Best Practices in Mathematics Education

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Best Practicesin Mathematics Education

• DR. TOM OTTINGER
• Reinhardt College
• 7300 Reinhardt College Circle
• Waleska, GA 30183
• 770-720-5596
• tpo_at_reinhardt.edu

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Goals of Mathematics Instruction

• Reason mathematically
• Evaluate mathematical arguments both formally and
  informally
• Use the language of mathematics to communicate
  ideas and information precisely
• Make connections among mathematical topics and to
  other disciplines
• Adapted from the Executive Summary of the
• Georgia Performance Standards

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Thinking Skills Blooms Taxonomy

• Knowledge Recall data or information.
• Examples Recite a policy. Quote prices from
  memory to a customer. Knows the safety rules.
• Key Words defines, describes, identifies,
  knows, labels, lists, matches, names, outlines,
  recalls, recognizes, reproduces, selects, states.

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Thinking Skills Blooms Taxonomy

• Comprehension Understand the meaning,
  translation, interpolation, and interpretation of
  instructions and problems. State a problem in
  one's own words.
• Examples Rewrites the principles of test
  writing. Explain in ones own words the steps for
  performing a complex task. Translates an equation
  into a computer spreadsheet.
• Key Words comprehends, converts, defends,
  distinguishes, estimates, explains, extends,
  generalizes, gives examples, infers, interprets,
  paraphrases, predicts, rewrites, summarizes,
  translates.

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Thinking Skills Blooms Taxonomy

• Application Use a concept in a new situation or
  unprompted use of an abstraction. Applies what
  was learned in the classroom into novel
  situations in the work place.
• Examples Use a manual to calculate an
  employees vacation time. Apply laws of
  statistics to evaluate the reliability of a
  written test.
• Key Words applies, changes, computes,
  constructs, demonstrates, discovers, manipulates,
  modifies, operates, predicts, prepares, produces,
  relates, shows, solves, uses.

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Thinking Skills Blooms Taxonomy

• Analysis Separates material or concepts into
  component parts so that its organizational
  structure may be understood. Distinguishes
  between facts and inferences. 
• Examples Troubleshoot a piece of equipment by
  using logical deduction. Recognize logical
  fallacies in reasoning. Gathers information from
  a department and selects the required tasks for
  training.
• Key Words analyzes, breaks down, compares,
  contrasts, diagrams, deconstructs,
  differentiates, discriminates, distinguishes,
  identifies, illustrates, infers, outlines,
  relates, selects, separates.

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Thinking Skills Blooms Taxonomy

• Synthesis Builds a structure or pattern from
  diverse elements. Put parts together to form a
  whole, with emphasis on creating a new meaning or
  structure.
• Examples Write a company operations or process
  manual. Design a machine to perform a specific
  task. Integrates training from several sources to
  solve a problem. Revises and process to improve
  the outcome.
• Key Words categorizes, combines, compiles,
  composes, creates, devises, designs, explains,
  generates, modifies, organizes, plans,
  rearranges, reconstructs, relates, reorganizes,
  revises, rewrites, summarizes, tells, writes.

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Thinking Skills Blooms Taxonomy

• Evaluation Make judgments about the value of
  ideas or materials.
• Examples Select the most effective solution.
  Hire the most qualified candidate. Explain and
  justify a new budget.
• Key Words appraises, compares, concludes,
  contrasts, criticizes, critiques, defends,
  describes, discriminates, evaluates, explains,
  interprets, justifies, relates, summarizes,
  supports.

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Thinking Skills Blooms Taxonomy

• Knowledge
• Comprehension
• Application
• Analysis
• Synthesis
• Evaluation

Higher Order
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Concepts versus Skills

• Knowledge
• Comprehension
• Application
• Analysis
• Synthesis
• Evaluation

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Goals of Mathematics Instruction

• Reason mathematically
• Evaluate mathematical arguments both formally and
  informally
• Use the language of mathematics to communicate
  ideas and information precisely
• Make connections among mathematical topics and to
  other disciplines

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Concepts versus Skills

• Reason mathematically
• Evaluate mathematical arguments both formally and
  informally
• Use the language of mathematics to communicate
  ideas and information precisely
• Make connections among mathematical topics and to
  other disciplines

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Success in Mathematics
Connections
Concepts
Problem Solving
Skills
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Success in Mathematics

• Students must be given the time and the
  guidance to construct their own understandings of
  mathematics as opposed to memorizing the
  understandings of others.
• Georgia Department of Education

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Best Practices

• Explanation and justification as an integral part
  of student work
• Active involvement of students
• Exploration, investigation, and/or discovery
• Discussion, collaboration
• Multiple representations, including words,
  pictures, graphs, tables, symbols
• Connections to other areas of mathematics, to
  other curriculum areas, and to students concerns
  and interests
• Some open-ended questions, problems, activities,
  or investigations
• Appropriate use of technology

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Appropriate Use of Technology

• Use as a tool for exploration and investigation
• Use to facilitate development of conceptual
  understanding
• AVOID use as a substitute for understanding
  (dont teach mindless button-pushing)
• AVOID use as an end in itself
• (use technology to teach math dont teach
  technology)

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Effective Teaching Plans

• Objectives
• Determine what is to be taught
• Determine how it is to be taught
• Procedures
• Provide a plan for accomplishing objectives
• Incorporate best practices
• Assessments
• Include both formative and summative
• Guide current and future instruction
• Show what students know and can do as well as
  what they dont know or cant do