This study investigates the longer-term associations of preschool quality with the development of mathematical skills during elementary school, taking into account early and subsequent learning environments at home and at elementary school. The arithmetic skills of a German sample of 554 children in grades 1-3 (ages 7:5-9:3 years) were analyzed using latent linear growth curve models to test the extent to which the quality of preschool math instruction is related to entry skills in grade 1 and rates of change over time from grades 1-3. In addition, we asked whether preschool quality interacted with quality of the home environment (HLE) during early or middle childhood in predicting math skills. Results show that initial mathematical skills at grade 1 were predicted by numerical skills at preschool age, and socio-economic status of the family. Moderator analyses revealed that middle childhood HLE moderated the preschool quality effect on the initial status of mathematical skills in grade 1 in such a way that preschool quality was associated with mathematical skills at grade 1 when middle childhood HLE was in the higher range. Growth in mathematical skills between grade 1 and 3 of elementary school was positively predicted by preschool quality even when controlling for the quality of the subsequent learning environments. Furthermore, elementary school quality was positively related to growth in mathematical skills during the observed period between grade 1 and 3. Moderator analyses revealed that effects of elementary school and preschool are additive as no significant interactive effects between quality in elementary school and preschool have been found. The study highlights the importance of high quality preschools for child development during elementary school. (author abstract)