1.
Were there any topics that you had seen before, but you understand better as a result of working through it again?
Chapter 11 Reflection
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
Section 11.2 Worksheets
PDF Version of these Worksheets
1
external/worksheets/11-Worksheets.pdfWorksheet Worksheet 1: Questions about the Content
2.
Were there any ideas that you had never seen before?
3.
Based on your experience, which of these ideas seems the most important to understand well?
4.
Did any part of the presentation make you curious about math in a way that went beyond the material? Are there questions or ideas that you would like to explore?
Worksheet Worksheet 2: Questions about You
1.
How has your mathematical writing evolved from the beginning of the course? Do you find yourself thinking in different ways?
2.
Did you have any "Aha!" moments where you had an insight into something that you had not noticed before?
3.
What is the biggest mathematical connection that you made?
4.
What is your level of confidence in mathematics? Is this higher, lower, or about the same as it was at the beginning of class?
