BUILDING A LOVE OF MATH FROM K TO 12

BY MAURA C. CICCARELLI, FREELANCE WRITER

Games

Career exploration

Digital art created from complex equations

Card and dice games

Online competitions

Virtual investing

Origami

Chess

These are just some of the ways Tower Hill math teachers in every grade bring math alive to convey ever-more-complex mathematical concepts. These can promote a love of problem-solving while they have fun doing it.

“We believe that learning math is a participation sport,” says Math Department Chair Noreen Jordan, who also teaches Upper School math. “Students are engaged and challenged in the classes and instead of sitting at a desk and doing rote work through worksheets, they absorb the information presented by conversing and collaborating about processes and applications.”

Yes, math may be difficult to learn. But, Jordan hopes that by the end of every year “most of the students feel a sense of accomplishment and understand that learning math is not about earning a grade, but it is more about building skills by process of trying and failing and trying and succeeding.”

Lower School

“In Lower School, students are building their understanding of operations,” says Michelle Coulter, who has been teaching at Tower Hill for 30 years and became a teaching and learning specialist last year to primarily support students in math.

“As a way to build fluency with the concepts of addition, subtraction, multiplication and division, we play games,” she says. “Students learn a variety of games using cards and dice, as well as engage in activities involving drawing to visually represent math facts. This helps students build their fluency and efficiency with math facts in a way that is engaging, collaborative and fun.”

Recently, after teaching a card game to a small group of second graders, one student asked when they were going to do math. “When I told him the game was our math activity for the day, he exclaimed, ‘That was math? It was fun!’”

Another popular program is Math Olympiad, a competition for grades 4-8 in the U.S. and around the world to promote problem solving, mathematical reasoning and flexible thinking, as well as fostering student’s creativity and ingenuity.

“We begin exploring Math Olympiad problems in fourth grade by encouraging students to find their unique ways to derive solutions,” says Coulter. “They often work collaboratively and share their answers to deepen their understanding of multiple methods. When students start Middle School, they enter the contest officially and work independently to solve the problems.” Coulter says she models a positive example about math by sharing her enthusiasm for the subject with them.

“I feel it’s so important for our youngest Hillers to develop confidence and a positive attitude as a foundation for their future learning,” she explains. Also, students write on whiteboards to explore and record their thinking and take risks.

“It makes math less threatening,” she says. “I constantly reinforce that it’s okay to make mistakes, which are an integral part of learning. I also feel that students become more engaged in math when they are collaborating with their peers to solve problems. Our students are encouraged to share different ways of deriving solutions.”

She adds, “I hope students come away with the understanding that there is not only one way to solve a math problem and that we can learn from the different methods shared by our classmates.”

Middle School

Making math fun helps students gain understanding of more complex math concepts, too, says Paul Mulvena, Middle School math teacher and Assistant Head of Middle School.

“Cherie Martinez’s and Kristie Campbell’s fifth and sixth grade math classes participate in the NBA Math Hoops, which is sponsored by the NBA and the Philadelphia 76ers,” she explains. “Students play a board game that incorporates math and sportsmanship along with strategy and sometimes luck.”

Throughout the year, they compete with their partners in a weekly match against other fifth and sixth grade teams, with the top two teams from each grade competing in a regional tournament. Students learn fundamental math skills along the way.

In November, the eighth grade honors algebra and geometry classes used equations to create pixel-based art that looks like block-based images on old-school arcade, computer and video game consoles.

“They worked with the algebra concept of systems of equations with two variables,” Mulvena explained. “By applying the algebraic strategies to solve linear systems, students created their own systems with specific parameters set for their solutions; students worked backward with their solutions to create these linear systems. In the creation of this project, students designed a unique pixel art image on Google spreadsheets. Using conditional formatting, each system solution is linked to the pixel art image. When solutions are entered into the appropriate cells, part of the student’s designed image appears. Plus, students also learned to utilize an equation editor application in their project.”

In sixth grade, students create a career poster, called “Math: Who Needs It.” Students research a math career of interest to them and create a poster to explain important aspects of the career in addition to how math is needed in the field.

The idea was inspired by Mulvena’s own experience as a student in school. He had interviewed his cousin who worked in construction and learned that the Pythagorean Theorem was used to calculate the dimensions of a sloped roof, properly sized beams and how much material would be needed to shingle it.

“At the time, he did not exactly remember that it was called the Pythagorean Theorem, but I felt proud to be able to connect his explanation with the theorem,” he says.

