Final answer:
Sam Houston's third goal was to gain recognition of Texas independence from other nations.
Step-by-step explanation:
The third goal of Sam Houston during his first term as President of Texas was to gain recognition of Texas independence from other nations. He sought to establish the Lone Star Republic as an independent entity, separate from Mexico, and recognized by the international community. By securing formal recognition from countries such as France, Great Britain, Belgium, and the Netherlands, Houston aimed to solidify the standing of Texas on the global stage and protect it from Mexican attempts to reclaim it. Neither creating public schools, expanding Texas into an empire, nor selling parts of Texas to help pay the republic’s debt were among Houston's primary objectives during his first term.