Inspired by the observation that infants acquire phonemes common to adults without having the capability to articulate, nor having a priori knowledge about the relationship between the sensorimotor system and phonemes, a constructivist approach to building a robot that reproduces a similar developmental process is conducted. Two general issues are addressed: what are the interactive mechanisms involved and what should be the behaviour of the caregiver/teacher? Based on findings in developmental psychology, it is conjectured that: (a) the caregiver's vocalization in response to infants' cooing reinforces the infant's articulation along the caregiver's phonemic categories; and (b) the caregiver's repetition with adult phonemes helps to specify the correspondence between cooing and the caregiver's phonemes as well as determining the acoustic properties of the phonemes. The robot consists of an artificial articulatory system with a five-degrees of freedom mechanical system deforming a silicon vocal tract connected to an artificial larynx, an extractor of formants, and a learning mechanism with self-organizing auditory and articulatory layers. Starting off with random vocalizations, the system uses the caregiver's repetitive utterances to bootstrap its learning. In order to resolve the arbitrariness in determining proper articulations, the torque to deform the tract and its resultant deformation are minimized. The experimental results, discussion and future issues are given.