Refugee data

At an assembly in the fall at Washington International School had a guest speaker from the organization Free Syria speak to our students about the current crisis. She gave the students more of a background the crisis and referenced data on the amount of refugees. This inspired me to do some research and to encourage a student to do a mathematical paper on the topic.

I looked for the data on the amount of Syrian refugees leaving as well as the amount of refugees that other countries have historically accepted and registered. I found raw data from the World Bank on countries from 1990 to 2014. (If you have not looked at the World Bank’s data, I highly recommend seeing what they have based on topics). In my spare time, I have been sorting the data and looking for trends, as any math teacher would do. Recently I sorted the countries by income level based on the World Bank’s definition and already stated in the data sheet. The graphs of the totals since 1990 of the countries based on income is displayed in the following graph using Excel. Screenshot 2015-11-29 11.35.33

I find it rather surprising that the High Income countries admit fewer refugees than most other countries. When looking at the data of the High Income countries closer, Quartile 1 and median are relatively close.

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I made another graph of individual High Income countries: USA, France, Germany, Canada, Sweden, and UK. Screenshot 2015-11-29 11.51.29

With the exception of Germany, most of the graphs gradually increase or decrease. When looking at the graphs of the 5 statistical measures, we can see that Germany’s data influences the standard deviation. For the graph of the USA there is an interesting spike in 2006. What explains that spike in USA’s policy?

I am going to continue to run different statistics in preparation for my grade 9 statistics unit. I am curious what is happening with the Low & Middle Income countries that allows them to admit more refugees.

Student work is Amazing

My students amazed me with their attention to detail with the Linear Programming art assignment. The objective of the assignment was to use linear programming to make an art piece, but I also wanted students to have the option to challenge themselves and be exposed to other types of functions. I introduced the students to sliders so that the students would have the structure and confidence to work with unfamiliar functions. Here are a couple of examples of their work.

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Alexandra’s Desmos graph of an eye

Alexandra pays great attention to details and was motivated to make an eye. Her process was so methodic and her conversations with her peers and me about the functions she needed to use focused on the attributes of the graphs you only wish your students would eventually notice. She played around with ellipses but noticed that she could not get the crease of the eyes. She was explaining her problem and I suggested using parabolas and was able to discuss cusps that occur in graphs. In her write up for the assignment she was able to reflect on the different aspects of the functions she used. In her reflection she wrote:

I was finished with the eye very soon after I started working on it, and I decided that I wanted to challenge myself even more. I attempted to draw eyeliner on the eye and draw an eyebrow as well. I experimented with parabolas and modified some equations and added sliders to figure out the correct equations and finally they turned out the way I wanted them to.

Lily wanted to work do a character with more than just linear lines and choose Carl Fredricksen from the movie Up. The emotion and facial expression she captured only using functions is true to the character. In Lilly’s reflection she discussed her use of different types of equations and use of sliders.

Lilly’s Desmos graph of Carl Fredricksen, from Up

“I had reached a point where I knew I had to start putting in my circles, parabolas and ellipses. …. I realized that my hesitation to begin using the equations for circles, parabolas and ellipses was because I felt that the equations were a bit intimidating. …. more values are involved; the more numbers there are, the more intimidating the equation becomes. ….. The use of sliders made creating equations and graphing lines go much more smoothly and much quicker, making work more efficient and less time consuming, allowing me to complete it on time.”

The assignment and the graphing tool desmos provided a situation for the students to take risks, explore different types of functions and be motivated to find equations that would best work in their art piece.

Function Art

Last week I had the privilege of presenting and attending the Project Zero conference in Amsterdam. The sessions were inspiring and I am looking forward to putting these ideas into practice. I attended the session at the COBRA museum and my group was guided by Claire Brown from the Thinking Museum in Amsterdam. We looked slowly at a painting using a variety of thinking routines to take in a painting rather than spending the average 15-30 seconds. We spent 30-45 minutes describing colors and hues then dissecting shapes, figures, perspectives and themes. Spending this time discussing and methodically going through seemingly simple aspects of the artwork we all came away with a deeper understanding of the artwork and appreciation for the artist’s process.

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View finder
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Partners: one describing the artwork and the other sketching.

One idea that came from the session was from an activity we started out doing. We were paired up each group given a view finder and a clip board. One person used the viewfinder and faced the painting, the other faced the opposite direction with the clip board. The partner looking at the painting had 10 minutes to describe the painting and his/her partner would have to draw. Both jobs were equally difficult, as we had to be very precise in describing the lines, and shapes in our view finder.

I want to modify this activity for my students to describe an artwork while we are working on functions.

Instructions for Function Art:

  1. Pair students up
  2. One student has a rectangular view finder with a grid or coordinates marked out.
  3. The student that sketches will have gridded paper with the similar coordinate plane.
  4. The student describing the artwork will have to use functions to describe the lines and brush strokes in the painting. Students should be specific on the functions’ characteristics and placement.
  5. Give the students 10-15 minutes on the task and have them switch.

Now I have to pick a painting that uses a variety of functions….. any suggestions?

Linear Art Assignment

This week I started my grade 9 students on a project that I got from NCTM’s article The Algebra Artist, by Darin Beige. The task has students use Desmos to make a drawing using restrictions on domain and range to limit lines and inequalities to shade areas of the graph. Before starting the activity I had the students solving systems of equations through graphing and graphing systems of inequalities. We did a few linear programming exercises by hand and then with Desmos so the students could get familiar with the Desmos.

Here  is The linear Art AssignmentThe panda I created using Desmos

The students have one week to complete the assignment.

I created a Panda using Desmos to show my students. (If you use the browser and login to save your creation.)  It was helpful for them to see examples then they did some research online to get ideas on what they wanted to create.

Beige, Darin. “The Algebra Artist.” Mathematics Teacher 108.4 (2014): 258-65.