To Discover or not to Discover!

Dedication: I dedicate this and everything I do to the one educator who helped me appreciate the value of learning in the grandest of fashions, my late father Ibrahim Nadji (RhA!) Thank you Didi and may Allah (SWT) reward you for your dedication to raising educated citizens!



Discovery must be part and parcel of every curriculum. STEM and STEAM curricula attempt to rectify what most educational systems have ignored for a long time. The building process that students engage in increases the chance for encountering various levels of discovery. This approach is going to become the focus of future physics lessons that my students and I are going to embark upon during second semester ISA. In the meantime, I thought I needed to get my students to embark in the process of formula/relationship discovery on their own without any intervention from me.

Since the time that I adopted the use of the modeling approach a few years back, I always played the role of moderator during whiteboarding sessions. This, as cool as it is, still left me unsatisfied as an educator. After all I have not empowered my students to become discoverers on their own. Therefore, I decided this year to step back for once and let the students take the reigns of discovery themselves. What follows is an outline of how one of the first and most successful "let-go" experiences my students and I have ever experienced thus far.

Context of the Experiment [The Pre-Lab & Linearizaion]: 

The experiment's goals included amongst other objectives a couple of things; discovering the lens/mirror equation and learning the concept of linearization. This latter concept is not as intuitive as it may seem and as such, I decided to have a whole separate pre-lab to assist students understanding it. So, I shall describe the pre-lab first and then I go onto describing the main lab experiment along with its ensuing discovery process.

The pre-lab set up consists of setting up two plane mirrors as a wedge on top of a polar graph paper as shown in Figure 01 below.

Figure 01

The students are to figure out what relationship, if any, exists between the angle of the wedge and the number of reflection images. They are to vary the angle from 15° to 180°. After which, the students completed their whiteboards following the template the whole class agreed upon. Below are images of the template (Figure 02) along with samples from some of the groups' generated whiteboards (figures 03-05).

Figure 02

Figure 03

Figure 04

Figure 05

As is customary in my classes, I ask one group to do something different than the rest of the groups. This would allow for the whiteboarding sessions to be better and more fruitful discussion sessions. During the white boarding session the works displayed in all whiteboards are discussed and the major relationship of the pre-lab or lab is deduced. Figure 04 above shows such a different group whose members were asked to graph the number of images vs. the reciprocal of the angles rather than the angles themselves. This opened up the door for introducing and discussing linearization.

Before the discussion part commenced, the whiteboards were shown to everyone in the class and the groups were to visit each whiteboard and critiqued it using the criteria shown in Figure 06 below.

Figure 06

 The use of Post-Its turned out to be impractical because the Post-Its left falling. So, I suggested that the students from each group write their critique using their lab group color around the whiteboard and the main classroom whiteboards. The resulting work looks similar to the one shown in Figure 07 below.

Figure 07

The whiteboarding session consisted of me pulling a student's name at random each time. The student would be asked to provide a comparison and a contrast between the various boards. And as major ideas emerge, I commit the outcomes to one of the classroom the smartboards. This process continued until the major relationship of the pre-lab emerged. In this case, the kaleidoscope formula emerged very so beautifully. And more importantly, the concept of linearization was introduced as a cool tool at the students' disposal whenever a non-linear situation would arise in future labs.

Context of the Experiment [The Main Lab & The Discovery of the Lens/Mirror Equation]: 

Now that the students became somewhat familiar with the concept of linearization, we moved onto the main lab experiment. First, the students played with curved mirrors and lenses and recorded observations in an activity that is described in the previous post. Second, the students were introduced to the concept of the power of a lens and then they set out to measure the power of each of their group's assigned lens. Each lens has a cover that contains a dimensionless number that the students were to figure out that it matches with the given lens's power. Figure 08 below shows the students engaged in such direct measurement process. Note 1: Ideally, this experiment is to be done outside with the sun as the source of light. But, the weather forced us to use a light source that is very high in the dome of our rotunda. Note 2: This actually opened up the discussion of what it means to have a source very far away and its implications?

Figure 08

Once the power of each group's assigned lens were ascertained, the students were presented with the main lab experiment set up as shown in figures 09 and 10 below.

Figure 09

Figure 10

In the old days, I used to have the students use a lit candle or a light bulb as the object whose image is to be analyzed. But, as soon as iPhones and mobile devices became prevalent, I began having students use pictures in their iPhones or mobile devices as objects instead. The image of the students' chosen picture is obtained at various distances away from the lens each time. The chosen object distances and their corresponding image distances are gathered, recorded, and then plotted. As usual, one group is asked to plot the reciprocals of the distances rather than the distances themselves. After this, the groups set their whiteboards as they did in the pre-lab and figures 11 and 13 show samples of such boards from different sections.

Figure 11

Figure 12

Figure 13

As the boards show, the linearization process has begun to sink in but not fully yet. After all some of the students still are having problems understanding what linearization really means. This is reflected in the kind of labels and units the students have been giving in their respective whiteboards.

Discovery Time!

