I obtained a Bachelor of Fine Arts (BFA) from a 4-year school. I got to experience fine arts training as well as computer-based design training. We learned art and design fundamentals and, importantly, learned how to be visual problem-solvers. I have worked in many different industries with that degree (publishing, museums, product design firm, ad agency, technology company). The basic design training I got made all those industries accessible to me, because I left school with a solid portfolio, had internship experiences, and knew how to apply design skills to real-world problems--no matter what kind! Technology will always change--the tools you use will change along with it. But learning design thinking and methods will last your entire career.
Hello, These days, designers need to be multi-faceted means need to know more than one topic. Technical knowledge, Product management along with concepts of User Experience would be very useful for designers. In addition, if you know market information for which you are designing a product it would be a great career move. I would suggest first focus on technical degree / experience in the area which you want to be a designer and then add-on trainings/certifications such as Design-thinking, Product Management, User Experience would be greatly useful. MBA would be add-on in my view, which would provide you business perspective as well.
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Second to Nicole's comment. A solid foundation will help you in your entire career. Design is something quite unique. At the end of the day, it is not about a specific design field you are in, it is about using your design skills and approach to solve problems of the field you are in. Of my over 20 years of design career, I have designed products, environments, services, and strategy.