In this "Math Chat" we will explore three topics. First, Michael Starbird's methods and vision for "effective thinking through mathematics". Second, using puzzles to explore and practice effective thinking. We will examine four example puzzles he and his student Scott work through (and a bonus puzzle by Derek Muller). Finally, we will discuss NetLogo, an agent-based programming language and modeling environment, based on several introductory videos by Melanie Mitchell.
The featured videos total an hour and a half, but if you follow all of the links there is an additional hour if you are feeling more ambitious. Each video is short: the longest one is only 18 minutes long. As always, watching the videos is optional, but will give you more grist for the discussion mill.
• In this video Starbird introduces his five strategies to effective thinking:
• In this exquisite video Starbird relates a story about a trumpet player to explain the first strategy of effective thinking, namely, to understand deeply, in particular, to understand simple things deeply:
• In this video Starbird powerfully explains the importance of making mistakes and learning from them:
• Link to the full 27 minute playlist for "Effective Thinking Through Mathematics" (includes 2 videos not highlighted totaling 5 minutes).
• Starbird introduces puzzles as a tool for practicing and evaluating strategies for effective thinking:
• The Meanie Genie Puzzle:
• The Pirates and Admirals Puzzle:
• Whom do you trust Puzzle:
• A Shaky Story Puzzle:
• This playlist includes the four introductory puzzles and other introductory material but no solutions (14 minutes).
• This playlist includes the four puzzles above plus videos where Starbird guides Scott in the practice of effective thinking. Warning: two of the puzzles are solved in the videos. Try to solve the puzzles on your own before watching the whole playlist. 52 minutes.
• Bonus puzzle by Derek Muller (can you guess the rule before Derek gives the answer?):
• Melanie Mitchell's Introduction to NetLogo (Download NetLogo through this link; Download Mitchell's "Getting Started with NetLogo" (pdf, 863k), Download the code for AntsNew.nlogo):
• A simple NetLogo model:
• A more advanced NetLogo model:
• This is the complete playlist for an Introduction to NetLogo with Melanie Mitchell. It includes four additional videos plus the three above (1 hour, 11 minutes). Additional resources needed for the extra videos: 1) Homework (pdf, 68k), 2) Download OneAnt.nlogo (12k), and 3) Download MultipleAnts.nlogo (12k).
Here are some of the questions we might discuss:
• What do you think of Michael Starbird's five strategies for effective thinking?
• Can we learn effective thinking from studying mathematics?
• With the five strategies for effective thinking can anyone learn how to do mathematics better? If not, what additional strategies are required? Or is mathematics the purview of only those with certain cognitive capabilities?
• Is reviewing and mastering the basics essential for high performance thinking in any field?
• Is learning from mistakes important for effective thinking? Do mistakes guide our work in solving problems and thinking effectively?
• How is one supposed to use "raising questions", following the "flow of ideas" and change or growth as tools for effective thinking?
• What did you learn from solving the four Starbird puzzles and the bonus Derek Muller video? Did you use the strategies for effective thinking? What strategies did you use? Can puzzles help us understand the qualities of effective thinking?
• What do you think of NetLogo? Is computer simulation a tool for effective thinking? Is agent-based modeling mathematics? Is building a mathematical model, in NetLogo for example, a way to make mathematics and effective thinking more broadly accessible?
• What examples from the NetLego models library did you explore?
• Is NetLogo a programming environment that you might consider using? For what projects?