Koedinger, K. and Nathan, M. 2000. Teachers and researchers

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Class Presentation by Melina Day based
on Teachers and Researchers Beliefs About the
Development of Algebraic Reasoning
Koedinger, K. and Nathan, M. (2000). Teachers
and researchers beliefs about the
development of algebraic reasoning. Journal for
Research in Mathematics Education, 31 (2).
Retrieved March 19, 2006 from
http//links.jstor.org/sici?0021-8251282000003
29313A23C1683ATARBAT3E2.0.CO3B2-C
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Types of Problems
original study 76 high school students
result unknown
start unknown
(arithmetic level)
(algebra level)
story problem (verbal)
symbolic equation (number sentence)
story problem (verbal)
symbolic equation (number sentence)
37
word equation (verbal)
word equation (verbal)
73
59
53
67
54
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Types of Problems
study following year 171 high school students
result unknown
start unknown
(arithmetic level)
(algebra level)
story problem (verbal)
symbolic equation (number sentence)
story problem (verbal)
symbolic equation (number sentence)
29
word equation (verbal)
word equation (verbal)
80
60
56
74
48
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• start unknown (algebra) problems
• are harder for students than
• result unknown (arithmetic
• problems)

Generalizations

• symbolic equation problems are
• harder than word equation
• problems story problems

this surprised me!

• verbal algebra problems are equal
• in difficulty to symbolic
• arithmetic problems

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4 Types of Solution Strategies Students Used
guess-and-test
arithmetic
unwinding (word backwards)
algebraic
highest likelihood of success (70)
with start unknown problems
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• researchers need to know
• misconceptions teachers have
• about algebra problem solving

Solution?

• then they could consider new
• approaches for improving
• teachers understanding of
• students thinking

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STUDY

• 67 teachers (7th-12th grade math)
• same state
• wide variety of settings of
• teaching
• recruited from a teacher
• workshop

Who Were the Participants?

• 35 researchers
• throughout the U.S.
• recruited from Internet
• discussion group on algebraic
• thinking instruction

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STUDY

• teachers and researchers were
• asked to rate problems from
• easiest to most difficult

What Was the Procedure?
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overall, both groups thought this was the easiest
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teachers rankings sequencing in the math books
were aligned
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Conclusion
Studies found
more research on development of students
algebraic reasoning problem solving must be
examined before teachers make curricular decisions
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Conclusion
Studies found
students learn better with the Verbal Precedence
Model
educators need to know students alternative
reasoning strategies (ex. guess and test
unwinding)
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• allow students to try to solve
• problems using a variety of
• methods

Classroom Application

• address informal methods during
• instruction build on them as a
• means to teach formal algebraic
• methods

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Work Space
Can you solve the problem using a different
strategy?
A Strategy Another Student Used to Solve the
Problem
A Strategy Another Student Used to Solve the
Problem