Category: OpenLab Assignments (Page 2 of 2)

OpenLab #3: The MIU puzzle

We are going to play a game with strings of symbols.  This game was invented by a man named Douglas Hofstadter and found in his book Gödel, Escher, Bach. Here are the rules:

Suppose there are the symbols ‘M’, ‘I’, and ‘U’,¬†which can be combined to produce strings of symbols called “words”, like MUI or MIUUU. The MIU game asks one to start with the word MI¬†and transform it using the following rules, to obtain some goal word (which is given to you). ¬†The rules state:

  1. You must always begin with the word MI.
  2. You may add a U to the end of any string ending in I. For example: MI to MIU, or MUUII to MUUIIU.
  3. You may double any string after the M¬†(that is, change Mx, to Mxx, where ‘x’ represents any string of symbols). For example: MIU to MIUIU
  4. You may replace any III with a U. For example: MUIIIU to MUUU
  5. You may remove any UU. For example: MUUU to MU

WARM UP.  In each example, start with the axiomatic word MI and show, step-by-step, how to obtain the goal word (in each step, state which of the rules you used). These are just for practice (you do NOT need to submit your answers).

Example 1: Goal word MIU
Example 2: Goal word MIIU
Example 3: Goal word MIIUIIU
Example 4: Goal word MUUII
Example 5: Goal word MUUIIUIIU

Example: Goal word MUI
Solution:
Step 1: MI  (we always start with this word)
Step 2: MI to MII (rule 3)
Step 3: MII to MIIII (rule 3)
Step 4: MIIII to MUI (rule 4)
DONE!

Assignment (due Thursday, 9/15): Your assignment has three parts.

PART 1. ¬†First, create an MIU puzzle — that is, make up a goal word, and post it in the comments. Your¬†goal word should be between 8 and 16 letters long. ¬†Try to make it¬†tricky to reach, requiring at least four steps to reach (but the more the better!). ¬†See if you can find a clever use of the rules!

PART 2. ¬†The second part of your assignment is to solve someone else’s puzzle. ¬† Type your solution step-by-step, indicating which rule you used at each step. ¬†Leave your comment as a response to their puzzle. ¬†Only one solution per puzzle!

PART 3.  The third part of your assignment is to write a short paragraph (at least 3 sentences) responding to the following prompt.  Be sure to respond to each part:

Writing Prompt, MIU puzzle: ¬†Did you enjoy this assignment? Why or why not? ¬†Describe a connection between this assignment and our work in the class. ¬†(If you don’t believe there is a connection, try to imagine why we are doing this). ¬†Leave your response in the comments.

OpenLab #2: Mathography

This assignment is due Thursday, September 8, at the start of class.

Assignment.  Choose ONE of the following two topics.  Write a reply to this post, responding to the topic.  Begin by telling us which topic you chose. (1-2 paragraphs).

Topics.

  1. Sometimes people can recognize a time when their opinion of math dramatically changed either for the better or the worse. If such a time happened to you, tell us about it.
  2. Choose an experience you had in which you suddenly understood a math concept (it could be any kind of math, from elementary school up through college).  Describe what happened.  Do you think you could explain it to others in a way that they could have the same flash of understanding?

Extra Credit. ¬†For extra credit, write a response to one of your classmates’ comments. ¬†Do you feel the same, or different? ¬†Did you learn anything? ¬†Did you get any ideas about teaching, or about learning?

Why are we doing this, anyway?¬† We are following two ideas that have come up already in class — things that may¬†not¬†seem related to learning math, but research shows that engaging in these activities can¬†dramatically¬†increase the amount that you learn, and change the way you learn it. ¬†The first is¬†writing¬†‚Äď something not typically associated with mathematics. ¬†When you express your ideas in words, it forces you to think them through very carefully, detail by detail. ¬†A great way to check and see if you really understand something is to try to explain it to someone else, either out loud or in writing. ¬†Example: if you know how to add fractions, try teaching it someone who doesn‚Äôt know how. ¬†The second is called¬†metacognition, or ‚Äúthinking about thinking.‚ÄĚ ¬†This happens when you think about what was going on in your head while you were working on a problem or trying to learn a new idea. ¬†What train of thought did you follow? ¬†Where did you get stuck, and what did you do next? ¬†What were you feeling at the time? and so on. ¬†Combining writing and metacognition can be a tremendously powerful tool in identifying the ways we learn best and the ways we make mistakes, and learning to improve. ¬†However, like any skill, it takes practice. ¬†That‚Äôs why we‚Äôre getting started by writing a little about our past experiences with mathematics.

OpenLab #1: Advice from the Past

A year ago I taught this same course.   At the end of the semester, I gave my students the following assignment:

Imagine that you are invited to speak on the first day of MAT 2071, to give advice to entering students. ¬†Write at least three sentences … describing what you would tell them.

To see the assignment and the students’ responses, follow this link.

Your assignment, due at the beginning of class next Thursday, September 1st, is to:

  1. Read through ALL the responses (there are 19 of them).
  2. Write a reply to this post (1 paragraph) responding to all of the following:
    1. What advice seemed most relevant to you personally? Why? (you can copy/paste a short statement, or put it in your own words)
    2. Based on this advice, what changes can you make right now to help you succeed in this course?

Extra Credit. For extra credit, write a response to one of your classmates’ comments.  Do you have any advice?  Be kind.

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