We examine the cosmic star formation rate (SFR) and its dependence on galaxy stellar mass over the redshift range 0.8< z< 2 using data from the Gemini Deep Deep Survey (GDDS). The SFR in the most massive galaxies (M*> 10 10.8 M☉) was 6 times higher at z= 2 than it is today. It drops steeply from z= 2, reaching the present-day value at z~ 1. In contrast, the SFR density of intermediate-mass galaxies (10 10.2 M☉≤ M*< 10 10.8 M☉) declines more slowly and may peak or plateau at z~ 1.5. We use the characteristic growth time t SFR≡ ρ/ρ SFR to provide evidence of an associated transition in massive galaxies from a burst to a quiescent star formation mode at z~ 2. Intermediate-mass systems transit from burst to quiescent mode at z~ 1, while the lowest mass objects undergo bursts throughout our redshift range. Our results show unambiguously that the formation era for galaxies was extended and proceeded from high-to low-mass systems. The most massive galaxies formed most of their stars in the first~ 3 Gyr of cosmic history. Intermediate-mass objects continued to form their dominant stellar mass for an additional~ 2 Gyr, while the lowest mass systems have been forming over the whole cosmic epoch spanned by the GDDS. This view of galaxy formation clearly supports" downsizing" in the SFR where the most massive galaxies form first and galaxy formation proceeds from larger to smaller mass scales.