This paper aims at shedding light on what students can "construct" when they learn science and how this construction process may be supported. Constructivism is a pluralist theory of science education. As a consequence, I support, there are several points of view concerning this construction process. Firstly, I stress that constructivism is rooted in two fields, psychology of cognitive development and epistemology, which leads to two ways of describing the construction process: either as a process of enrichment and/or reorganization of the cognitive structures at the mental level, or as a process of building or development of models or theories at the symbolic level. Secondly, I argue that the usual distinction between "personal constructivism" (PC) and "social constructivism" (SC) originates in a difference of model of reference: the one of PC is Piaget's description of "spontaneous" concepts, assumed to be constructed by students on their own when interacting with their material environment, the one of SC is Vygotsky's description of scientific concepts, assumed to be introduced by the teacher by means of verbal communication. Thirdly, I support the idea that, within SC, there are in fact two trends: one, in line with Piaget's work, demonstrates how cooperation among students affects the development of each individual's cognitive structures; the other, in line with Vygotsky's work, claims that students can understand and master new models only if they are introduced to the scientific culture by their teacher. Fourthly, I draw attention to the process of "problem construction" identified by some French authors. Finally, I advocate for an integrated approach in science education, taking into account all the facets of science learning and teaching mentioned above and emphasizing their differences as well as their interrelations. Some suggestions intended to improve the efficiency of science teaching are made.