Those questions are perfectly normal to have, and I think they can be incredibly helpful if you allow them to alert yourself to the way God moves in your life. The answers don't always come easily or clearly, but that can be a good thing. The search for meaning can train us to keep our eyes expectantly on the Lord through every circumstance, and teach us to watch for His hand at work in our lives.
God might have placed you in your teaching situation for one particular student who desperately needs someone to show him or her love. Or maybe He wants you where you're at because the adults around you need encouragement. It could be that God wants you to be a force for positive change in a school or school system that doesn't put the needs of children first. It could be all of those things, and more.
The place you're at might be dark, but you can be confident that God wants to use you to shine a light there. Continually returning to that belief makes it a lot easier to get through the hard times. When a student seems impossible to handle, think to yourself, What is the reason God wants him/her in my classroom instead of someone else's? What can I offer this student because of God's love? Shift your outlook from Why do *I* have to deal with this? to How does God want to use me in this situation?
Keep looking to the Lord for your purpose. Ask Him to help you embrace your job in its totality: the parts you love, the parts you don't, the parts you think you can't possibly handle for a second longer. Pray that God would keep you focused on the things He wants to accomplish in and through you. Ask that He would make you aware of the little miracles He's accomplishing and the way He's growing you through your trials.
You can start small if you need to: What is one way that you know God wants to use you in your current teaching position? Share your thoughts in the comment section. Then return to that thought again each morning before you start work, and again each time it gets hard, and again at the end of the day when you think back on the way that God strengthened you and provided for you.
God wants to do exceedingly, abundantly above all that we could ask, think, or imagine. May we open our eyes and see the ways that He is working.