USING CUISENAIRE RODS TO TEACH STUDENTS ABOUT FRACTIONS

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USING CUISENAIRE RODS TO TEACH STUDENTS ABOUT
FRACTIONS
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Introduction

• Focus is on adult learners
• Traditional-age college students
• Older college students
• We have found that our students often have
  trouble with basics mathematics skills
• Nationwide, over 20 of college freshmen take
  remedial mathematics courses
• About 40 of Felician freshmen take remedial
  mathematics
• About 60 of freshmen at two-year colleges take
  remedial mathematics

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Research Question

• Do Cuisenaire rods have a role in helping adult
  learners make sense of fractions?

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Theoretical Framework

• Manipulatives can help elementary students make
  sense of fractions
• Maher, Martino Davis (1994) Steencken (2001)
  Bulgar (2002) Reynolds (2005)
• Manipulatives must be used properly
• Kamii, Lewis, and Kirkland (2001)
• College students can benefit from rich
  mathematical experiences
• Glass and Maher (2002)

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Rationale for This Study

• Research has shown that Cuisenaire rods have
  helped elementary students make sense of
  fractions
• Our students have often been unsuccessful in
  performing basic operations on fractions when
  taught via traditional methods
• Students are unable to recognize when an answer
  does not make sense

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Our Data

• Sample of about 30 students
• Students in developmental classes based on
  placement test scores (Felician)
• Students in a math methods class for elementary
  teachers (Kean) who identified themselves as
  having difficulties with fractions
• Students in a math content class for elementary
  teachers (Felician)
• Data sources
• Classroom observations and teachers notes
• Student work

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Background

• Common characteristics of students
• Relied on rules which were sometimes imperfectly
  recalled
• Did not relate fraction problems to real
  situations
• Did not recognize unreasonable answers
• Errors similar to those made by elementary school
  students
• Adding numerator and denominator
• Cross multiplying

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Focus of This Paper

• Using Cuisenaire rods to explore basic operations
  with fractions
• Investigations with rods1
• Exploring relationship among the rods, including
  fractional relationships
• Assigning fraction names to the rods
• Comparing fractions with rods

1 Explorations to Build Meaning about Fractions,
by Elena Steencken, Robert B. Davis Institute for
Learning, Rutgers The State University of New
Jersey
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Fraction Problems

• Rationale
• To assess students understanding
• To improve students understanding
• Problems discussed
• The chocolate bar problem
• Division problems
• Multiplication problem

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The Chocolate Bar Problem

• I had a chocolate bar. I gave 1/2 of the bar to
  Jason and 1/3 of the bar to John. What fraction
  of the chocolate bar did I have left?
• Use Cuisenaire rods to model your answer.

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One Chocolate Bar Answer
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Division Problems

• What is 6 divided by 2?
• Build a model to justify your solution
• What is 6 divided by 1/2?
• Build a model to justify your solution

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Division Problem 1