The beginning has begun; learning to teach future learners.
In mathematics, when you learn something new it mostly like will be used to build of something else you're going to use in the future. Some of the first and most basic concepts you learn are used repeatedly throughout your career as student, such as fractions, addition, equations, linear functions and so on. As you use these things over the years, for some people, it starts to become second nature, something you don't really have to think about. When you're put in a situation where you have to think about your thinking, those second nature concepts become almost a challenge. You've been doing it for so long, it's not something you think about anymore.
I am currently enrolled in Math 229, which is teaching middle grades math and I am also an SLA facilitator for Math 097, which is elementary algebra. I am also in three hundred level courses and yet I am being challenged equally by a 300 level course as a 097 and 229 course. How is that possible? Thinking about your thinking is difficult! Both 229 & 097 have forced me to think back to those surface level concepts and process how I solve those problems. Then on top of that, forcing myself to think about different ways to solve the problems and not just my "go to thinking." Why is that so important? Why do I need to know different ways to solve a problem and fully understand why I may solve a problem a certain way?
I've already learned so much being an SLA facilitator and if one thing is true, it's that students need to be engaged for them to fully understand the concepts. The surface level concepts that are so crucial to the rest of the semester need to be taught and learned really well. This means that you can't move on to the bigger concepts until the class has mastered those first basic concepts. I've realized in Math 229 the importance of being able to explain things in many different ways. There are so many different kinds of learners and if you're teaching in one way, you might not reach half the class and therefore they may not be engaged in your teaching. For example, I could've sat through the same math classes for 6 years as Sue. Those concepts we learned became second nature to me because all our teachers gave lots of practice problems and that's how I learn best. Those same concepts are not second nature to Sally because she is a visual learner and needs thing to be applied to the real world in order for her to fully understand. Being engaged makes a difference in what you learn. As you can see, learning to teach to your audience is a big concept to grasp.
In closing, how do you teach those crucial topics to students, keep them engaged in your instruction, and make sure your using many different methods in teaching it? A good question that I am still learning the answer too. I think it starts with establishing a teaching style, but being flexible enough to understand that it may change every year, or even every month. I have a youtube video below that discusses the importance of keeping students engaged and few ideas on how to do that. It's interesting to think that just changing a story problem to a topic that interests the class could change how much they're engaged in the concept your teaching.