Miranda v. Arizona

In the last unit of Policy at GCE, we learned about the Judicial branch of the US Government. More specifically, we explored the similarities and differences between federal and state courts, looked at how court systems work, and talked about the supreme court and the duties it holds. As we got deeper into the unit, we learned about specific and notable supreme court cases like Brown v. Board of Education. For our Field Experience, we visited the Cook county criminal courthouse and got to see first hand the happenings in a courtroom. For this Action Project, we were asked to choose any supreme court cases, decide weather or not we though the decision that was made was just, and support our conclusion.

Redesigning an Urban Space

In my last unit of Urban Planning at GCE, we learned about the history and purpose of both modern and ancient cities. In our Internal Investigation, we experienced a more history focused unit to analyze what cities did to thrive and survive, what worked, and what did not. In our External Investigation, we chose a city and did research on its urban planning. Then, we compiled our findings and explained how we think the city could have done better. For this Action Project, we were asked to pick an urban area that we wanted to redesign and improve.

2016-2017 Service Learning Hours

Throughout my 2016-2017 school year at GCE, I pursued multiple opportunities to gain service learning hours. Most of my time was spent at school helping out and preforming school improvement activities. Some examples of this is hanging up art/sound panels, restoring broken or damaged areas, or cleaning up storage spaces and classrooms. Doing work around the school has taught me a lot about doing different kinds of handiwork and working with power tools. Hearing other students and staff members say that they appreciate the newfound organization and art that I helped put up made it much more fun to try to improve the school in many ways. Hopefully, as other students see what cool things they can do to help the school, they participate in making new and creative things to beautify the space.

LS. (2017) GCE Lab School

World War II: Policy and Justification

In the second unit of Policy and GCE, we learned more about the Executive branch of the US Government. In our Internal Investigation, we explored the powers of the Executive branch and what it has the right to do in the government according to the Constitution. During one FE to the Chicago History Museum, we went to a Spies and Espionage exhibit that had lots of information relating to the wars, conflicts, and policies we were studying in class. For this Action Project, we were asked to write an essay that speaks our opinion on weather or not we though a war of our choice in US history was justified.

CNN. (2016) German Troops Marching

As many know, World War II began with Germany invading Poland in 1939. The Germans, being upset from the outcomes of WWI and the Treaty of Versailles, were evidently not very happy with many parts of Europe. Using this hatred to fuel his rise to power, Adolf Hitler and the Nazi Party quickly became a large force in Germany (US Army). After the inciting incident in Poland occurred, it was not long before the world began splitting itself into different sides of the fight. While over 30 countries were involved in WWII, the primary conflict was split between the two major powers: Axis and Allies. The Axis powers included Japan, Germany, and Italy. The Allied powers included Britain, France, China, Soviet Union, United States, and others (History.com). One of the most important events for the US during WWII was the bombing of Pearl Harbor in 1941. This was the primary reason that the US ended up entering the second World War. Because of it’s need to protect itself and defend the values it holds, the United State’s entry into World War II was justified.

The US president at the time of entry, Franklin D. Roosevelt, played a large part in both the US’s participation in WWII and generating support from other countries and the American people. According to History.com’s page on Roosevelt, “On December 8, 1941, the day after Japan bombed the U.S. naval base at Pearl Harbor, Roosevelt appeared before a joint session of Congress, which declared war on Japan.” According to the Constitution, the power to declare war lies with Congress. As we can see, Congress was, in the end, the deciding factor as to whether or not the US participated in the war. However, it seems that Roosevelt appeared at the session of Congress to express his support for the country’s entry into the war. Later in that same History.com article, it says “Roosevelt spearheaded the alliance between countries combating the Axis, meeting frequently with Churchill and seeking to establish friendly relations with the Soviet Union” and “he spoke constantly on the radio, reporting war events and rallying the American people in support of the war effort”. Based on these two quotes, it is obvious that Roosevelt was at the helm of the War against the Axis powers, wanted the American people to rally behind his cause, and was a large influence on the other countries apart of the Allied powers.

