The nature and origin of mathematical skills (pp. Representation and retrieval of arithmetic facts: A network-interference model and simulation. Mechanisms of simple addition and multiplication: A modified network-interference theory and simulation. Learning and Individual Differences, 6(1), 1–36.Ĭampbell, J. An evaluation of evidence supporting fact-retrieval models. Organizational Behavior and Human Decision Processes, 76(1), 70–88.īaroody, A. Resource-allocation strategies: A verbal protocol analysis. Human memory: A proposed system and its control processes. Journal for Research in Mathematics Education, 26(5), 396–421.Ītkinson, R. The frequency of arithmetic facts in elementary texts: Addition and multiplication in grades 1–6.
Cognitive arithmetic: A review of data and theory. The results of this study indicate that (1) the retrieval method, procedure method, and mental arithmetic method are the three main calculation methods of abacus arithmetic, each of them having some variations (2) experts tend to use the retrieval method, while novices tend to use the mental arithmetic method (3) the retrieval method and mental arithmetic method are applied more for simple operations and addition problems, while the procedure method is applied more for complicated operations and subtraction problems.Īshcraft, M. The experiment in the study invited 36 participants including 12 vocational high-school students as junior experts, 12 ordinary high-school students as novices, and 12 bank clerks as senior experts to validate the 3 × 3 × 2 experiment. This model describes three methods for solving abacus arithmetic problems: retrieval method, procedure method, and mental arithmetic method and three external factors that affect the choice of those methods: level of expertise, level of difficulty, and type of operation. With a real abacus, constant practice is indispensable in achieving virtuosity in calculating speed.Based on the literature review about abacus arithmetic, this study proposes a model of the cognitive process of Chinese abacus arithmetic. Abacus Apps on touch-screen tablets are better simulations. The Java version of the abacus is a limited simulation of the real device because the fingering technique is completely obfuscated by the mouse. In certain calculations, the middle finger is used to move beads in the upper deck. Beads in lower deck are moved up with the thumb and down with the index finger. With a Chinese abacus, the thumb and the index finger together with the middle finger are used to manipulate the beads. Proper finger technique is paramount in achieving proficiency on the abacus. Similarly, the fourth column representing the number 7, is counted with 1 bead from the top-deck (value 5) and 2 beads from the bottom-deck ( each with a value of 1, totaling 2) the sum of the column ( 5+2) is 7. Referring to the Figure/Applet above, the third column (from the left), representing the number 8, is counted with 1 bead from the top-deck (value 5) and 3 beads from the bottom-deck ( each with a value of 1, totaling 3) the sum of the column ( 5+3) is 8. If your browser is Java-capable then the applet, above, will identify the parts of the abacus in your browser's status-area as you move your mouse-pointer over it the beads will move when you click on them and the value of each column will be displayed on the top frame. Abacus Applet: Numeric representation of the number: 87,654,321. Floating point calculations are performed by designating a space between 2 columns as the decimal-point and all the rows to the right of that space represent fractional portions while all the rows to the left represent whole number digits.
The right-most column is the ones column the next adjacent to the left is the tens column the next adjacent to the left is the hundreds column, and so on. CountingĪfter 5 beads are counted in the lower deck, the result is "carried" to the upper deck after both beads in the upper deck are counted, the result (10) is then carried to the left-most adjacent column. PREPARING THE ABACUS: The abacus is prepared for use ("zeroed") by placing it flat on a table and pushing all the beads on both the upper and lower decks away from the beam by sliding the thumb along the beam.īEAD VALUES: Each bead in the upper deck has a value of 5 each bead in the lower deck has a value of 1.īeads are considered counted, when moved towards the Beam- the piece of the abacus frame that separates the two decks.
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