Journal of Math Circles

Article Title

Dots Explode in Hawaiʻi

Biographical Sketch

Veny Liu, Dr. Veny Liu is an Assistant Professor of Mathematics at the University of Hawaiʻi - West Oʻahu. She has been part of The Math Teachers' Circle at Hawaiʻi (MaTCH) Leaders for the past 4 years.

Laurie James, Dr. Laurie James is an Assistant Professor of Math Education at the University of Hawaiʻi – West Oʻahu. She engages students in productive mathematical struggle, connecting math to outdoor life experiences, and making math fun through projects. Her research interest focuses on using math manipulatives and interactive games in grades K-5, the integration of technology into the elementary classroom, and environmental education that creates lasting change.


Teachers are wonderful advocates of mathematics for future generations, and they are continually looking for ways to get students more engaged in mathematics. Through visuals and hands-on activities, the Exploding Dots concept can help teachers and students understand many elementary arithmetic and algebra topics. The implemented tasks promote problem-solving by allowing multiple entry points and varied solution strategies. This paper explored this idea beyond drawing clusters of dots by Locking Legos activity. With a thorough understanding of math content, participants in multiple Math Teachers’ Circle of Hawai‘i (MaTCH) meetings expressed confidence in creating and developing meaningful and relevant differentiated learning opportunities, which include teacher candidates through classroom activities and demonstrations. This paper presents these participants' experiences of a simple concept that grew into a mathematical story.

Description of Program

In 2011, Math Teachers' Circle at Hawaiʻi (MaTCH) was started at the University of Hawaiʻi at Manoa, located in the southern part of the island of O‘ahu. The fundamental beliefs of MaTCH involve the development of personal mathematical and pedagogical knowledge through ongoing dialogue. The MaTCH meetings focus on promoting hands-on activities to embrace, engage, and empower learning through productive challenges that ignite participation in mathematical problem solving activities. MaTCH has evolved to become a professional learning community of students, teachers, mathematicians, and mathematics educators, where they meet regularly to engage in mathematical problem solving activities and pedagogical discussion. In the past four years, MaTCH has expanded to the Leeward (western) side of O‘ahu.

Website: https://math.crdg.hawaii.edu/match/

Contact: Veny Liu (venyliu@hawaii.edu) and Laurie James (ljames7@hawaii.edu)