Unfortunately, in Roosevelt’s efforts to protect his people, he made a mistake with a policy he implemented during the war. According to the Chicago History Museum (CHM), “In 1942, Roosevelt signed executive order 9066, authorizing the military to forcibly relocate and intern people it considered a security risk”. In the panic and fear of the recent attack on US territory, Roosevelt tried to contain any possible threat to the US. This would seem a reasonable action on a small scale. However, according to the same CHM info source “120,00 people of Japanese ancestry--most of them US citizens living on the West Coast--were interned primarily because of their ethnic origin”. What seemed to be a way to isolate and contain serious and legitimate risks to safety of American citizens turned into a fear-fueled witch hunt for any person who looked to be of Japanese descent. This executive order was both unjust and unconstitutional based on the fifth amendment. According to the Constitution, “No person shall...be deprived of life, liberty, or property, without due process of law”. People were being interned and promptly stripped of their liberty just because of their ancestry and without a proper trial or law process. Therefore, this executive order was unconstitutional and should have never been allowed to go into effect. Even though US’s entry into WWII was justified because of our need to protect ourselves, president Roosevelt should've gone to the length of creating an unconstitutional executive order to increase security.

Overall, it is understandable and reasonable to me why the US and president Roosevelt joined World War II. The attack on Pearl Harbor and the need to protect our country from the foreign threats of the war made it almost impossible to stay uninvolved. However, Executive order 9066 was not a just way of increasing the safety of Americans. In order to prepare our country from future threats and to equip ourselves with the right means to ensuring security, it is important for us to analyze both the successes and mistakes that have been made in the past.

Works Cited

"Franklin D. Roosevelt." History.com. A&E Television Networks, 2009. Web. 21 May 2017.

N.d. Exhibit: Spies, Traitors, and Saboteurs. Chicago History Museum, Chicago.

U.S. Constitution. Amend. V.

US Army. "The Outbreak of War." Brief History of the U.S. Army in World War II. N.p.: U S Govt.

Printing Office, 1992. N. pag. Print.

"World War II History." History.com. A&E Television Networks, 2009. Web. 21 May 2017.

Saving Energy

In the second unit of Urban Planning, we talked about the math, history, and applications of electricity. In our Internal Investigation, we learned about the war of the currents between Thomas Edison and Nikola Tesla. We also talked about the math behind electricity and used snap circuits to get a hands on experience. In our External Investigation, we did research about how things in our home use electricity and what some energy efficient alternatives are. For this Action Project, my partner LD and I made our own circuit and compared each part to energy efficient appliances you can find in a home.

Letter to a Government Represenative

In my first unit if Policy at GCE, I learned about the Legislative branch of the United States Government. In the Internal Investigation, I learned about the representatives that make up congress and what the process is of making a bill into a law. For the Action Project, I was asked to choose a bill that is currently in the process of becoming a law and write to a legislator that has the power to vote on that bill. For my project, I chose an Illinois state bill called the Reasonable Use of Force Act and decided to write to my local representative Sara Feigenholtz.

---

LS
GCE Lab School
1535 N Dayton St.
Chicago, IL 60642

April 30, 2017

Representative Sara Feigenholtz
3223 N Sheffield Ave
Chicago, IL 60657

Everyday people across the world get abused by the power of the police force. We see it it the news what must feel like every other week. In order to prevent this brutality, we cannot just simply ask the world to stop. In order to fix this widespread issue, we have to start small and then push for larger action. I write to you today asking for your support of the Reasonable Use of Force Act. If this act is passed, we can take a step towards a future where police action is more regulated and in turn, the safety of the lives of those who are being policed increases.

As you may already know, the Reasonable Use of Force Act does many things to ensure that people being handled by an officer are done so more cautiously and appropriately. According to the Illinois General Assembly website, the act covers the following points:

• Peace officers shall only used the amount of force that is absolutely necessary to perform a lawful task, successfully perform an arrest, overcome resistance, control a subject, or protect themselves or others from harm

• Prohibits the officer from preventing a subject from breathing 

• Limits an officer's ability to place a subject on their stomach unless necessary for the safety of the officer or others 

• Prohibits the use of a choke hold unless deadly force has been authorized 

• States that officers must monitor and seek medical attention for an arrestee after control has been obtained

