Last modified: 2018-07-07
Abstract
In adding and subtracting two numbers, arithmetic capability is required for elementary students. Mastering place value on the concept of numbers is very important, since a number is determined by the order or number position (Walle, 2013). The concept of place values ​​of multidigit figures is essential for learning an advanced mathematics. Although the place value material performs a basic knowledge, but there are still many elementary students who have difficulties in understanding the concept. Elementary students are still difficult to write the number symbols, understanding the value of the place, even still difficulties in the operation of the count (Selvianiresa, 2017). To find out difficulties that faced by students in solving the place value problems, one firstly needs to analyze the strategies applied by students. Moreover, students’ misunderstanding of  place value of multidigits’ numbers, can be indicated from the strategy used. It is emphasized that there is a relationship between mathematical ability and constructed strategy.
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This descriptive-qualitative study aimed to investigate student strategies in solving place value problems. This study involved the 4th grade students of elementary school consisting of 12 students at a tutoring institute ASUB in Surabaya. All subjects were given two tests, namely maths ability test which was to determine the student's maths abilities (high maths’ ability, medium maths’ ability, and low maths’ ability) and the place value test which was to find out any strategy employed by students. Three volunteer students were selected as research subjects and were individually interviewed based on the answer of the place value test. Our result showed that subjects with high maths’ ability were able to convert the given block problems to correct numbers, and capable in using mathematical notation, as well as providing good reasons for adding multiple multidigit numbers according to the given problem. Medium maths’ subjects were utilized one by one counting the given block problem, then represented in the correct numbers. He was able to use mathematical notation well, and had tried one by one the numbers given to add two numbers. In contrast, low maths’ ability subjetc solved the given problem by counting each block and representing into multidigit numbers. He unfortunately did not implement maths’ notation when adding two multidigit numbers. Although he had tried to work out the given problem, by adding one by one two multidigit numbers, but he faced such difficulties to obtain the required number.
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Figure 1 The answer of medium mathematical ability subject
In Figure 1 the answer a medium mathematical ability subject tried one by one the numbers in the known circle to perform number 50 corresponding to the asked number.
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Figure 2 The answer of high mathematical ability subject.
In Figure 2 the answer a high mathematical ability subject employed his reasoning in solving the problem. A high mathematical ability subject did not try one by one a known number to obtain a number 50 corresponding to the appropriate number. But a high mathematical ability subject considered the place value at each known number in the circle of the question.
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The results of this study concluded that each category of mathematical ability has a varied strategy. Subjects with high mathematics ability had knowledged of the place value very well. The strategy used was by looking at the pattern on the unit and tens of each known numbers and provided the appropriated reasonings. Subjects with medium mathematics ability had understood the place value were good nough. The chosen strategy was trial and error by selecting one by one of proposed numbers to perform a number as asking in the question. Meanwhile the strategy utilized by the subject with low mathematical ability was the same as  that of the subject of medium mathematical ability, but he did not mention all known pairs of numbers as involving in the question.
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