A mind for numbers

Focusd and Diffuse Mode

Since the very beginning of the twenty-first century, neuroscienists have been making profound advances in understanding the towo different types of networks that the brain switches between-highly attentive states and more relaxed resting state networks.

Focused moid thinking is essential for studying math and science. It involves a direct approach to solving problems using rational, sequential, analytical approaches. The focused mode is associated with the concentrating abilities of the brain's prefrontal cortex, located right behind your forehead. Turn your attention to something and bam-the foicused mode is on, like the tight, penetrating beam of a flashlight.

 

Diffuse mode thingking is also essential for learning math and science. It allows us to suddenly gain a new insight on a problem we've been struglgling with and is associated with "big-picture" perspectives. Diffuse mode thinking is what happens when you relax your attention and just let your mind wander. This relaxation can allow different areas of the brain to hook up and return valuable insights. Unlike the focused mode, the diffuse mode seems less affiliated with any one area of the brain-you can think of it as being "diffused" throught out the brain.

 

THe diffuse mode must have clay to make bricks!

 

Learning involves a complex flickering of neural processing among different areas of the brain, as well as back and forth between hemispheres.

 

focused, diffused

 

The Einstellung effect is a frequent stumbling block for students. It's not just that sometimes it is tough even figuring out where to begin, as wehn tackling a homweork problem. You bumble about your thoughts far from the actual solution because the crowded bumpers of the fucused mode prevent you from springing to a new palce where the solution might be found.

 

This is precisely why one significant mistake students sometimes make in leanring math and science is jumping into the water before they learn to swim. In other worlds, they blindly start working on homework without reading the textbook, attending lectures, viewing online lessons, or speaking twith someone knowledgeable. This is a recipe for sinking. It's like randomly allowing a thought to pop off in the focused mode pin ball machine without paying any real attention to where the solution truly lies.

 

If you are trying to understand of figure out something new, your best bet is to turn off your precision focused thingking and turn on your "big picture" diffuse mode, long enough to be able to latch on to a new, more fruitful approach. 

 

"when I wans learning about the diffuse mode I began to notice it in my daily life. For instance, I realized my best guitar riffs always came to me when I was 'just messing around' as opposed to when I sat down intent on creating a musical masterpiece (in which case my songs were often cliched and uninspiring). Similar things happened when I was writing a chool paper, thrying to come up with an idea for a school project, or trying to solve a difficult math problem. I now follow the rule of thumb that is basically: The harder you push your brain to come up with something creative the less creative your ideas will be. So far, I have not found a single situation where this does not apply. Ultimately, this means that relaxation is an important part of hard work and god work for that matter"

 

To figure out new ideas and solve problems, it's important not to only to focus initially , but also to subsequently turn our focus away from what we want to learn.

 

 

 

 

One of the first steps toward gaining expertise in math and science is to create conceptual chunks mental leaps that unite separate bits of information through meaning.

 

 

1. The first step in chunking then is to simply focus your attention on the information you want to chunk. When you first begin to learn something, you are making new nueral patterns and connecting them with preexisting patterns that are spread thtough many areas of the brain. Your octopus tentacles can't make connections very well if some of them are off on other thoughts.

 

2. The second step in chunking is to understand the basic idea you are trying to chunk.

 

3. The third step to chunking is gaining context so you see no just how, but also when to use this chunk. 

There are chunks related to both concepts and procedures that reinforce one another. Solving a lot of math probelms provides an opportunity to learn why the procedure works the way it does or why it works at all.... it also makes it much easier to apply your knowldedge to novel problems, a phenomenon called transfer.

 

Attempting to recall the material you are trying to learn retrieval practice is far more effective than simply rereading the material. 

 

Make your knowledge second nature

 

 

We procrastinate about things that make us fell uncomfortable.

 

THe better you get at something, the more you'll find you enjoy it.