Building Academic Skills in Context: Enhancing Mathematics Achievement through CTE Instruction

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Building Academic Skills in Context Enhancing
Mathematics Achievement through CTE Instruction

• Leslie Carson
• leslie.carson_at_sreb.org

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Welcome
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Group Norms and Housekeeping

• Group Norms
• Participate
• Ask questions of each other
• Work toward solutions

• Housekeeping
• Restrooms
• Breaks
• Lunch
• Punctuality

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Communities of Practice

• Offers the more powerful conceptual model for
  transforming schools
• (R. DuFour)
• Collaborative Teams
• Collective Inquiry
• Action, Orientation and Experimentation
• Continuous Improvement
• Results Orientation
• Lets form communities.

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The Power of Team Dynamics

• Instructions in planner
• 20 minutes to plan, practice
• I will act as timekeeper and give the start
  signal
• After the challenge, there are reflection
  questions to ponder
• GOAL Build the tallest free-standing structure

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Essential Questions

• Why is helping students understand math
  everyones job?
• What does math look like in the non-math
  classroom?
• How do math and CTE teachers support student
  understanding of math?

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At the turn of the 20th century, we were an
experience rich, information poor society.
Today we are an information rich experience poor
society. Dale Parnell
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Preparing our Students to be Successful
Mathematically

• Previously it was enough for our students to
  just be able to solve a given math problem such
  as
• What is 45 divided by 7?
• Reading off of a calculator, the answer is
  6.428571429

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The Good News Is..
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Did you know?2005 Skills Gap Report-National
Association of Manufacturers

• 84 of employers surveyed believe public schools
  are failing to prepare students for the
  workplace.
• The biggest deficiency is in areas of science and
  mathematics, noting that
• word problems seldom resemble real-world
  experiences
• mathematics teachers teach standard approaches
  (e.g. algebraic symbol manipulation) to the
  detriment of mathematical reasoning.
• too often students' mathematics experiences are
  characterized by repetition learning rather than
  problem solving

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Did you know?

• 1/3 of NASA employees were born on the Indian
  subcontinent
• The Visionarys Handbook 2000 Watts Wacker
  Jim Taylor w/Howard Means

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Did You Know?

• American Industry is spending nearly as much
  each year to educate their employees
  mathematically as is spent on mathematics
  education in public schools
• A selection from Numeracy by Lynn Arthur Steen

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Lynn Authur Steen, St. Olaf College

• Children learn to read and write not solely
  because of their language arts instruction in
  school, but equally because of the reinforcement
  provided by other school subjects, and by their
  environment at home. Where reading and writing
  are not reinforced at home, the progress of
  learning is much slower.

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Lynn Authur Steen, St. Olaf College

• (Mathematics) is rarely reinforced, neither in
  school nor at home. Parents, coaches, and
  teachers of other subjects seldom make the effort
  to engage children in activities that would use
  mathematical or statistical methods--perhaps
  because the adults themselves tend to avoid such
  methods.

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U.S. Ranked 24th out of 29 OECD Countries in
Mathematics
Organization for Economic Cooperation and
Development (OECD), PISA 2003
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How can we fix it?
"Somebody has to do something, and it's
just incredibly pathetic that it has to be us."

• Jerry Garcia of the Grateful Dead

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As any wise old farmer can tell you, you dont
fatten your lambs simply by weighing them
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Common Misconceptions about Learners Sue E.
Berryman and Thomas Bailey, The Double Helix of
Education and the Economy (New York Institute on
Education and The Economy, Columbia University,
1992), 45-68

• People predictably transfer learning from one
  situation to another.
• Learners are passive receivers of wisdom-empty
  vessels into which knowledge is poured.
• Learning is the strengthening of bonds between
  stimuli and correct responses.
• What matters is getting the right answer.
• Skills and knowledge, to be transferable to new
  situations, should be acquired independent of the
  contexts of uses.

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Cognitive Science Questions about the Teaching
and Learning Process

• How do the human mind and body work in their
  learning capacity?
• How can an understanding of the mind/bodys way
  of learning be used in educational settings?

