Comprehensive Balanced Mathematics Model Middle School

1
Comprehensive Balanced Mathematics ModelMiddle
School

• Okaloosa County School District
• Dr. Lynda Penry

2
Elements of the Comprehensive Mathematical Model

• Components of Mathematics
• Math Model Examples
• Principles of Mathematics
• Descriptors
• Best Practices
• Self-Reflection Survey
• Resources

3
Components

• Problem Solving
• Reasoning and Proof
• Communication
• Connections
• Representation

4
Problem Solving

• Unless students can solve problems, the facts,
  concepts and procedures they know are of little
  use.
• Example
• Create four towers (single cube wide) of
  differing heights using 1-inch cubes, beginning
  with a single cube. Determine the surface area
  of each tower.

5
Reasoning and Proof

• Mathematics should make sense to students
• Example
• Describe the pattern relating the surface areas
  to the towers as they become taller. Build one
  more tower to test your pattern.

6
Communication

• An important step in communicating mathematical
  thinking to others is organizing and clarifying
  ones ideas.
• Example
• Express the pattern (relationship) in a
  mathematical sentence (equation).

7
Connections

• Students build new understandings on previous
  knowledge
• Students build new understandings between
  mathematics and other subject areas
• Students build new understandings between
  mathematics and every-day life.
• Example
• How would the pattern change if the towers are
  double wide rather than single? Draw 4
  double-width towers on dot paper to test your
  prediction.

8
Representation

• Students can develop and deepen their
  understanding of mathematical concepts and
  relationships as they create, compare, and use
  various representations.
• Example
• Create a table of values and graph representing
  the relationship of the height of the single-wide
  towers and their corresponding surface areas.
  You may use computer software or a graphing
  calculator.

9
Questions to Foster Mathematical Understanding

• Does anyone have the same answer but a different
  way to explain it?
• Can you convince us that that makes sense?
• Can you model that to prove your thinking?
• Does that always work?
• How does this relate to ?
• Can you give us an example of ?

10
Principles of Mathematics

• The Equity Principle
• The Curriculum Principle
• The Teaching Principle
• The Learning Principle
• The Assessment Principle
• The Technology Principle

11
Self-Reflection Survey

• Individual reflection
• Based on Best Practices of the Principles of
  Mathematics

12
Resources

• Web sites used in OCSD classes
• Principles and Standards for School Mathematics -
  NCTM