# Shredded Documents

Concepts

• Logic
• Regression (in MAA)

MEA Description: Shredded Documents provides students with a hands-on experience developing an algorithm to solve a tangible problem. This task requires students to develop a procedure to develop a quantitative method for analyzing if the scans of two shreds should be rejoined, as well as developing a brute force algorithm in MATLAB to perform the reassembly. The motivation for developing the procedure is established by using a realistic context in which a company specializing in security software development wishes to design software to aid in the reassembly of shredded legal documents. The company intends to use their software to assist government lawyers in their case against a fraudulent tire company. Student teams of four are required to establish a procedure for performing the reassembly using quantitative methods. The students then apply the procedure to an actual shredded document to analyze the correctness of their algorithm.

MAA Description: The MAA extends the MEA by having students implement a given de-shredding algorithm using MATLAB. Focusing on the use of looping structures, user defined functions, and image processing, the algorithm makes use of linear regression to rank how well two strips align.

Implementation Strategy:

1. Individual Activity ï¿½ Students individually begin to articulate how they would measure how well two strips align. The focus is at developing a mathematical algorithm for ranking how well two strips align.
2. Team Activity ï¿½ In teams of four, students read the interoffice memo from the security company client, which establishes the need to create a procedure to reassemble shredded documents.
3. Homework Activity - Continuing in their teams, students revise their procedure based on feedback provided by their teaching assistant.
4. MAA Activity - Individually, students develop a sequence of user defined functions in MATLAB to load shredded images, quantitatively assess how well any two strips align, join strips, and gradually build a complete reassembled image

Six Principles:

Principle Description How the principle is addressed in the MEA?
Model Construction Ensures the activity requires the construction of an explicit description, explanation, or procedure for a mathematically significant situation
Describe the mathematical model the students will be developing when solving this MEA:
• What are the elements?
• What are the relationships among elements?
• What are the operations that describe how the elements interact?
Elements  Shreds
Operators  Alignment, Rotation
Relationships  Reassembly instructions
Reality Requires the activity to be posed in a realistic engineering context and be designed so that the students can interpret the activity meaningfully from their different levels of mathematical ability and general knowledge
Describe the context. What is the story?
What knowledge will students need to bring to this problem?
What background information must be provided?

Describe how the problem is open-ended.
Essentially a realistic jigsaw puzzle. Corporations exist that professionally do this - Church Street Technologies
Self-Assessment Ensures that the activity contains criteria the students can identify and use to test and revise their current ways of thinking
What is provided in this MEA that students can use to test their ways of thinking?
Can they read a shredded document reassembled using their procedure?
Model-Documentation Ensures that the students are required to create some form of documentation that will reveal explicitly how they are thinking about the problem situation
What documentation are the students being asked to produce in this MEA?
Step-by-step algorithm
Construct Share-Ability and Re-Usability Requires students produce solutions that are shareable with others and modifiable for other engineering situations
What will indicate to the students that a sharable, reusable, or generalizable solution is desired?
Sharable  They should produce a reorganization method.
Generalizable  Should be able to convert this to a method for other reassembly projects
Effective Prototype Ensures that the solution generated must provide a useful prototype, a metaphor, for interpreting other situations
What are other examples of structurally or conceptually similar problems that would required a similar solution?
General assembly schemes, developing step-by-step instructions for someone else.

Author Information:

• Original Author(s):
• Matthew A. Verleger
• Assisted by:
• Tamara Moore
• Euridice Oware
• Carla Gerberry
• Irene Mena

Files:

• MEA Documents
• Extension Documents

History:

• Spring 2006 - Modified to push more quantitative elements into lab. Reused in ENGR106
• Fall 2005 - All components used in ENGR106