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ERIC Number: EJ1021713
Record Type: Journal
Publication Date: 2013
Pages: 10
Abstractor: As Provided
ISSN: ISSN-0020-739X
On Roots and Squares--Estimation, Intuition and Creativity
Patkin, Dorit; Gazit, Avikam
International Journal of Mathematical Education in Science and Technology, v44 n8 p1191-1200 2013
The paper presents findings of a small scale study of a few items related to problem solving with squares and roots, for different teacher groups (pre-service and in-service mathematics teachers: elementary and junior high school). The research participants were asked to explain what would be the units digit of a natural number to be squared in order to obtain a certain units digit as a result. They were also asked to formulate a rule--an algorithm for calculating the square of a 2-digit number which is a multiple of 5. Based on this knowledge and estimation capability, they were required to find, without using calculators, the square roots of given natural numbers. The findings show that most of the participants had only partial intuition regarding the units' digit of a number which is squared when the units' digit of the square is known. At the same time, the participants manifested some evidence of creativity and flow of ideas in identifying the rule for calculating the square of a natural number whose units digit is 5. However, when asked to identify, by means of estimation and based on knowledge from previous items, the square roots of three natural numbers, only few of them managed to find the three roots by estimation.
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Publication Type: Journal Articles; Reports - Research
Education Level: Elementary Education; Higher Education; Postsecondary Education; Junior High Schools
Audience: N/A
Language: English
Sponsor: N/A
Authoring Institution: N/A
Grant or Contract Numbers: N/A