Estimation and the General Estimating Ability of Secondary Students - an Overview

[Abstract] Mathematics and Science education at secondary level emphasizes the importance of teaching measurement. Any continuous measurement like measuring length, time etc. is not exact, at best an "estimate". Estimation offers approximate and real values for practical utility. Estimation can be qualitative or quantitative. Living beings practice qualitative estimation, using sensory signals, all the time. Learned individuals make quantitative estimation, for specific needs. It is possible to define and measure General Estimating Ability. This paper discusses estimation and suggests a model to score, grade and categorize the estimator. [Keywords] Estimation; general estimating ability; grading and categorization; mathematics; science education; secondary students Introduction We count, we measure and we also estimate. Counting is taught at an early childhood, followed by measuring and computing certain physical quantities like length, mass, time etc. Correct measurement of various attributes of physical quantities, use of few measuring devices, appreciating their limitations etc., find due place in school education, leaving estimation to relative neglect. A student who is capable of estimating and is willing to apply this capability to guess the solution of a problem can be expected to be more motivated to solve it (Polya, 1965). The National Council of Supervisors of Mathematics, using the Euclid Conference Report (National Institute of Education, 1975) as a basis for developing a position paper on basic skills, included estimation within the 10 basic skill areas in need of development. The ability to estimate has been identified as one of the basic competencies recommended that every one should have (Carpenter et al., 1976). But, most textbooks give little attention to the development of estimation skills (Freeman, U Kuhs et al., 1980). In everyday situation involving numbers estimation is often more useful than precise calculation (Buchanan, 1980). Further, teaching students to estimate will improve skills in computation and in problem solving (Schoen et al., 1981). Wide spread use of computing technology places emphasis on estimation for verifying the reasonableness of computation and the need to formulize these techniques in considering assumptions underlying mathematics instruction (Levin, 1981). The Conference Board of the Mathematical Sciences (NSB Commission, 1982) recommended that substantially more emphasis be given to the development of estimation skills. Interestingly, we find many children and adults too are poor estimators (Underbill, 1983). New Jersey Mathematics Curriculum Framework (1996) observes; any continuous measurement is inexact and it is at best an 'estimate'. Estimation of measures should be a focus of any work that students do with measurement. Third International Mathematics and Science Study (TIMSS) includes information from over 40 countries and measures mathematics and science abilities in elementary, middle and high schools comprising problem solving ability, number sense, measurement and estimation. The new world class standards for US schools as identified by 47 states in 1998 had outlined K-12 standards in mathematics, includes; fostering estimation skills in students is a commendable goal. However, warns not to overemphasize estimation. We need a way to teach children how to formulate a response that is sensible and based on reason. For example estimates should fall in a reasonable range (Kuwahara, 2001). Estimation and Estimating Ability According to Webster's Third New International Dictionary (1993) Estimation is to arrive at a value judgment that is often valid but incomplete, approximate or tentative. A judgment made from usually mathematical calculation especially from incomplete data. Estimation is a rough or approximate calculation (as of the number, amount or size of any thing). The International Encyclopedia of Education (1985) observes: "In general usage, estimation is synonymous with judgment or opinion associated with value, worth, or significance. …