This paper considers a group of preservice teachers' construction of concept maps derived from y = x + 5 and y = [pi]x[squared] with emphasis on their conceptual understanding of function. The two statements are perceived to represent a number of different concepts with indications of compartmentalized knowledge structures that might prevent the preservice teachers from building rich conceptual structures. The preservice teachers' view on the concept of function contrasts with a view where the function concept is a unifying concept in mathematics with a large network of relations to other concepts. Different properties and categorizations of functions are less frequently recognized. In the preservice teachers' response of drawing concept maps there are signs of metacognitive activity. (Contains 1 note and 2 figures.) [For complete proceedings, see ED496848.]