• The research is inconclusive as to the prerequisite relationship between conservation and a child’s ability to measure attributes. One exception is that conservation seems to be a prerequisite for understanding the inverse relationship between the size of a unit and the number of units involved in a measurement situation. For example, the number expressing the length of an object in centimeters will be greater than its length in inches because an inch is greater than a centimeter (Hiebert, 1981).
• Young children lack a basic understanding of the unit of measure concept. They often are unable to recognize that a unit may be broken into parts and not appear as a whole unit (e.g., using two pencils as the unit) (Gal’perin and Georgiev, 1969).
• Figueras and Waldegg (1984) investigated the understanding of measurement concepts and techniques of middle school students, with these conclusions:
1. In increasing order of difficulty: Conservation of area, conservation of length,
and conservation of volume.
2. Measurement units are used incorrectly by more than half of the students.
3. Students are extremely mechanical in their use of measuring tools and counting iterations of equal intervals.
4. Students find areas/volumes by counting visual units rather than using past “formula” experiences, even if the counting process is tedious or complex.
5. Student performance on measurement tasks decreases significantly when the numbers involved are fractions.
The researchers suggested that “a fixed measuring system is introduced far too early in the curriculum of elementary school, thus creating a barrier to the complete understanding of the unit concept” .
• When trying to understand initial measurement concepts, students need extensive experiences with several fundamental ideas prior to introduction to the use of rulers and measurement formulas:
1. Number assignment: Students need to understand that the measurement process is the assignment of a number to an attribute of an object (e.g., the length of an object is a number of inches).
2. Comparison: Students need to compare objects on the basis of a designated attribute without using numbers (e.g., given two pencils, which is longer?).
3. Use of a unit and iteration: Students need to understand and use the designation of a special unit which is assigned the number “one,” then used in an iterative process to assign numbers to other objects (e.g., if length of a pencil is five paper clips, then the unit is a paper clip and five paper clips can be laid end-to end to cover the pencil).
4. Additivity property: Students need to understand that the measurement of the “join” of two objects is “mirrored” by the sum of the two numbers assigned to each object (e.g., two pencils of length 3 inches and 4 inches, respectively, laid end to end will have a length of 3+4=7 inches) (Osborne, 1980).
• First, the manipulative tools used to help teach number concepts and operations are “inexorably intertwined” with the ideas of measurement. Second, the improved understanding of measurement concepts is positively correlated with improvement in computational skills (Babcock, 1978; Taloumis, 1979).
• Students are fluent with some of the simple measurement concepts and skills they will encounter outside of the classroom (e.g., recognizing common units of measure, making linear measurements), but have great difficulty with other measurement concepts and skills (e.g., perimeter, area, and volume) (Carpenter et al., 1981).
• Students at all grade levels have great difficulties working with the concepts of area and perimeter, often making the unwarranted claim that equal areas of two figures imply that they also have equal perimeters. Perhaps related to this difficulty, many secondary students tend to think that the length, the area, and the volume of a figure or an object will change when the figure or object is moved to another location (K. Hart, 1981a).
• Students initially develop and then depend on physical techniques for determining volumes of objects that can lead to errors in other situations. For example, students often calculate the volume of a box by counting the number of cubes involved. When this approach is used on a picture of a box, students tend to count only the cubes that are visible. The counting strategy also fails them if the dimensions of the box are fractions (K. Hart, 1981a).
• The vocabulary associated with measurement activities is difficult because the terms are either entirely new (e.g., perimeter, area, inch) or may have totally different meanings in an everyday context (e.g., volume, yard). Furthermore, students do not engage in enough physical measurement activities for the necessary vocabulary to become part of their working vocabulary (K. Hart, 1981a).
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