6 comments on “Just how silly is a 45-day weather forecast? And while we’re at it, just how good is a 2-day forecast?”

Just how silly is a 45-day weather forecast? And while we’re at it, just how good is a 2-day forecast?

Artifact

crappuweather

I’ve got bad news for everyone here in the Fort Collins area: there’s a chance of showers on Labor Day (September 2). It’s a shame because the following Monday (September 9) shows a mostly sunny day, with a high of 77 degrees. (I am writing this on August 8.)

Seriously, AccuWeather? Yes, AccuWeather is releasing a 45-day weather “forecast”, although it’s actually just more of a trendline (it will be colder in October than it is now in August, probably a safe bet). It will predict the highs, lows, and chance of precipitation up to 45 days in advance. Presently, I cannot quantify how terrible these forecasts will be, but they will be terrible.

So that’s the silly portion of this blog post. To me, the more interesting questions are as follows.

Guiding Questions

  • Is a 2-day forecast error prone? What about a 7-day? At what point to weather forecasts become statistically useless?
  • Is there a regional difference in weather forecast error?
  • Which weather forecast models are more accurate for your region?

Suggested Activities

  • Solicit predictions. How accurate do you think weather forecasts are? Do you think a 2-day forecast is appreciably more accurate than a 5-day forecast? Do you think it depends on the region you’re checking (i.e. does, say, a dry climate have more error than a wet climate? do the coasts have more forecast error than the plains?)? Can we quantify any of this?
  • Start collecting data. Keep track of the 2-, 3-, 5-, 7-, and shoot, the ridiculous AccuWeather 45-day forecasts. Compare it to the recorded data (you could stick a max/min recording thermometer out your window, or check archived data). Grab the highs and lows, and possibly recorded rainfall. Yes, the 45-day forecasts won’t start paying dividends for a couple months, but that’ll be some pretty rich data (“rich” has a couple different meanings in this case) to have collected. And thankfully, if you’re teaching Algebra 1, a lot of curriculum maps out there don’t have the “Statistics” unit until late in the year.

How to collect the data? Well, Google Forms makes it nice and easy to record data. See, look, I made a Google Form for you and your students to use. The only tricky part will be some spreadsheet column manipulation, correlating the forecasts with the appropriate weather data collection dates.

  • Develop a method to calculate the error of the forecast. Depending on the grade level, your class could certainly develop an error model based on whatever sophistication you feel appropriate. Maybe an elementary class will just take the differences between the forecasted and collected highs and lows. Maybe a middle or high school class will develop something more sophisticated. Something like Mean Square Error should do nicely.

MSE

MSEhuman

  • Compare model to model; compare region to region. Which weather model was the most accurate for your region? What if you just took the average of all the forecast models? Would that result in a better prediction? Some forecast sites to check:
  • Toward the end of the year, have students begin making their own Highs, Lows, and Precipitation prediction. By the way, these competitions happen all the time in the atmospheric science community. Maybe after some year-long analysis, your last couple weeks are spent gaming around students making their own predictions. They can look at all the forecasts and make a judgment. There are several ways to “score” it, some are more intense (scroll down to “scoring”) than others. Like collecting the data, Google Forms could be helpful.

If you’re looking for a long-term project that all students can access and be involved in (low barrier of entry, high ceiling), you could do worse than tracking weather forecast accuracy.

Teacher’s Edition

I’ve got some news that will probably shock you: 2- and 3-day forecasts are actually pretty good. And they’re getting better.

But this is me telling you that things are getting better and just citing some peer-reviewed research. That’s not necessarily what we do here. This is where you and your students could potentially come in.

For more on weather and weather forecasting, NCAR/UCAR has some excellent resources.

Update 8/9/2013:

Huge thanks to Frank (@fjvitale) for finding some graphs that better show improvement in TEMPERATURE forecasting. Here’s one that shows the error of MAX temperature forecasting for several different day forecasts since 1972.

