Real Math Is Wonderful

by Radhika Zahedi (Math Program Coordinator, The Gateway School of Mumbai)
Perceptions of Math

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I have been teaching math for 10 years and have lost count of how many times people have shared this cartoon with me! Far too many people have negative associations with math. I have seen math draw out reactions ranging from anxiety to hatred.
Why do so many people hate math?
I think the only possible explanation is that these people have never had the opportunity to experience real math. They’ve probably just got some irrelevant, mundane version from poor teaching and textbooks. It is like deciding you hate a #1 hit song solely based on a rendition from your tone deaf friend. The real song is amazing, but all you’ve been exposed to is your friend’s badly sung version and so obviously you think it is horrible (Read the first two pages of A Mathematician's Lament for an eloquent description of this music analogy).
A possible cause
So, to restate my hypothesis: People dislike math because they have only been exposed to a dull version of math. Let’s define dull math.

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A dull math experience consists of mechanical math exercises, often without understanding. It is usually purposeless learning of disconnected topics in which students have no idea why they are learning what they are learning, or where it can be used (The pie chart joke alongside is a great representation of this perception!).
Real Math versus Dull Math
At the heart of mathematics lies Problem Solving. In order to understand dull math better we will compare dull math problems from traditional classrooms with real math problems that arise in our lives. Given below are two math problems on Area.
  • Problem 1: Real math problem (Design a playground)
  • Problem 2: Dull math problem (Area of a rectangle)

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Real Math Problem versus Dull Math Problem
How are these two problems different?
Purpose: A real math problem is purposeful and usually arises out of a need. We design a playground because it serves a purpose and so we are motivated to do it by the need itself.
In contrast, dull problems like Problem 2 are usually purposeless exercises without a meaningful context (This lovely saying comes to mind: Math - the only place where people buy 60 watermelons and no one wonders why…).
Critical thinking and creativity : Real math problems like Problem 1 are much more complex. Before we even begin planning a solution to the playground problem we need to ask many questions just to understand the problem. “How big is the area? Which age group will be using it? What is our budget? What time frame are we looking at?”. We need to really take in the problem and think critically about it. Real math problems are complex because they require you to ask questions to define the problem and consider many variables. Also,they can be approached in many ways and often have multiple solutions based on the needs. For example, if we need to create a small space for football practice we may divide the area up one way but if we need to incorporate a law requiring allocation of a certain percentage of the land for trees we may divide the area in a different way.
In contrast, dull problems (seen in abundance in math textbooks) are typically straightforward because they are devoid of meaningful context and can be solved by using a standard procedure or formula.
Collaboration and resourcefulness: Real math problems can rarely be approached independently. For example, designing a school playground would require the architect to collaborate with the school leaders and school community to understand needs, equipment manufacturers to know what is available or is to be ordered, contractors to understand how and when it can be constructed etc. The architect would probably refer to other designs or consult with a team to generate and execute ideas. Real math problems require you to collaborate with people. Sharing ideas and using strengths of different people allow us to come up with the most innovative solutions.
In this 21st century it would also most involve extensive use of technology, for example the use of a Computer-aided design (CAD) program for creating designs. Real problems require us to experiment with and leverage modern technology.
In contrast, dull (textbook or exam) problems are typically required to be solved individually and in many cases do not even allow the use of a calculator, leave aside modern technology.
Would the purposeless and prescriptive nature of dull math excite you? Or would it make you believe that math is just plain horrible?
A real math project
The good news is that real math can be brought into the classroom too. Last month my students worked on a real math problem similar to Problem 1 - they took up a 2 month

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design project. The plan was to turn our classroom into a study space and create a 3D model to depict their designs. Here is a picture of their model about half way through:
From the numerous discussions that took place during the process, I have listed a few comments that I believe are representative of the above mentioned criteria - purpose, critical thinking, creativity and collaboration.
Purpose/ Context:
“Miss my father was an architect, he used to design stuff just like this!”
“We saw scale models just like this at the art exhibition we just visited. Except those were created for film sets.”
Critical thinking and Creativity:
“Miss I don’t think the square footage of my space is the same as N’s! Both areas don’t look like they are 40 square feet each! I am going to recheck.” (student grabs the measuring tape and proceeds to measure the space.)
“Miss can I please add a loft to my design, I will have much more space with a loft!”
“Can I fit a hammock in my space?”
“Oh no, This table is too big for my space! Maybe I can fit one in if I attach one to the wall”
Collaboration and resourcefulness:
“Ms. M what do you do if the client doesn’t like your designs? How do you rework it? What about the additional costs?” (to the guest architect)
“Eeeeeeeee this tool is soooo cool! I can view my design from all angles!”
“Let’s use the online converter to see how much this area is in square inches”
This was the first time that I had experimented with a project that spanned over two months and it brought out aspects of learning that I had not witnessed in my classes before. My students, some of them ‘math-haters’, were engaged and enthusiastic for the entire duration. One math-hater even announced during a whole school sharing that she was excited about her math project.
I can compare this to classes early on in my career when I used a dull approach. In those classes the discussions really just included comments like “What is the formula for area? What is the unit for measuring area? What answer did you get?”
Imagine a future where math lovin’ is such a common trait that society ends its portrayal as a rare quality possessed only by a nerdy few. Let our kids experience real math and it can be a reality. As you ponder over this, I will leave you with two amusing images from the internet, presumably created by some fellow math enthusiasts.

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Image sources:
http://illuminations.nctm.org/uploadedImages/Content/Lessons/Images/6-8/solution.jpg
http://rlv.zcache.co.uk/hippopotenuse_postcard_by_sandra_boynton-r0e98550d4c4045878ecc6b344d27712e_vgbaq_8byvr_324.jpg
http://40.media.tumblr.com/1a9035e2d98c0bd71e44de377315deed/tumblr_nx5uag3ccH1r52l3qo1_400.png
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