Congratulations! if you are reading this you have successfully found Open Lab and our class web site. Remember you must register as a member of Open Lab (follow the directions on the first page) and as a member of this class (see directions under help). You must be a participant in the class to post assignments and comments. If you have any problems or questions, e-mail me (BMishara@citytech.cuny.edu). The staff of Open Lab are also extremely helpful and quick to respond.
Getting Started
On our Open Lab site we will be thinking and writing about structures and mathematics. The study of structures is based on science and mathematics. I think everyone acknowledges these facts. But writing??!! What does that have to do with either subject? A lot it seems. Research shows that by writing and thinking about mathematical processes dramatically increases student understanding and learning. When you describe the reasoning you used to solve a problem, you must think through the steps very carefully and in detail. Writing accomplishes this. Teaching or explaining solutions verbally is also an excellent learning technique. We will be doing this in class. The focus is not so focused on the “right” answer, but rather your understanding of the parameters.
I will also ask you to think and write about how you worked on a problem. This is called metacognition, or “thinking about thinking.” What goes on in your head when you work on a problem. What are your feelings – panic, anxiety, confidence? Where do you get stuck and what can you do next? Recognizing your thoughts identifies obstacles to learning. And this is the beginning of a solution. Metacognition also illustrates your learning style. Reinforcing this style increases understanding and learning.
At first these techniques might seem odd. Give them a chance. Like any skill it takes practice. (With thanks to Jonas Reitz)
