Shredded Documents
Concepts
 Logic
 Regression (in MAA)
MEA Description: Shredded Documents provides students with a handson 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 deshredding 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:
 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.
 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.
 Homework Activity  Continuing in their teams, students revise their procedure based on feedback provided by their teaching assistant.
 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:

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 openended. 
Essentially a realistic jigsaw puzzle. Corporations exist that professionally do this  Church Street Technologies 
SelfAssessment 
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? 
ModelDocumentation 
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? 
Stepbystep algorithm 
Construct ShareAbility and ReUsability 
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 stepbystep 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: