I ran into this when working up an exponential growth problem (http://systry.com/precalculus/ebola-2014/) for my son’s precalculus class. The CDC had data on the number of Ebola cases which could be modeled with an exponential growth curve at the time. However, the math needed correction because of a sudden increase in cases. The CDC readily admitted they believe the cases were unreported by a factor of 1.5 to 2.5. Thus, a human eye on the data to recognize that and make an adjustment was necessary.

Later, when the curve could be modeled nicely by a logistics curve, the equation (http://systry.com/precalculus/ebola-2014-revisited/) was still incorrect in predicting the end of the epidemic. As teachers we would like to be able to button everything up and wrap it in a bow, but the real world seldom works that way.

We are trying to address this at the university (Newcastle) where I work by introducing into our mathematics teacher training degree a course in modelling (using problems where progress can be made with only school level mathematics).

Love to hear more about this. dan@mrmeyer.com if I can be of service.

The problem of assessment still remains though. The external examinations sat by our school students don’t involve any modelling activity.

Not just a NSW issue. I have yet to see a good (valid, reliable, practical) assessment of modeling.

We are trying to address this at the university (Newcastle) where I work by introducing into our mathematics teacher training degree a course in modelling (using problems where progress can be made with only school level mathematics). The problem of assessment still remains though. The external examinations sat by our school students don’t involve any modelling activity.

Every time I watch one of yours, I think of moments I sat and watched, thinking this would make a great! classroom poser — but didn’t take out my camera! (Large thunk of palm to head!)

I know that facepalming feeling!

Maybe useful context: for every video or photo I post there are five more on my camera. That’s to say, I capture lots of math, most of it useless for public / classroom consumption. But I find the act of capturing math sharpens my senses to the math around me. Constant capturing prepares me to notice the great math when it crosses my path.

I’m worry about it. I’m worry about not to find enough situations in which we need quadratics, trigonometric, exponentials,… functions to modelize. Is it because we oversimplify the model or is it because the 99% of situations could be modelized by afine function?

It it’s the second, our students tend to modelize things always with afine functions because “it’s always this way” ;-)

Just a thought,
Xavier

Last year, when my students did estimation180.com, we would enter “too low”/”too high” values that were (roughly) the median “too low”/”too high” choices for the class. (Somebody would suggest a value, people would raise their hands for whether they agreed it was too low/high, and we’d adjust/check a few times till we had a value where about half the people raised their hands.)

This seemed to work amazingly well to give high-quality lower and upper bounds. We could all tell the class median values were consistently better than any individual’s would have been over time. It also meant that everybody had input into the class low/high boundaries.

(The class median probably would have worked well for the actual estimate, too, but they took turns giving that one individually along with their own reasoning.)