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A
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How Do New Pieces of Information Fit?
Learning often occurs only when students process
new information or knowledge in such a way that
it makes sense in their frame of reference
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Students can increase high level mathematics
understanding through experiences.
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And by Collaborating with Their Peers.
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Learning in Context Involves

• Linking new information to students familiar
  frame of reference
• Hands on activities combined with teacher support
  to allow students to discover new understandings
• Application of new knowledge to real world
  situations
• Working in collaborative groups to solve problems
• Transfer understanding to new situations and
  problems

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Why is relevancy important?

• Example Learning a Code

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A

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Now

• Spell the word FACE in Code.
• Lets see how you did!

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a
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Algebra students feel the same way about what
they learn in algebra. The out of context codes
for letters make just as much sense to them as
using x and y as variables.
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Traditional mathematics education presents the
concepts first and applications second
This logical approach is successful for a
limited segment of abstract thinkers in our
student population. Many students have difficulty
assimilating abstract theories. These students
learn from educational programs that emphasize
hands on learning. They need to experience it.
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Learning Mathematics should be based on
understanding concepts and on doing mathematics,
not on memorizing rote procedures
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Why Should CTE Teachers Care About Mathematics?

• NCLB / AYP
• Students indicate they do not like mathematics
  because they do not see the use for it. CTE
  courses fill that need.
• CTE Teachers can provide the relevance for
  motivation and the frame of reference so that CTE
  students value mathematics.
• The CTE classroom also provides the environment
  where students can develop high level math skills
• 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.

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CTE Classrooms Provide the Perfect Learning
Environment

• The purpose of Perkins IV- The purpose of this
  Act is to
• develop more fully the academic and career and
  technical skills of secondary
• education students and postsecondary education
  students who elect to enroll in
• career and technical education programs, By
• 1st of 7 building on the efforts of States and
  localities to develop challenging academic and
  technical standards and to assist students in
  meeting such standards, including preparation for
  high skill, high wage, or high demand occupations
  in current or emerging professions
• 2nd of 7 promoting the development of services
  and activities that integrate rigorous and
  challenging academic and career and technical
  instruction, and that link secondary education
  and postsecondary education for participating
  career and technical education students

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Did You Know?

• Daggett, 2005
• Studies have shown that students understand and
  retain knowledge best when they have applied it
  in a practical, relevant setting.
• According to Daggett, at the high school level,
  CTE programs provide the most effective learning
  opportunities.
• Not only are students applying skills and
  knowledge to real-world situations in their CTE
  programs, but also they are drawing on knowledge
  learned in their core subjects.

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Often, mathematical and CTE skills are chunked,
making transfer to the mathematics classroom and
standardized tests difficult
Pythagorean Theorem?
3-4-5 Angle?
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Often the mathematics in CTE is bypassed or
minimized by teaching students shortcuts.

• CTE students often learn shortcuts to bypass or
  memorize mathematical processes. CTE courses can
  be used to create teachable moments for
  understanding mathematics.

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Reading, Mathematics, and Science HSTW Scores for
Students
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CTE Programs Provide Focus Foundation
Context
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Why Is It Important That CTE And Academics Work
Together?

• Example Picture Recall

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We bring different pieces of information to the
team!
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Team Member Roles

• Math Teachers
• Collaborate to find and emphasize embedded math
  in CTE.
• CTE Teachers
• Collaborate to provide relevancy in Academics.
• CTE and Math Teachers
• Consult with each other to implement successful
  instructional strategies.

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Important to remember

• CTE teachers should introduce the CTE concepts
  first and then emphasize the math concepts
• Mathematics teachers should introduce the math
  concepts first and then emphasize the CTE
  connections to provide relevancy

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The teaming of math teachers and CTE teachers
merges context and content.

• Historically, this has not happened naturally.
  There must be a concentrated effort.

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What Can Mathematics and CTE teachers do?

