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


1
Building Academic Skills in Context Enhancing
Mathematics Achievement through CTE Instruction
  • Leslie Carson
  • leslie.carson_at_sreb.org

2
Welcome
3
Group Norms and Housekeeping
  • Group Norms
  • Participate
  • Ask questions of each other
  • Work toward solutions
  • Housekeeping
  • Restrooms
  • Breaks
  • Lunch
  • Punctuality

4
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.

5
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

6
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?

7
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
8
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

9
The Good News Is..
10
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

11
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

12
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

13
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.

14
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.

15
U.S. Ranked 24th out of 29 OECD Countries in
Mathematics
Organization for Economic Cooperation and
Development (OECD), PISA 2003
16
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

17
As any wise old farmer can tell you, you dont
fatten your lambs simply by weighing them
18
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.

19
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?

20
A
21
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
22
Students can increase high level mathematics
understanding through experiences.
23
And by Collaborating with Their Peers.
24
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

25
Why is relevancy important?
  • Example Learning a Code

26
A

27
Now
  • Spell the word FACE in Code.
  • Lets see how you did!

28
a
29
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.
30
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.
31
Learning Mathematics should be based on
understanding concepts and on doing mathematics,
not on memorizing rote procedures
32
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.

33
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

34
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.

35
Often, mathematical and CTE skills are chunked,
making transfer to the mathematics classroom and
standardized tests difficult
Pythagorean Theorem?
3-4-5 Angle?
36
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.

37
Reading, Mathematics, and Science HSTW Scores for
Students
38
CTE Programs Provide Focus Foundation
Context
39
Why Is It Important That CTE And Academics Work
Together?
  • Example Picture Recall

40
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41
We bring different pieces of information to the
team!
42
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.

43
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

44
The teaming of math teachers and CTE teachers
merges context and content.
  • Historically, this has not happened naturally.
    There must be a concentrated effort.

45
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

46
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.

47
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.

48
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

49
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

50
SREBs Criteria for Authentic Anchor Project
Units
51
Overview Eight Steps to Develop Authentic
Integrated Projects
52
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.

53
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.

54
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?
55
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.

56
Define
  • AXIS
  • SOLUTION
  • RANGE
  • YARD

57
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.

58
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.

59
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.

60
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.

61
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.

62
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).

63
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
64
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?

65
AUTHENTIC INTEGRATED PROJECT UNIT CONCEPTS Step
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
66
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

67
What do the embedded math standards look like?

68
AUTHENTIC INTEGRATED PROJECT UNIT CONCEPTS Step
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
69
Step Three Choose literacy and habits of
success strategies you will use as you teach the
project unit.
Listening
Speaking
70
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

71
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

72
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.

73
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.

74
AUTHENTIC INTEGRATED PROJECT UNIT CONCEPTS Step
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
75
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

76
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

77
What does varying levels mean?
  • Getting to mastery
  • at the proficient level is the key!
  • Basic
  • Proficient
  • Advanced
  • Stem Questions from Blooms

78
Where can we find good examples of 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

79
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80
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81
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.

82
Standardized Tests
  • The project assessment should include items that
    might appear on
  • state assessments
  • ACT
  • SAT

83
ACT- The edges of a cube are each 3 inches long.
What is the surface area, in square inches, of
this cube? F. 9 G. 18 H. 27 J. 36 K. 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

84
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

85
Process Form for Creating Mathematics/CTE
Authentic Problems
  • Examples
  • Work as a team
  • to write an authentic
  • problem

86
How Do We Help Students Learn Problem Solving?
  • RAP Sheet
  • Think Aloud
  • Socratic
  • Questioning

87
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.
88
The Corandic
89
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?

90
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.

91
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.

92
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.

93
Project Activity Worksheet
Day Career/Technical Course Instructional Activities Math Course Instructional Activities Field Trips Guest Speakers



Chart It
Example
94
Project Activity Worksheet
Day Career/Technical Course Instructional Activities Math Course Instructional Activities Field Trips Guest Speakers



Chart It
95
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.

96
Chart It
  • Make sure your work is charted and hung before
    you leave!

97
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.

98
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

99
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

100
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.

101
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.

102
What is the Cycle of Learning?
  • Get started
  • Engage
  • Explore
  • Explain
  • Practice together
  • Practice in pairs
  • Practice alone
  • Evaluate
  • Close

103
Cycle of Learning
  • For all classes
  • Creates a pattern of learning
  • Moves students into deeper understanding
  • Allows for formative assessment

104
First Getting Started
  • Quick
  • All students can be successful.
  • Not new learning.
  • Establishes routine.

105
Second Engage
  • Introduces focus for the day
  • Provides relevance for the lesson
  • Provides motivation for learning

106
Third Explore
  • Creates personal learning
  • Sets the stage for content
  • Allows for interaction
  • Creates investment in content

107
Fourth Explain
  • Multiple types
  • Short bursts of new content
  • Within context of exploration
  • Teacher talk

108
Fifth Stages of Practice
  • Practice together
  • Practice in small groups
  • Practice alone

109
Sixth Evaluation
  • Formative assessment usually
  • Indicates mastery or re-teaching
  • Usually brief
  • Often informal

110
Seventh Closing activities
  • Bring closure to each class
  • Enhance retention
  • Improve parent relations

111
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

112
Project Planning
  • This is where you put everything together into
    a clearly articulated series of daily that ensure
    instructional time is used wisely.
  • Example

113
Using the Cycle of Learning
  • Lets build a daily lesson plan together for one
    of the authentic integrated units developed
    today.

114
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

115
Complete Daily Lesson Plans!
  • As team members, continue working on the unit
  • Email me if you have questions

116
Instructionally..
  • Does the project present learning activities to
    students following the seven elements?

117
Action Planning Using 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?

118
Remember the goal
  • Supersize Opportunities for Students to Embrace
    Mathematics

119
Ticket out the door!
  • Last page in your handout!
  • Thank You for Being Here!
  • See ya next time.
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