(Instructions on using the multiplayer aspect are on my blog here: http://liketeaching.blogspot.co.uk/2013/07/lesson-sketch-online-bearings-game-gets.html)

I really like how simple and uncluttered your version is, and I REALLY like the opening ‘blind sailor’ that builds a need for bearings.

From mine I prefer that you can watch you and your classmates racing against each other (increasing motivation to make a quicker time).
I also tried to get in ‘reverse’ bearings questions to raise the ceiling of the app, though I’m not entirely how successfully it worked.

I’m guessing bearings are written differently in the US to the UK (ours are a three digit integer angle measured clockwise from north).

Is that also an example of a language problem? They have an incorrect understanding of what the notation for the equation *means*? (Genuinely curious about this; I often wonder whether math education couldn’t effectively pillage instructional techniques from the study of languages–inflected languages in particular.)

Many short cuts are basically ways to think in terms of language instead of math.

@Ian – interesting. I’d agree that the student who can follow one of those sets of directions but not the other needs some linguistic work. What would the converse look like? Are there situations where a student grasps the language and vocabulary but not the underlying math? What would that look like for the same example?

Many students wouldn’t be able say much if you asked them what they know about about canis lupus familaris. That doesn’t mean they don’t know anything about dogs. Learning words to describe dogs is not directly related to learning about dogs. Learning the meaning of notation or language that can be used in math is not always directly related to learning the underlying math. Too often what passes for math learning is actually language learning.

Suppose a student is able to follow these instructions: put a dot that is 2.5 units to the right and 4 units above the first dot. But cannot follow these: plot a point at (2.5, 4). This student needs to learn some language, not math, in order to get the second task done.

Is there a difference between vocabulary and language learning and math? If so, what is it?

I really like how the angle is expanded out as the next bearing is set (maybe slow it down a bit). This activity is a nice way to introduce and get a little practice with bearing notation. Nice clean look as well.

Coming to an understanding that “20 degrees South of East” means to going mostly to the right and a little bit down is vocabulary or language learning, not math. The proportional reasoning with the 10 mile map key and the angle estimation introduces some relatively routine math (low floor). I would love to see a twist that leads to a mathematical puzzle or decision or strategizing – raise the ceiling as you say.

It is great that students get to pick their own routes. Why not make the optimal route less obvious in a straightforward way? Maybe the speed differs in different parts of the ocean due to currents/winds, so the shortest path is not always the quickest path. Give them an opportunity to do some reasonable analysis that will improve a route — doesn’t even matter if they find the optimal one.

I am completely sympathetic to the programming difficulties that may be involved in bringing in additional features. It is still a nice tool for working with the language of bearing notation and eyeballing distances and angles.