Math Activities in Images

I apologize to my readers for the long time since I last posted; a busy schedule has not been kind at all!

I would like to let a few images speak for some aspects of this year's math.

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Of course, these are not the only pictures that give away how much coolism did occur in math this year but at least they convey some ideas.

What do you think these images conjure up in your mind curriculum-wise, learning-wise, and math-wise?

Thank you for taking the time to read the post and please leave comments that reflect your thoughts.

Musings of a Nadjling!

As we were driving back home from his percussion lesson, Omar (the 12-year old Nadjling) said, "Baba, future does not exist." 

"How so?" I replied. 

He said, "Well, future is not here, it is unknown, and when it occurs it is present. So, there is only past and present." 

This took me by complete surprise and I retorted, "This is an interesting thought and I would have to think about it."

Then, the math connection came when he continued, "The future is undefined and when it is experienced it is not a future; it is the present then." The Physicist in me could not help but think of contrast between the deterministic interpretation of the world by classical Physics versus the quantum mechanical probabilistic approach to physical phenomena. In addition, I thought of the wave function collapse from a "nebulous/combined state" to a definite state once one performs an experiment with elementary particles.

For a kid to hit on an idea such as this is fascinating. So, I encouraged him to jot down such things when he thinks of them in the future.

Afterwards I gave Omar the example of how knowing the current position, velocity, and acceleration of a probe we are sending to Pluto for instance, we can predict its future position, velocity, and acceleration and this is how we are able to get such probes that far and with incredible precision. I was trying to convey the idea of the deterministic nature of classical Physics. 

But, before I went far with the idea, he interjected by mentioning the take-home test that he mentioned earlier in our trip and he was going to take when we get back home and said, "I am going to cheat." Alarmed by unethical behavior I was going to start giving him a big lecture but he interrupted by explaining, "I have to do a decay experiment and instead of taking out sixes of dice, I will just take out evens." I said, "Why would you do that?" He replied, "This way the decay rate will be a half." To this I commented, "This is not cheating; this is clever! But, why take out the evens and not the odds?" To which he answered, "Evens have only one prime number." Ok!

Fast forward and Omar is at home. He thought he had 100 dice (the required starting number given in the test directions) around the house but he found only 49. So, he shared with me the following thought, "Would it be ok to just use 49 and whatever I get I divide by 49 and multiply by 100 to make the experiment match a 100-dice roll?" This being a test, I told him that would have to be his decision. Deep inside, the father in me could not help but feel proud of the kid's divergent thinking and resourcefulness. In the end he decided to keep the experiment simple, straightforward, and he used 100 coins.


Omar is lucky that his father knows about math and is willing to give-and-take with him in such musings and I just hope that the many Omars out there would be equally fortunate and benefit from such exchanges with adults (teachers, parents, older siblings, etc.) around them. So, if we (the math/science teachers) are the only adults that kids may get this mental gymnastics opportunity from we must seize it with earnest passion and great patience for it would help them grow as thinkers and flourish as math/science lovers.

Happy Valentines Day & please share musings of your students or your own kids in the comments section.

Thank you and take great care! :-)

Sinusoid Lab Activities

Nothing helps students get a good handle on mathematical concepts than lab activities that addresses the subtleties and true meaning of the underlying components that accompany such concepts.

Following is a description of a set of lab activities that deal with the sinusoid and its usefulness in trig and in many real life situations that are periodic in nature. 

Day 1: Students were handed a plot, that I obtained in an experiment I conducted as a test run (see still image of video shown below), to model it themselves using the sinusoid (transformed basic sine function) involving the h & k form. First the students had to work alone, then with a partner, and then in a group to assist one another with the modeling process.

Test Run by Mr. Le Nadj! of the Lab the students are about to conduct themselves!

Day 2: Students were handed a data set to enter the first two columns in their respective TI calculators and as a class we worked together to plot the data, model them ourselves as a class, and then the class was broken into three groups whose assignment was to carry out the same process but for columns one and three, one and four, and one and five respectively. The rest of the work consisted of students competing for the best fit equation generated by hand and the group member with the equation that fit the best than her/his group peers will be treated to delicious sweets. No TI sine regression was allowed.

Day 3: Students's regression equations were pitted against one another for each group and the best fit equations were identified and the equations owners were treated to double sweets while the rest of the folks (who did attempt a decent fit of some sort) got single sweets. Afterwards, the sine regression functionality in the TI calculator was introduced and now the students were ready to carry out the lab activities themselves. The setups, the procedures, and all technology matters were introduced. Following, are the pictures of the various setups.

First Setup: The pendulum is facing the motion detector that is resting on a make-shift bubble gum box. The students in this group will alternate in collecting data onto their respective laptops. From the camera perspective, another group is going to use LoggerPro's video capture of the same motions of the pendulum (see picture below.)

Second Setup: The pendulum motion is recorded laterally by the members of another group using LoggerPro's video capture of the same motions of the pendulum that the first group is recording. The idea here is to allow for cross referencing and checking of the various group members' data and results.

Third Setup: An iPad is hanging as a bob from a spring that is attached to a force probe. The oscillatory motion is recorded in two ways, the acceleration of the iPad using SPARKvue app from within the iPad itself (see next pictures) and force using Vernier's dual force probe whose results are fed directly to LoggerPro of the students' laptops. Once again the idea here is to allow for cross referencing and checking of the various group members' data and results using two different means of gathering data related to the same motion.

Day 4: Students did the actual lab; the scene was lively, the graphs were gems (an example is shown below), and the thinking and enthusiasm were Coolism! 

The graph of the oscillatory motion of the iPad shows three parts, the hand picking the iPad to start the recording of the motion, the oscillation, and final the hand picking the iPad again to stop recording the motion.

Once the data collection process was completed and every student obtained her/his data and graphs on their respective laptops, the task of switching LoggerPro's form to theform. This part ended up being the homework that was due next day; every student had to complete the form change and make the predictions requested in parts B, C, & D listed in the lab sheet (shown at the end of this post).

Day 5: Students showed their form changes and their predictions, compared their respective constants, and then discussed their predictions and how they would be checked empirically.

As a whole the activity was not just fun but also led to many insights. The experiment is still in progress in that a followup lab that will make the oscillations dampened shall ensue when exponential functions come into the picture.

Thank you for reading the post and please provide some feedback, suggestions, or variations you deem worth consideration. 

Thank you and take great care! :-) 

Hand Outs: