Extensions to SHM in AP-Physics

Introduction:
It is very important that students in AP-Physics classes be pushed to go beyond the usual curriculum material. We owe it to them to conduct harder labs that would push their thinking and analysis limits.

What to do?
As an option that instructors may choose is to extend regular topics to include situations that are different, unusual, or simply more difficult to arrive at definitive answers. For instance, this year, the subject of Simple Harmonic Motion (SHM) was expanded to include the following extensions and twists.

Example 1: [From Simple Pendulum to Compound Pendula]
In this case, the students are handed rectangular wooden blocks and triangular prism wooden blocks and are asked to make predictions regarding these compound pendula. For instance, what would the period be? Will it depend on mass? Will the amplitude matter? How would this kind of pendulum compare to a simple pendulum? etc.

Student was using her mobile device to measure the period.

Example 2: [From SHM to Damped Oscillations]
In this case, the students are presented with a situation where the would collect data involving a spring-mass system whereby the mass is oscillating in water as opposed to in the air as is usually the case in regular labs. The following images show the lab set up and the results of the activity.

Closing Thoughts:

Student appreciate being challenged, especially in courses such as AP-courses where the expect an added level of difficulty and rigorousness. The added benefit of such extensions is that it offers instructors the chance to detect and address any lingering misconceptions related to simpler items from the regular curriculum. This is bourn by the fact that students who have gaps in their understanding of regular material, this gaps are bound to surface in these new challenging settings. And as such, these challenging additions may serve as a safety valves that enable us, educators, to address less understood concepts in our main curriculum.

Thank you for taking the time to read this blog entry and I hope you would add your own comments on the subject matter. What kind of extensions do you have your own students contemplate and go through?

Dance of the Changes: ∆p vs. ∆K

Once momentum p and kinetic energy K were derived and the connection between them was established, our task as a class was to find any connections, if any, between ∆p & ∆K. The derivations shown below were conducted in class with the participation of everyone using what I call "Stand/Sit Participation Method". This ensures that every student is active in the derivation process from beginning to end with emphasis on understanding all along.

Students were asked to compare and contrast the two relationships that were derived and only then did the following slide show up.

This, my friends, led to the Free Body Diagrams (FBD) challenges activity that eventually  led to the formulation of Newton's 2nd Law of Motion (N2L.)

A simple harmonic oscillator (SHO) attached to a force probe with a motion detector set below the mass that is attached to the spring provided the conformation of N2L.

The above derivation is aimed at achieving three goals.

1) To help students realize that Physix concepts are not disconnected islands, rather they are individual cells within the organism of Physix knowledge.

2) To establish the emergence of acceleration as a quintessential aspect of any changes in the state of motion of particles.

3) To overemphasize the complementarity between between space and time that relativity asserted and Heisenberg's Uncertainty Principle alluded to in Quantum Mechanics.

Thank you for reading this post and I look forward reading your valuable comments.   

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

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).

Physix Curriculum Map a la Mr. Le Nadj!

Students love Modern Physics topics. Unfortunately, most introductory Physics courses eschew Special Theory of Relativity (STR), General Theory of Relativity (GTR), and Quantum Mechanics (QM) because of their perceived difficulty.

For the past four years, I have been introducing more and more of STR early on in the year/semester. But, this year I used STR as a means of introducing classical Physics concepts such as kinetic energy. The mind map below summarizes the gist of this approach. It is important to mention that the Modeling Approach serves as the backbone and the glue that holds this teaching method together. Thus, the use of many abbreviations that only modelers would know.

Physix a la Mr. Le Nadj! Curriculum Map

In future posts, I shall address each of the branches. I shall also give samples of presentations material, examples of students reactions/reflections, and typical artifacts that assist in making the case for such a pedagogical approach.

Please, feel free to share your thoughts in the comments area so that readers like you would benefit from them personally or their students indirectly. Thank you

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

Is this The Mother of All Formative Assessments or What?

