Abstract: Strategic problem solving is a very effective approach for children to acquire cognitive ability. Siegler (1983) has revealed four basic addition strategies: counting fingers, fingers, verbal counting, and retrieving. However, his studies merely focus on strategies involving children’s natural acquisition and self-discovery mechanisms. Furthermore, these calculation strategies are limited to single-digit addition and subtraction.
Participants included 171 Chinese children in three fourth-grade classes at a Chinese Experimental Elementary School, composed of 88 boys and 83 girls. In the pretest of the study, all the three classes were equivalent with respect to the students’ arithmetic level and the instructors’ teaching capacity. From the three classes, two were randomly selected to serve experimental groups and one as the control group. During the strategies training period, the three groups were instructed by their original teachers. The two experimental groups were trained using the teaching models designed by researchers—one group used the expositive model and the other, the exploratory model. On the other hand, the control group was taught using the teacher’s original method. The independent variables constituted the different teaching methods, and the dependent variable was the level of the students’ arithmetic. This paper discusses the following three main aspects. First, it compares the effects of the researchers’ methods and the teacher’s original method on students’ calculating performance in the posttest. Second, it compares the effectiveness of the expositive and exploratory methods by analyzing the posttest results. Finally, it explores the students’ utilization deficiency by evaluating the effects of the training strategies in the delayed posttest that took place 45 days after the completion of the training.
By comparing the experimental groups with the control group, this study showed that in the experimental groups, students’ calculating performance, calculating speed, and learning interest were raised significantly through the shortcut strategy training. In the delayed posttest, the result reveals no obvious difference between the test papers containing clues to prompt students to use strategies and the test papers without such clues. This indicates that utilization deficiency can be avoided as long as the training method is appropriate. Finally, there is little difference between the effect of the exploratory and expositive teaching methods used in this study. This is probably because Chinese students have been accustomed to the latter style. They may need time to adapt to the exploratory teaching method.
Based on this study, we can conclude that the level of the students’ arithmetic ability, their calculating speed, and learning interest can be raised significantly through the specialized training strategy described in the paper; strategy utilization deficiency can be avoided as long as the training method is appropriate

Key words: elementary school children, shortcut calculation, strategy training, utilization deficiency, delay