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 [email protected]. Welcome. Group Norms: Participate Ask questions of each other Work toward solutions. Housekeeping: Restrooms Breaks Lunch Punctuality. - PowerPoint PPT PresentationTRANSCRIPT
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Building Academic Skills in Context: Enhancing Mathematics Achievement
through CTE Instruction
Leslie Carson
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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
Let’s 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
Textbook
p. 4
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Essential Questions:
Why is helping students understand math everyone’s 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…
Textbook
p. 6
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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 Visionary’s 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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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.
Lynn Authur Steen, St. Olaf College
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(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.
Lynn Authur Steen, St. Olaf College
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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?
Jerry Garcia of the Grateful Dead
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“As any wise old farmer can tell you, you don’t fatten your lambs
simply by weighing them”
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• 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.
Common Misconceptions about LearnersSue 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
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•How do the human mind and body work in their learning capacity?
•How can an understanding of the mind/body’s way of learning be used in educational settings?
Cognitive Science Questions about the Teaching and Learning Process
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A
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Learning often occurs only when students process new information or
knowledge in such a way that it makes sense in their frame of
reference
How Do New Pieces of Information Fit?
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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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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
Learning in Context Involves:
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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.
Let’s 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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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.
Traditional mathematics education presents the concepts first and applications second
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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
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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.
D
R T
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Reading, Mathematics, and Science HSTW Scores for Students
57%
31%
69%
45%
63%
38%
0%
10%
20%
30%
40%
50%
60%
70%
Reading Mathematics Science
IntegratedAcademics
No Integration
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CTE Programs ProvideFocus 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 TeachersCollaborate to provide relevancy in Academics.
CTE and Math TeachersConsult 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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SREB’s Criteria for Authentic Anchor
Project Units
Textbook
p. 7
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Overview: Eight Steps to Develop Authentic Integrated Projects
Textbook
p. 8
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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.
Textbook
p. 8
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Step One: Identify a major project with embedded mathematics content.
A. In your teams, CTE teachers share a major project they will complete with students. The project selected should be rich in embedded mathematics.
B. Break down into the activities that make up the project and consider making adjustments that add math rigor.
C. Identify the CTE concepts in each activity.
D. Identify the CTE vocabulary.
Textbook
p. 9
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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.
Textbook
p. 9
Workbook
p. 2
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AUTHENTIC INTEGRATED PROJECT UNIT CONCEPTSStep One:
SEE SAMPLE
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
Textbook
p. 10
Workbook
p. 2-3
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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?
Textbook
p. 9
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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
Workbook
p. 2-3
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Step Three: Choose literacy and habits of success strategies you will use as you teach the project unit.
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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
Textbook
p. 11
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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
Textbook
p. 12-13
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Exploring Habits of Success- INSERT Strategy
1. Read the description of the Habits of Success assigned to your team.
2. Place a by each bulleted item that you have a strategy for.
3. 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
Workbook
p. 3-4
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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
Textbook
p. 14
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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
Textbook
p. 14
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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 Bloom’s
Textbook
p. 14-17
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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/startsearch.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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The project assessment should include items that might appear on
state assessments ACT SAT
Standardized Tests Textbook
p. 18-19
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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. 942B. 1,885C. 2,262D. 9,047E. 11,310
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Guidelines for Developing Authentic Problems
1. Apply desired math content.
2. Use a non-contrived scenario.
3. Include real-world numbers with appropriate units of measure.
4. Remain faithful to the selected occupational area.
5. Include some extraneous data.
6. Avoid hand-holding or step-by-step guidance.
Examples
Textbook
p. 21
Textbook
p. 22-23
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Process Form for Creating Mathematics/CTE Authentic Problems Workbook
p. 6-8
Examples
Work as a team to write an authentic problem
Textbook
p. 24-26
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How Do We Help Students Learn Problem Solving?
RAP Sheet
Think Aloud
Socratic
Questioning
Textbook
p. 27-28
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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.
Textbook
p. 29
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The CorandicTextbook
p. 30
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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 CBL’s and CBR’s 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 classroom—to 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 frame’s 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 theorem—both in CTE and traditional math problems—as 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
Textbook
p. 31
Workbook
p. 9
Example
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Project Activity Worksheet
Day Career/Technical Course Instructional Activities
Math Course Instructional Activities
Field Trips Guest Speakers
Workbook
p. 9
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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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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.
This involves: Coordinating the instructional
activities and assignments from previous steps into a coherent plan which students complete.
Textbook
p. 32-34
Example
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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.
Workbook
p. 11-13
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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.
Workbook
p. 14-15
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What is the Cycle of Learning?
Get started Engage Explore Explain Practice together Practice in pairs Practice alone Evaluate Close
Textbook
p. 35
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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 TwoGetting Started Getting StartedEngage EngageExplore Practice in teamsExplain Practice alonePractice together EvaluateClosure 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.
ExampleTextbook
p. 36-37
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Using the Cycle of Learning
Let’s build a daily lesson plan together for one of the authentic integrated units developed today.
Workbook
p. 16-17
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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?
Workbook
p. 20
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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?
Workbook
p. 21-22
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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….
Textbook
p. 38