Unlike previous instances and in previous years, I decided this time around that I am not going to lead or moderate the whiteboarding session at all. Instead I asked the groups to send a delegate to the main classroom boards each. I called these individuals the Discovery Delegates. Once they were selected and went up front, I informed the delegates that they all are Mr. Le Nadj! now. I handed one of them my deck of index cards that has the names of all the students in the class. This delegate would be the person who selects students at random to ask them to provide comparisons and contrasts. I handed the other individuals a stylus each for writing major ideas on the classroom smartboards. I then informed the class that I was going to sit back, videotape the white boarding session, and be quiet until the Big Kahuna is discovered. This is the lens/mirror equation, which I did not give the students its name yet so that they would not look it up.

Rules: The students were instructed that (i) they have 23 minutes to arrive at the Big Kahuna, (ii) they are not allowed to use their laptops except for one of them wishing to recheck their LoggerPro's experiment file, and (iii) they must deduce the Big Kahuna only from the whiteboards at hand and not using anything else. To increase the incentive for everyone in the class to contribute to this whole new experience, I declared that each section is competing with all my other physics sections for a pizza party or a pie party if they beat everyone else to the discovery within the allotted time or they accomplish the feat in the quickest time. As far as I can tell, they were not aware of what relationship they were going after. The ensuing process convinced me that that was indeed the case.

The images listed as figures 14 through 17 below give a hint of what had transpired in one of the sections. But, it must be stated that nothing would recapture the charged, magnificent, and exhilarating atmosphere that permeated throughout the whole process (once I figure out how to hide students' faces in some the videos, I may add them to this or future post.) This discovery process was one of my and I hope my students' most climactic and superb educational experience thus far!

As soon as the timer went up, I asked one of the delegates to put their Big Kahuna inside a red rectangle. Figure 14 shows the formula they arrived at. Note: The smartboard app contains more than the slide shown here. The one shown in Figure 14 below is the class's last and final slide.

Figure 14: The "focal length" statement was kept to reflect the struggle the students had in interpreting their own terms along the way. One of the videos clearly demonstrates what had transpired.

I asked the students to stand in front of their claimed formula so that I take a picture of them with it. But, as is clear from the picture, shown in Figure 15, except for two students the rest of the students were not willing to own up to it yet because they were not certain that it was indeed the major formula or not. I did not divulge anything yet at the time this picture was taken.

Figure 15: The rectangles are covering some of the students' eyes and IDs to conceal their identity. 

Finally the students were told that their Big Kahuna was none other than the lens/mirror equation. Immediately afterwards, I wrote the lens/mirror equation on the smartboard below their own as shown in Figure 16. The students were ecstatic and Figure 17 shows their elated and pride-full state. 

Figure 16: The Lens/Mirror equation!

Figure 17: The Pride & Joy are Evident, aren't they?

The Aftermath?

Once we established the lens/mirror equation, we set out to apply what I have taught the students to do before one accepts any newly established relationship. The students chorused the two litmus tests! So, we tested the Big Kahuna for dimensional analysis, litmus test one, and it passed with flying colors. Then, we tested it for extreme and special cases, litmus test two, as follows (please, refer to figures 18-20 below) and the discovered formula also passed this test with flying colors.

Figure 18: Extreme Case of Flat Mirror where image is a virtual image located behind the mirror.

Figure 19: Extreme Case of a Far Away Object, which justifies  the rotunda direct measurement results. 

Figure 20: Special Case of a Source at the Focal Point 

As soon as we were able to complete the top two cases of litmus test two, the class came to a close. The students' reactions were indescribable. One of them flatly stated, "I am very proud of myself." Two other students, realizing that they may not be in the same section next semester, quipped that they have to have a class reunion to celebrate this memorable discovery. The atmosphere was super-charged overall!

What's next?

Now that the lens/mirror equation has been established, the students are going to begin the numerical work. I already produced a set of Youtube videos where I went through examples of how this seminal relationship along with the formula for magnification are  used to solve a wide range of optics problems. In addition, the students are going to go back to their qualitative observations from weeks ago to make sense of them quantitatively now for lenses as well as mirrors.

Observations & Closing Comments:

1) Students can and relish the very idea of taking matters on their hands.

2) Students need to be given chances to discover things fro themselves even if they wrestle with the process.

3) During the whole discovery process only one student was a bit disengaged but his peers literally called upon him to get up from his seat and be part of the whole experience. It was very encouraging to witness such team spirit.

4) Some of the least participating students in this section were all over the place on their own contributing in grand and wonderful fashion. They did this without any prompting from me nor their classmates. I am very proud of them and I am thankful that it took such activity to bring about their flowering as proactive learners.

5) Now that the door has been opened, there is no closing. Giving students the reigns of the discovery process, as was done in this session, is here to stay.

6) Next, I would like to add another layer to the discovery process, hands-on discovery. I am going to challenge the students to design a device that performs a task based on all of the concepts they have learned in optics. This hopefully would align our curriculum more closely with STEM and STEAM approaches to learning.

7) Last but not least, please, use the comments area to share your thoughts, reactions, or similar experiences your students and you went through. Thank you

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?

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

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! :-)