Lamson Library: Metaliteracy: 2. An Approach to Solving Any Problem

Now that you've focused your topic

1. Think about what you hope to learn and what skills you might like to develop.

2. Consider what you know about the topic and what you want to learn. Devise a Plan.

3. Carry out the plan. As you complete the assignment, add new searching skills to what you already know.

4. Reflect on the project once you complete it. Did you learn new skills? Did you accomplish what you identified as desirable goals when you were in the thinking stage?

First:

Understand the Problem
(Metacognition* -- Thinking about Thinking)

Think about How You Could Solve it.

Anagram: DRY OXTAIL IN REAR

Clearly state the problem**:

I need to rearrange the fifteen letters [DRYOXTAILINREAR] into a single English word.
I must use all of the letters, but each letter only once. Therefore, the English word will have fifteen letters.
I've seen anagrams before. For example, letters in the word DORMITORY can be rearranged to spell DIRTY ROOM.
I'll know I've succeeded when I've used all fifteen letters to form one English word.

From a metacognition standpoint, think about how you think about puzzles. What might you get out of doing puzzles other than the right answer?

Sources:

* Metaliteracy is not a linear process. You would use all four domains throughout your investigation of a topic. But at this stage you could consider the value of metacognition, thinking about your thinking. For example, what could you hope to accomplish by doing this puzzle beyond solving the puzzle? It turns out there could be many benefits. Research shows that working on puzzles:

helps memory
increases the ability to concentrate
helps with collaboration skills
aids face recognition
relieves stress
increases visual-spatial reasoning
improves attention to detail
delays Alzheimers

The schema for metaliteracy was developed by Trudi Jacobson (University at Albany) and Tom Mackey (Empire State College). This interpretation was derived from: Forte, M., Jacobson, T., Mackey, T., O'Keefe, E., & Stone, K. (2014, September 11). Goals and learning objectives: Developing metaliterate learners [Blog post]. Retrieved from Metaliteracy website: https://metaliteracy.org/learning-objectives/

**The renowned mathematician, George Pólya, claimed that skipping this step is the reason many problems go unsolved or are solved incorrectly. This puzzle and the recommended steps to solve it come from: Pólya, G. (1957). How to solve it: A new aspect of mathematical method. Garden City, NY: Doubleday Anchor Books. (pp. 161-162)

Second:

Devise a Plan
Consider What You Know (Cognition*)

What data are available? What information might help? How could I approach the problem methodically -- step by step?

Devise a Plan, Evaluate Data*:

Anagram: DRY OXTAIL IN REAR

Gather data and create a solving strategy**:

The data:
- There are eight consonants: (D,L,N,R,R,R,T,X)
- There are seven vowels: (A,A,E,I,I,O,Y)
What I already know about the English language:
- Seven vowels might mean seven syllables (unless there are diphthongs, e.g. io, ea, etc...)
- Long English words (this one has fifteen letters) frequently have common prefixes and common suffixes.
My personal experience:
- Having the letters in alphabetical order doesn't help.
Expert advise:
- Will Shortz, the New York Times crossword puzzle editor, says it's easier to recognize anagrams if you arrange the letters randomly within a circle.

The Plan (Solving Strategy):

1. Form a list of prefixes and suffixes.

2. Write prefixes and suffixes on paper

3. Arrange remaining letters randomly
in a circle between the prefix and the suffix.

4. Rearrange the letters using trial and error.

Sources:

* Metaliteracy is not a linear process. You would use all four domains throughout your investigation of a topic. But at this stage you could consider the value of cognition, what you know. However, you'll want to be aware of what you know and what you learn throughout the process. The schema for metaliteracy was developed by Trudi Jacobson (University at Albany) and Tom Mackey (Empire State College). This interpretation was derived from: Forte, M., Jacobson, T., Mackey, T., O'Keefe, E., & Stone, K. (2014, September 11). Goals and learning objectives: Developing metaliterate learners [Blog post]. Retrieved from Metaliteracy website: https://metaliteracy.org/learning-objectives/

Third:

Carry Out Your Plan (Behavioral*)

Try Your Plan. Be Flexible if you get Other Ideas.**

Anagram: DRY OXTAIL IN REAR

1. Form a list of prefixes and suffixes.

Prefixes:

anti-
de-
en-
extra-
in-
inter

Suffixes:

-al
-ary
-ation
-ial
-ed
-er
-ion
-tion
-ity
-ly
-ty
-y

2. Write prefixes and suffixes on paper

extra	dryoiinr	al
extra	doilinr	ary
extra	droaiinr	ly

3. Arrange remaining letters randomly in a circle between the prefix and the suffix.

4. Rearrange the letters using trial and error.

Anagram: DRY OXTAIL IN REAR

Sources:

* The schema for metaliteracy was developed by Trudi Jacobson (University at Albany) and Tom Mackey (Empire State College). This interpretation was derived from: Forte, M., Jacobson, T., Mackey, T., O'Keefe, E., & Stone, K. (2014, September 11). Goals and learning objectives: Developing metaliterate learners [Blog post]. Retrieved from Metaliteracy website: https://metaliteracy.org/learning-objectives/

Metaliteracy is not a linear process. You would use all four domains throughout your investigation of a topic. But at this stage you could consider the value of the behavioral domain, what do you actually do to solve the problem? What skills could you develop along the way?

Fourth:

Reflect on the Experience (Affective*)

Unfortunately, George Pólya doesn't include this important fourth consideration in his "steps," but metaliteracy does. Recognize that the four domains of metaliteracy all interact with each other all the time. Being aware of the affective domain throughout the process could help motivate you and give you a feeling of confidence and pride in your efforts. The way these steps were arranged makes it look like problem solving is a linear process. It isn't. Although you might be able to apply metaliteracy concepts to Pólya's steps, understanding metaliteracy might be more helpful to you because it is a way for you to continually take in the big picture.

Source:

*The schema for metaliteracy was developed by Trudi Jacobson (University at Albany) and Tom Mackey (Empire State College). This interpretation was derived from: Forte, M., Jacobson, T., Mackey, T., O'Keefe, E., & Stone, K. (2014, September 11). Goals and learning objectives: Developing metaliterate learners [Blog post]. Retrieved from Metaliteracy website: https://metaliteracy.org/learning-objectives/

Try this problem on your own:

Metacognition: Thinking about thinking.

In this stage you think about how you'll go about solving the problem. The first step is to clearly state and understand the problem. Remember that Prof. Pólya says that not stating the problem clearly is the main reason people fail at coming up with a solution. In this example, the problem is already clearly stated. But the metacognition work isn't done. Think about what you hope to learn or gain from working on this problem

Problem:

"A bear, starting from the point P, walked one mile due south. Then he changed direction and walked one mile due east. Then he turned again to the left and walked one mile due north, and arrived exactly at the point P he started from. What was the color of the bear?"

Cognition: What you know (or what you learn)

I can assure you that you already know everything you need to know to solve this problem. You just have to realize that you know it. Think about the problem and what you know.

Behavioral: What you do to solve the problem.

Can you identify what you did to solve the problem. What steps did you take? Perhaps you could plot the path of the bear on a piece of paper.

Affective: How you feel about the problem.

How does working on solving the problem make you feel?

Perhaps it's a sense of accomplishment. A feeling of pleasure that you solved the problem. Amusement when you come up with the answer.

This puzzle comes from: Pólya, G. (1957). How to solve it: A new aspect of mathematical method. Garden City, NY: Doubleday Anchor Books. (p. 234)

Now that you've focused your topic

First: Understand the Problem (Metacognition* -- Thinking about Thinking)

Think about How You Could Solve it.

Clearly state the problem**:

From a metacognition standpoint, think about how you think about puzzles. What might you get out of doing puzzles other than the right answer?

Second: Devise a Plan Consider What You Know (Cognition*)

What data are available? What information might help? How could I approach the problem methodically -- step by step?

Devise a Plan, Evaluate Data*:

Gather data and create a solving strategy**:

The Plan (Solving Strategy):

Third: Carry Out Your Plan (Behavioral*)

Try Your Plan. Be Flexible if you get Other Ideas.**

Fourth: Reflect on the Experience (Affective*)

Try this problem on your own:

Metacognition: Thinking about thinking.

Problem:

Cognition: What you know (or what you learn)

Behavioral: What you do to solve the problem.

Affective: How you feel about the problem.

First:

Understand the Problem
(Metacognition* -- Thinking about Thinking)

Second:

Devise a Plan
Consider What You Know (Cognition*)

Third:

Carry Out Your Plan (Behavioral*)

Fourth:

Reflect on the Experience (Affective*)