Looking at Math in a Different Way

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Ebola, it is something that my students have been worried about since the first person on American soil was diagnosed on Sept 25th.  Even though I live in Northern Minnesota, my student really took interest in the disease.  I have been thinking about things to talk and work with them on about Ebola, and last night on Twitter my idea solidified when I caught #Edbola chat.  We have been looking at many different graphs in my Math class, and students were intrigued by the contact mapping officials were doing for those who were in contact with man diagnosed with Ebola.  I decided to have students create their own map of possible exposure given certain constraints.

 

We decided that a person with ebola was contagious for only 2 days.  That person would only come into contact with 5 people each day.  I asked my class to create a mapping of this scenario to determine how many people could possible be exposed to the ebola virus after 5 days.  Students quickly got to work, and after two minutes of creating a map, wrinkled their papers up and asked for new ones.  When this started to become it’s own epidemic, I pulled the class back together and asked what difficulties they were having in creating their maps.  The list I received was:

  1. I am not sure how to display possible contacts
  2. I am not sure how to show exposure for two different days
  3. The paper is too small
  4. I don’t know what type of map to make
  5. The map gets very hard once you get past the first two days
  6. I can’t make enough lines or symbols for my map, they get too crowded or small

For my class, student assignments are just that- student created ones.  For questions 1,2 and 4 I talked with students about the assignment- what it asked them to do and what they thought it should look like.  I would then have students just quickly sketch out a mapping that they envisioned.  This took a little coaxing, students typically do not want to do anything they perceive as “work” unless it is the end product.  I reassured them that the reason I wanted them to do this was not for an accurate mapping, but just as a quick visual for both of us so we knew where to start.  I then asked students to analyze that design, what could they anticipate as problems and what did they need to adjust to make sure they were able to display the information they wanted.  This step proved to be key, many students understood the need for the sketch and appreciated that they were able to create a small-scale version instead of attempting it right away and making errors.  They were also able to better handle questions 3,5 and 6 now that they had a clear picture of what they were attempting and anticipated possible roadblocks.

I purposefully kept the mapping to an 8.5×11″ paper, because I wanted students to realize the implications of the disease.  As it turned out, many students were not able to fit the whole 5 days on the mapping- which really solidified the idea that disease spread and containment is a serious issue in cases like this.  Here are a few examples of student work.

ebola mappings

I then asked students how many people would be exposed to the virus over this time, just to give students a numerical idea of how quickly this virus can spread even under these controls.  Students spent the rest of the day grinding the numbers out.  They chose brute force in an attempt to answer this question.  There were many mental breakdowns during this hour, but they were focused and engaged- they wanted to find the answer and did not quit on the problem, so I let them struggle.  At the end of class I told them they could take their mappings home, I wanted them to be able to clearly explain to me their strategy for finding their total exposure count.  I also reminded them to be mathematicians, to keep their eyes open to what they were asked to do and to look for strategies to get the answer.

The next day was an interesting discussion, one that I decided to keep whole group instead of breaking off into smaller ones.  We discussed many different ways to count the number of exposed people, why they worked, what they missed, and compared them to one another.  In the end students came up with the following method for counting the number of people exposed to ebola:

Ebola Contact

In the end, we took a real subject and explored it mathematically.  There were many great discussions between the students, and I got to see a side of their learning that is hard to expose.  They were surprised at the number of people who could be effected in such a controlled time, and this project has stuck with them as they hear about Ebola through the CNN Student News.

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