Islamic Art Exploration

My goal as an educator this year is to intentionally focus on the cultural side of mathematics through authentic applications.  During the geometry unit in pre-algebra, my students explore the intersection of geometry and Islamic art. After studying quadrilaterals, we started playing with 5 and 7 overlapping circles through activities outlined in the book Islamic art and Geometric Designs. Screen Shot 2018-02-01 at 6.37.56 PM.png The activities expose students to the regular shapes that can be made from circles. At first, we worked with compass and rulers, and I gave students the option to work on GeoGebra.

Two videos that explain the process and significance:

The students worked on their project over a week. We first looked at developing an appreciation of the creation process, then started analyzing photos. I used some designs from Eric Broug’s book to help students explore the patterns in the designs and deconstruct designs.

Here is a link to analyzing a pattern tile, Complex Islamic Geometry. Some imagines are taken from Eric Broug’s book and a Thinking Routine from Agency by Design (Parts Purposes, Complexities).

After going through examples and making connections between geometry properties and overlapping circles, we started on the project. Instructions for students Islamic Art Project.

Students used GeoGebra or compasses to create different pattern tiles. We used about 2-3 class periods for students to create a design then one lesson to work on the write-up. I did not assign homework through the process as I wanted to make sure to be available to answer their questions and provide technical help. Upon completion as hosted a Gallery walk to observe student work. I invited fellow teachers, administrators and Grade 2 students joined us since they were kicking off their Geometry unit. It was beautiful to see the students give the second graders a guided tour.IMG_3988.jpg

Overall the students improved describing their process, their use of mathematical vocabulary, comfort level with GeoGebra, and learned about some of the cultural significance of geometry to Islamic Cultures.



Student work 2
This student highlighted different parts of her design to explain her process



The newly renovated Renwick Gallery in Washington, DC is a perfect place to start off 2016 by seeing the exhibit Wonder. The exhibit features nine artists’ installations that give the visitor a sense of wonder. I absolutely loved walking through the beautifully restored building to observe thoughtful pieces created with care and precision. Through the exhibit I kept rerunning the Project Zero Thinking Routine I see… I think… I wonder….. 

Through the various rooms there are quotations about wonder. One that I found thought provoking “It is not understanding that destroys wonder, it is familiarity”  John Stuart Mill, 1865.

The symmetry in Jennifer Angus’s installation of unaltered insects was fascinating, playful and made your skin crawl a little while taking in the details and features of the insects.

The Gabriel Dawe installation of Plexus A1 is just breath taking. I would love to see if I could do a lesson on vectors and intersecting planes for the color refractions he creates through the use of string. If any of you math educators have ideas on this type of lesson please share 🙂 I will see what I can come up this semester.

This slideshow requires JavaScript.

At the risk of being to familiar with the art piece, I played around with Geogebra‘s 3D modeling to construct the basic shape and see of the intersecting thread. Figure 1 is the first model with the lines on the floor perpendicular to the lines on the ceiling. The figures are not to scale.

Figure 1

After looking at the photos again I notice that the lines on the ceiling were more angled. The angles are shown in Figure 2. I am interested to know how the Dawe planned the strings line of the intersection. Also, how can you mathematical maximize the intersection string line? When thinking of this from color theory point of view, you can also look at each intersection points of the individuals lines as color mixtures.

Figure 2

I wonder how the tightness of the string effects the intersection of the planes, also how to describe the planes mathematically? In a way it reminds me of the mathematical models that May Ray used in his Human Equations exhibit at the Philips Collection last spring.

If you have an idea or insight on this installation please share. It definitely brings out a lot of wonder even as I become more familiar with the problem.

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.

Screenshot 2015-11-29 11.57.48.png

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.

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.

Slow Data Collection

Inspired by a Project Zero principal investigator, Shari Tishman, idea of ‘Slow Looking’, my students will participate in Slow Data Collection in preparation for our statistics unit. For the first semester my grade 9 students will collect data about the amount of water bottles we are saving by refilling cups and/or reusable bottles. I made a google form for the students to easily collect and record the data. The students self managed the groups to see who documents which of the five water fountains around campus. We will use this information in the second semester during our statistics unit as well as information on a trash audit that the school’s environmental club will be doing this fall.

This project is being conducted at Washington International School
Water fountain with counter. This project is being conducted at Washington International School

My goals for the project is for my students to have a better understanding of the limitations of data collection and how there are so many factors that come into play when doing a study. I also want them to problem solve through the process, make recommendations to the school community based of the water usage and be curious about other information we could collect in their environment. I am currently working on getting guest speakers from climate change to come in and speak to the students about their study.  I am really excited about the project and hope that it brings about a change in perspective of what statistics is to my students as well as being more aware of their own environmental impact.