One of the most well known instances of excessive use of force by Illinois police officers was the brutal killing of Laquan McDonald in October 2014. According to CNN, during this incident, McDonald was shot 16 times while walking away from officers and not posing any severe threat. It should have been obvious here that using deadly force on a person who is not threatening the lives of any living thing around him would have been the wrong way to handle the situation. Maybe if the Reasonable Use of Force Act had been in place at that time, officers may have thought more about how to handle the situation before exerting force. According to Daily News, in another instance in 2014, 43 year old Eric Garner was killed after an altercation with police which he ended up in a choke hold. In the video evidence provided, it it clear that Eric Garner was no threat to the officer nor anybody around him. While arguing with one officer, another jumped from behind him and placed him in a choke hold to wrestle him to the ground. During this time, Garner repeatedly exclaimed that he could not breathe. After a while, officers let him go to see he was unconscious and later proclaimed dead. With the amount of officers surrounding Garner and the fact that he was posing no threat to any officer or person on street, there was no reason that the officer should have 1) put Garner in a choke hold and stopped his breathing 2) wrestled Garner to the ground and forced him on his stomach. Neither of these actions were warranted and both are prohibited in the Reasonable Use of Force Act. In order to prevent things like this from happening in the future, this Act needs to be passed.

Since I do live in Chicago, I’ve bared witness to many arrests and police encounters all over the city. However, one particular situation that I saw many years ago still sits sharp in my memory as if I had seen it minutes ago. At a park somewhere within the city my friends and I witnessed 2 men fiercely arguing. Some passerby must have called the police because within a few minutes they had arrived. Even though the men had not shown a distinct desire to physically hurt one another, the officers that arrived there thought it would be appropriate to use physical force on these people to force them away from each other. One of the officers practically tackled one of the men to the ground and began arresting him. The other officer, seemingly a bit more sensible, only pushed the other man away and held him at bay. While the situation wasn’t necessarily a violent one, as a smaller kid it really made me scared of the police. How could they so easily exert physical force upon people who didn’t seem to be doing anything wrong in the first place? Why were the people who were supposed to be keeping peace, so keen on inciting violence? Again, if this Act is passed in Illinois, these situations will have smaller chance of occurring.

Some people like President of the Fraternal Order of Police Kevin Graham, might say that this Act being proposed is just another way the public can criticize the Chicago police force or that this law would just be a way to take necessary power away from the police. According to Chicago Reader, Graham has said “In the past, the media has often not portrayed the Chicago Police in a good light. We want to make certain that our members and the citizens of Chicago realize that we are the good guys." and "We will no longer be victimized by a biased anti-Police media." It seems to me that people like Graham try to rally around trying to brighten the image of the police in the face of the public rather than reflecting upon their mistakes and trying to better themselves in the future. At this point in time, the way the public sees the police does not matter as much as how the police are are treating the public and keeping them safe. Instead of worrying about how people see his police force, Graham should be backing legislation like the Reasonable Use of Force Act and pushing for more ways to keep altercations between the police and the public fair and law abiding.

Overall, the ways that the police treat the public is still a massive problem all over the country. However, I write to you specifically because the Reasonable Use of Force Act is still an active bill in the Illinois General Assembly. I hope that after reading this letter, you have felt my passion for this issue and can empathize with me. Furthermore, I hope that as a woman with a seat at the General Assembly, you can take a stand with your power and push this bill through the process and into a law.

Building Bridges

In our first unit of our first course in Spring Term called Urban Planning, we learned about the structure and math behind bridges. During the Internal Investigation, we explored the different kinds of bridges that exist and when and why they are used in different situations. We also talked more about the math behind triangles and how they are used in certain types of bridges. In the External Investigation, we went and found a bridge somewhere in our city on our own time and did a small research assignment about it. For our Action Project, we were asked to build a bridge using only 60 popsicle sticks, glue, and the knowledge we've gained so far.

The Best Playlist

For my first and only unit in my class Mixtapes, we learned how to analyze music for it's history and inner workings. For our internal investigation, we grew our vocabulary by reading about Ratliff's definitions. We also learned how certain notes can make people feel certain things by studying major and minor keying. In our many Field Experiences, we went to multiple places to increase our knowledge of as it exists in different environments. For our Action Project, we were asked to curate a music playlist with our added commentary that used what we learned in the unit to analyze and connect with our chosen songs.

Secretary of Education

In our final unit of Argument, we learned how to synthesis. In our Internal Investigation, we looked at how people throughout history synthesized in their arguments. For this Action Project, we were asked to investigate the role of a member of the president's cabinet. Then, we had to prove why this position was useful, why the current occupant was a good choice in the eyes of the president, and choose our own nominee for said position.

