Measurement in society

Summary: Accuracy and precision are important in the many systems of measurements used in various spheres in society.

Imagine how chaotic the world would be if people could not measure anything! People would not be able to keep track of time, would not know weights or heights of people (or of anything else in the world), could not calculate the distance between any two points, and would not have recipes to cook properly. Indeed, the list of everyday activities that would be impossible to do in the absence of measurement is endless. Thus, measurement is an essential part of everyday life. Measurement is a fundamental part of mathematics research and curricula and there are many types of measurements in society. Some measurements elucidate productivity or change. Others measure large-scale aspects of society, like gross domestic product (GDP). Area measurements have practical applications in areas like surveying and interior design. Measurements are fundamental in drug dosing labels, quality control, missile launches, and in many other applications and fields. Because of its critical and practical importance, measurement is an extensively studied concept in pre-K–12 mathematics education.

Measurement Systems

Numerous measurement systems have been developed and used since ancient times, the earliest of which used body parts as the unit of measurement. The many, diverse measurement systems were a source of confusion, not only among nations, but also among different fields within a nation. To establish common units of measurement and promote their use, a treaty titled the “Convention of the Metre” was signed by 17 countries on May 20, 1875. The Convention of the Metre established three international organizations—the International Bureau of Weights and Measures (BIPM), the General Conference on Weights and Measures, and the International Committee for Weights and Measures—to oversee issues related to measurement in the member nations.

In 1960, the 11th General Conference on Weights and Measures developed and adopted a unified measurement system named International System of Units (SI) to promote a worldwide measurement system. The SI is based on seven dimensionally independent units: meter (the unit of length; abbreviated as m), kilogram (the unit of mass; abbreviated as kg), second (the unit of time; abbreviated as s), ampere (the unit of electric current; abbreviated as A), kelvin (the unit of thermodynamic temperature; abbreviated as K), mole (the unit for amount of substance; abbreviated as mol), and candela (the unit of luminous intensity; abbreviated as cd). Although the spelling of the base units may differ in different languages, the symbols are the same world-wide. The SI is an evolving measurement system to keep up with ever-growing measurement needs. The BIPM, which is comprised of many countries, ensures that measurements throughout the world are traceable to the SI. The BIPM is related to other significant international organizations such as the International Commission on Illumination, the International Atomic Energy Agency, the International Laboratory Accreditation Cooperation, the World Health Organization, and the International Organization of Standardization. Such a worldwide organization to oversee the uniformity of measurements explains clearly the reason for the crucial emphasis on measurement in mathematics curricula.

The United States has its national standards for measurement and measuring devices explained in the U.S. Code. Because measurement and measurement devices are a part of everyday life and are used in various businesses and for commercial purposes, the U.S. Code, published by the Office of the Law Revision of the House of Representatives, includes a chapter titled “Weights and Measures and Standard Time” under the Title 15. The chapter sets standards for weight and measurement devices to enforce accuracy and to ensure equity in the marketplace. In the early twenty-first century, the acknowledgement of measurement in the U.S. Code as a chapter containing 267 sections under nine subchapters is a sound indicator of the importance of measurement in human life.

Accuracy and Precision in Measurement

Any measurement is an approximation to the real value of a quantity. The length of the previous sentence might be 12 centimeters (cm), but in millimeters (mm) it would be 121 mm; 12 cm is not equal to 121 mm. The reason behind the difference between these two measurements is the second measurement is more accurate than the first one. Can it be measured more accurately? This question yields to the need for accurate measurement. One millimeter in this example can be ignored, but an inaccuracy of a mere millimeter in a missile launch may result in a disaster. Improvements in measurement systems are extremely important to make measurements as accurate as possible.

In measurement, the most accurate and precise results are desired. “Accuracy” in measurement refers to the extent to which a measured value matches the correct value. “Precision,” on the other hand, refers to the reliability of a measurement and how close individual measurements are to each other. Measurement units and devices in different fields of study are not static; rather, they evolve to improve accuracy and precision. In the United States, the National Institute of Standards and Technology (NIST) is a federal agency that employs mathematicians and scientists, among others, whose main tasks include the advancement of the science of measurement and measurement standards. NIST, together with partners from the government, industry, and academia, also develops measurement tools for different sciences. The services of NIST include verification of the accuracy of measurements, instrument calibration (for example, calibration of dimensional, mechanical, or electromagnetic instruments) to improve measurement quality, and the development of innovative measurement methods.

Although accuracy and precision are always desirable in measurement, in some fields quality of measurement is more crucial. For example, the National Aeronautics and Space Administration (NASA) uses various instruments to measure temperature, pressure, load, and acceleration, and to make other critical measurements for its test programs. The Measurement Standards and Calibration Laboratory of the White Sands Test Facility, which supports an extensive number of test programs, performs instrument calibrations to ensure measurement quality is compatible with recognized national standards that are traceable to NIST. In NASA’s test programs, any error in measurements in any equipment may cause not only the deaths of highly trained astronauts but also the loss of millions of dollars. Accurate and precise measurement therefore underpins the success of NASA missions, including launching spaceships and ensuring their safe return to Earth.