The day started as a usual Physix day full of anticipation for what young brain may teach me today. A favorite Clickerism of mine was the prelude to a session whereby I would verify the extent to which my students understood the just completed Uniformly Accelerated Particle Model (UAPM). This Clickerism (shown below) is one of Eric Mazur's ConcepTests and I have used it since I purchased his book way back.

Courtesy of Eric Mazur

The response system gave a sobering initial distribution. So, I let the Peer Instruction process take its course and the correct choice emerged triumphantly. But, as if struck by a lightning of dissatisfaction mixed with a stroke of pure educational hunch, I turned to a group of students while pointing to the smartboard. I tasked this first group with inventing their own graph that would only satisfy option one amongst the multiple choice questions (refer to figure below.)

Group 1 Task

Then I turned to another group of students and another until I got four groups in total whose tasks are shown in succession below.

Group 2 Task

Group 3 Task

Group 4 Task

The students jumped on the tasks with much appreciated interest and curiosity. Once all groups were done, I summoned the first group's representative to the smartboard to draw their group's invention. During that time I asked the rest of the class to draw the velocity vs. time graph that corresponds to the original graph to keep them active and engaged in the learning process. But, as soon as the students completed the group's invention, another stroke of inspiration hit and I thought why not make a Clickerism out of this situation and create more chances for students' give-and-take. So, I asked the class to clap for the representative and got the clicker system ready for a Valid or Not Valid (T or F) that the whole class has to vote on. All agreed except for one student who dissented and I asked who it was and what was the dissent for? The student replied that the units were not correct and since the favorite color of this student is white I wrote their suggested amendments in white.

Note: It is a tradition of mine to honor the student who proposes amendments, suggestions, or answers by using their favorite color for such updates on the smartboard.

  

First Group's Invention is shown in Blue while the Proposed Classmate's Enhancements are shown in White. 

Had it not for the new fortunate twist to this old Clickerism of mine I would not have caught the representative's confusion of unit and variable representing respective physical quantities.

Representative after representative went to the smartboard to share their group's inventions. During the smartborad work the students are given other tasks to keep them productively busy thinking about the original given graph of the Clickerism. And after each invention another round of validity assertion is conducted with the response system. Every ensuing discussion was better, deeper, and richer than its predecessor! The whole class was so animated that later that day some of my colleagues were wondering what was going on in the classroom. Below are the inventions of the other groups and some additional ones involving the same formative assessment idea but from other sections I teach.

Second Group's Invention is shown in White while the Proposed Classmate's Enhancements are shown in Light Blue.

Third Group's Invention is shown.

Fourth Group's Invention is shown.

First Group Invention of Another Section is shown. 

Second Group Invention of Another Section is shown. 

Third Group Invention of Another Section is shown. 

Fourth Group Invention of Another Section is shown. Note: This group requested to have three graphs instead of just one. Just as class was being dismissed students were still standing by the smartboard talking about these graphs. One student then offered the purple statements and I wrote them in his favorite color to honor his non-Physics thought out of the box.

I wish there was a way to convey the amount of thoughtful energy that was present during these impromptu sessions of creativity, multiple assessments, and sheer fun that the students were having.

Many an educator would rush to loath multiple choice questions for various good reasons but a twist such as the one presented here rendered such a question a treasure trove of informative assessments! Is this the Mother of All Formative Assessments? It certainly is not but it surely felt as such for my students and me at the conclusion of each class period.

Lessons Learned:

1) In education, planning is definitely good, but being flexible enough to consider off the cuff ideas is equally, if not more valuable.

2) Multiple choice questions can still lead to good education if used effectively such as was related in this post.

3) Peer Instruction is definitely a powerful educational tool and the use of technology renders it more efficacious.

4) Letting the reigns of thought turns students into better inventive young Physicists.

5) As educators, we must always challenge our selves to consider new approaches and twists, especially with methods we tend to employ routinely.

Now your turn!

