Download Alabama Course of Study

Professional Development: Grades 9 – 12 Phase I
Regional Inservice Center
Summer 2011
PART A
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Components of the Course of Study
High School Course Progressions/Pathways
Standards for Mathematical Practice
Literacy Standards for Grades 6-12
◦ History/Social Studies, Science, and Technical Subjects
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The Big Picture
◦ Domains of Study and Conceptual Categories
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Learning Progressions/Trajectories
◦ Vertical Alignment of Content
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Addressing Content Shifts
Early Entry Algebra I
◦ Considerations/Consequences
Goal
Conceptual Categories
Domains of Study
Position Statements
Standards for
Mathematical Practice
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Preface
Acknowledgments
General Introduction
Conceptual Framework
Position Statements
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Equity
Curriculum
Teaching
Learning
Assessment
Technology
Standards for Mathematical Practice
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Directions for Interpreting the Minimum
Required Content
GRADE 4
Students will:
Cluster
Domain
Number and Operations in Base Ten
Generalize place value understanding for multi-digit whole
numbers.
Content
Standards
6. Recognize that in a multi-digit whole number, a digit in one place
represents ten times what it represents in the place to its right.
[4-NBT1]
7. Read and write multi-digit whole numbers using base-ten numerals,
number names, and expanded form. Compare two multi-digit
numbers based on meaning of the digits in each place using >, =,
and < symbols to record the results of comparisons. [4-NBT2]
8. Use place value understanding to round multi-digit whole numbers
to any place. [4-NBT3]
Content
Standard
Identifiers
ALGEBRA II WITH TRIGONOMETRY
Students will:
FUNCTIONS
Conceptual
Trigonometric Functions
Category
Cluster
Content
Standards
Domain
Extend the domain of trigonometric functions using the unit circle.
32. Understand radian measure of an angle as the length of the arc on
the unit circle subtended by the angle. [F-TF1]
33. Explain how the unit circle in the coordinate plane enables the
extension of trigonometric functions to all real numbers, interpreted
as radian measures of angles traversed counterclockwise around the
unit circle. [F-TF2]
34. Define the six trigonometric functions using ratios of the sides of
a right triangle, coordinates on the unit circle, and the reciprocal of
other functions.
Content
Standard
Identifiers
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Standards for High School Mathematics
◦ Conceptual Categories for High School Mathematics
 Number and Quantity
 Algebra
 Functions
 Modeling
 Geometry
 Statistics and Probability
◦ Additional Coding
 (+) STEM Standards
 (*) Modeling Standards
 ( ) Alabama Added Content
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(+) STEM Standards
Geometry
22. (+) Derive the formula A = (1/2)ab sin(C)
for the area of a triangle by drawing an
auxiliary line from a vertex perpendicular
to the opposite side. [G-SRT9]
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(*) Modeling Standards
Algebra I
28. Relate the domain of a function to its
graph and, where applicable, to the
quantitative relationship it describes. * [F-IF5]
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Added Content Specific to Alabama
Geometry
35. Determine areas and perimeters of
regular polygons, including inscribed or
circumscribed polygons, given the
coordinates of vertices or other
characteristics.
•Description of Standards
•Relation to K-8 Content
•Content Progression in 9-12
•Narrative
•Domains and Clusters
•Standards for
Mathematical Practice
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Appendices A-E
◦ Appendix A
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Table
Table
Table
Table
Table
1:
2:
3:
4:
5:
Common Addition and Subtraction Situations
Common Multiplication and Division Situations
Properties of Operations
Properties of Equality
Properties of Inequality
◦ Appendix B
 Possible Course Progressions in Grades 9-12
 Possible Course Pathways
◦ Appendix C
 Literacy Standards For Grades 6-12
History/Social Studies, Science, and Technical Subjects
◦ Appendix D
 Alabama High School Graduation Requirements
◦ Appendix E
 Guidelines and Suggestions for Local Time Requirements and Homework
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Bibliography
Glossary
Required for All Students
• Algebra I
• Geometry
• Algebra II with Trigonometry or Algebra II
Courses Must Increase in Rigor
New Courses
• Discrete Mathematics
• Mathematical Investigations
• Analytical Mathematics
The Standards for
Mathematical Practice
Standards for Mathematical Practice
“The Standards for Mathematical
Practice describe varieties of
expertise that mathematics
educators at all levels should
seek to develop in their students.
These practices rest on important
“processes and proficiencies”
with longstanding importance in
mathematics education.”
(CCSS, 2010)
Underlying Frameworks
National Council of Teachers of Mathematics
5 PROCESS Standards
•Problem Solving
•Reasoning and Proof
•Communication
•Connections
•Representations
NCTM (2000M). Principles and
Standards for School Mathematics.
Reston, VA: Author.
Underlying Frameworks
National Research Council
Strands of Mathematical Proficiency
•
•
•
•
•
Conceptual Understanding
Procedural Fluency
Strategic Competence
Adaptive Reasoning
Productive Disposition
NRC (2001). Adding It Up.
Washington, D.C.: National
Academies Press.
