66
performed by an institution, the performance of a company, or the wealth of a
nation, all of which are sometimes claimed to be measurable by computing given
mathematical functions. In these cases one can interpret measurement as a tool not
only for the acquisition of information on the measurand, but also, and even before,
for gaining knowledge about the general property under consideration.
The case of reading comprehension ability is interesting in this respect, given
how it has changed historically. In the nineteenth century, one procedure for checking whether students could read was that they were asked to read a text aloud, and
often also asked to recite parts of the text from memory (Matthews, 1996; Smith,
1986). Thus, at that point of time, the (implicit) property definition was something
like “ability to accurately read a text out loud”. With time, it was realized that students could succeed at such tasks without understanding the content of the text passage. This led to the advent of silent reading tests, where reading comprehension
ability was assayed by the interaction of the reader with comprehension questions
(Pearson, 2000), generically called “items”. Thus, at this later point, the property
definition (still implicitly) changed to something like “ability to demonstrate understanding of the content of the text (and the question)”. An early test of this sort was
developed by Frederick Kelly (1916), and an example question from it is shown in
Fig. 1.1. The questions were chosen to be likely to generate incontrovertibly correct
or incorrect responses. The indication of a student’s reading comprehension was
then the number, or percentage, of the test items the student answered correctly.
3.4.2 Measurement and measure
In the framework of necessary conditions for measurement introduced in Sects. 2.2
and 2.3—measurement as an empirical and informational process, designed on purpose, whose input is an empirical property of an object and that produces information in the form of values of that property—a further specification is appropriate,
about the very distinction between measurement and measure.
The ancient Greek verb for has the root “metr-” (μετρ), from
which the term “metrology” derives, highlighting the relation of the concepts. However, we see a more difficult relation between
the concepts designated by the nouns “measure” and “measurement”.
The Euclidean tradition is sometimes thought of as “the earliest contribution to
the philosophy of measurement available in the historical record” (Michell, 2005:
p. 288),
20
as witnessed by the oft-quoted first definition of Book 5 of the Euclid’s
Elements: “A magnitude is a part of a[nother] magnitude, the lesser of the greater,
when it measures the greater” (Euclid, 2008: V.1, emphasis added). Hence the
hypothesis that the nouns “measurement” and “measure” refer to the same entity
20 More broadly, the importance of this contribution is also highlighted by the consideration that
“Euclid’s Elements, written about 300 BC, has probably been the most influential work in the history of science” (Suppes, 2002: p. 10).
3 Technical and cultural contexts for measurement systems
performed by an institution, the performance of a company, or the wealth of a
nation, all of which are sometimes claimed to be measurable by computing given
mathematical functions. In these cases one can interpret measurement as a tool not
only for the acquisition of information on the measurand, but also, and even before,
for gaining knowledge about the general property under consideration.
The case of reading comprehension ability is interesting in this respect, given
how it has changed historically. In the nineteenth century, one procedure for checking whether students could read was that they were asked to read a text aloud, and
often also asked to recite parts of the text from memory (Matthews, 1996; Smith,
1986). Thus, at that point of time, the (implicit) property definition was something
like “ability to accurately read a text out loud”. With time, it was realized that students could succeed at such tasks without understanding the content of the text passage. This led to the advent of silent reading tests, where reading comprehension
ability was assayed by the interaction of the reader with comprehension questions
(Pearson, 2000), generically called “items”. Thus, at this later point, the property
definition (still implicitly) changed to something like “ability to demonstrate understanding of the content of the text (and the question)”. An early test of this sort was
developed by Frederick Kelly (1916), and an example question from it is shown in
Fig. 1.1. The questions were chosen to be likely to generate incontrovertibly correct
or incorrect responses. The indication of a student’s reading comprehension was
then the number, or percentage, of the test items the student answered correctly.
3.4.2 Measurement and measure
In the framework of necessary conditions for measurement introduced in Sects. 2.2
and 2.3—measurement as an empirical and informational process, designed on purpose, whose input is an empirical property of an object and that produces information in the form of values of that property—a further specification is appropriate,
about the very distinction between measurement and measure.
The ancient Greek verb for
which the term “metrology” derives, highlighting the relation of the concepts
the concepts designated by the nouns “measure” and “measurement”.
The Euclidean tradition is sometimes thought of as “the earliest contribution to
the philosophy of measurement available in the historical record” (Michell, 2005:
p. 288),
20
as witnessed by the oft-quoted first definition of Book 5 of the Euclid’s
Elements: “A magnitude is a part of a[nother] magnitude, the lesser of the greater,
when it measures the greater” (Euclid, 2008: V.1, emphasis added). Hence the
hypothesis that the nouns “measurement” and “measure” refer to the same entity
20 More broadly, the importance of this contribution is also highlighted by the consideration that
“Euclid’s Elements, written about 300 BC, has probably been the most influential work in the history of science” (Suppes, 2002: p. 10).
3 Technical and cultural contexts for measurement systems