A Balanced Mathematics Framework K - 12

1
A Balanced Mathematics Framework K - 12

• BOE work session
• May 21, 2012

2
Tonights Agenda

• Brief introduction of the Common Core State
  Standards (CCSS)
• Common Core State Standards for Mathematics
  (CCSSM)
• Why a Balanced Mathematics Framework, K - 12

3
Common Core State Standards

• The Common Core State Standards Initiative
  (CCSSI) is a state-led effort coordinated by the
  National Governors Association (NGA) and the
  Council of Chief State School Officers (CCSSO).

4
Common Core State Standards

• Not a Federal Mandate
• 46 States have Adopted Standards
• For first time, consensus on the essential
  knowledge and skills for college and career
  readiness
• Are Fewer, Clearer, and Higher
• Reframing what we expect students to accomplish

5
NH Common Core Message

• Common Core State Standards Solve Three Specific
  Problems
• Increased Skill Demand and Competition
• Students Not College and Career Ready
• Variance Across the Country in standards and
  expectations
• (zip code should not dictate expectation)
• NH Dept. of Education, 12/2/2011

6
Common Core Mathematics

• Focus key ideas, understandings and skills
  identified for each grade and course
• Coherence across grade levels and link to major
  topics within grades
• Rigor at all grade levels, all students
• Conceptual understanding
• Procedural skill and fluency
• Application

7
Focus

• There are two to six critical areas for
  instruction for each grade level, model course or
  integrated pathway (K-12).
• They bring focus to the standards at each grade
  by providing the big ideas that educators can use
  to build their curriculum and to guide
  instruction.

8
Focus
Each grade includes an overview of cross-cutting
themes and critical areas of study
9
Coherence

• Each concept in each grade builds on what you
  learned before
• Learn about related topics in a way that
  reinforces the core learning
• A constant effort to rethink what we learn in
  math, so it links to core understanding

10
Domain Progressions
K K 1 2 3 4 5 6 7 8 HS
Counting Cardinality Counting Cardinality
Number and Operations in Base Ten Number and Operations in Base Ten Number and Operations in Base Ten Number and Operations in Base Ten Number and Operations in Base Ten Number and Operations in Base Ten Number and Operations in Base Ten Ratios and Proportional Relationships Ratios and Proportional Relationships Number Quantity
Number and Operations Fractions Number and Operations Fractions Number and Operations Fractions The Number System The Number System The Number System Number Quantity
Operations and Algebraic Thinking Operations and Algebraic Thinking Operations and Algebraic Thinking Operations and Algebraic Thinking Operations and Algebraic Thinking Operations and Algebraic Thinking Operations and Algebraic Thinking Expressions and Equations Expressions and Equations Expressions and Equations Algebra
Operations and Algebraic Thinking Operations and Algebraic Thinking Operations and Algebraic Thinking Operations and Algebraic Thinking Operations and Algebraic Thinking Operations and Algebraic Thinking Operations and Algebraic Thinking Functions Functions
Geometry Geometry Geometry Geometry Geometry Geometry Geometry Geometry Geometry Geometry Geometry
Measurement and Data Measurement and Data Measurement and Data Measurement and Data Measurement and Data Measurement and Data Measurement and Data Statistics and Probability Statistics and Probability Statistics and Probability Statistics Probability

11
Rigor

• Equal emphasis at all grades for all students
• Conceptual Understanding
• Practical skills and fluency
• Application

12
RigorFluency Fast and Accurate

• Grade Required Fluency
• K Add/subtract within 5
• 1 Add/subtract within 10
• 2 Add/subtract within 20
• Add/subtract within 100 (pencil
  and paper)
• 3 Multiply/divide within 100
• Add/subtract within 1000
• 4 Add/subtract within 1,000,000
• 5 Multi-digit multiplication
• 6 Multi-digit division
• Multi-digit decimal operations
• 7 Solve px q r, p(x q) r
• 8 Solve simple 2X2 systems by inspection