The Standards for Mathematical Practice
Mathematically proficient students:
Standard 1: Make sense of problems and persevere in
solving them.
Standard 2: Reason abstractly and quantitatively.
Standard 3: Construct viable arguments and critique
the reasoning of others.
Standard 4: Model with mathematics.
Standard 5: Use appropriate tools strategically.
Standard 6: Attend to precision.
Standard 7: Look for and make use of structure.
Standard 8: Look for and express regularity in repeated
reasoning.
1.
2.
3.
What does this standard look like
in the classroom?
What will students need in order
to do this?
What will teachers need in order
to do this?
Adapted from Kathy Berry, Monroe County ISD, Michigan
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Analyze givens, constraints, relationships
Make conjectures
Plan solution pathways
Make meaning of the solution
Monitor and evaluate their progress
Change course if necessary
Ask themselves if what they are doing makes
sense
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Make sense of quantities and relationships
Able to decontextualize
◦ Abstract a given situation
◦ Represent it symbolically
◦ Manipulate the representing symbols
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Able to contextualize
◦ Pause during manipulation process
◦ Probe the referents for symbols involved
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Construct arguments
Analyze situations
Justify conclusions
Communicate conclusions
Reason inductively
Distinguish correct logic from flawed logic
Listen to/Read/Respond to other’s arguments
and ask useful questions to clarify/improve
arguments
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Apply mathematics to solve problems from
everyday life situations
Apply what they know
Simplify a complicated situation
Identify important quantities
Map math relationships using tools
Analyze mathematical relationships to draw
conclusions
Reflect on improving the model
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Consider and use available tools
Make sound decisions about when different
tools might be helpful
Identify relevant external mathematical
resources
Use technological tools to explore and
deepen conceptual understandings
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Communicate precisely to others
Use clear definitions in discussions
State meaning of symbols consistently and
appropriately
Specify units of measurements
Calculate accurately & efficiently
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Discern patterns and structures
Use strategies to solve problems
Step back for an overview and can shift
perspective
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Notice if calculations are repeated
Look for general methods and shortcuts
Maintain oversight of the processes
Attend to details
Continually evaluates the reasonableness of
their results
The Standards for [Student]
Mathematical Practice
SMP1:
SMP2:
SMP3:
SMP4:
SMP5:
SMP6:
SMP7:
SMP8:
Explain and make conjectures…
Make sense of…
Understand and use…
Apply and interpret…
Consider and detect…
Communicate precisely to others…
Discern and recognize…
Note and pay attention to…
Mathematical
Practice
Mathematical
Content
Algebra Task 3 Sorting Functions
This task gives students the chance to:
• Find relationships between graphs,
equations, tables, and rules.
• Explain reasoning for answers.
www.insidemathematics.org
Algebra Task 3
Sorting
Functions
Algebra Task 3
Sorting
Functions
www.insidemathematics.org
Algebra – 2008
Copyright © 2008 by Noyce Foundation.
All rights reserved.
The information provided in the following slides
is for professional development only.
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Making connections between different
algebraic representations: graphs, equations,
verbal rules, and tables
Understanding how the equation determines
the shape of the graph
Developing a convincing argument using a
variety of algebraic concepts
Being able to move from specific solutions to
thinking about generalizations
Algebra – 2008
Copyright © 2008 by Noyce Foundation.
All rights reserved.
The Standards for Mathematical Practice
Mathematically proficient students:
Standard 1: Make sense of problems and persevere in
solving them.
Standard 2: Reason abstractly and quantitatively.
Standard 3: Construct viable arguments and critique
the reasoning of others.
Standard 4: Model with mathematics.
Standard 5: Use appropriate tools strategically.
Standard 6: Attend to precision.
Standard 7: Look for and make use of structure.
Standard 8: Look for and express regularity in repeated
reasoning.
Student A
Student B
The Standards for [Student]
Mathematical Practice
“Not all tasks are created equal, and
different tasks will provoke different levels
and kinds of student thinking.”
Stein, Smith, Henningsen, & Silver, 2000
“The level and kind of thinking in
which students engage determines
what they will learn.”
Herbert, Carpenter, Fennema, Fuson, Wearne, Murray, Oliver, & Human, 1997
But, WHAT TEACHERS DO
with the tasks matters too!
The Mathematical Tasks Framework
Tasks as
they
appear in
curricular
materials
Tasks
are set
up by
teachers
Tasks are
enacted
by
teachers
and
students
Student
Learning
Stein, Grover, & Henningsen (1996)
Smith & Stein (1998)
Stein, Smith, Henningsen, & Silver (2000)
Standards for [Student] Mathematical
Practice
The Standards for Mathematical
Practice place an emphasis on
student demonstrations of learning…
Equity begins with an understanding
of how the selection of tasks, the
assessment of tasks, and the student
learning environment create inequity
in our schools…
Leading with the
Mathematical Practice Standards
You can begin by implementing the 8
Standards for Mathematical Practice now
Think about the relationships among the
practices and how you can move forward to
implement BEST PRACTICES
Analyze instructional tasks so students
engage in these practices repeatedly