Does C P P C Conceptual versus Procedural Understanding

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Does C P P C ?Conceptual versus Procedural
Understanding

• Dr. Jeremy Winters
• ElEd 6550

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Psychological Considerations to Teaching Math

• Mathematics should be
• A natural outgrowth of the childrens lives
• Interesting for the students
• Challenge their imagination
• Beget creative solutions

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Logical Approach

• Usual Order
• This approach does not ensure student success.
• Need to complement with Psychological approaches.

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Psychological Approaches

• Piaget Stages of Development
• 1. Sensorimotor (0-2 years)
• Imitate sounds and actions, and recognizes that
  objects still exist when they are out of sight.
• 2. Preoperational(2-7 years)
• Child gains an initial use of language and the
  ability to think in symbolic terms

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Psychological Approaches

• Piaget Stages of Development
• 3. Concrete Operations (7-11 years)
• Physical objects provide the medium for learning
• Children discovery objects can be changed or
  moved and still retain many of their
  characteristics and that these changes can be
  reversed
• 4. Formal Operations (around 11)
• Adults may never fully operate at this level
• Students can think logically about abstract
  problems.

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Piagetian Terms

• Conservation (age 7)
• Assimilation and Accommodations
• Children should be involved in inventing
  mathematics. It is through experiences that
  children discover relationships and solve
  problems. (Constructivism)

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Hot Air Balloons

• Your entry
• Things I want you to know
• Examples
• Students at Scales Elementary School

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Conceptual versus Procedural Knowledge

• What are they?
• From the Hot Air Balloon Activity
• Students taught in a way that relies too heavily
  on rote memorization isolated from meaning have
  difficulty recovering and retaining math concepts
  and generalizations. - Sherman
• Does C P P C?, notice neither is alone

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Concepts

• Concepts can not be known until they are
  experienced.

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Conceptual versus Procedural Knowledge

• What Barney has to Say

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The Dissimilar Learner

• Long-term understanding and skill achievement are
  established together when students successively
  build upon concepts in a guided discovery process.

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The Dissimilar LearnerMathematics Learning5
Interrelated Strands

• Conceptual Understanding
• Comprehension of ideas
• Procedural Fluency
• Flexible and accurate skills and procedures
• Strategic Competence
• Ability to formulate and solve problems
• Adaptive Reasoning
• Capacity to reflect and evaluate ones knowledge
  and ability to reason
• Productive Disposition
• Habitual inclination to make sense of and value
  what is being learned

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The Dissimilar Learner

• One who has experienced little or no success in
  all five areas or lack any understanding in one
  complete area.

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The Dissimilar LearnerDesigning Lessons for
Success

• Connect new concepts to those the students know
  and are actively engaged in at a concrete level
  of understanding
• Students represent understanding with pictures or
  diagrams
• Students attach numerals and number sentences to
  the drawings
• Students practice skills and algorithmic
  procedures through a variety of activities and
  reinforcement lessons.