Math is an interesting teachable. While I do not have a formal education in math, the two areas that I am most well versed in, physics and chemistry, are math heavy topics.
In fact, the most common barriers and bumps, in those courses, are math skills. So, I have spent much of my time teaching physics and chemistry, teaching math.
Grade 9 math is simple on the surface, but that's only because of my background in other sciences. I find that the spectrum of students is wider in this course, and the classroom management aspects, are just as significant as covering the topics.
I like to teach the course with short, traditional lessons, followed with plenty of time to practice problems.
As we build our foundational math skills, in this course, students may be able to appreciate some of the more interesting topics in science. In the past, this has included conversations about space, medicine, or the analytics to sports.
This is a unique course in that it is one of the first courses where the spectrum of individuals is shrunken. From my experience, the students in this course have rounded their studying and practice habits fairly well, which allows us to move at a quick and heavy pace. I always remind the students how challenging the course is, but they have seemed to respond favourably to the challenge.
In the past, I have taken students on less traditional field trips (if time permitted), to places like the park, or mini golfing, or to play laser tag. This makes the course more memorable, but also gives students an opportunity to see math outside of their classroom, in an environment where they can enjoy themselves.
Applied math is such a fantastic course. It exposes students to some useful topics, like statistics and measurement, but does not demand as much of the theory that Pre-Calculus would.
I have learned a lot, teaching applied courses, along with my students because we live in such a fortunate time, with all the technology available to us, that we can always see the content from another perspective.
10 years ago, for instance, all students would learn how to use the graphing features of a TI-83 series calculator. How many of those students used those skills beyond high school? Today? We have wonderful apps, such as Desmos and Wolfram Alpha, which make accessing the content so much more enjoyable.
The grade 12 component of this stream is arguably the most useful high school course.
The content, in essentials, is quite low intensity. I find that classroom management has been a greater factor than conveying the content to students.
With that being said, for students who have little to no interest in pursuing anything that requires a deep math background, essentials is the perfect course, to keep kids exposed to math without overwhelming them with practice.
This was the math that was most interesting to me, as a student. Now, after experiencing calculus proper, and courses that utilize derivatives and integration, I think I have an even greater appreciation for the high school preparatory courses.
These courses are intense. However, the spectrum of students taking pre-calculus is so fine tuned, that we are able to work at a fast and heavy pace.
In addition, by the time students are able to enroll in pre-calculus, they are also able to enroll in some of the heavier science courses, which reinforce the utility of pre-cal.
Pre-cal would be the most traditional class I would teach. It would be designed to prepare students for the intensity of a calculus course.