- Go back through the exercises in the last four sections of this chapter. Complete any items you did not complete the first time through. Prepare any that we have not discussed in class so that you will be ready to present them.
Now we take a short break to revisit and consolidate the learning you have done so far. Revisit the reading and the exercises you have done in Chapter Two: Linear Equations. The important feature of this work should be learning to think about your own thinking. This sort of meta-cognition characterizes expert learners. Eventually, you want to be able to monitor your work at all times and recognize when you understand deeply and when you do not. This will allow you to self-correct.
To help you get started with meta-cognition, I listed learning goals in each section. To go further, you need to explicitly go through the process of reviewing what you can do and what you cannot. Here are some prompts to help you get started with this process.
- Review the learning goals from each section. Can you do the things described? Can you do them sometimes, or have you mastered them so you can do them consistently?
- Look through all of the tasks and go deeper into them. Can you connect each exercise to one of our pictures? Try to build a mental model of how the exercise and its solution work.
- If your first solution to an exercise involve a “guess-and-check” approach, can you now complete the exercise in a purposeful and systematic manner?
- Make a list of concepts or exercises that are not clear to you. Phrase each item in your list as a question, and make each question as specific as possible. Talk with fellow students or your instructor until you can answer your own questions.