Binary and Hexadecimal Number Systems

In one of my many Workshops at GCE called Math Problem Solving, we were given the freedom to research and follow any challenging math concept we wanted. This workshop was new and very special in the sense that we were given the responsibility to keep track of our own work and go at our own pace. For my topic, I chose to learn about binary and hexadecimal (hex) number systems because I am majoring in computer science next year.

When I first started my research, I chose to learn the basic concepts of binary. This meant learning how the number system is structured, how to convert it to base 10 or hexadecimal, and how to add, subtract, and divide in binary. My most valuable resource was Kahn Academy. They have many videos on binary and hex and different things you can do with them. This video gave me my basic understanding of binary:

Basically, when learning about number systems, the most important thing to look at is place value. If you look at base 10 (what we use), you see that the first place value is 1s, then 10s, then 100s, and so on. It is called base 10 because each place value is a power of ten. The 1s are 10 to the 0th power because that equals 1, the 10s are 10 to the 1st power because that equals 10, the 100s are 10 to the 2nd power because that equals 100, and so on. If we look at the number 251 in base 10. By looking at the place value, you see that we have 2 "100s", 5 "10s", and 1 "1s". Add those together and you get 251.

 Both binary and hex are very similar. For binary, the only numbers we can use is 1 or 0. Also, the place value for each place one of those numbers can go changes. Another word for binary is base 2. In base two, each place value is two to the power of a number rather than ten to the power of a number in base ten. So, the first place is still the 1s because 2 to the power of 0 equals 1. But, the next place is the 2s place because 2 to the power of 1 is two. Then, the third place is the 4s place because 2 to the power of 2 is 4. Just like base ten, the places go on and on like this infinitely. Since binary only has the numbers 1 or 0, each place value can only have 1 or none of said value. To look at an example, if we had the number 1011 in binary, you'd covert it to base 10 like so: In the 1s place we have 1 so that is one 1. In the 2s place we have a 1 so that is one 2. In the 4s place we have a 0 so we have zero 4s. In the 8s place we have a 1 so that is one 8. Add that together and you get (1x1)+(1x2)+(0x4)+(1x8)=11. So, 1011 in binary equals 11 in base 10. 

Hexadecimal is very easy once you understand the basics of place values in the number system. Another name for hexadecimal is base 16. So, hex uses 16 numbers. However, we are used to the base 10 system where we only have 10 numbers (0,1,2,3,4,5,6,7,8,9). In hex, the numbers we use are 0,1,2,3,4,5,6,7,8,9,A,B,C,D,E,F. While this seems confusing, the letters that follow the numbers correspond to numbers that we see in base 10. A=10, B=11, C=12 and so on. Also, since hex operates in powers of 16, the place values are 1s, 16s, 256s, 4096s and so on for infinity. As an example, if we had the number 6A4 in hex, you'd convert it to base 10 as follows: In the 1s place we have 4 so thats 4 ones. In the 16s place we have A so we have eleven 16s. In the 256s place we have 6 so we have six 256s. Add everything together and you get (4x1)+(16x10)+(256x6)=1700. So, 6A4 in base 10 equals 1700.

As for applications of these concepts, I learned in my research that binary is used mostly in computers and are the way that computers carry out their operations. In computer circuits, something is either on or off. Thus, in binary, 1 stands for on and 0 stands for off.

Designing a Clock

In the third and final unit of Light, Sound, and Time, we learned about Time. Moreover, we studied how gravity affects time and how time and space are related. We also looked at different time telling devices and instruments like pendulums and sundials. For the math section of the unit, we learned how to figure out longitude and latitude, how to calculate arc length, and how to calculate the period of a pendulum. For our Action Project, we were asked to design a time telling device based off of our research we did on ancient clocks.

For my clock, I combined the main ideas from each unit into one device. The clock I designed uses Light and Sound to communicate the Time. In order to tell the time with light, the device starts dim and gradually increases/decreases the brightness as the day goes on. While when the peak of brightness happens is programmable, it would originally be set to noon to mimic the real sun. In order to tell time with sound, a constant sound is emitted throughout the day with a increase/decrease in frequency as the day goes on.

