When playing games with his friends and family during an annual vacation, Taylor Gibson was intrigued by a specific line in the rulebook for a card game. The line, which followed a few pages of instructions on the game’s intricate rules, said “start playing and it will all become clear.” 

The instructions basically encouraged players to do a practice round, exploring the rules in a hands-on way to help reinforce their understanding. It’s a concept that Gibson, a math instructor at the North Carolina School of Science and Mathematics and executive director of the Ryden Program for Innovation and Leadership in AI, believes can be applied to the K-12 math classroom. 

“That just resonated with me so strongly as an educator because I think a lot of times in education we start with the rulebook. We ask our students to memorize all of the rules before we start playing a game. We ask them to do that when we’re giving a classroom lecture; we quiz them on the rules, maybe at the end of every week, to make sure that they remember all of the rules, but we’re asking them to do that in this vacuum,” Gibson said. 

Gibson delivered the keynote speech, entitled “Play the Practice Round First: Building Math Instruction Before the Rulebook,” during the 10th annual Math Summit held at NC State on Aug. 4. The event, which is sponsored by the NC State College of Education and the Triangle Math Alliance – a regional consortium of the Chapel Hill-Carrboro, Durham, Johnston, Orange and Wake County public schools – and funded by the Goodnight Educational Foundation, is designed to help practicing teachers learn more about best practices for mathematics teaching and learning.

During his talk, Gibson noted math often starts with giving students abstract formulas and expecting them to apply those formulas to real-world concepts. Instead, he believes that instead of starting with the “rulebook” of abstract concepts and formulas, students should get a “practice round” where they develop ideas through simulation and experiences, and formalize that learning afterwards. 

“Playing the practice round first, building the intuition with your students, will help whatever formalization we’re trying to build come a little bit easier,” he said. 

He walked teachers in attendance at the Math Summit through an example by having them roll dice to calculate the odds in a game of Yahtzee of rolling ones or sixes to inform their playing strategy. 

In a similar classroom activity, Gibson would have students begin by rolling the dice by hand, and then move on to a digital app where they could replicate multiple rolls at once to see a bigger data set. Students would then go on to quantify what they observed and build a probability tree, moving from the tangible dice to the abstraction of data. 

“Creating these opportunities for students to play and learn and build that intuition is really going to help that learning process,” he said. 

Research backs Gibson’s idea of a “practice round,” showing that learning through simulation not only encourages interaction and collaboration between students but also reduces extraneous cognitive load by helping students focus on concepts and ideas rather than rote calculations. 

Research also shows that students who learn through simulations, and continue to do so, more successfully retain the information they learn in order to apply it later on. 

“We’re teaching them these skills that we hope are durable,” Gibson said. “So, the idea that we can go this route and have them actually remember all the stuff that we spent time helping them develop is important,” 

Although his background is in high school statistics, Gibson noted that the benefits of learning and inferring about data through doing can be applied to all grades, from kindergarten through college. 

For example, for younger learners, collecting data can be as simple as taking a poll about favorite music genres. Students can begin by collecting data from their classroom and then move on to polling the grade and school, thinking about what the most probable top answer will be based upon data collected from each previous sample group. 

For more advanced classes, students could collect data samples and create a dot plot by hand, and then compare how different samples are different and discuss how and why that’s possible. The most advanced students would then shift from guided, hands-on activities to autonomous collection based upon their own developed questions and using what they’ve learned to develop their own solutions. 

“This idea of simulating things in the real world helps make math meaningful for your students,” Gibson said.