Several models have been proposed to describe how people select and execute strategy. They found that the strategic performance was impacted by many factors, in which EFs (central executive functions) were included. Up to now, several researchers have investigated the specific roles of shifting, inhibition and updating on arithmetic strategy use. However, the role of dual-task coordination in arithmetic strategy use is still unclear. Although strategy execution can be impacted by presentation mode in conflict monitoring, the evidence is inadequate obviously. 54 adult participants were chosen randomly for Exp 1 (includes 26 participants) and Exp 2 (includes 28 participants). By controlling presentation mode and numbers of reaction, the present study combined the no-choice condition from the choice/no-choice paradigm with the revised psychological refractory period paradigm. To examine how dual-task coordination and task presentation mode influence the efficiency of strategy execution in first estimation reaction, we divided the experiments into random mode and fixed mode. Experiment 1 and Experiment 2 were conducted in random mode and fixed mode, respectively. Both of them adopted a 2 (response situation: single /double) × 2 (task presentation sequence: computational estimation rendering first / graphics rendering first) × 2 (no-choice method: rounding up / rounding down) within-subject design. Results were indexed by accuracy, reaction time and dual-task coordination cost (difference between double and single responses). Results showed that the reaction time of rounding-up strategy was significantly longer than rounding-down. Computational estimation in dual-response situation was worse than in single-response situation. The accuracy of estimation in dual–response situation was lower and reaction time was longer than single-response situation. Single or Double responses of estimation strategy affected the efficiency of reaction. Specially, estimation performance in dual-response was considerably worse than single-response, and the dual-response had greater effect on the complex rounding-up strategy. Dual-task coordination cost was influenced by the random sequence of tasks and strategy difficulty. With the task presentation mode fixed, dual task coordination cost decreased or even disappeared. Dual-task coordination influenced estimation efficiency of strategy execution by the number of responses and task presentation mode. Despite the fact that both fixed and random mode affected the estimation strategy execution, dual-task coordination cost in random mode was more. Strategy execution process is influenced by numerous factors. In addition to cognitive system (e.g., effort, accuracy and time) and environmental factors referred by cognitive niche theory, it was also affected by task presentation mode, that is, the effect of working memory itself.