Please, use the comments area to enrich this post with your own ideas, takes, and reactions. Thank you

Initial Forays Into the World of Modeling in Physics Instruction

Introduction: I was fortunate to be accepted to participate in the Modeling Workshop that was conducted by the North Central region of Michigan via COOR ISD this summer. 

Goal: Since I was teaching a summer course at the same time that the workshop has been conducted, I thought I would put some of what I have learned to the test immediately to gain more hands-on experience with the modeling approach to instructing Physix before the following academic year begins.

Philosophy: I think one's success with new approaches to instruction would have higher chances of success if one allows the new methods (Modeling approach in my case) to seamlessly blend with her/his way of doing things. In other words, one has to own her/his Modeling way.

The Nadj! Approach Constant Velocity Particle Model: 

1) I like starting my Physix units by having students analyze art pieces and extract preliminary Physix concepts out of them. In this case, the students were shown a visual art piece (see image below) & a video that shows the Berlin philharmonic under the directorship of maestro Herbert Von Karajan conducting playing the last movement of Beethoven's 9th symphony. Students were to compare & contrast the two art pieces Physix-wise, a class discussion ensued, and the idea of motion and movement emerged naturally from the experience.

2) Couple of Clickerims were given to prep the students for the Constant Velocity Particle Model lab.

3) Following is a sequence of pictures that shows some aspects of the modeling process.

Task Board that explains to students what their respective boards must contain.

One of the group's set up for the CVPM lab (notice the little tabs for time calls.)

   

Student sets her iPhone to videotape the motion of her group's buggy.

CVPM lab run of one of the groups.

Boards set for whiteboarding sessions! :-)

4) The students' engagement, the ideas they had to generate, the details they had to wrestle with, the whiteboarding session that ensued, and the levee of understanding reached were all a marvel thing to witness.

This is just a snapshot of what had transpired this summer and hopefully more Coolisms will emerge as I become more familiar with the method and the wonderful outcomes it seems to readily yield.

Thank you for reading this blog post and I encourage you to comment about similar experiences you had, suggestions you may offer, or pedagogical ideas this may have triggered in your mind. Please, commit your thoughts to the comments area. 

Model away, Model all the way! :-)    

Physix in Images 2013-2014

First: I apologize for the lack of activity in my blog.

Second: There were precious moments in Physics (3 sections) & Astronomy (new section) and I thought instead of blabbering about them I should just let some pictures convey the extent of the fun as well as learning.

The Smiles of Pride! :-)

Tip of the Hat to Sir Isaac Newton!

When Physix meets Art; only Coolism ensues! :-)
A Cool Student PhysArt Project

Nothing beats the connectedness between Physix concepts!
Mechanical Systems (spring/mass) in Series/Parallel to contrast with Electrical Systems In Series/Parallel

Students love it when Experts present their work!
Dr. Brian McNamara discusses his work on Supermassive Black Holes & Exploding Galaxies!

Star Gazing Extravaganza wraps up a Cool First Year of Astronomy, look at the wide smiles! :-)

Optics meets Art! Backyard of our classroom with the Physix room acting as a Camera Obscura!

iPad used to generate Motion Diagrams. How cool is that?

Physix of Motion meets Art! iPad used to generate the corresponding Motion Diagram.

Testing Hypotheses about Combinations of Human Electric Generators (Take I)

Testing Hypotheses about Combinations of Human Electric Generators (Take II)

Taking the concept of Combinations of Human Electric Generators to its Ultimate Finale!

Students getting close & personal with Optics, Lens Equation Lab!

Physix meets Art, slide from a student's project presentation!

Physix meets Art (refer to previous image!)

Astronomy Lab on Plasma & Light Spectra, Sweet! :-)

Astronomy class experiencing Motion Diagrams (look closely to see the blue dots!)

Third: I hope the above excite you to share your own cool images from last year of Physics or Astronomy.

Thank you for taking the time to view/read the post and I hope you would be kind to leave some comments.

Thank you and take great care! :-)