Effective thinking through Mathematics - A Philadelphia meetup.

On the 4th Saturday of the month the Philadelphia Math Counts meetup meets at the greatest coffee shop in Philly, Capriccio Cafe & Espresso Bar, to spread Math culture in the city of Philly by discussing videos and books. This month, the meeting is on July 26th and the discussion is on Michael Starbird's Effective Thinking through Mathematics videos. As per the usual order of the group, you don't need to see the video to join in the discussion, just come with an interest in the material and two dollars to help make sure we get to continue doing this. Everybody from novices with questions to experts with answers are welcomed, because the regulars fall under both categories. It's fun, informative, and there is a ton of coffee involved. Or tea or bagels, if that's your thing.

Some thoughts and a brief overview of Starbird's videos. In his 1st video, he explains it as a self help sort of thing, a way to train your mind for success. Fine, okay. But as the videos go on, it's more heuristics and effective ways to solve problems better. This is a fascinating field to me, and our group has already covered the book "How to Solve it" by George Polya, so I was interested to see if he added anything new to the discussion.
His five steps towards effective thinking can be applied to anything besides math. It's part of the point of the series. Their good tips.

1. Understand deeply. Mediate and observe you life, or the problem, and work to understand  "with nuance, precision, and depth."
2. Follow the flow of ideas. Ideas rarely come from air. They change and evolve over time and continue to do so as new knowledge and experience is applied to the idea.
3. Raise Questions. His suggestion is to get into the habit of asking questions about the problem. Is there more to the problem that I'm not seeing? Can this be ex tented? The most important one is, have I've seen a similar problem, and can I adapt an old answer to a new problem?
4. Make mistakes. It has been said time after time again that making mistakes is the best way to learn. BUT there is more to this than just make mistakes. By combining this one with the first one, you do learn. Otherwise, you are doomed to repeat the same mistake and never going forward. Make mistakes, and reflect on them.
5. Change. Strive to change. Become better than you are. Grow your personality.

I'm not going to lie, self help anything is something that makes me uneasy. A strange statement, but it's something that bugs me like salesmen or policemen acting like their best friends in the world. I've only watched the videos so far, and haven't taken the course, so I can't comment on how you use this in a daily life. As a way to solve problems though, the information is invaluable. Starbird does offer practice problems, too, with the goal being to practice the steps laid out in the videos. The problems are not tough at all, and really just require the person to sit down and focus on them. I've worked on one so far.
The admirals and pirate puzzle is 3 pirates and 3 admirals both make it to a river at the same time. There is one boat that can hold 2 people and, since it's a boat, it needs at least 1 person in it to row it. If the pirates outnumber the admirals on either side of the river, they will kill the admirals. How do you get everyone across the river with no bloodshed?
It's a variation on the goat, cabbage, and wolf problem. An old problem. I've come up with an answer, but I'm not so sure when to share it. Maybe later this week, maybe you'll just have to come the meetup if you want to hear my answer. Don't know.
I don't want to sound too hard on these videos. His stories on two of techniques are good and illustrate his point. But, I guess I just don't know what level this aimed at. These seem easy, but he's acting like he's addressing this to people who've already graduated. Well, I have the link to the full course, so I'll watch more of it and try to come back with a more in depth thought on it. Stay tuned later this week when I talk about the netlogo videos that the group will also be discussing.