13
Rigor

• (8) Pre-K-12 Standards for Mathematical Practice
• Expertise for students at all grade levels
• 1. Make sense of problems and persevere in
  solving them
• 2. Reason abstractly and quantitatively
• 3. Construct viable arguments and critique the
  reasoning of others
• 4. Model with mathematics
• 5. Use appropriate tools strategically
• 6. Attend to precision
• 7. Look for and make use of structure
• 8. Look for and express regularity in repeated
  reasoning

14
SMARTER Balanced Assessment Consortium

• Heres a sample

15
Nashua needs

• To develop students who
• Are fluent in basic arithmetic skills
• Think critically
• Solve problems
• Synthesize math concepts in order to apply to
  real world problems
• Assess the validity of the solution
• Communicate their thinking

16
Recommendations

• Provide on-going professional development
• Pedagogy
• Striking a balance between computation practice
  and fluency and deeper conceptual elements of
  math
• Content and its applications
• Collaboration to develop a math instructional
  framework that is independent of textbook series
  or program
• Vertical and horizontal collaboration

17
How do we proceed
18
Mathematics Steering Committee Investigations

• Selection of an instructional mathematics
  framework that
• Can be used by all teachers of mathematics, K -12
• Is independent of a specific math program or
  textbook series
• Increases teachers understanding of mathematics

19
Relationship to Strategic Plan

• Goal Promote increased student learning and
  achievement through all teaching and learning
  practices to maximize each students personal
  growth and meet district, state, and federal
  standards of accountability.
• Nashua Strategic Plan, page
  2
• Strategy Implement Balanced Mathematics as a
  framework for mathematics instruction K 12

20
Balanced Mathematics Framework, K - 12

21
Balanced Mathematics Framework, K - 12

• First, what it is not
• It is not a mathematics curriculum
• It is
• 5 essential components for any mathematics
  instruction K 12
• Computational Skills (Math Review and Mental
  Math)
• Problem Solving
• Conceptual Understanding
• Mastery of Math Facts
• Common Formative Assessment

22
Math Review and Mental Math

• Simple system for reviewing basic computational
  skills
• Part I Students do selected problems
• Teacher selects one problem based on standards
  and skill needing reinforcement and practice
• Teacher circulates as students work
• Part II Processing the Math Review
• Emphasize number sense and reasonableness of
  answers
• Use math vocabulary
• Uncover common mistakes

23
Mental Math

• 5 minute work out for the brain mental practice
  in computing basic number facts
• One more/less, doubles, counting by 2s, 5s, 10s,
  vocabulary
• Say out loud, process together

24
Problem Solving

• The problem -solving step of a balanced math
  instructional framework provides students with a
  dual opportunity to
• Apply the mathematics they are learning
• Communicate their mathematical thinking to others.

25
Problem Solving

• At each level (elementary, middle, and high) the
• framework provides a suggested instructional
  sequence
• to teach students how to mathematically solve an
• application problem and communicate both orally
  and
• in writing the process they used.

26
Conceptual Understanding

• Developing students conceptual understanding is
  at the heart of effective mathematical
  instruction aimed at deepening students
  understanding of the unit and central math focus

27
Conceptual Understanding

• Teaching for meaning
• Network of ideas
• Logical relationships
• Making connections
• Transferring for understanding

28
Mastery of Math Facts

• Mastery of math facts is necessary for students
  to be able to solve problems accurately and in an
  appropriate amount of time.
• Professional development will provide teachers
  with new strategies to teach math facts with
  mastery.

29
Common Formative Assessment

• Assessment FOR learning
• Includes instructionally embedded activities
• Teacher developed
• Yields rich diagnostic information
• Occurs while material is being taught
• Informs and focuses instructional decisions

30
In Review

• You have had -
• A glimpse of the Common Core State Standards
• A look at the new assessment measure which will
  replace the NECAP
• An opportunity to see one of our strategies to
  improve math instruction through a common
  instructional framework K - 12