• Implement authentic anchor projects that become
  places where students use mathematics
• Require students to solve authentic adult-like
  problems
• Have students use tools of the trade to complete
  tasks

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Good reasons for integration

• Integration is how people work in the real world.
• Academic and CTE teachers expand their repertoire
  of teaching strategies.
• Enhances student motivation.
• Enhances student career planning.
• Promotes professionalism among teachers.
• Improves academic achievement.

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What is integrated embedded CTE learning?

• NOT inserting mathematics in the CTE curriculum
• Is unwrapping embedded mathematics in the CTE
  Authentic Anchor Projects students complete
• NOT turning CTE teachers into mathematics
  teachers
• Is looking at how the mathematics can be
  emphasized, made more rigorous, and academic
  language included in the projects and problems
  CTE teachers teach.

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What is Authentic Academic Learning?

• Not setting aside the math curriculum
• Is providing real life scenarios and projects for
  math concepts
• Not turning math teachers into CTE teachers
• Is bridging the language of math to the language
  of CTE and providing opportunities to practice
  authentic problem solving and application

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Important to remember

• CTE teachers should introduce the CTE concepts
  first and then emphasize the math concepts and
  necessary components
• Mathematics teachers should introduce the math
  concepts first and then emphasize the CTE
  connections to provide relevancy

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SREBs Criteria for Authentic Anchor Project
Units
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Overview Eight Steps to Develop Authentic
Integrated Projects
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Seven Elements for teaching mathematics through
authentic integrated project units

• CTE teacher introduces CTE lesson.
• CTE teacher assesses students math awareness.
• CTE teacher works through embedded example.
• Math teachers work through traditional examples.
• CTE and math teachers work through related,
  contextual examples.
• Students demonstrate understanding in CTE and
  math classes.
• CTE and math teachers formally assess students.

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Step One Identify a major project with embedded
mathematics content.

1. In your teams, CTE teachers share a major project
   they will complete with students. The project
   selected should be rich in embedded mathematics.
2. Break down into the activities that make up the
   project and consider making adjustments that add
   math rigor.
3. Identify the CTE concepts in each activity.
4. Identify the CTE vocabulary.

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Is the Math in CTE Courses the Same as that in
Academic Math Courses?
Usually the math is the same but the terminology
is often different.
Pitch or slope?
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Bridging the Gap Between Academic and CTE
Vocabulary

• We often use
• Different words for the same concept (pitch,
  slope, grade, incline, steepness, elevation)
• Different meanings for the same word
• Directions
• Before going any further, you will need a piece
  of paper and something to write with.
• You will see four words. Write each word on your
  paper as you see it and then write the first
  definition of that word that comes to mind.

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Define

• AXIS
• SOLUTION
• RANGE
• YARD

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AXIS

• Science the second vertebra in the neck, which
  acts as the pivot on which the head and first
  vertebra turn
• Agriculture central part of plant the main part
  of a plant, usually the stem and the root, from
  which all subsidiary parts develop
• Geometry one of two or more lines on which
  coordinates are measured. Often on a graph two
  axes form its left and lower margins.

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RANGE

• Transportation distance traveled without
  refueling the farthest distance that a vehicle
  or aircraft can travel without refueling.
• Agriculture open land for grazing farm
  animals a large area of open land on which farm
  animals can graze. 
• Construction north-south strip of townships a
  north-south strip of townships six miles square
  and numbered east and west from a meridian in a
  U.S. public land survey.

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RANGE Continued

• Mathematics set of values the set of values
  that can be taken by a function or a variable.
• Statistics extent of frequency distribution the
  difference between the smallest and the largest
  value in a frequency distribution.

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SOLUTION

• Science fluid with substance dissolved in it a
  substance consisting of two or more substances
  mixed together and uniformly dispersed, most
  commonly the result of dissolving a solid, fluid,
  or gas in a liquid. It is also, however, possible
  to form a solution by dissolving a gas or solid
  in a solid or one gas in another gas.
• Mathematics value satisfying an equation a
  value for a variable that satisfies an equation.

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YARD

• Business Slang for one billion dollars. Used
  particularly in currency trading, e.g. for
  Japanese yen since on billion yen only equals
  approximately US10 million. It is clearer to
  say, " I'm a buyer of a yard of yen," than to
  say, "I'm a buyer of a billion yen," which could
  be misheard as, "I'm a buyer of a million yen.
• Agriculture livestock enclosure an enclosed
  area of land for livestock.