Similar the light aspect of the clock, the sound tells time by increasing/decreasing the frequency and can also be programmed to have the peak happen at different times of the day. The program that the device would be set on when it was first turned on would be to start emitting a sound with a frequency of 150 Hz at 12am. For 12 hours until noon, the sound would increase in frequency at a rate of 0.4861 Hz per minute. Once it hits the peak of 500 Hz it would start to decrease at the same rate until it hit 12am again to repeat the cycle. Also, the volume is adjustable and comes with the option to toggle it on and off so the sound is not bothersome.

Like we learned in unit two, the frequency of the sound wave is tied to the pitch of the sound. The higher the frequency of the wave, the higher the pitch. Also, we used the equation 340.29 m/s (speed of sound)= wavelength x frequency. If we wanted to test this equation, we could look at the lowest frequency of the clock (150 Hz) and find its wavelength by dividing the speed of sound by 150 Hz. So, 340.29/150= 22.686. The wavelength of a wave with a frequency of 150 Hz is 22.686 m.

Primarily this clock was made to be a cool and new way to tell time. However, it also allows people who are either blind or deaf to see or hear time. People who need this device to tell time are more likely to buy it so that is why it was designed with those people in mind. But, there is no limit on who can enjoy the device. Also, because there is the option to program the cycle of the sound and light, the user can make it so they wake up to a soothing dim light and a low but relaxing tone.

The idea of using light to tell time is not new. The most common example of how ancient civilizations practiced this is the sundial. The earliest record of the use of the sundial goes all the way back to ancient Egypt. To tell time, the sundial relies on the sun's change in position in the earth's sky. As time goes by, the shadow casted by gnomon (the part in the middle of the sundial that sticks upward) gets moved around the face of the sundial.  To read the time, people just see where the tip of the shadow is casted around the numbers on the face (just like a traditional analog clock). My clock is  similar to this old time invention because of its use of light. However, my design is in no way an improvement of this ancient clock. The sundial would be a way more accurate way to tell time than my device would be. However, my device was not made to be a precise way of keeping track of time. It was more for a novelty and to help those who cannot see a normal clock.

The measurements of the clock would be approximately 5in Tall x 10in Long x 3 in Wide. Because of this, the volume would be around 150 in^3.

Citations

Marie, Niclas. "When Time Began: The History and Science of Sundials." Time Center. TimeCenter,

n.d. Web. 26 Feb. 2017.

Student Representation

In our second unit of Argument at GCE, we looked at the constitution and how it presented arguments. In our internal investigation, we discussed how the US government works and more importantly, how the different branches of government interact with each other. For our external investigation, we went to a courthouse to watch a trial and visited an Alderman to see how arguments are constructed in court and how elected officials view/use the principals of argument. For this Action Project, we were asked to come up with an amendment for the Code of Conduct. The amendment could change anything that we have the ability to support with logical reasons and solid arguments.

Cartoon jury (2008) bethtgirl

The above image symbolizes my argument because it shows a fair trial by jury and represents the how the disciplinary council could be more fair and just with student representation. 

The part of the code I am amending involves who is a part of the disciplinary council. Currently, the person who is supposed to represent the interests of the student is the Director of Counseling. In the Code of Conduct, it says: “The Counselor’s primary role in the Disciplinary Council is to be an advocate for the student and to facilitate conversation between the members of the Disciplinary Council.” There have been reports of unfair treatment and decisions coming out of the council that do not fully take into account the need of the student. Thus, I am proposing an amendment to the Code of Conduct that allows a randomly picked student to be involved in the disciplinary process per student request.

P1: Students have bias to their peers in the decisions made and the opinions put forward.
P2: Students “on trial” has a right to privacy during the disciplinary process.
P3: Having a student on the council would infringe on the student in question’s right to keeping their issues private between them and the staff.
P4: Discipline can only be dispensed by professionals
C: Therefore, students should not have a place on the disciplinary council.

