1 Mapping children’s Mapping children’s understanding of understanding of mathematical equivalence mathematical equivalence Roger S. Taylor, Bethany Rittle- Roger S. Taylor, Bethany Rittle- Johnson, Percival G. Matthews, Johnson, Percival G. Matthews, Katherine L. McEldoon Katherine L. McEldoon
24
Embed
1 Mapping children’s understanding of mathematical equivalence Roger S. Taylor, Bethany Rittle-Johnson, Percival G. Matthews, Katherine L. McEldoon.
This document is posted to help you gain knowledge. Please leave a comment to let me know what you think about it! Share it to your friends and learn new things together.
Transcript
1
Mapping children’s Mapping children’s understanding of understanding of
mathematical equivalencemathematical equivalence
Roger S. Taylor, Bethany Rittle-Johnson, Roger S. Taylor, Bethany Rittle-Johnson, Percival G. Matthews, Katherine L. Percival G. Matthews, Katherine L.
McEldoonMcEldoon
• Goal of “Algebra for All” motivated National Mathematics Panel (2008) report on how to improve students’ readiness for algebra
• To meet this goal, must re-conceptualize algebra as a continuous strand from elementary through high school (NCTM, 2000)
Algebraic ReasoningAlgebraic Reasoning
2
• Previous research has shown that knowledge of the equal sign and equivalence (or equality) is critical for learning algebra (Carpenter, et al., 2003; Knuth, Stephens, McNeil, & Alibali, 2006)
• Equivalence is the principle that two sides of an equation represent the same value
• Provides the foundation for two key algebra proficiencies (Kieran, 1992):
• Understanding the equivalence of expressions
• Competence at performing the same operation on both sides of an equation
• Is accessible to elementary school children (Baroody & Ginsburg, 1983; Jacobs et al., 2007)
Algebra & EquivalenceAlgebra & Equivalence
3
• Many children view the equal sign operationally, as a command to carry out arithmetic operations (Baroody & Ginsburg, 1983; Carpenter, et al., 2003; McNeil & Alibali, 2005)
• Define “=“ as meaning “add up the numbers”
• Solve equations incorrectly when operations on the right side of the equal sign, such as: 3 + 5 = __ + 6
• Reject number sentences such as 3 + 5 = 5 + 3
• Children need to develop a relational view of the equal sign
ES4: (L2) Which answer choice below would you Put in the empty box to show that two nickels are the same amount of money as one dime? Circle your answer.
a)+b)=c)5¢
12
Equal Sign Wright MapEqual Sign Wright Map
Respondents | Items
ES1: (L3) What does the equal sign (=) mean?
ES5: (L3) Is this a good definition of the equal sign? Circle good or not good.• The equal sign means the same as.