Why are chimneys like party poppers?

We are nearing the final stages of the English and Maths project, where a bunch of Yr9 students are using their understanding of how pollution spreads to convince the local residents and the planning officials that building 4 factories in the heart of the Olympic Park is a bad idea. Jess wrote about the project planning here, and the press attention here.

The mathematical foundation for the argument against the factories has constantly shifted over the past term. Both frustrating and rewarding. Here is the journey, starting in October.

  1. Initially I assumed that any theoretical understanding of pollution would be difficult for a nurture group, probably delving into multi-variable differential equations.
  2. Therefore, we at first planned to record levels of pollution in the local area, and use this data to predict what the pollution might be like after the construction of concrete factories. We were very kindly given a class set of tags that paired with phones to give data. Unfortunately the data was not detailed enough, logistically it was difficult to go out and record high quality data, and not every student had a phone. The dream of students independently going out and using their phone to change the world was somewhat dashed. That said, a few students do continue to use their tags and record the pollution in their daily lives – small win.
  3.  If measuring air pollution was not going to work, would we have to go back and understand the theoretical models? A few weeks of emailing around pollution scientists in London and treading water in lessons ensued. Elsa, from Southbank University, came and spoke to the class, and taught me about the Gaussian Plume Model. We had found an equation that could map out spread of pollution.untitled-picture
  4. First attempt: students to understand the equation and substitute in the relevant variables (for example, distance away from concrete factory and speed of wind). I made a beautiful but hopelessly complicated flowchart to aid this process.untitled-picture
  5. The equation was too unwieldy. Next step: I plug the numbers into the equation (or sometimes students use a ready-built calculator to do it themselves, and the students plot the graphs and analyse the results. Plotting graphs with very small and very big numbers involved revealed great teaching points about rounding and scale.untitled-picture

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We discovered that the students were having difficulty understanding the variables affecting how dirty the air that you breath in is. For example, what does “distance from chimney to my location”? Building on an idea from Jess I made a double-lesson analogy of Chimney as party popper, with the exploding paper representing the pollution. untitled-picture

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Distance to factory, distance to side of factory, and height of chimney, become real.

 

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Conclusions 

  • Through this tortuous journey of dead-ends and frustrated ideas we (accidentally?) exposed the students to a variety of mathematical ideas. Had we gone straight to Stage Five: plotting graphs and analysing them, then there would have been no data collection, no understanding of equations, no algebraic substitutions.
  • The fact that we teachers genuinely had no idea of how to solve the problem gave us intellectual excitement throughout the project, useful in pumping up the students and our lessons.
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