This paper demonstrates that a teachable agent (TA) can play a dual role in an online learning environment (OLE) for learning by teaching--the teachable agent working as a synthetic peer for students to learn by teaching and as an interactive tool for cognitive task analysis when authoring an OLE for learning by teaching. We have developed an OLE (called APLUS) on which students can interactively teach a TA (called SimStudent) how to solve problems. APLUS has a cognitive tutor embedded (aka meta-tutor) that provides students with adaptive feedback and help on how to solve problems. The results showed that the expert model created by SimStudent was highly accurate with more than 0.95 precision and recall scores on two different task domains (equation solving and fraction addition). The cost analysis showed that although the authors need to provide SimStudent with task dependent Java code, the amount of code written was relatively small--about 1000-2000 lines of code in 20 to 50 classes. Those findings imply that the TA has practical potential to help authors of APLUS create a domain expert model for the embedded cognitive tutor and the tutoring interface used for the OLE. It was also observed that the failure of TA to learn expected cognitive skills helps the author identify missing essential cognitive factors that must be encoded in the OLE.