The Excitement of Discovering Mathematical Ideas on Your Own

Mathematical Curiosity and Exploration

Take a moment to ponder the symmetric dot pattern shown above.  What does the pattern make you wonder?  What do you notice about the pattern?  How does this pattern make you feel?  What questions could you ask about the pattern?

These questions were posed by Matt Roscoe in the opening paragraph of a recently published study titled “Using Tile Farm to Support Emerging Multiplication.”

Roscoe, a math professor at the University of Montana, with a strong interest in investigative and exploratory math education lessons, was keen on discovering what math second graders could unearth by analyzing symmetric dot patterns made in Tile Farm Studio.

Initially, Roscoe showed the pattern above to students and asked what they noticed or wondered about it.  Students had many diverse observations.  One student said it was a “triangle full of dots”.  Another noticed it had “groups of ones, twos, and threes”.  Another student saw the pattern as a “triangle made out of triangles”.  After one student pondered how many dots there might be in the pattern, Roscoe gave students the challenge of trying to figure out how many dots there were in the symmetric dot pattern shown above, and the three shown below.

Pure dot patterns made in Tile Farm Studio, and found in Tile Farm Playground’s Notice & Wonder, allow for students to discover math on their own, while also teaching empathy, as students discover the many different pathways to a correct answer reflect the diversity of human thought.

Discovering Math on Your Own Is Exciting

The beauty of Roscoe’s approach lies in its simplicity.  By presenting students with intriguing patterns and encouraging them to explore, he tapped into their innate curiosity.  The students weren’t just learning math; they were discovering it.

As the students delved deeper into the patterns, they began to see the underlying mathematical principles. They started recognizing the symmetries, the repetitions, and the multiplicities.  Even though they hadn’t learned about multiplication in school yet, some students began to group the dots and ”invented” multiplication on their own to find the total number, showcasing an organic understanding of the concept.

But the real magic happened when students realized that there were multiple ways to approach and solve the problem.  This not only deepened their understanding of math, but also opened a window into the diverse thought processes of their peers.  By discussing and comparing their different approaches, students gained insights into how others think, fostering understanding and empathy.

Perhaps the most significant takeaway from Roscoe’s study, however, is the sheer joy and excitement the students exhibited.  They weren’t just solving problems; they were embarking on mathematical adventures, making discoveries, and experiencing the thrill of insight.

The Lessons section of Tile Farm Studio is full of lessons that put creativity and exploration at the forefront of math learning.  In the video above, you can learn how to build your own pure dot patterns—like the ones found in Roscoe’s paper—in Tile Farm Studio.  Subscribe to the Tile Farm YouTube channel for more videos like this.

Bringing the Magic of Mathematical Discovery to Your Home

Notice & Wonder is a collection of 7 daily patterns found in Tile Farm Playground meant to stimulate math talk, curiosity, and wonder—in a similar way to Roscoe’s paper. Studies show that parents engaging in simple math talk activities like Notice & Wonder with their children is a great way to boost mathematical achievement and understanding. Notice & Wonder is a low floor-high ceiling activity—meaning it is appropriate for people of all ages and intellects—which makes it a perfect activity to do together as a family. Try heading to Tile Farm Playground, doing Notice and Wonder with friends or family today, and seeing what math you discover!

Interested in experiencing math in a completely different way?  Sign up for Tile Farm today! 

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Alex Romero, Chief Experience Officer

Alex has an MS in biochemistry and molecular biophysics from Caltech, and has extensive experience both as a research scientist and as an elementary school math and science teacher. He is passionate about art and innovation, and making the math learning experience as beautiful as possible.