Another field where measurement accuracy has critical importance is the health industry. Cancer is one of the most serious diseases that the human race has faced so far. Almost 13% of all deaths in the world were caused by cancer in 2004. Radiotherapy, which uses high-energy radiation to kill cancer cells, is one of the most frequent methods used to treat cancer patients. However, radiotherapy not only kills cancer cells but kills healthy cells as well. Before the start of a cancer treatment, doctors conduct a simulation to locate the patient’s tumor and the normal tissues around it. In order to provide effective treatment, the next step is to measure the dose of the radiotherapy required and the safest angles to deliver the radiation to kill cancer cells. Measurements taken for radiotherapy have to be as precise as possible because the amount of radiation required to kill a cancer cell differs by the type of cancer cell and there is a risk of damaging the normal tissue during the radiation delivery. Sophisticated computers capable of making sensitive measurements are used for radiotherapy planning. Thus, human error in measurement is decreased. Advancements in technical equipment used in cancer treatment help to increase the effectiveness of the treatment and decrease the deaths caused by cancer. Monitoring the patient’s temperature and thermal dosage in real time provides doctors the opportunity to treat tumors as closely as possible while keeping the adjacent healthy tissues safe.

Measurement in Everyday Life

Measurement is a pervasive mathematical concept in everyday life, so it has many applications to a variety of careers, such as health sciences, architecture and construction, interior design, carpentry, meteorology, and public safety. Precise measurement is crucial in healthcare, as monitoring patient condition has critical importance. Thus, choosing effective measurement devices and obtaining accurate measurements (for example, of weight, blood pressure, or blood sugar) are essential aspects of healthcare professions. Also, healthcare professionals frequently use measurement conversion on the job. Doctors, nurses, and pharmacists convert between English and metric systems, or between Celsius and Fahrenheit, when they collect patient information on weight or temperature or when calculating appropriate medication dosages to administer. Measurement conversion is a particularly important competency for pharmacists, as they convert among different measurement systems such as metric, apothecary, and avoirdupois systems when they calculate medication dosages and fill orders.

Measurement is among the essential mathematics concepts applied in architecture, construction, and related careers. From the design and scale models of a project to its actual construction, precise and accurate measurement is vital. Measurement is also used extensively by interior designers as they improve the aesthetics and function of interior spaces. Interior designers have to determine precise measures of virtually all parts of a space to most effectively utilize the space and to decide the type, size, and placement of furniture or fixtures. Designers need to have precise area measures of walls, floors, or countertops to determine the size and number of tiles needed to cover these surfaces. Indeed, site measure and survey is an essential routine for interior designers in which they get measures of a space and draw an outline of the space, including dimensions.

Carpentry is another occupation for which measurement is substantially important. An old saying emphasizes the significance of measurement in carpentry: “Measure twice, cut once.” Because precise measurement is at the heart of good carpentry work, carpenters use various specialized measurement tools, such as a combination square (to accurately measure 45 degree and 90 degree angles), carpenter’s square (to plot right angles), and T-bevel (to set and transfer angles), in addition to the regular metal tape measures and folding rulers.

Although most people are familiar with thermometers and their uses, many may not know about various other measurement scales meteorologists use to organize and record weather conditions. Meteorologists use anemometers to measure wind speed or pressure, ceilometers to measure the thickness and height of clouds, barometers to measure atmospheric pressure, and high-tech sensors to measure humidity. People have always been interested in reliable and long-term weather forecasts. Although weather predictions are increasingly accurate and can be made for increasingly longer terms, meteorologists are continuously searching for methods to improve weather predictions. In this effort, innovative measurement devices in meteorology are being developed using the most up-to-date technology to make more accurate and precise weather and climate predictions.

Measurement also has significant applications in public safety. To maintain public travel safety, the Transportation Security Administration (TSA) utilizes the most advanced imaging technology, such as millimeter wave scanners to screen passengers for metallic and nonmetallic threats that might be anywhere on the body without physical contact. Millimeter wave scanners use electromagnetic waves to produce a black-and-white image in seconds. These scanners transmit extremely high radio frequencies, a wavelength of 1–10 mm, from two antennas to construct a three-dimensional image of the person scanned. The energy each radio wave reflects back from the passenger’s body to the scanner is transmitted to a computer. Then, software measures the energy for each radio wave reflected from the passenger’s body to construct an accurate and precise three-dimensional image of the passenger for security check. With the help of such detailed three-dimensional images, any hidden object can easily be identified by security. For such an imaging technology to be used in areas requiring high security needs, like airports, the technology needs to provide fast, accurate, and reliable images. Further, imaging technology developers should consider the amount of radiation emitted by a person who is screened. With more accurate and reliable measurements using advanced imagining technologies, human life can be protected both by eliminating possible threats to public safety and by decreasing side effects of such screening technologies.

