Definitely yes! The themes of Problem Solving, Reasoning and Proof, Mathematical Communication, Mathematical Connections, and Mathematical Representations run through all math courses. You can best prepare yourself to teach math by paying attention to developing your abilities in these five areas.

What do the NCTM's Principles and Standards for School Mathematics say about this?

What do the Texas State Board for Educator Certification Standards and the Texas Essential Knowledge and Skills say about this?

Use of technology is another thing to pay attention to as you select and take your math courses. You will use technology in M 315C (Functions and Modeling) and in M 358K (Applied Statistics). Some sections of M 333L (Structure of Modern Geometry) use the software Geometer's Sketchpad; signing up for these sections can help you gain facility with this software as well. Be sure to take advantages of any other opportunities you can to become familiar with a wide variety of technological tools that can help you as a math teacher.