Introduction to Statistics and IB math exploration

I have not posted for a while but interesting math still has been adding up.

I posted previously about iTunes and statistics. I recently revised the activity to compare more countries and introduce statistics. The students were give data from USA, Australia, Nigeria, India, and Germany and put in groups to look through the top 20 sales in iTunes.

While the students sorted the data they listened to the songs, discovered Bollywood, Highlife from Nigeria and realized the Justin Bieber was a hit across the board. Here is the student handout. I distributed using google docs so the students could edit the document together and have it as a record.

Lesson1studenthandoutiTunes

The second activity investigated how statistics can be used to change policy. The students first watched The Story of the Plastic Water bottle to understand . And then were given data from Rock Creek Conservancy  on trash pick ups from the last years. Students were given an introduction on excel formulas, how to sort data and needed to use statistical measures to investigate trends. The goal was to look at the local level, national and global, as well as exposed the students to the amount of plastic in our water ways.

More to come…

 

Wonder

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.

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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. 

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.

I made another graph of individual High Income countries: USA, France, Germany, Canada, Sweden, and UK. 

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.

Normally distributed Groceries

 

Recently when looking up a grocery store on my phone on google maps I noticed the following graph on popular times.

Google provides data/predictions for customers about when people typically visit the specific store. I am not sure how the data is collected, so if any one knows please share.

I used these graphs in a statistics lesson after I had introduced normal distributions. We talked about who this information is important to and estimated the standard deviation on a curve that looked normal. We discussed the missing information on the y-axis as well as how a store opened 24 hours would have a different standard deviation and possible shape to the graph. Then we looked at the rest of the week.

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The students were able to recognize patterns in the specific store and relate it to human behaviors in the work week, we estimated the mean for each graph. We also discussed other locations through Washington, DC and if they would have the same types of distributions. Would stores downtown have a different distribution from stores in the suburbs? Will all types of stores have a similar distribution based on location or is it more based on the type of store (for example, grocery, hardware, clothing).

It would be interesting to see how Thanksgiving preparation will affect the graphs.

“That’s so cool!!”

When I was visiting friends in NYC for Halloween weekend I made a trip to the Museum of Mathematics, or MoMath. I went with two former colleagues, a physics teacher and history teacher. We began our visit to the interactive museum on the floor zero, ground floor. There is a stool  inside a circle of strings attached to the ceiling. Once you sit down you spin the stool to activate the strings creating a hyperbolid around you.

Then onto the bikes!Inspired first by G. B. Robison in 1960 who came up with the flat tire bike. Macalester College’s Math professor Stan Wagon made a flat tire tricycle to ride on a straight track with a catenaries. MoMath has a similar type of circular track with two sizes of tricycles. Of course I had to try! It is amazingly smooth ride with three different sized tires. Wolfram has a simulator of the different types of tires and planes to use.

Amanda Riske riding the square tire tricycle

We played video game that would graph your velocity and acceleration on the running track. On floor -1 we were greeted by a wall of magnetic tangrams. We made designs and completed Escher like tessellations. There were logic puzzles, an interactive light board to walk on, and spinning tops to sit on. All of the exhibits were not so much about the history of math but the play in math. Two hours flew by! I had a wonderful time, and loved hearing other people in the museum exclaiming “That’s so cool?” If you are in NYC or planning a visit soon, I highly recommend stopping at MoMath.

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.

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.

View finder

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 Assignment. 

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.

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.

Statistics lesson: Justin Bieber was the common denominator.

For my grade 12 class we reviewed the five statistical measures with the following activity. I found a website that releases the data for the top selling songs on iTunes for the past 24 hours, called Digital Sales Data.  We did the activity on September 3rd which was after Justin Bieber’s new single What do you mean? was released.

Outline of activity:

• The students were in groups of 3-4 students and each group was given data of the top 25 selling song from a different country: USA, Finland, Australia, Malaysia, and Nigeria.
• Each group had to find the 5 statistical measures and we compared as a group.

What was interesting was that Finland and Nigeria had similar types of numbers, The students were a little confused about if the units were in the thousands or just units as some of the data was so small. One student pointed out that Finland owns Spotify so we talked about the economies of the countries. We also talked about why the values were so different discussing the population of the countries and buying power. It would have been helpful if I had the countries’ population and GDP to compare.

Overall it was a good activity that brought in a global perspective and interesting to see what types of music are listened to elsewhere and helped the students stay focused and interested. We found that Justin Bieber was the top selling in all the countries. We also were able to talk about grouped data and deciding on appropriate class grouping ranges depending on the data given and discussed the standard deviation of each set.

Here is and example of the data from the USA and Finland.