Measurement in Pre-K–12 Mathematics Curricula

The study of measurement starts before kindergarten, and most children of pre-K and kindergarten age can acquire considerable knowledge of measurement. Providing young children with motivating opportunities to explore measurable characteristics of objects such as size, weight, and length and engaging them in activities that require comparing and ordering objects by these characteristics can help them develop the concept of measurement. For example, children can order their toys by their size, make short and long (or big and small) animals using clay, or match items of the same size. An activity that can help children start developing an understanding of area might be covering a large flat surface using small sizes of the same surface (such as leaves or cookies) and making comparisons between surface areas (for example, a larger leaf or a smaller cookie). Children can develop a general idea of volume as they pour water from a wider to a narrower container, or from a taller to a shorter container. Parents can also contribute to their children’s learning of early measurement concepts and appropriate measurement terms by making comparisons using terms such as “big,” “bigger,” “small,” “smaller,” “light,” “lighter,” “heavy,” “heavier,” “tall,” “taller,” “short,” and “shorter” when referring to objects or people in their daily conversations. In their daily routines, children encounter various opportunities to develop an understanding of time and its measurement. For example, children can understand the day and night cycle and sequences of their daily activities (washing hands before meals and brushing teeth after meals). The waiting periods for major events that children look forward to, such as special days and holidays, can provide opportunities for children to understand concepts of day, week, month, and year. Young children can learn various measurement devices within daily contexts as they associate money with buying things, clocks and calendars with time concepts, or thermometers with temperature.

In addition to making comparisons and ordering familiar objects, children should experience the process of measurement. Before being introduced to standard units of measure, such as inches or feet (or equivalent units in the metric system), children typically start measuring using nonstandard measurement units. For linear measurement children can measure the length of a table using their hands, the height of a chair using paper clips, or the distance between two points using their feet. Children can explore measuring area as they cover different sizes of flat objects with uniform blocks. An activity for children to learn about volume measurement is placing uniform cubes in a box and counting the number of cubes used to fill up the box. Balance scales can be used to provide children with comparisons of weights of different objects, such as comparing an eraser’s weight to a pencil’s weight. Children can also weigh objects with nonstandard units using balance scales. They can weigh a book using unifix blocks or a pencil using paper clips. The Illuminations Web site of the National Council of Teachers of Mathematics (NCTM) provides various lesson samples that can be used in preschool classrooms or at home to teach children measuring with nonstandard units. When measuring with nonstandard units, students can conceptualize that they determine the total length, area, volume, or any attribute of interest as they repeatedly measure using the same measurement unit.

After children experience the measurement process using nonstandard units, they will be better prepared to explore measuring with standard measurement tools and units. Measuring with standard units as well as nonstandard units is among NCTM’s measurement standards for grades pre-K–12. According to NCTM standards, pre-K–12 students also should be able to choose appropriate measurement units and tools to measure different attributes. Students can be introduced to standard measurement tools, such as tape measures, scales, or rulers, with activities that allow them to experiment with the measurement process. For example, to learn measuring weight using a scale and to gain an idea about weights of different objects, students can weigh themselves and various items such as a bag, a book, or fruit on a scale and record the weights. As students weigh using the scale, they will recognize the units of measurement. After students gain some experience with measuring weights, an enjoyable activity might be to ask students to estimate weights of things that they identify in the classroom.

Throughout elementary and middle school, students learn conversions within a measurement system; measure time, area, volume, temperature, and angle size using appropriate measurement units and tools; find the areas of rectangles, triangles, parallelograms, circles, and irregular shapes; and calculate volumes and surface areas of rectangular solids, cylinders, and trapezoids. In later grades, students are expected to analyze measurement precision and accuracy and approximate measurement error.

An important concept that students need to learn when they study measurement is “estimation.” Students in early grades can determine common or personal referents (for example, the width of an index finger is 1 centimeter) as they estimate different attributes, such as length and weight of common objects. As students move on to higher grades, they should be prompted to estimate perimeters, areas, and volumes using benchmarks. Students in college explore the theory of measurement. For instance, they use techniques from calculus to represent the length of a curve and the notion of a metric space is defined in topology. Mathematicians measure hard-to-define quantities, like the length of a coastline, refine and improve systems of measurement, and also research related concepts in the field of measure theory.

Bibliography

Confer, Chris. Sizing Up Measurement: Activities for Grades 3–5 Classrooms. Sausalito, CA: Math Solutions Publications, 2007.

Drum, Randell L., and Wesley G. Petty, Jr. “2 Is Not the Same as 2.0!” Mathematics Teaching in the Middle School 6, no. 1 (2000).

Howarth, Preben, and Fiona Redgrave. Metrology: In Short. 3rd ed. Albertslund, Denmark: Schultz Grafisk, 2008.

National Council of Teachers of Mathematics. “Illuminations: Resources for Teaching Math.” http://illuminations.nctm.org.

National Council of Teachers of Mathematics. Principles and Standards for School Mathematics. Reston, VA: National Council of Teachers of Mathematics, 2000.

Nowlin, Donald. “Precision: The Neglected Part of the Measurement Standard.” Mathematics Teaching in the Middle School 100, no. 5 (2007).