Saturday, November 2, 2013

Geometry of Number Lines Makes Uncertainties Visible


Uncertainties tend to give students a hard time. So, I decided to approach this vital concept of Physics a bit differently this year by emphasizing the use of number lines as visual aids. This, would enable students, to not deal with uncertainties as pure abstract numbers only, rather they would graph them on number lines to reach better conclusions regarding uncertainties. 

The Nuts & Bolts:

In this experiment, a precursor to the actual Free Fall lab, the students dropped rulers to determine their respective reaction times and then, using their group's collective uncertainty number line (see images below) they decided (as a group) which student should be their stopwatch timer for the subsequent main lab activity. In addition, the students had to provide at least one complete sentence detailing their justification as to why they picked their respective group's timing person.

Following is a sample of my students' initial rough dabbling with such new approach. I am proud of them and the genuine effort they devoted to the activity!

This is Group 3's take on the matter & it is so easy for students to see unusual outcomes this way! Coolism! :-)
This is Group 4's take on the matter. The language is a bit more precise (pun intended) than I have ever had in previous years. The potential of this method is promising! Coolism! :-)


Of course, this visual approach may not be earth shattering but the beauty of it is in the following touches:
1) It makes the invisible, visible! Pedagogically speaking, this should improve understanding.
2) The connection this approach establishes with a math concept (number line) that students would rarely see/use outside of their math class. Physics adds Coolism to math!
3) This approach already seems to offer students a better and slightly more sophisticated way of expressing their thoughts vis-a-vis terms they need to learn to use carefully in their lab analyses such as accuracy, precision, uncertainty.

Coolism Request:

Please, add to the Coolism, by commenting on this approach and suggesting adjustments you would make to allow it to be more useful to our students conceptually speaking. 

In addition, share your own successful approaches so that together we enrich our respective students' experience with the concpet of uncertainties. 

Thank you 


  1. I like this a lot. The notion of making the invisible visible is a powerful one in this instance. I really liked how some groups chose the most precise person (Robert at the top) and others just chose the one who's average was the smallest. Did you have a conversation about which of those approaches would be most useful? Also, please share this approach with us on Wednesday when we tackle uncertainties in the Global Physics Department.

    1. (1) Thank you for taking the time to read the post and thank you squared for commenting. (2) No we did not have a conversation yet for this was done just last Thursday and also I would like to let the results of the actual data collection process of the subsequent lab provide the students with further insights into the matter. (3) I would love to share the approach with our Global Physics Department colleagues..

  2. I agree- I've bookmarked this post for use next year when I introduce the idea of uncertainty. It's certainly true that a lot of students don't conceptually understand uncertainty and simply do it because they're required to. I like how this makes the uncertainty easily visible and can open up a discussion about what makes a "good" set of measurements.

    Thanks for sharing!