The argument above shows the assumed opinions of the people who originally created the Cod of Conduct. It describes how they would've thought and it helped me to think in their shoes when constructing my argument. In multiple cases, I have heard testimonies from students (former and current) that consistently say that the current student representative/mediator in the disciplinary council does not always represent the perspective of the student. By leaving the student to fend for themselves, they are much less likely to effectively present their side of the story and defend themselves. By adding a student representative, students being processed by the council can now have someone to relate to, feel supported by, and get defended by during the entire process. My changes to the rule are described in the syllogism below:

P1: The student rep does not have to have an empowered position on the council. Only a position that allows the representative to help the student in question explain their side and provide support.
P2: Student privacy and how it’s kept/broken is up to the student in question. It should be up to the student as to whether or not they want a representative and if they should know the details of the situation.
P3: With the point of GCE being a Lab school being constantly brought up, it would be counterintuitive to deny student representation based on the status quo definition of professional.
C: Therefore, students should have a place on the disciplinary council.

With this amendment, students will have more trust in how the staff deals with disciplinary actions. More students would be less resilient of the decisions that come out of the council. A student that supports my amendment by being a co-signer recently said this when discussing the details change: “Having a student on the disciplinary council would broaden the perspectives and make sure all sides of the story is heard and taken into fair account. It would also ensure all decisions made are justified.“ -SG

Building a Guitar

In the second unit of my STEAM course Light, Sound, and Time, we learned all about sound. By looking sound both in a science perspective and a mathematical perspective, we were able to learn how sound travels and how we can use math to calculate different features of the wave. For our Action Project, we were asked to make a makeshift guitar. By doing this, we could demonstrate both our knowledge of the math behind waves and how sound travels through a guitar.

Diddley Bow (2017) LS

In our internal investigation, we looked at how sound travels. What we discovered was that sound travels at a speed of ~343 meters per second. We also learned how the amplitude of a sound wave affects the volume and how the frequency and wavelength affect the pitch. In my makeshift guitar, the sound gets created by strumming the sting. Then, the vibrations travel down the length of the string and into the tin can. There, the sound gets amplified and the sound waves go out the open end of the can.

Harmonics (2017) LS

To make my guitar, I used a tin can, a piece of wood, screws, a battery, and a guitar string. The string I used was 0.02 in thick. I first put a hold in my can with a sharp object. Then, I secured the tin can with one screw on each side. To put the string on, I winded the string on one each on each side of the guitar, making sure to pull it tight and run it through the hole in the tin can. You can hear me playing my diddley bow here.

Diagram (2017) LS

The calculations I did on my guitar were based off of the trapezoid shape that the string makes with the top of the wood. I turned the top half of the trapezoid into a triangle to use trigonometry to find the measurements of some of the angles. The length of the string from he can to the battery was 13.5 in, the length of the wood from the can to the battery was 13 in, the height from the top of the wood to the string by the tin can was 0.5 in, and the height from the top of the wood to the string by the battery was 0.25 in. I used the inverse tangent of angle y to find it's measurement then used that information and my knowledge of triangles to find the rest of the angles. I also found the volume of the tin can by using the formula v=pi*r^2*h and I got 35.5 in^3. Finally, I found the thickness of my string to be 0.02 in.

Calculations (2017) LS

My Declaration for a New Course

In the first unit of Argument at GCE, we learned about how to properly structure our own arguments. To give us historical context as to have this has been done successfully, we analyze the Declaration of Independence and how the colonists made their argument against King George. For our Action Project, we were asked to write our own declaration for a new course at GCE using the concepts that we have learned. For my declaration, I choose to write about an advanced mathematics course.

LS. (2017) Class Discussion

As much as I’ve loved my time at GCE, there are also some things I would change if I could. One of these things is college readiness and the level of math. Because of the way GCE structures and teaches classes, I feel that many students are not as prepared as they could be for the next step in their academic careers.

I believe that education is not a privilege. Every person in the world deserves the right to know how to have the basic skills to function in a sophisticated society. The purpose of school is to prepare for the future. For some people it’s preparing for a deeper level of education and for others it could be starting their careers. Either way we learn things in school that are essential to all potential paths. I propose a class called advanced mathematics. In this course, students will have a personalized program to propel them to the highest level of math before they graduate. However, the goal of the course is not only to help students learn a higher level of math, but to also help them understand why they are learning it and where they could potentially use it later in life. Also, I hope that after taking this course, student will better understand the reason why they are learning math in school.

Personally, I've always loved doing math. Because of this, I think it's easier for me to understand the true value behind it. I've also been in many situations when applying to a school were certain a certain level of math was needed to apply but I hadn't reached it yet.