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YARD Continued

• Agriculture land around a house the area of
  land immediately surrounding a house, often
  covered with grass or landscaping. 
• Agriculture winter grazing area an area of land
  where deer, moose, or other animals graze in
  winter.
• Mathematics imperial unit of length a unit of
  length equal to 0.9144 m (3 ft).

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Authentic Anchor Project Unit Development
Template

• Step One Describe a CTE project rich with
  embedded mathematics that you will be teaching
  soon.
• Include the
• essential questions for the unit.

Chart It
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Guiding Questions/Essential Questions

• Open-ended
• Drive all instruction
• Higher order and stand the test of time. Even
  when curriculum changes, the essential questions
  are still there.
• At least one connects to students real life
• Examples
• What is the price of eggs in China?
• How would the price of eggs in China effect the
  cost of things in the US?

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AUTHENTIC INTEGRATED PROJECT UNIT CONCEPTSStep
One
Identify, in order, the activities that make up the project CTE Concepts to be Covered Mathematics Concepts to be Covered Tools Needed Habits of Success/Literacy Vocabulary
           
           
           
           
Chart It
SEE SAMPLE
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Step Two Identify the embedded mathematics to
be taught through the authentic integrated
project unit.

• CTE teachers explain project objectives so that
  mathematics teachers can help discover the
  embedded mathematics.
• Identify the math tools and vocabulary
• Tools to help with this process
• School/district pacing guides
• Competency Checklist

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What do the embedded math standards look like?

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AUTHENTIC INTEGRATED PROJECT UNIT CONCEPTSStep
Two
Identify, in order, the activities that make up the project CTE Concepts to be Covered Mathematics Concepts to be Covered Tools Needed Habits of Success/Literacy Vocabulary
           
           
           
           
Chart It
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Step Three Choose literacy and habits of
success strategies you will use as you teach the
project unit.
Listening
Speaking
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The Big Six Literacy Strategies Any Teacher Can
and Should Use

1. Summarizing
2. Paraphrasing
3. Categorizing
4. Inferring
5. Predicting
6. Recognizing Academic/Technical vocabulary

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Habits of Success.

• 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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Exploring Habits of Success- INSERT Strategy

• Read the description of the Habits of Success
  assigned to your team.
• Place a by each bulleted item that you
  have a strategy for.
• Place a ? by each bulleted item that you do not
  have strategy for.

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Exploring Habits of Success- INSERT Strategy

• 3. Look for people in the room who have a where
  you have ? and interview them.
• 4. The goal is to have at least one new strategy
  under each Habit of Success category.

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AUTHENTIC INTEGRATED PROJECT UNIT CONCEPTSStep
Three
Identify, in order, the activities that make up the project CTE Concepts to be Covered Mathematics Concepts to be Covered Tools Needed Habits of Success/Literacy
         
         
         
         
Chart It
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Step Four Develop a summative unit exam to
assess students understanding of mathematics and
CTE concepts used in the project.

• Dictates what students should know and be
  able to do, includes a traditional paper and
  pencil assessment, and a rubric for the
  Culminating Task.
• Should also Include
• Performance assessment (if appropriate)
• Traditional problems found on college placement
  and state level exams
• Authentic Problems from the pathway

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Step Five Pre-assess students mathematics and
CTE knowledge and skills that are embedded in the
authentic integrated project.

• Identify prerequisite and new skills students
  need to be successful in the unit.
• Include
• Reading problems
• Procedural mathematics problems
• Assess various vocabulary, skills and
  understanding of mathematics content
• Varying levels of mathematics problems

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What does varying levels mean?

• Getting to mastery
• at the proficient level is the key!
• Basic
• Proficient
• Advanced
• Stem Questions from Blooms

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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)
• www.micron.com

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www.micron.com

• MACHINIST
• A worker in a lawnmower factory is asked to make
  the part shown below for a new lawnmower design.
  To program a machine to cut the part out, the
  worker must find the slope and length of edge D.