In addition to the Math Olympiad mentioned earlier, seventh and eighth graders participate in the SIGMA Math Competition, which applies their math knowledge in new ways by solving non-routine problems, as well as the online math competition called the Math League, which develops problem solving through competition. Eighth graders also take the American Math Competition (AMC 8) exam, which promotes problem-solving skills.

In addition, all Middle Schoolers can join origami and chess clubs as well as play The Stock Market Game, a virtual program organized by the University of Delaware to teach financial literacy.

Mulvena says he knew he wanted to be a teacher by second grade. Today, he operates by the concept that you need to “reach” students before you can “teach” them. He often quotes the famous Kung Fu television series line, “Patience, young grasshopper,” when kids want to zoom ahead before developing a firm foundation of math concepts.

“Math is not about just memorizing,” he notes. “Math investigates quality, structure, space and change. Understanding where each student is in their life-long journey of learning and providing the opportunities, resources and time to help them develop is critical to their growth, progress and success.”

“By having students complete the Desmos project it gives them an opportunity to apply what they know into something tangible. They get to see math in action and how it can actually create something meaningful in the moment.”

Upper School

“Math gets such a bad rap and I have tried to make it a point to provide a positive classroom experience for my students,” says Upper School math teacher Jordan. “At its essence, mathematics is the study of patterns, so I like to begin the school year with an activity that exposes students to all kinds of patterns that may not necessarily include numbers.”

This includes incorporating logic puzzles and games with visual patterns such as SET and Uzzle in class to help students develop reasoning skills while having fun.

Jordan notes that Tara Tatasciore’s classes periodically play a game called SKUNK that helps students develop a sense of how probability works.

In addition, Tatasciore and fellow teacher Nicole Keith use an online tool called Desmos, including its graphic calculator, which can do much more than the handheld calculators students usually use. The graphing projects show students how math and art are connected by asking them to create a design using mathematical equations that they have learned.

“The assignment is open ended but does have certain requirements depending upon which course the student is in,” says Tatasciore. “It enables students to blend their mathematical knowledge with their creative skills. Students gain a better understanding of how graphs behave while making beautiful art.”

Keith says she uses Desmos to help students visualize the functions they are learning.

“Desmos itself would often share images that students had created on its website, and I thought it would be interesting to have our own students take on the project,” she says. “I started in 2016 with my precalculus students. In this course, students learn conic sections, which includes the study of circles and ellipses. With this information in their back pocket it makes the Desmos project more interesting since the students can include circular shapes and not just lines and curves.”

She adds, “A lot of the really cool applications come later in mathematics when students have already decided how they feel about math. By having students complete the Desmos project it gives them an opportunity to apply what they know into something tangible. They get to see math in action and how it can actually create something meaningful in the moment. That is also why we can do the project over multiple years—the students learn and grow and can improve the complexity of their designs.”

Additionally, she says, having students apply their current knowledge to something outside of mathematical applications gives them a window into the possibilities of a math-based career.

“A lot of students often equate mathematics with engineering but have no idea what that looks like in reality or what other options there are. Math is often seen as this clinical pursuit while in reality there is a lot of creativity that is connected to the subject. Having space and time to create for the sake of creation brings a lot of our students joy and gives them a chance to see how fun math can really be,” she says.

Keith, who has been teaching algebra II, precalculus and calculus during her eight years at Tower Hill, says she’s always very upfront with her students. While mathematics can be difficult, that is actually part of the fun of learning it. She tries to balance challenging materials by helping students get through by taking smaller steps, which makes math feel achievable.

“I always try to make the classroom environment one where students feel comfortable asking questions and a place where all ideas are valued,” she says. “If a student has a different way of solving a problem, we often dive into that idea together as a class and discuss the pros and cons of the different methods. I strive to make the classroom feel like a team and where we are all working towards the same goal together.”

Math From Start To Finish

“Math is like building a tower of blocks,” notes Mulvena, who has been at Tower Hill since 2009. “Our Lower School teachers do a phenomenal job developing the foundation. In Middle School, we make sure that the foundation remains strong as we build upon it in preparation for the students’ later math studies in Upper School and beyond.”

“Our students do so much reading and writing in our humanities classes, I think it is a welcome change for them to come over to the math and science building to use a different part of their brain,” adds Jordan, who has taught math for more than three decades and has been math department chair for the last six years.

“We value careful and deep thinking in our classes—students learn to reason, think and listen to each other,” she says. “They share ideas about problem solving and are encouraged to come up with new ways to tackle problems. Presenting students with an unknown and then having them work together to arrive at a solution is valuable practice for any field or future job.”