Number Sense – Space and Time

Took a day off from my #MTBoS30 challenge yesterday as I was hiking in New Hampshire with 8 of our boys. Beautiful view from the top despite rain in the morning:


There wasn’t a ton of math happening, but one thing was surprising, and a bit worrying on the theme of number sense. The hike was 5 miles round trip. 2 miles up, including a number of sections like this:


And 3 miles back down. The first mile, both up and down, was less than half an hour for the group. But the last half-mile to the summit, mostly climbing up steep trail like the picture above, took over an hour. My students were very attentive to the signs marking mileage coming up, and weren’t too focused on how long it was taking. Heading down, however, they really struggled to get an idea of how far we were from the trailhead, or how long that would take. They didn’t think that 3 miles was a big deal as we started on the trail down, but were surprised to hear that we probably had more than an hour left after making about a mile of the way down. Then, upon hearing that they were still a mile from the bottom, several students were horrified that they were so far away, unaware of how fast we were moving on the relatively flat lower portion of the trail.

This isn’t a big deal, or a red flag for me mathematically. This type of number sense is tough for many adults, and we were tired and impatient after a long hike. That said, we spent some time this year talking about distance-speed-time questions, and while they often struggled with concepts, it’s a skill I would love them to take to high school, and I didn’t see it in practice. It makes me curious what kind of concrete activities could give students a sense of space and time that they could apply to their everyday lives.

So many questions.

2 thoughts on “Number Sense – Space and Time

  1. banderson02

    We do an overnight hike with our 8th graders, and their sense of time and distance is also very off. I realize that night hiking makes this type of estimation especially tough, but when you make comments like “we are halfway to our next break” they still ask 5 minutes later how far or how much longer to break.
    Reading this, I am thinking I will try and prep students for this type of internal calculation, thanks for the idea!

  2. dkane47 Post author

    I wonder how this is related to the inability to delay gratification that we all see with middle-schoolers — any time we do estimation or prediction tasks around time, the answers vary enormously, much more so than with spatial sense in my experience.


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