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Standardized Tests

• The project assessment should include items that
  might appear on
• state assessments
• ACT
• SAT

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ACT- The edges of a cube are each 3 inches long.
What is the surface area, in square inches, of
this cube?F. 9G. 18H. 27J. 36K. 54

• In Context- The youth center has installed a
  swimming pool on level ground. The pool is a
  right circular cylinder with a diameter of 24
  feet and a height of 6 feet. A diagram of the
  pool and its entry ladder is shown below. To the
  nearest cubic foot, what is the volume of water
  that will be in the pool when it is filled with
  water to a depth of 5 feet?
• A. 942
• B. 1,885
• C. 2,262
• D. 9,047
• E. 11,310

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Guidelines for Developing Authentic Problems

• Apply desired math content.
• Use a non-contrived scenario.
• Include real-world numbers with appropriate units
  of measure.
• Remain faithful to the selected occupational
  area.
• Include some extraneous data.
• Avoid hand-holding or step-by-step guidance.
• Examples

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Process Form for Creating Mathematics/CTE
Authentic Problems

• Examples
• Work as a team
• to write an authentic
• problem

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How Do We Help Students Learn Problem Solving?

• RAP Sheet
• Think Aloud
• Socratic
• Questioning

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Steps 6 7 Designing Engaging Instructional
Strategies
Step Six Identify instructional strategies CTE
teachers will use to engage students with
mathematics embedded in the Authentic Anchor
Project Unit. Step Seven Identify
instructional strategies math teachers will use
to engage students by providing relevance for the
math content.
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The Corandic
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Engaging Instructional Strategies that aim toward
college readiness.

• Cooperative learning
• Project-based learning
• Socratic method
• Anticipation guides
• Videos
• Readings
• Demonstrations
• Multi-intelligences approach

• Technology integration
• Blogs
• YouTube
• Graphing calculators
• CBLs and CBRs
• Excel
• Literacy Strategies
• Use of manipulatives
• Others?

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Notes

• Bring both CTE and mathematics knowledge base
  into discussions.
• Mathematics teachers help CTE teachers develop
  ways to teach mathematics.
• CTE teachers help mathematics teachers understand
  the CTE well enough to develop contextual
  problems for use in the mathematics classroomto
  give mathematics students a reason to understand
  the mathematics.
• Both CTE and mathematics need to share in
  preparation of students for high-stakes exams.

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Remember the seven elements

1. CTE teacher introduces CTE lesson.
2. CTE teacher assesses students math awareness.
3. CTE teacher works through embedded example.
4. Math teacher works through traditional math
   examples.
5. CTE and math teachers work through related,
   contextual examples.
6. Students demonstrate understanding in CTE and
   math classes.
7. CTE and math teachers formally assess students.

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Seven Elements A sample from the building trades

1. CTE teacher points out that carpenters (students)
   must ensure 90-degree (square) corners on their
   building project.
2. Assess students math awareness as it relates to
   CTE.
3. CTE teachers walks through the original problem
   of ensuring a wall frames rectangular shape,
   gradually introducing the math formula and
   terminology of the Pythagorean theorem. CTE
   teachers uses both math and CTE vocabulary.
4. Mathematics teachers teaches Pythagorean Theorem
   in the traditional manner.
5. CTE and mathematics teachers assign construction
   problems to which the Pythagorean theorem can be
   applied.
6. Students demonstrate their understanding of
   Pythagorean theorem through project completion.
7. The students complete their building project, as
   well as a worksheet practicing the Pythagorean
   theoremboth in CTE and traditional math
   problemsas a part of a formal assessment. In
   the mathematics class, students apply the
   Pythagorean theorem in traditional and contextual
   problems as a part of a formal assessment.

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Project Activity Worksheet
Day Career/Technical Course Instructional Activities Math Course Instructional Activities Field Trips Guest Speakers



Chart It
Example
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Project Activity Worksheet
Day Career/Technical Course Instructional Activities Math Course Instructional Activities Field Trips Guest Speakers



Chart It
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Team Planning Time for Steps 6 and 7

• Consider the strategies that CTE teachers might
  use to teach the mathematics
• Consider the strategies that academic teachers
  might use to relate the mathematics embedded in
  the project to traditional mathematics concepts.
  

