Derivation of classical Kinetic Energy formula from STR

This year, thanks to NMC's media folks, I was able to use a lightboard (click here to read an article that describes how to build one) to put together two videos about Special Theory of Relativity (STR).

The first video (see the link shown below), goes through the process of deriving the classical formula of kinetic energy (K) from its relativistic sibling. The student were sent the link shown below and were asked to view it, take notes on it, record the said notes onto their IONs (Input/Output Notebooks), and then write a reflection paper on the subject matter as well as the video itself.

Kinetic Energy in STR Video (12:52 min): https://www.youtube.com/watch?v=-RfR-3-jiv4

The second video contrasts the two relativity relationships as understood by Galileo on one hand and the one formulated by Einstein on the other hand. The latter is also used to assist students in their understanding of how light speed remains constant in all inertial frames of reference.

Galilean vs. Einsteinean Relativity (6:21 min): https://www.youtube.com/watch?v=NGpVPG8Uilw

Once the students' reflections papers were collected, I challenged the students to justify the reasoning behind the Physicists insistence on inventing yet another relationship (that of K) that depends on the same physical quantities, mass and velocity.

Once satisfactory responses were obtained, I stated, "Now that we established connections between momentum p and kinetic energy K, would there be any relationship between ∆p & ∆K?" This led to the changes presentation, which I shall address in the following post.

After watching the two videos listed above, please, share your thoughts, reflections, and ideas about how you might use them in your own curriculum. Thank you

Dedicated to the memory of my beloved father (RA).

Geometry of Number Lines Makes Uncertainties Visible

Introduction:

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! :-)

Reflections:

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