10.28 Part 2: Analysis!

Note:  discussion of the reflective writing for the persuasive essay, and posting materials for the Grade-so-far for the Persuasive writing is in the previous blog post.

Analysis.
During the second half of class discussing analysis.  We worked together, as a class and in groups to solve a logic puzzle using analytic process.  As we worked on the puzzle, we paid attention to the "moves" we were making, and wrote a list on the board to name and describe our analytic process.  The purpose of this exercise was to make us more conscious of what we do when we analyze, and to develop a shared vocabulary to talk about the moves we make during analytic process.

You all use analysis all the time.  Before we began working on the puzzle, I gave you a rather technical definition of what analysis is.  I said analysis is the process of looking at a system or process or other object in terms of its parts.  The parts are named and classified (categorized) in terms of their features.  The analyst then lookes for patterns in the relationships among the parts.  This is a lot to take in - so the next thing we did was to talk about the ways you use analysis in your everyday life.  We talked about how you might use analysis when you "comparison shop" = by identifying what you like and don't like about the various options.  This is an analytic process.

Solving the sequence puzzle.

 1. DEFINE the problem/question 

This step included deciding what your task was (what you had to do)  and ORIENTING to the data (deciding the perspective or focus for your analysis).  In this case, this process involved ooking at the grid of shapes, reading the question at the bottom of the page. So initially the problem was "to identify the missing shape."  But to solve this problem, you also had to decide what "order" the shapes were in - whether they were arranged right to left, left to right, top to bottom, bottom to top, sudoku fashion, or. . .?  And the only way to know if you'd chosen to right "frame" for looking at the problem, was to solve the problem (find and answer that would explain the data).  So there was an element of trial and error even in definining the problem.

 

2. Identify or categorize the elements of the puzzle

Categories = groups of things with shared features - so in some ways, this step involved a kind of unconscious noticing of the differences/similarities of elements (diamonds, clubs, squares, hearts, etc).  Those siilarities and differences are the the features (shape, orientation, color) of the different elements.  You identified 8 different elements.  Some of you counted them.  Some of you looked for local patterns iat this point (step 4), and then "tested" your patterns by looking to see if they applied to the whole puzzle. 

In a way, this was a beginning of looking for patterns.

This step sometimes included counting the elements within a category (how many of each kind of shape/color/orientation) and it sometimes included noticing LOCAL groups or clusters (like the groups of two symbols of the same kind) and counting that as a category.

Looking at a LOCAL group (just part of the problem) so you could concentrate on a smaller, more manageable piece of data.  I think every group made important progress through looking at small, local groupings as a way to predict what other local groupings would be. 

3. Name/identify FEATURES within data = deciding which FEATURES in your data were essential features (relevant to the pattern you were trying to find) and which were incidental.

You noticed that there were different shapes,

That some of the shapes were oriented differently

That the shapes were different colors

Before you could talk about patterns, you needed to NAME and classify the features of your data.  You then could have a discussion about whether or not those features were relevant to the puzzle's solution.  In this case, shape and orientation were important within the global pattern, but color was only important in that it was fixed for particular shapes.

4. Look for patterns

 In this step you looked at the features, categories and local groups you identified as ways to talk about repetitions, relationships, and larger sequences. 

You identified lots of different local patterns = which shapes ALWAYS went together, or the order in which shapes followed one another.  

To develop different patterns - your looked at the puzzle from different ORIENTATIONS, and you also looked at particular, local sections as a way to consider part of the puzzle at a time

5. Pose local theories (connect to  patterns that are "out there" in the world).

Once you noticed a pattern in color, or sequence, or grouping  - you formed an idea of what that pattern might look like if it were true for the whole puzzle.  The idea of what a pattern would look like when it applies to ALL your data is a theory.

Theories often are connected to patterns that you already know.  For example, you "read" the puzzle from right to left (for different reasons) and from top to bottom, some of you connected to the 3X3 matrices of sudokus, and some of you tried columns).  Each of these decisions represents a "theory" about how the puzzle was oriented/organized.

Some of you noticed that there was a black shape in every row but the last one, and guessed the club (which is the right answer) => but the wrong reason.  There is also a diamond in every row but the last one => the REAL answer is about the sequence of the shapes (a  GLOBAL theory- a theory that can explain everything in the puzzle). Some of you theorized that the club occurred next because of the sequence (which shapes were always on either side of the upside down club)=> this was the right LOCAL theory, but it was not a GLOBAL theory (one that could account for all the data - and predict what would happen with additional data).

6. Test your theories!

 Once you had a local theory (about two shapes always following each other, or being above each other, or about the color distribution, or about symmetry) you tested your theory by checking to see if the pattern you identified applied to the WHOLE puzzle. 

If the theory didn't FIT (explain what you could see) and WORK (allow you to generate or extend the data further by predicting the pattern) - you decided the theory was wrong - and cycled back through the steps - re-thinking the names and groupings and patterns that you had already tried. You might even need to go back and re-define the problem.

7. Use local theory to pose GLOBAL theory (to explain the whole system)

Once you found a theory that seemed to fit and work for part of the puzzle - the next step is to see if you can use your theory to predict what would happen in new situations.  For this puzzle - the correct answer allows you to name the right "shape" at any point in the series.

You did a great job on this!  Both on naming what you did during analysis AND in solving the puzzle.

In the end, we oserved that analysis, like writing, is recursive -in that you work through "loops" - start over, get to a place where something doesn't work, and start over again.

We also (re)defined the terms we used to talk about analysis:

categories, elements, features, local theories, global theories, fit, work.  

You will want to go over these words so we can talk about what we are doing as you do your analyses in this unit.  

For next class:

Read:  Zinczenko (p. 391); Warner (p. 400). 

Write:  Finish yor persuasive essay, and put all work to be graded in your portfolio

In next class, we will start by nailing down the main points in each of the essays.  Then we will work as a class and in groups to analyze the arguments made in these two texts. 

Good class and see you Thursday!