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Chart It

• Make sure your work is charted and hung before
  you leave!

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Step Eight Describe how students will
demonstrate their understanding of CTE and
mathematics knowledge and skills as they complete
the project.
Example?

• This involves
• Coordinating the instructional activities and
  assignments from previous steps into a coherent
  plan which students complete.

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Step Eight Describe how students will
demonstrate their understanding of CTE and
mathematics knowledge and skills by completing
the project.

• This also involves
• Creating rubrics for mathematics and CTE
  components of the project.
• Determining when co-teaching can and will take
  place
• Developing community resources
• Providing performance guidelines
• Writing a scenario or problem for students to
  solve
• Developing extra help strategies for students who
  do not meet mastery at the proficient level

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Step Eight Describe how students will
demonstrate their understanding of mathematics
knowledge and skills by completing the project.

• Most important to remember
• Require students to demonstrate understanding at
  varying levels of difficulty (basic, proficient,
  advanced)
• Assess learning through performance-based
  assessments AND using test items found in college
  placement exams and state level accountability
  tests

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Team Planning Time

• With your community, complete a Project Outline
  which thoroughly articulates how students will
  demonstrate understanding of both technical
  competencies and mathematics competencies.

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Reflections on Work Using SREB Criteria

• As a team, analyze your project using the
• Checklist for Quality Authentic Integrated
  Project Units
• Note any adjustments or improvement that need to
  be made.

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What is the Cycle of Learning?

• Get started
• Engage
• Explore
• Explain
• Practice together
• Practice in pairs
• Practice alone
• Evaluate
• Close

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Cycle of Learning

• For all classes
• Creates a pattern of learning
• Moves students into deeper understanding
• Allows for formative assessment

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First Getting Started

• Quick
• All students can be successful.
• Not new learning.
• Establishes routine.

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Second Engage

• Introduces focus for the day
• Provides relevance for the lesson
• Provides motivation for learning

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Third Explore

• Creates personal learning
• Sets the stage for content
• Allows for interaction
• Creates investment in content

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Fourth Explain

• Multiple types
• Short bursts of new content
• Within context of exploration
• Teacher talk

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Fifth Stages of Practice

• Practice together
• Practice in small groups
• Practice alone

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Sixth Evaluation

• Formative assessment usually
• Indicates mastery or re-teaching
• Usually brief
• Often informal

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Seventh Closing activities

• Bring closure to each class
• Enhance retention
• Improve parent relations

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The Cycle can take more than one day!

• Sample two day cycle
• Day One Day Two
• Getting Started Getting Started
• Engage Engage
• Explore Practice in teams
• Explain Practice alone
• Practice together Evaluate
• Closure Closure

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Project Planning

• This is where you put everything together into
  a clearly articulated series of daily that ensure
  instructional time is used wisely.
• Example

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Using the Cycle of Learning

• Lets build a daily lesson plan together for one
  of the authentic integrated units developed
  today.

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Write a Daily Lesson with your school team!

• Using your authentic integrated unit, develop a
  daily lesson plan for the CTE teacher and a daily
  lesson plan for the mathematics teacher.
• One Day for Math and One Day for CTE

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Complete Daily Lesson Plans!

• As team members, continue working on the unit
• Email me if you have questions

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Instructionally..

• Does the project present learning activities to
  students following the seven elements?

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Action PlanningUsing the Team Action Plan

• Identify next steps to completion of the
  skeleton unit, including implementation of the
  unit.
• How will you finish planning together?
• When will you teach the project?
• How will you share with others what you are
  learning?
• What will you bring to the follow up meeting?
• What data will you share with your community in
  follow up meetings?

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Remember the goal

• Supersize Opportunities for Students to Embrace
  Mathematics

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Ticket out the door!

• Last page in your handout!
• Thank You for Being Here!
• See ya next time.