Fifteen elementary and secondary teacher candidates solved sixteen integer addition and subtraction problems during think-aloud interviews. Investigators further probed participants' solution strategies as well as what they noticed first when starting a new problem. Task analyses of participants' solutions led to the creation of two distinct maps detailing the procedural relations among and conceptual elements underlying the six problem types. The task analysis results indicate that participants relied on procedural knowledge and had weak strategic knowledge with little focus on number values in their four main solution strategies. These findings highlight possible areas for instruction to support conceptual understanding. [This research was funded by a Purdue Research Foundation Year-long Grant. For the complete proceedings, see ED584443.]