Section 11.1 A Pause for Reflection
Congratulations! You have just completed the "main trunk" of the course. The algebraic skills that we have been discussing are the foundation of college level mathematics. But that doesn't mean that there's nothing more to learn. Mathematical knowledge is deeply scaffolded. And weaknesses in the lower level can manifest in an unstable understanding down the line. What we have done up to this point is attempt to plug the biggest holes as fast as possible so that you can move forward in your college level math courses. It's really just a patchwork job that tries to get you to a place where you have a decent chance of being successful at that college level coursework.
The sections that follow are going to be focused on getting deeper into the foundation in search of filling the cracks that lie beneath the surface. As we follow the different "branches" of mathematical thinking, the hope is that you will come to a new and deeper understanding of ideas that you have seen for years. Some of these ideas may help feed directly into your college level work, but other things may simply be about uncovering a new perspective of mathematics.
As we have been emphasizing throughout this text, there is more to math than just executing calculations. Yes, that's a part of it, but there's an element of communicating and understanding the ideas and a curiosity for how ideas fit together. Ultimately, this is all about building a mindset towards mathematical thinking that is robust enough to help you be successful at whatever you do. One of the reasons that mathematical skills are so highly valued is not because there aren't a lot of people who can do the raw manipulations (we have computers to do that for us), but it's because there aren't a lot of people who can meaningfully interpret that information and apply it to new situations.
For these reasons, it's important to take a pause every now and then and think about what's happening beyond just the calculations and think about what's happening to your mindset as you've been working your way through the content.
In this portion of the course, we have covered the following topics:
Basic Algebraic Presentation
Variables in Expressions and Equations
Like and Unlike Terms
Simplifying Expressions and Solving Equations
Variables and Substitutions
The Properties of Exponents
Products of Polynomials
Common Factors
Factoring Quadratic Polynomials
Reading Mathematical Expressions