What factors into the decision making process…a Quadratic-factoring modeling problem

Scheduling isn’t often thought of as a STEM (science, technology, engineering and math) career, but who could deny the thinking involved is mathematical?

A Scenario

Jeff is setting up a training conference for English and math teachers.  He needs to send four employees to the site to run two separate sessions.  Two will be lead presenters and two will manage the logistics.  Jeff must choose whom to send out from 16 employees within his non-profit organization.  What advice would you give?  Factor in all the constraints, weigh the benefits, and be ready to argue your position.

Diagram

diagram

Constraints

  • Ann is a great presenter but does not work well with other women.
  • Joan can either present or handle logistics
  • Ed is great with logistics but not much of a presenter
  • Greta is a mediocre presenter but better with logistics
  • Sam is a great presenter but doesn’t communicate well with Ed
  • Cara is a take-charge (but rigid) logistics manager
  • Joe is a great presenter, but often requires last-minute changes with logistics
  • Fred can only present ELA and is terrible with logistics
  • Paul can present Math, but is even better with logistics
  • Amanda is great with logistics, gets along with everyone but has young children and frequently misses work
  • Greg is amazing with logistics but has health issues and frequently misses work
  • Rhoda is a fairly good math presenter, but doesn’t get along with Joan
  • Nick can present ELA, but refuses to travel with Rhoda
  • Beta is a very laid back logistical person, sometimes misses a few details.
  • Zane is a reasonable good ELA or math presenter
  • Jon can do logistics in an ELA setting, but is totally lost in a math setting

Connections

This thought process above is mirrored in the process of factoring a quadratic by guess and check.  Depending upon the number of factors in the leading coefficient and the constant, there can be many possibilities and considerations.  Memorizing those considerations (can’t have two even numbers because then a two could be factored out…) is not the point of the exercise.  Rather, the factoring process allows students a means to develop the skill of systematically organizing and considering options.  Students analyze constraints and outcomes and select a pair of numbers that meet them.  This thought process is used virtually everywhere there are complex problems to be solved.  I was talking with a young man today who told me about his job as a bond analyst.  He selects from some options, and filters them through constraints, researches, and repeats the process until he finds what appears to be a good buy.  That is a process of making educated guesses and checking the outcomes , in this case, over time.  Here is a video that also mirrors the thought process of factoring a quadratic by guess and check:  video

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