A good example of how people in the past used math to be successful is how Mary Jackson, Katherine Johnson, and Dorothy Vaughan helped NASA do calculations for their space missions. Not only were these three people women, they were also African American. These women used math to liberate them from the idea that women could not do a "man's" job. Also, while not directly related to math, Phyllis Wheatley tried to promote change in other while her poems. In a way, I'm doing something very similar with this course. Something needs to change with how students think of math at GCE and around the world and I hope this course can help to start to do that.

Guiding Question: How can students use math to prepare for their future?

Course Details:

- The course would be one full term towards the end of senior year. However, in order to prepare for the SAT, the school may choose to teach it to juniors during the winter or spring.

- Most deliverables would not be large assignments. Each piece of homework would be small but focused on ensuring each student retained the information taught each day. New concepts would not be introduced in at home deliverables.

- The resources I would need are as follows: math teacher, classroom, writing materials

p1: Math is used in almost every aspect of your day and knowing more about it can save you money and valuable time. Also, even if you do not decide to go to college, knowing math can get you better paying job positions.

p2: A higher understanding of math can help you get into a better school or further your academic endeavors.

p3: The literal learning of math teaches a discipline of memorization and helps students develop conflict resolution/problem solving skills.

c: Math is an extremely valuable skill to learn for futures may or may not contain academic pursuits.

Overall, this syllogism tries to explain that both the principal of learning math and math itself can be valuable in anybody's life. That math can be valuable not only in the way that many people have viewed it, but in new ways that most high school students don't yet understand.

Usually, when people think of an independent study, they think of one person working alone all the time. However, collaborating with others can eventually lead to you being better as an independent learner. This is because after getting taught by someone else or working with another person, you can better apply the new tools and techniques youve learned to your independent studies.

Building a Camera

In the first unit of my STEAM course Light, Sound, and Time, we learned about the many different aspects of light. During our internal investigation, we explored light waves, radiation, and the electromagnetic spectrum. We also learned about similar triangles and graphing skills to help us understand the math concepts behind the waves of light. For our Action Project, we had to make a camera and use it to show our knowledge on the behavior of light and reflection/refraction. To demonstrate our mastery of the math learned in the internal, we applied our knowledge of similar triangles to create a diagram of how our camera captured the light.

LS Camera (2017) LS

In order to capture the light of an image, my camera has a very small pinhole opening in the front as well as a cover to prevent light from entering the camera while I'm not taking a picture. When light enters the pinhole, it gets inverted and projects the image on the other side of the camera. To capture an image, I put a piece of photosensitive paper inside it and let it sit out with the pinhole exposed for 2 minutes However, for some reason, the picture I took did not come out right and just showed darkness. Along with the photo taken with my camera, I also did a photogram. In order to do this, I placed objects on photo paper and while in a dark room, shone light over the objects and paper for 5 sec and then developed the photo.

When constructing my camera, one of the first things I did was paint the entire inside of it black. This is because black absorbs light while white will reflect it. Black will also ensure that the inside of the camera stays as dark as possible and does not ruin the film.

Photogram (2017) LS

During our Internal Investigation, we learned about the differences and similarities between reflection and refraction. Refraction describes light passing into a different medium and bending. Reflection is when light bounces off of surface. Based on these definitions, neither apply to my camera. The light in my camera is simply projected through the pinhole and onto the film. Another thing we learned about was whether light was a particle or a wave. According to our findings, light is both a particle and a wave depending on the situation. Since light can pass through another beam of light, it can be a wave. Since light can transfer energy when it hits a metal sheet, it can be a particle. In my camera, light behaves like a wave because of how it passes through the pinhole and onto the photosensitive paper.

Math Diagram (2017) LS

The diagram above describes the relationship between the object I photographed, the pinhole of my camera, and the distance between the pinhole and the paper. My object was 6.25 in tall, the height from ground to the pinhole is 5 in, and the distance from the pinhole to the film is 5.25 in. Using these three measurements and what I learned about similar triangles, I calculated the distance the light traveled from the object to the paper and the angles between the light and various parts of the camera. As shown above, the light rays pass from the right where the object is, to the left where the film is. This not only gives me a better understanding of the path of the light waves, but also applies the math concepts of trigonometry/geometry that we learn in class.