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July-August 2015
 
 

Let’s Embed Decision Analytics into Middle School Mathematics to Make Math More Relevant to Students’ Lives
From Kenneth Chelst

Kenneth ChelstMiddle school mathematics develops and builds skills that provide the foundation for learning algebra. One interrelated set of critical skills involves learning about ratios, proportions, rates and percentages. A standard word problem is as follows:

There are thirty children in a class. The ratio of boys to girls is 3:2. How many boys and girls are there in the class?

This simple example illustrates the lack of relevance that pervades math word problems. Here are some of my concerns.

  • How would someone know the ratio is 3:2 if they had not counted the number of boys and girls in the first place?
  • Why is anyone interested in the number of boys and girls in this class?

Additional shortcomings include

  • There is nothing of interest to discuss in the example.
  • The example involves finding the single correct answer.

Decision makers and analysts use mathematics to explore a range of solutions and not just to find the single correct answer. In most real-world contexts there is lots to discuss. This example can be transformed and made substantive by focusing on a decision in the future and not a description of what is.

A group of 60 students are going on a sports outing. The ratio of boys to girls is 3:2. The trip organizers want to plan the program around one of three possible sports: basketball, volleyball or softball. In fairness, they would like to keep the ratio of boys to girls the same on each team.

  1. If they go with basketball teams of five students, how many teams would there be? How many boys and girls would be on each team?
  2. If they go with volleyball teams of six students, how many teams would there be? How many boys and girls would be on each team?
  3. If they go with softball teams of nine students, how many teams would there be? How many boys and girls would be on each team?

The first question is straightforward and helps students understand the context. The second question also looks simple until you realize that it is not possible to keep the ratio of 3:2 with six students. In the “real world” the numbers do not work out perfectly. This opens up the opportunity to discuss solutions that are close to this ratio. What other factors could be used to make the teams more balanced? One precocious student might even question the underlying assumption that it is important to keep the ratio of boys to girls equal to 3:2. In the third example, nine does not go evenly into 60. In addition, teams of nine also cannot maintain a 3:2 ratio. However, there is a simple alternative. Each team is given a reserve player so teams of ten are formed.

This simple transformation brings the concepts of analytic decision making to a problem context children can relate to. Students are using ratios to explore the solution space. There may be no one correct answer. It offers broad opportunities for discussion around the importance of knowing ratio of men to women in many contexts.

Dr. Kenneth Chelst is Director of Engineering Management and Professor of Operations Research in the College of Engineering at Wayne State University. He led the NSF grant that developed the MINDSET curriculum that uses math-based decision-making tools from Operations Research to present standard mathematics concepts in a non-calculus fourth-year mathematics course. See more at: http://www.mindsetproject.org.

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