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Aluminum Crystal Size

Concepts

  • Algebra
  • Dimensions and Units
  • Statistics

MEA Description: Aluminum Crystal Size provides students with an opportunity to work with images and utilize actual procedures used in industry. This task requires students to develop a procedure to measure the average crystal size of aluminum crystal images of three different samples. The motivation for developing the procedure is established by using a realistic context in which the quality of aluminum being produced is trying to be improved and can be assessed based on the size of the aluminum crystals in a sample. Student teams of four are required to establish a procedure for measuring the average crystal size. The students then apply their procedure to three different samples.

Implementation Strategy:

  1. Team Activity � In teams of four, students read background material describing the crystaline properties of aluminum. They are then asked to develop a procedure to take magnified images of aluminum and calculate an average crystal size.
  2. Homework Activity - Continuing in their teams, students read about a commonly used procedure to calculate crystal sizes known as the Average Grain Intercept (AGI) method. Students are then asked to write a document explaining how the AGI method is similar and differrent to their own method, as well as to apply the AGI method to a set of aluminum crystal images.
  3. MAA Activity - Individually, students develop a sequence of user defined functions in MATLAB to load an aluminum crystal image and quantitatively assess the average crystal size using the AGI method.

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?
The students need to develop a procedure for quantifying average size of irregularly shaped objects (given their own definition of average size) using microscopic images. The data that the students must work with is imbedded in three different monochromatic images. Each image is at a different scale.
Student are expected to apply algebra, dimensions, and units, and perhaps even statistics, to measure average size.
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.
The client is an unspecified aluminum company. This client needs a procedure for quantifying the quality of the aluminum being produced.
Knowledge & Background Needed: It is expected that students would apply algebra, dimensions, and units, and perhaps even statistics, to this problem. In addition, it is not known whether students would have been exposed to the concepts of average size and measuring the size of irregularly shaped objects.
Open-ended: The fact that there are a number of established methods for quantifying average size of irregular objects ensures the creation of a very open-ended problem that is mathematically significant.
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?
The test cases in the Aluminum Crystal Size problem consist of three images of aluminum samples. The students must apply their procedure to each of these images. The images are monochromatic pictures of surfaces where the intensity of the color of the surface is an indicator of differing crystals. The x-y scales on the images are given with appropriate units.
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?
Student teams are asked to respond to the client in the form of a memo. The memo must include the procedure for quantifying the average aluminum crystal size and the results of applying the procedure to the sample images.
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: The student teams are being asked to create their procedure for the aluminum company client.
Re-usable: The implication is that the client will apply this procedure to other aluminum samples.
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?
It is anticipated that students will use the following knowledge and skills imbedded in this MEA in subsequent courses and engineering practice:
  • defining "average size"
  • graphical representation
  • dimensions and unit conversions
  • scaling
  • statistics

Author Information:

  • Original Author(s):
    • Keith Bowman

Files:

History:
Tested in ENGR106 - Spring 2005