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Greater than, less than, equals to : kindergartners' use of symbols to represent such relationships
Author
Hoo, Carmen Ka Mun
Supervisor
Ng, Swee Fong
Abstract
Relationships such as equivalence, „greater than‟ and „smaller than‟ can be represented using concrete aids, pictures, language and symbols. The capacity to represent such relationships can form the basis of children‟s understanding of mathematical relationships such as equations and inequalities. Children may find representations using concrete aids or pictures more meaningful than those represented using language and mathematical symbols.
In the early 60s‟ Davydov experimented with a new curriculum which explored whether algebra could be taught in primary school in his homeland Russia. Of particular significance, he focused on whether children as young as first grade could express relationships demonstrated using concrete objects schematically and then as mathematical equations or inequalities using letters and mathematical symbols such as „=, >, and <‟. Because of the Cold War very little was known of the Russian‟s work which only gained prominence when the English translation of it appeared in his 1962 paper published in Sovetskaia Pedagogika.
This exploratory study, the first of its kind in Singapore, seeks to replicate a part of Davydov‟s seminal work. I examined the capacity of 5- and 6-year old kindergartners learning to use concrete aids, language and letters and symbols (=, < and >) to represent relationships of equivalence and inequality. Because the intended kindergartners of this study were younger than the first graders in Davydov‟s work, a pilot study was conducted to ascertain the suitability of Davydov's tasks. Based on the findings of the pilot study, a series of selected tasks were administered to 16 kindergartners from two different pre-schools.
Most of the kindergartners were able to use "=‟, "<‟ and ">‟ symbols to record the equivalence and inequality relationships represented by the concrete materials. When given equations and inequalities as stimulus, many of the kindergartners could also fill in missing symbols to represent equations and inequalities in both directions, for example, either as A = B or B = A. The kindergartners were more successful representing equivalent relationships than non-equivalent ones.
Implications of the findings on teaching and learning of how mathematical relationships can be represented were discussed. These are suggested to impact not only kindergartners but higher levels as well.
In the early 60s‟ Davydov experimented with a new curriculum which explored whether algebra could be taught in primary school in his homeland Russia. Of particular significance, he focused on whether children as young as first grade could express relationships demonstrated using concrete objects schematically and then as mathematical equations or inequalities using letters and mathematical symbols such as „=, >, and <‟. Because of the Cold War very little was known of the Russian‟s work which only gained prominence when the English translation of it appeared in his 1962 paper published in Sovetskaia Pedagogika.
This exploratory study, the first of its kind in Singapore, seeks to replicate a part of Davydov‟s seminal work. I examined the capacity of 5- and 6-year old kindergartners learning to use concrete aids, language and letters and symbols (=, < and >) to represent relationships of equivalence and inequality. Because the intended kindergartners of this study were younger than the first graders in Davydov‟s work, a pilot study was conducted to ascertain the suitability of Davydov's tasks. Based on the findings of the pilot study, a series of selected tasks were administered to 16 kindergartners from two different pre-schools.
Most of the kindergartners were able to use "=‟, "<‟ and ">‟ symbols to record the equivalence and inequality relationships represented by the concrete materials. When given equations and inequalities as stimulus, many of the kindergartners could also fill in missing symbols to represent equations and inequalities in both directions, for example, either as A = B or B = A. The kindergartners were more successful representing equivalent relationships than non-equivalent ones.
Implications of the findings on teaching and learning of how mathematical relationships can be represented were discussed. These are suggested to impact not only kindergartners but higher levels as well.
Date Issued
2010
Call Number
QA135.6 Hoo
Date Submitted
2010