Great question! I am glad to hear you are interested in a potential career as a High School Math Teacher. I taught High School English so I cannot speak to the part about teaching Math content. However, I wanted to provide some insight as to what it is like to teach High School and in the adolescent grades.
Teaching as was brilliantly stated in the answer above, is a highly rewarding and fun, yet challenging career. You get to help promote lifelong learning and be a catalyst for encouraging adolescents to be the best that they can be and reach heights they may never have thought possible. For me, one of the most fun parts about the career was the enthusiasm and energy that students brought each day. You get to foster this excitement and energy by creating fun and relatable lessons. Depending on the school you teach in, you may have more autonomy than others in what you get to teach and how you get to teach it. For Math, the curriculum guide will dictate what you need to teach, however, how you choose to teach this content and get it across to your students is entirely up to you!!! I truly enjoyed lesson planning and coming up with creative ways to engage my students and make learning not only fun, but relatable and memorable.
Teaching however, does require long hours, contrary to what people may think. Not only did I teach, but also was the Advisor for the Freshman Class and coached soccer, baseball and track. After practice and meetings, I then had to grade papers and make sure to refine my lesson plans for the next day. I created my yearly lesson plans in advance, however, I would have to adjust for things like snowdays (I taught in the Northeast) or just a class maybe not progressing at the rate I expected. I also used quizzes and tests to tell me which areas I needed to review and re-teach, so I made sure to plan and incorporate those review sessions into my plans.
Teaching requires special talents and skills and it is not for everyone. You may want to consider tutoring, observing in school (I reached out to some of my former teachers to shadow their classes) and researching college programs. I would definitely recommend doing some work with kids prior to embarking on a college path (working at a summer camp or summer enrichment program is a good idea) because in most, if not all, teacher education programs, Student Teaching comes at the very end, in your last semester which is late in a college degree course to decide you do not like it. With that said, at the high school level, in college you typically major in both your content area (Math) and Education which provides you with a double major and two degrees that you can use regardless of whether you decide to further pursue teaching or not. Math also translates very well into the Computer Science and programming world.
I hope this helps and I believe that you will have a fun and rewarding career as a High School Math Teacher!!!
Here are a couple things you may want to do to get a better sense of whether you'd like teaching.
1. Tutor 1:1 and move into small group
2. Shadow a few math teachers across different grades and subjects. Write down what you like and don't like. Ask teachers what they had to do to prepare for and following the lesson.
I am also a former math teacher. There are great benefits to this career that would fit your interests - you get to work with math every day, you get to work with students, you have summers off. But, there are also great challenges. Depending on the district you work in, administration can be challenging to deal with, parents can be challenging, students can be challenging. It really depends on the town/city/state that you are working in. In the end, the challenges outweighed the benefits for me, and I now work on math curriculum for a publishing company. I really enjoy the work I do, and both my schooling and teaching experience have greatly helped me to be successful in my new role.
At the end of the day, only you can know what's best for you! If you think you would love teaching - go for it! But also know that there are other options for you if teaching isn't what you expected it to be. I do not regret my choice to begin my career in education, and am excited to see where else my path will take me.
I taught math to high school students for several years, mostly when I was straight out of college with a BSc in Math. It was rewarding to bring what was logical to me to the classroom and help those who found math hard, but were then able to understand it then enjoy it. It took quite a bit of preparation to figure out how to present the materials, which media I would use, which problems to use as class examples, then measure the students' grasp. This is an age group where a lot of empathy and focus needs to be provided to address any emotional or behavioral issues, and recognize when extra individualized tutoring or counseling is needed. It was really rewarding to see the students take some of the newer concepts, then go off on their own and work projects that resulted in computer generated graphics, drawings or applied studies.
The key component here is competency in the general area of mathematics if you want to be a high-school math teacher. I would suggest that you major in mathematics in your undergraduate curriculum.