Limits as Buffering

I was trying to make limits more interesting for my students and promote better understanding, and I came across this blog post that compared limits a moment when you are watching a video (in this case a soccer game) and your computer goes black for “buffering”. Click on this link for a better explanation:

http://betterexplained.com/articles/an-intuitive-introduction-to-limits/

Putting these screen shots on separate slides, students used what they knew about minutes 3:58, 3:59, 4:01, and 4:02 to predict what happened at exactly minute 4:00.

This led to students making tables for functions and comparing”buffering” to ERROR (on the calculator).

After the first day, I noticed a few students who were exploring a limit as x approaches 4 by making a table with x-values 1, 2, 3, 4, 5, 6. I wanted to emphasize the importance of “zooming in” further. So on day two I made my own set of screen shots (this time using a volleyball game), and I showed screen shots of minutes 2:00, 3:00, 5:00 and 6:00. We discussed how screen shots of these moments was not enough info to predict what happened at 4:00. Too much could have happened between minute 3:00 and minute 5:00!

We were able to come back to the comparison between the soccer game and the volleyball game screen shots throughout the week.

Lastly, I want to mentioned that Bowman has a great blog post on limits with an activity that I also used one day:

http://bowmandickson.com/2011/09/29/students-identifying-misconceptions-instead-of-me/

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1 Comment

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One response to “Limits as Buffering

  1. Jasmine

    I read a few blog posts before I get up each morning. Most of them are not directly related to what I’m teaching that day, but give me some food for thought as I make coffee and shower. Occasionally something is prefect for that day, and this was one of them. Thank you for sharing the better explained site. The soccer shots were absolutely prefect for my class today. It also reminded me that I don’t have to do anything amazingly original for a blog post to be useful. I’m going to write a post this weekend! Thanks for the inspiration!

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