We are surrounded!!! -- by Axelle Faughn and Kathy Jaqua

So I have to admit we ARE having a lot of fun with these Mathematical Selfies projects... but what do students get out of them? Well... here are a few students' quotes that speak for themselves.

• On different ways of perceiving mathematics: “It is interesting to see how people’s personalities and interests play into the different ways in which they view math.  Some people saw math at their place of work, others in their hobbies, and some in tasks they do every day.”
  
  
• On developing mathematical awareness: “I have enjoyed watching my eye for math in the world grow.  I now notice math  much more frequently in the outside world, and I feel like the more I learn about math the better off I am.”
  “I cannot not see it anymore, mathematics is everywhere!”
• On popularizing mathematics beyond the mathematics classroom: “I have begun to talk about math that I find in the world with my friends and family, and they think that it is pretty cool!”
• On personal satisfaction: “I enjoyed the “hunt” for physical representations and got satisfaction from finding good photo comparisons.”
• On uncovering the building blocks of mathematics: “I never realized there were triangles in all these objects!”

These genuine student reactions are certainly exciting, however we are interested in further exploring potential outcomes of mathematical selfies projects and activities such as:

1. Assessing student understanding and identifying underlying misconceptions
2. Encouraging access and equity through student participation
3. Encouraging family and community involvement in mathematics
4. Developing Mathematical Language use in and outside of the classroom
5. Identifying common thinking and visualizing patterns in students
6. Engaging and having fun with mathematics

In this post let us focus on point 1. Assessing student understanding and identifying underlying misconceptions. The following picture submission by a student enrolled in an introductory college course is a good example of how selfies can help us with formative assessment.

Clearly, although the student had learnt an appropriate definition for the concept of function, this knowledge did not accurately translate in their representation and interpretation of the mathematical object. Indeed, when working with the graphical representation of a function, they were identifying the output as the location of a point on the plane, rather than the y-coordinate associated with a given input x. This misunderstanding may not have been apparent had the student not had to create both a visual representation and a verbal explanation of what they saw in the selected picture. So the picture submission was helpful in catching this misconception and making sure it could be addressed early on.

As one of our students advised:“Keep your eyes open and pay attention to math.  You are surrounded!” -- to which I shall add, "not only notice it, but also talk about it, as this may reveal understandings far beyond what the eye can see".