This paper utilizes concept mapping as a tool for conscious and deliberate knowledge building in mathematics and its extension to algorithms. Currently, alleged defects in mathematics education are obvious: instead of conceptual elaboration, everyday praxis relies on routine computations that are likely to lead into alienated concepts with weak connections to prior knowledge. A concept map visualizes the existing conceptual structure, and whenever new information is brought in, it will be placed in the map by clearly explicating its linkage to the previous concepts. In the Finnish mathematics education, such new knowledge is programming content that is integrated into elementary school mathematics in 2014 Finnish National Curriculum. This content is crystallized as the requirements of computational and algorithmic thinking, the utilization of respective data structures, and adequate amount of hands-on practice to internalize good coding conventions. This study examines secondary (N = 19) and higher education students (N = 10) and their conceptual knowledge of mathematics concentrating on the domain of algorithms in particular. The concept maps drawn by the students are evaluated using the SOLO taxonomy. To conclude, a consensus map of algorithms is represented and linked to the elementary mathematics syllabus.