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Estimation in Schools resulted in an MPhil awarded by the Institute of Education (1992). Please make use of my work in any way you see fit.
You have the choice of viewing the research in several different ways and clicking on any underlined word will result in transfer to that part of the Website or if you've decided this is not your cup of tea, go back to the Home Page.
I have developed an Estimation Teaching Programme based on the Research and this can be viewed and then perhaps you will want to see the rationale as developed in the research.
A brief Synopsis (the Abstract of the MPhil)
Or a Chapter at a time of interest to you. Each Chapter is available as a pdf file and the size of each file is given after the Chapter number or the entire MPhil also as a large pdf file.
CHAPTER 1 is "An Overview of the Research" and the descriptions below for each chapter alleviate the need to produce this chapter.
The following aspects of the research can be accessed independently but there are references to other aspects which can be seen if the MPhil is read in its entirety.
Chapter 2 (167 KB) The Nature of Estimation - Discusses the various types of estimation defining terms where necessary concentrating on Computational & Quantitative Estimation
Chapter 3 (75 KB) The Value of Estimation - Relates my reasons to believe that estimation is both valuable and important to the mathematics curriculum.
Chapter 4 (315KB) Studies of Estimation - Discusses the work of other researchers in the field. A major problem encountered in the literature search is the scarcity of research which has included data.
Chapter 5 (70 KB) Preliminary Research - Interviewing pupils while they engaged in estimation activities was used in the early stages of the work.
(It probably best to read the following two chapters together but click them in order)
Chapter 6 (165 KB) & Chapter 7 (783 KB)- Discuss the development of a pair of tests to assist me in determining areas of estimation which would be worth greater investigation and a full discussion of the results of these tests is given here. Two major areas of interest arose from these tests. The graph below shows an interesting distribution which is investigated.
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Chapter 8 (1662 KB) A New Criterion of Reasonableness - One problem encountered earlier in the research was the variety of criteria used by the different researchers preventing ease of comparison between studies. The graphs below show typical distributions for questions with large magnitude answers.
A question occurred to me i.e. "Is an estimate of 50 000 for a collection of 100 000 objects equivalent to an estimate of 5 for a collection of 10 objects? Is it reasonable to assess on a straight percentage basis? A full description of the development of a Criterion Of Reasonableness (COR) is given to assess estimates of large quantities.
Chapter 9 (1417 KB) Interviews to Address the Issues of Units of Measure and Large Magnitude - Discusses pupil's inability to estimate quantitative measures expressed in metric terms and large magnitudes within the same limits of reasonableness as other estimates.
Chapter 10 (1444 KB) Encouraging Estimation and Measuring Confidence Levels Raises Another Issue - Shows that pupils do not value the estimation process and confidence in their estimates lead to a view that confidence is related to gender.
(It probably best to read the following two chapters together)
Chapter 11 (87 KB) & Chapter 12 (130 KB) Describe Estimation as a risk-taking activity and links are shown between gender and risk-taking. A survey shows there are strong indicators that the gender of the pupil is a major factor in their willingness to engage in risk-taking and in their self-confidence.
Chapter 13 (253 KB) Conclusions and Suggestions for Future Research - Restates some of the conclusions reached during the study and suggestions for future research are given.
The entire MPhil Dissertation (6481 KB)