Weekend Warriors: Mathematical Selfies -- by Axelle Faughn

Access in Mathematics Education is a complex issue. It is no secret that students with privileged socio-economic backgrounds have better chances to succeed in school. Indeed, early exposure to books in the home, cultural activities outside of the home, and availability of educational resources are all determinant factors in later school performance. One could think however that mathematics to some extent stands apart from this trend since “being good with numbers” is often thought of as a natural skill rather than nurtured by the environment, and may not seem as closely affected by daily interactions in early childhood. Nevertheless, issues pertaining to access in mathematics education are significant enough that the National Council of Teacher of Mathematics issued the following position statement on the topic:

NCTM Position (https://www.nctm.org/Standards-and-Positions/Position-Statements/Access-and-Equity-in-Mathematics-Education/)

Creating, supporting, and sustaining a culture of access and equity require being responsive to students' backgrounds, experiences, cultural perspectives, traditions, and knowledge when designing and implementing a mathematics program and assessing its effectiveness. Acknowledging and addressing factors that contribute to differential outcomes among groups of students are critical to ensuring that all students routinely have opportunities to experience high-quality mathematics instruction, learn challenging mathematics content, and receive the support necessary to be successful. Addressing equity and access includes both ensuring that all students attain mathematics proficiency and increasing the numbers of students from all racial, ethnic, linguistic, gender, and socioeconomic groups who attain the highest levels of mathematics achievement.

In my own professional experience, I find that equity and access in the teaching and learning of mathematics involve multiple levels of complexity. Cultural differences may make access difficult as extensively advocated by the organization TODOS – Mathematics for all (https://www.todos-math.org/). Various diagnoses of learning and intellectual disabilities should also be taken into account when striving to make mathematics relevant and accessible to all students. Similarly, gender issues pertaining to access in STEM disciplines are well documented in the research. And the list goes on.

For this post, we chose to work with a group of students from Western Carolina University’s University Participant (UP) Program. As described on the UP Program website, “The WCU UP Program provides an inclusive, two-year, on-campus living and learning experience for college-aged persons with intellectual disabilities. The goal of the program is to facilitate UP students' transition from secondary school to adult life with education, employment and independent living.” 

In January 2018, my colleague Kathy Jaqua and I decided to offer a mathematical selfies workshop for these students as one of their “weekend warriors” organized activities. This was in part prompted by our desire to share the beauty and fun of mathematics with students who may not be aware that they are exposed to mathematical ideas on a daily basis. Indeed, after volunteering for the program for a few months, I realized that most of them did not enroll in college mathematics courses. Considering their busy schedule with work, classes, and other social participation activities, along with the bad rep that “math is hard stuff” and maybe not as useful as, say, a communication or a business class for promoting community integration, this was not surprising. Nevertheless, I suggested we still provide these students with access to some unusual and interesting aspects of mathematics through mathematical selfies. In previous posts I have already commented on how selfies can be used as a doorway into the mathematical realm for students who may not be inclined to explore this idea otherwise, a way to develop an appreciation for the subject matter. Our experience with the UP students is one more example of this.

When you consider working with students with disabilities, there is often an adaptive component involved. So I looked up Adaptive Mathematics to find out where we, as mathematics teachers, stood in that respect. It appears that most adaptive teaching approaches are heavy on using computer-based curricula. With the Mathematical Selfies, we propose a different, more hands-on, fun and team oriented approach to looking at mathematics. I always keep in mind that Play is recognized as an international human right by the World Health Organization. And I believe it has its place in making mathematics even more accessible to students with disabilities as a way to trigger their interest and possibly offer perspectives on and connections among topics which they may not have thought about previously. Image 1 shows how we captured their attention through an engaging mystery to solve. 

Image 1: Treasure Hunting as a goal to achieve

We started the day with a brainstorming session of how the students used math in their daily lives, with an emphasis on their workplace. This was well received as several of the second year students were able to share stories of how they used mathematics on the job, either working at a restaurant, or landscaping. Then students gathered in groups of 4 to engage in a mathematical treasure hunt around familiar places on campus. This activity is very play-like, goal oriented and builds team spirit along with a sense of competition. Several of the UP students have specific goals that they are working towards, therefore goal directed activities are familiar to them and a great way to engage and sustain effort/attention. The treasure hunt we used also presented some aspects of problem-solving strategies such as elimination, and was a perfect way to engage their brains towards logic and deductive reasoning, building cognitive skills as they had fun arguing and discussing the clues. 

And so they went…

College students spend a lot of time hanging out at the gym or at the cafeteria when they are not in class, studying, or at work. So it is no surprise that several of the mathematical pictures illustrating mathematical concepts such as operations were taken at the food court or exercise room that day.

Image 2: SUBtraction

 Image 3: Numbers on the Treadmill

The topics we selected for the workshop involved Shapes (triangles, circles, rectangles…), Numbers (whole, decimals, fractions…), Arithmetic operations, Measurement (units, volume, length, weight…), and Data (lists, tables, graphs…). For image 2, students as a group came up with the following description: “We like this picture because we love food!! We noticed the different sizes of sandwich 7” 10” and 14”. We also noticed the prices which have decimals, the calories and also how it’s in a list.” Students who submitted image 3 said they noticed “heart rate, distance, speed, inclimb, kilometers.”

Image 5: Lean Mean Vending Machine

Image 4: Circle of WCU                                                              

Exploring campus location with new mathematical eyes,    students also noticed the vending machines,
and some of the architectural features around.

In both of the above pictures, students mentioned the circular shapes. In particular for the WCU logo they highlighted the “evenness of all the circles and shapes.  It also has a clock, and a date because it’s important to keep track of time!” The group who selected the vending machine started to think deeper about number relationships and suggested the odd/even relationship based on the rows of the keypad. They also talked about “coding used in math with letters and numbers”. One of them even said he was interested in transaction and coding because his goal is to learn computer science.

In several of the descriptions, students alluded to the other goals they have to sustain daily, goals that might have been determined together with guidance from the UP Program staff for which they have reminders on their daily schedule of activities. Learning to keep track of time and be on time for your classes and meetings, managing eating portions, managing money, promoting a healthy lifestyle through exercise and proper hydration, as illustrated in the water bottle picture below.

Image 5: Our Goal of Drinking 2 Water Bottles a Day

“We found a water bottle that has units and volume and numbers. The bottle measures the amount of water.”  

 By the end of the morning, our weekend warriors seemed much better equipped to notice and talk about, or even write about the mathematics they encountered in their daily occupations. Several reported that they had learned that “everywhere you go you can come in contact with math”, or that “the world could not function without math”. Some were more specific in pointing out that they were able to recognize that math was an integral part of their campus community, although they don’t usually look for it. Several also said it was fun. Developing mathematical awareness and a sense of playfulness was the main purpose of our weekend warrior venture, and overall it was a huge success. I will leave it at these last two quotes to which I return often for their honesty and candor.

“Math is not only a bunch of incomprehensible numbers, and it is all around us in our everyday life. Math can be fun!”

“I learned that some people really see math everywhere!”

Weekend Warriors, January 27 2018