The purpose of this study was to investigate the reliability of children's verbal report, to identify the use of multiple strategies for solving of addition problems, and to retest the validity of 'the distributions of associations model' developed to account for the process of the strategy choice by Siegler. The subjects for this study were 45 first-grade students attending at N elementary school in Daegu city. The addition problem was consisted of 20 items with larger addends from 6 to 9, smaller addends from 2 to 8, and sums from 9 to 17. And children's strategy choice, response accuracy and reaction time was observed on those items. Each child's response for trial-by-trial was questioned and recorded by two investigators who have practiced on the test methods. For data analysis, regression method, Pearson's correlation analysis, and ANOVA was used. The results of the analysis indicated the followings: 1. Using the chronometry method only, the size of the smaller addend predicted linearly a time of the children's problem solving. 2. Using both the chronometry method and the children's verbal report, the reliability of the children's verbal reports was identified. 3. Basing the data from the children's verbal report, children used the multiple strategies(counting all, minimum, decomposition, guessing, retrieval) for the simple addition problem solving. 4. The inner validity of strategy choice model developed by Siegler was tested.