Algorithmic Thinking (AT) skills may be considered one of the necessary skills for everyone in the new century. Individuals and societies live in a time when they cannot avoid using information communication technologies (ICT). Hence, they need to be ICT literate. Teachers shall play an important role both for individuals and societies to address this need. However, are they ready to play such a role? This paper presents a suggestion for teacher training to help teachers how to play the role. The paper suggests including an elective course under the title AT into the computer science teacher training curricula and aims to present the course, progress and views of the students who took the course. A mixed-method approach was followed for the current study. The study was carried out with the participation of sixth-semester students of a Computer Education and Instructional Technology Department of an Education Faculty who may be considered prospective computer science teachers. Twenty-eight students were enrolled in the elective AT course offered for the period. Within the scope of the study, development of the course curriculum, instructional process of the course and evaluation of the course, in line with students' views and exam scores, are presented. Findings of the research suggest that the students find the Algorithmic Thinking course helpful for them to acquire some algorithmic thinking skills as well as some other academic and life-related thinking abilities. Also, the course may be considered as a necessary course particularly for the training process of computer science teachers. In addition, the students think that the offered course was effective and beneficial.