Previous computer-assisted problem-solving systems have incorporated all the problem-solving steps within a single stage, making it difficult to diagnose stages at which errors occurred when a student encounters difficulties, and imposing a too-high cognitive load on students in their problem solving. This study proposes a computer-assisted system named MathCAL, whose design is based on four problem-solving stages: (1) understanding the problem, (2) making a plan, (3) executing the plan and (4) reviewing the solution. A sample of one hundred and thirty fifth-grade students (aged 11 years old) completed a range of elementary school mathematical problems and empirically demonstrated. The results showed MathCAL to be effective in improving the performance of students with lower problem solving ability. This evaluation allowed us to address the problem of whether the assistances in various stages help students with their problem solving. These assistances improve students' problem-solving skills in each stage.