**Last week, we had a great debate about our expert’s last video OUR EXPERT ANSWERS #6: “How can we explain fractions without using division?” Some of you asked Sunil to explain how he came up with 6 as the LCD. But he did not give the answer…on purpose. He tells you why in this new article.**

## Do Not Deny Opportunities For Students To Struggle With Mathematics

“Mathematics is the art of explanation. If you deny students the opportunity to engage in this activity– to pose their own problems, to make their own conjectures and discoveries, to be wrong, to be creatively frustrated, to have an inspiration, and to cobble together their own explanations and proofs– you deny them mathematics itself.”

My video on seeing the division of fractions as a subtraction received many comments and social media shares! And, the prevailing question–dare I say, criticism–was that there was no explanation as to why I chose an array of six blocks to represent a whole, the number one!

I intentionally left that information out to generate a discussion, and to provide a fertile environment to probe the video for “missing information”. And while I do take some pride in being a math expert here at Buzzmath, I would like to think that it is more important to create a community of experts who inspire each other to make learning mathematics authentic and meaningful.

But those are words that are often casually tossed around in math education. What do we really mean by something like authentic? As most of you know, Buzzmath devotes enormous resources to the creation of rich and engaging Missions activities–where students solve math problems in the context of math history and along with mathematicians who contributed to the global understanding of the subject. As such, it only makes sense that when students learn mathematics, they go through the same intellectual and emotional struggles to understand mathematics.

There are no shortcuts, and yet, if we try to create them, we will do a disservice to the very essence of mathematics–success through struggle. With only success, we put inordinate and incorrect pressure on our students to be perfect and to be fast. In other words, to be completely counter to the development of mathematics.

Greater patience and resilience cannot be acquired unless we continually exemplify it through what we teach, how we teach and why we teach.

Answering that last question with honesty will reveal not only our potential as math teachers, but also our limitations. This potential should fuel the energy to break through our limitations–to see mathematics as one of the highest artistic achievements of our society.

“Mathematics is the music of reason. To do mathematics is to engage in an act of discovery and conjecture, intuition and inspiration; to be in a state of confusion—not because it makes no sense to you, but because you gave it sense and you still don’t understand what your creation is up to; to have a breakthrough idea; to be frustrated as an artist; to be awed and overwhelmed by an almost painful beauty; to be alive, damn it.”

Anything less, and the value of mathematics–and the struggle that is inextricably tethered to it–will be far less than what was intended and created.

However, in order for any of this positive struggle to have any resonance with our students, our own struggles with mathematics must be documented in the classroom. What problems stumped us as kids? What problems stumped us as teachers? Not only should this be shared, but it should be shared in a joyous and celebratory fashion!

Why?

To make mathematics a human experience…again.

**Sunil Singh,**

Math Specialist and Buzzmath expert