¶ … Value: Problem Solving and Written Assessment by: Sharon R. Ross
This paper provides an analysis of an article by Ross (2002), which describes the learning characteristics exhibited by young children in relation to a particular topic in mathematics, known as place value. Place value refers to the value assigned to each digit within a multiple-digit numeral, within the familiar decimal number system that is the basis for contemporary mathematics in academia and commerce. The premise of the article is that the concept of place value is inherently difficult for elementary grade students to grasp, and correspondingly difficult for instructors to teach. The reason for this difficulty is attributed to the complicated symbology inherent in the decimal system of numeration, which may be summarized as being the product of four mathematical properties, namely the additive, positional, base-ten and multiplicative elements inherent in each and every multiple-digit numeral. Ross (2002) describes a practical classroom study in which researchers analyzed the results of five problem-solving assignments administered to different groups of elementary school students between grades three and five. These assignments were designed to exercise the cognitive skills and aspects needed to deal with the four mathematical properties related to place value. Results of the experiment were compared between individual and collaborative group efforts to solve the assigned problems.
As such, the rightmost digit in a numeral preceding the decimal point represents "ones," the next digit to the left represents "tens," the third digit to the left represents "hundreds," and so on. Children in the Ross (2002) study were assigned five problem solving tasks in which they were called upon to use intuitive, pictorial and group discussion methods to decide upon the relationship between parts of a given numeral and the actual count of objects in a given collection. The mathematical content involved in each of these five exercises will now be examined.
1. 144 Squares problem
In this exercise, students were made to collaborate in groups of four to assess whether several paper shapes with slight modifications had the same area as a 12 cm x 12 cm square, whose area was 144 cm2. The shapes to be compared included two rectangles and a square with clipped corners. Students were asked to identify the significance of each of the three digits comprising the number 144 relative to the area of the shape.
2. 124 Cubes problem
Groups of students in this exercise were asked to exercise their three-dimensional visualization capabilities to identify all possible ways to construct 124 cubes, using a fixed number of blocks with base-ten dimensions. Students…
