Principled Knowledge Strategy

1
Principled Knowledge Strategy

• F. D. Rivera, Ph.D.
• Department of Mathematics
• San Jose State University
• Module 15, Session 4

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Principled Knowledge Strategy

• Three kinds of mathematical knowledge
• Conceptual knowledge
• Procedural knowledge
• Principled knowledge

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Principled Knowledge Strategy

• Conceptual knowledge knowledge rooted in a firm
  understanding of principles.
• In mathematics, this refers to the why aspect.

4
Principled Knowledge Strategy

• Procedural knowledge knowledge that is driven by
  the use of procedures and steps.
• In mathematics, this refers to the how aspect.

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Principled Knowledge Strategy

• Principled knowledge, a term borrowed from
  Lampert (1986) knowledge that is both conceptual
  and procedural.
• In mathematics, this refers to being able to
  perform the operations and to explain the
  validity of the operations.

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Principled Knowledge Strategy

• Procedure Principle strategy works better than
  Procedures-only strategy

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Example Algebra

• In using algebra tiles
• Good thing to do
• Were going to add this two polynomials, x2 and
  3x2. We could do this because both are similar
  terms (use manipulatives to show a piece of a red
  square and three pieces of another red square).
  So in all I have 4 red squares and this means
  4x2.

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Example Algebra

• Not so good
• Were supposed to add x2 and 3x2. Copy x2 and
  just add 1 and 3. You get 4x2.

9
Example Geometry

• Suppose students with learning disabilities in
  math have been asked to determine the area of a
  square whose side is 5 cm.
• Good thing to do
• In finding the area of this square, we know that
  a square
• is a rectangle with equal sides. So if you
  remember the
• formula for the area of a rectangle, A length x
  width,
• then the area of a square is A side x side.
  Hence, the
• area of this square must be A 5 x 5 which
  equals 25
• square cm. Dont forget to include the correct
  unit of
• measure. Since were dealing with an area of a
  figure that
• has both length and width, the measure has to be
  in
• square units.

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Example Geometry

• Not so good
• Were supposed to get the area of
• this square. So A s2. Just plug in
• the numbers and youre all set. So
• A 52 which equals 25.