You can find more forecasting verification graphs here.

(More of my posts on weather and climate.)

19 comments on “A non-linear approach to curriculum mapping”

A non-linear approach to curriculum mapping

I often hear teachers and parents talk about how math skills build on each other in a way that other subjects do not: you have to know how to add before you can subtract, you have to know how to multiply before you use exponents. This is certainly true to an extent, however, I’m wondering if we’re reinforcing these modes by our overly linear curriculum maps (*ahem*). In an inquiry based approach of mathematics, we often preach about “multiple solutions or solution paths” or “multiple entry points.” If we believe what we’re selling, doesn’t that fly in the face of a laddered approach to curriculum mapping? Are we just paying lip service to the whole “multiple solution paths” bit because we know the real way to solve the problem?

linear curriculum map
A linear curriculum map

I was talking with Kelly Renier (@krenier), director at Viking New Tech, and we began discussing the concept of “power standards” or “enduring understandings” or “What are the Five Things you want your students to know when they leave your class?” then build out from there. However, we didn’t discuss building those Five (or whatever number) Things out into linearly progressing units, but rather concentric circles.

concentric circles

Tasks and/or concepts may go in some ring of each of these concentric circles.

ccircles_tasks

Think of it as an outward moving spiral.

However, standalone, this still operates somewhat linearly: you start with the middle stuff (which is allegedly easier or essential) and progress outward, just like you would at the start of a unit, progressing to more complex concepts. But we make an entire curriculum of concentric circles and rotate from concentric circles cluster to concentric circle cluster every few days, or even in a week, potentially moving outward from the center of each set of concentric circles along the way.

ccircles_course
A [circular? iterative? vortex? Archimedean Spiral?] curriculum map.
There are two Moving Parts here, which probably should be addressed individually, but I’ve mashed together, either like a fluid Girl Talk album or Frankenstein’s Monster, take your pick.

  • Moving Part 1: Constructing units as concentric circles
  • Moving Part 2: Rotating through and revisiting topics

That said, I’m not sure you could do Moving Part 2 without doing Moving Part 1. We probably need a name for this type of Scope and Sequence / Curriculum Map: Circular Curriculum Mapping? Iterative Curriculum MappingArchimedean Spiral Curriculum Mapping?

This is getting a little mad-scientisty, I realize. Still, this may have a few potential benefits.

1) Students get to revisit a general topic every few weeks, rather than a one-and-done shot at learning a concept.

2) Students have time to “forget” algorithms and processes and when they see a scenario they have to fight their way through it accessing prior or inventing new knowledge, rather than relying on teacher led examples. Yes, I consider this a benefit.

3) Teachers may formatively assess more adeptly.

4) Students may see math as a more connected experience, rather than a bunch of arbitrary recipes to follow.

5) It probably better reflects the learning process, which happens in fits and starts, and frankly, cannot be counted upon to be contained within a specified time frame.

Personally, I find this framework compelling to a point. I think it better exemplifies recent research and advocacy toward math education. It certainly is messier than a linear approach to curriculum mapping. Your syllabus could potentially look elegant and beautiful or ugly and convoluted. Your administrator might back you, she might not. I’m guessing if you were forced to follow a district scope and sequence, or your math department wanted to be teaching the same things at the same time this would be a non-starter.

So this is just a sort of framework I’ve been playing around with, mostly in my head and I thought I’d throw it out there. I haven’t really developed anything useful. I’d be interested to hear your thoughts. How would you feel about a framework such as this? Do you think it adheres to best practices around mathematics instruction? Would this just work to create more confusion within students? Just how impossible would this be to develop in a public school? Maybe some math departments or curricula are already doing this or something like this? And if it does adhere to best practices and it isn’t implementable due to external constraints, then there may be additional implications for a teacher, school and district. For now, we’re just trying things on. And possibly tearing things apart and starting from scratch. Again.