The Border Problem: Figure out without talking, without writing, and without counting onebyone how m

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• The Border Problem Figure out without talking,
  without writing, and without counting one-by-one
  how many unit squares are in the border of a 10 x
  10 grid.
• Find at least one way to represent your method
  arithmetically, algebraically, geometrically, and
  verbally.

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Strengthening Standards, Instruction, and
Resources for Mathematics

• Barbara Libby, Director, Office of Mathematics,
  Science and Technology/Engineering
• Connie Louie, Director, Office of Instructional
  Technology
• Nancy Hanson, MCAS Alternate Assessment
  Specialist
• Sharyn Sweeney, Mathematics Coordinator, Office
  of Mathematics, Science and Technology/Engineering

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Purpose

• Reinforce the urgency to address the achievement
  gap in mathematics
• Share the work and considerations of the
  mathematics revision panel
• Show strategies for making standards accessible
• Identify the characteristics of an engaging
  standard-based mathematics classroom
• Share a variety of resources to support
  students

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Data

• What do the data tell us about mathematics
  achievement?

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Why the Border Problem?
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Learning Standards for Border Problem

• Students engage in problem solving,
  communicating, reasoning, connecting, and
  representing as they
• 6.N.9 Select and use appropriate operations to
  solve problems involving addition, subtraction,
  multiplication, division, and positive integer
  exponents with whole numbers, and with positive
  fractions, mixed numbers, decimals, and percents.
  
• 6.P.4 Represent real situations and mathematical
  relationships with concrete models, tables,
  graphs, and rules in words and with symbols,
  e.g., input-output tables.
• 6.P.5 Solve linear equations using concrete
  models, tables, graphs, and paper-pencil methods.
  
• 6.G.3 Identify relationships among points, lines,
  and planes, e.g., intersecting, parallel,
  perpendicular.
• 6.M.1 Apply the concepts of perimeter and area to
  the solution of problems. Apply formulas where
  appropriate

http//www.doe.mass.edu/frameworks/current.html
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Mathematics Curriculum Framework

• First Framework 1994
• Current Framework 2000
• Grades 3, 5, 7 supplement 2004
• Next Generation (under construction)
• Reviewed data
• MCAS, PISA, TIMSS, NAEP
• Read current thinking
• NCTM, National Mathematics Advisory Panel Report,
  21st Century Skills research
• Reviewed other frameworks
• Other states and other nations frameworks and
  standards
• Surveyed framework users
• Hosted informational public forums

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Revision Topics for Consideration

• Breadth and Depth
• Prioritize standards
• Problem Solving
• Include student reasoning/communication
• Vertical Alignment of Standards
• Preparation/Access to Algebra
• College and Career Readiness
• 21st Century Skills
• Financial Literacy
• Content Literacy and Mathematics
• Format
• Dynamic Document

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High School Pathways

• Mass Core
• 4 units of high school mathematics including
  Algebra II
• Take mathematics in senior year
• Challenge
• Appropriate course(s) for the students who are
  not recommended to take Precalculus or Calculus
• Options
• Bridge to Algebra II
• Quantitative Reasoning
• Discrete Mathematics
• Statistics/Probability

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Possible Pathways
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Border Problem

• How did you express your solution?

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Sometimes, It Seems Like This.
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Massachusetts Resource Guide A Model for
Teaching, Learning, and Assessment
Entry Points
http//www.doe.mass.edu/mcas/alt/resources.html
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Access to the General CurriculumMathematics
Number Sense and Operations
Grade 5-6 Learning Standard 6.N.9 Select and
use appropriate operations to solve problems
involving addition, subtraction, multiplication,
division, and positive integer exponents with
whole numbers and with positive fractions, mixed
numbers, decimals, and percents. Example (10 x
4) - 4 36 8 x 4 4 36
Essence Select and use appropriate operations to
solve increasingly complex problems.
Use math reasoning to solve less complex (lower
complexity) problems Example 10 x 4 40 40 - 4
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Add or subtract using manipulatives or real-life
objects. Example 1 cube 1 cube 2 4 books - 1
book 3
Solve simple one-step problems. Example 1 1
2 5 4 1
Entry Points
Standard as written
Less Complex More
Complex
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Using the Resource Guide

• Can the student address
• The standard as written for a student in that
  grade?
• If no, can the student address
• The standard at a slightly lower level of
  complexity ( i.e., a more complex entry point)?
  
• If no, can the student address
• The standard at an even lower level of complexity
  (i.e., a low complexity entry point)?

• If yes
• Pre-test the student Identify a skill at a
  challenging and attainable level
• Design instruction that allows student to
  demonstrate mastery
• Collect data and other evidence, as student
  learns the skill

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Essence Meaning of standard and topics covered
Standard as written
Entry Points related to meaning and topics
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Standards in Action
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Characteristics of a Standards-Based Mathematics
Classroom

• Development of the document
• Organization
• Selected Examples
• Research
• Potential Uses

http//www.doe.mass.edu/omste/news07/mathclass_cha
r.pdf
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Organization

• 8 Guiding Principles
• 20 Characteristics
• Most characteristics should be evident
• 80 Indicators
• Examples that one might see that demonstrates how
  a characteristic is implemented

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V. Teaching
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Teaching
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The Railside Study, Jo Boaler

• Five-year study of three high schools
• Guiding theme is equity for all students at
  Railside
• In year 4, 41 of seniors at Railside were
  enrolled in calculus, compared with approximately
  27 in the other two schools.
• Importantly, inequities between students of
  different ethnic groups disappeared or were
  reduced in all cases at Railside whereas they
  remained at the other schools that employed
  tracking.

Note Railside is a pseudonym for an urban high
school in California http//www.utdanacenter.org/
umln/downloads/sanjose06/railside_study.pdf
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Think about

• Which of these characteristics are currently
  strengths in your classroom or district?
• Which of these characteristics need additional
  strengthening to address achievement gaps?

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Resources

• ESEs Resources (at no cost to schools)
• Data Warehouse
• Curriculum Instruction Website
• Office for Mathematics, Science, and Technology
  Engineering (OMSTE) Website
• Resource Guide to the Massachusetts Curriculum
  Frameworks for Students with Disabilities
• Assistive Technology Website
• Massachusetts Thinkfinity Partnership
• MassONE Lesson Plan Tool

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Resources

• Other No Cost Resources
• WGBH Teachers Domain
• NCES Kids Zone
• Project Interactivate
• http//www.shodor.org/interactivate/activities/Sha
  peExplorer/
• National Science Digital Library
• The BBC

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Questions?

• Thank you

Barbara Libby, Director, Office of Mathematics,
Science and Technology/Engineering,
blibby_at_doe.mass.edu, 781-338-3460 Connie Louie,
Director, Office of Instructional Technology,
clouie_at_doe.mass.edu, 781-338-6865 Nancy Hanson,
MCAS Alternate Assessment Specialist, Office of
Student Assessment, nhanson_at_doe.mass.edu,
781-338-3625 Sharyn Sweeney, Mathematics
Coordinator, Office of Mathematics, Science and
Technology/Engineering, ssweeney_at_doe.mass.edu,
781-338-3504