratic method
• Anticipation guides
• Videos
• Readings
• Teacher Demonstrations

• Technology integration
• Graphing calculators
• CBLs
• Excel
• Literacy Strategies
• Use of manipulatives
• Multi-intelligences approach
• Practice Problems

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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.

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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.

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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.

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• 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

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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.

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• 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

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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

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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 dont understand

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• 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?

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Where Can I Get Help?

• HSTW trainer can provide state, district and/or
  school site workshops for teaching embedded
  mathematics
• National workshops planned on March 13-14, in
  Atlanta

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For more information, contactIvy Alford or
Leslie Carsonivy.alford_at_sreb.orgleslie.carson
_at_sreb.org
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Check Out Those Resources!
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Resources to Support Mathematics Integration

• For additional ideas visit the American Diploma
  Project Website.
• Core Subject Area Benchmarks
• Sample Workplace Tasks
• http//www.achieve.org/
• (select For Full Report on ADP)
• ACT EPAS Standards (act.org)

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Math Resources

• http//www.learner.org/exhibits/dailymath/index.ht
  ml From the Annenberg/CPB Project Exhibits
  Collection, the site discusses how math applies
  to daily life. (Topics include- Playing to Win,
  Savings and Credit, Population Growth, Home
  Decorating, Cooking by Numbers, The Universal
  Language)
• http//www.nsa.gov/teachers/teach00006.cfm
  Lesson plans for Elementary (Arithmetic, Data
  Analysis, Fractions, Geometry, and
  Probability/Patterns), Middle (Pre-Algebra,
  Algebra/Graphing/Statistics, Geometry, Number
  Theory, Interdisciplinary), and High School
  (Pre-Algebra, Algebra, Geometry, Trigonometry,
  Statistics, Pre-Calculus, Calculus, Internet,
  Science, Modeling) topics.

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Math Resources

• http//mathprojects.com/ The Math Projects
  Journal is dedicated to improving mathematics
  education by empowering teachers with innovative
  math lessons and ideas.
• http//education.ti.com/educationportal/activityex
  change/ActivitySearch.do?cidUS Texas
  Instruments lesson plans that correspond to the
  CBS series NUMB3RS for seasons 12.
• http//www.weallusematheveryday.com/tools/waumed/a
  ctivities_season3.htm CBS webpage with lesson
  plans for the current season (season 3)

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Math Resources

• http//www.bced.gov.bc.ca/careers/aa/lessons/math.
  htm Lessons developed by teachers of Applied
  Mathematics in British Columbia. These lessons
  are linked to specific occupations and encourage
  students to see where math is used in the real
  world. (Examples include the following
  occupations Firefighter, Lifeguard, Electrical
  Engineer, Event Planner, Vulcanologist, Roller
  Coaster Designer, Mechanical Drafter Designer,
  House Painter, Market Analyst, Computer Game
  Designer, Audiologist, Sportscaster, Animal
  Health Technologist, Golf Pro, Aerospace
  Engineer, and Piano Repair Technician)

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Math Resources

• http//www.micron.com/k12/math/index These
  real-world math problems were contributed by a
  variety of area businesses (in Idaho) and
  demonstrate the relevance of math in today's
  world. The intent of these lessons is to excite
  students about mathematics, to expose students to
  professions that employ mathematics, and to
  demonstrate the relevance of mathematics in
  solving real-world challenges. The lessons are
  organized by math strands (Numbers and Operations
  , Measurements, Algebra, Geometry, and Data
  Analysis and Probability) for easy searching.