The computing landscape has shifted towards multicore architectures. To learn about software development, it is increasingly important for students to gain hands-on parallel programming experience in multicore environments. This experience will be significantly different from programming for uniprocessors, because it involves a profound understanding of how to write software that is (1) free of concurrency bugs and (2) able to effectively utilize the underlying parallel hardware architecture. We present our work at Yonsei University and The University of Sydney to teach parallel programming to first and second-year undergraduate students. Our objective is to introduce parallelism early on in the curriculum, to instill it as a first principle of computation. We introduce a series of five parallel programming course modules suitable for a one semester introductory programming course. Each module teaches one fundamental concept of parallel programming: parallelism and execution indeterminism, thread-and-lock based programming, performance of parallel programs, hardware acceleration using OpenCL, and stream-parallel programming with StreamIt. We report our experience from four course offerings (2008-2011) at Yonsei University, and two course offerings at The University of Sydney. Over 73%of students surveyed enjoyed this multicore programming experience and preferred exposure to parallelism at this early stage of their CS education. Our course has been awarded an Intel microgrant for "Parallelism in the Classroom", and it is available online at Intel's Multicore Curriculum Initiative Website.