Early Algebra Working Group (8)

1
Early Algebra Working Group (8)

• What Early Algebra is not vis-à-vis pre-algebra
  (how it is commonly thought of).
• Historical overview, esp. relations among
  arithmetic and algebra
• Overview of algebra research (from an
  enculturation point of view)
• Sad stories (70s, 80s, and 90s)
• Arithmetic-hangover sign, buggy procedures,
  mal-interpretation, S-P problem, alienation,
  failure rates, Toshi-story re TIMMS
• Untapped potential
• Evidence of real potential Happy stories (90
  onwards)

2
Existing Examples Broad List (17)

• Variable and modeling
• Spreadsheet group
• Logo (Jill V.)
• From generalizing with open number sentences
• Quasi variables from arithmetic and geometry
• Tom C parts of Susie video
• Unexecuted expressions
• Fraction thinking
• Algebraic use of number (Zaskis)
• DAB on
• Functions
• Representations
• Variable number line

3
Detailed Examples

• From generalizing with open number sentences Tom
  Carpenter parts of Susie video (5)
• David Carraher
• 1. Functions (3)
• 2. Variable number line (1)
• Hawaii/Davydov (3)
• Quasi variables/algebraic use of number (include
  geometric example) (2)

4
Research Agenda/Implications

• Work to be done
• Research policy
• Issues needing attention
• Implications for algebra in grades 6-14

5
Research needed

• 1. Studies that look at how teachers adapt to
  change in early mathematics (towards early
  algebra). Their understanding of what the
  mathematics of early algebra means.
• 2. The study of long term interventions (with
  respect to teachers, students, etc)
• 3. What are the missing pieces before we can
  propose an early algebra curriculum. How to
  algebrafy the whole of early mathematics? What
  principles will help us algebrafy early
  mathematics, such as varying parameters in a
  mathematical task. How the understanding of
  number facilitate algebraic thinking? Research on
  approaches/assumptions behind how children think.
• 4. What are the implications of what we know
  about early algebra for the 6-14 in the K-5
  curriculum?
• 5. Does traditional arithmetic affect some
  childrens abilities to reason algebraically?
  How do mathematical learning and development
  evolve in new EA environments?
• 6. Systematic research on how students who are
  failing think. What factors do they attribute
  their failure to. What things do not make sense
  to them? What is it about the nature of the
  subject that makes students say It doesnt make
  sense?
• 7. Surveys on the uses of algebraic/algebrafy and
  how they relate to research.
• 8. Research on approaches/assumptions behind how
  children think.

6
Prepare for Representation Pluralism in 21st.
Century