Remember when math class used to be fun? Yeah, me neither. When I was a kid, math class consisted of completing worksheets with problems that had no apparent real-world relevance, learning algorithms straight from a textbook and memorizing the multiplication table and other figures. Sure, it was challenging, and I learned enough to get through my SATs, but it wasn’t a subject where I felt like I had any creative leeway or could have fun. And it certainly didn’t lead to a career that involved math.
What if math class really was fun when you were growing up? What if it was a subject you looked forward to or was even your favorite one? Would it have changed your outlook during those formative school years and maybe even your career path?
At Roland Park Country School, an independent school for girls in grades K-12, the mathematics department introduced an innovative curriculum three years ago known as “integrated math” to develop mathematicians who can transfer their skills to solve new and complicated problems, rather than simply memorizing one way of solving equations. Integrated math unites analytical and creative thinking, which helps students become more engaged and enthusiastic about the subject. Instead of teaching one math subject at a time, such as fractions or pre-algebra, the curriculum across the entire school focuses on problem-solving, critical thinking and connecting and building upon different math concepts and drawing from prior knowledge to encourage deeper learning. By teaching creative and flexible approaches to solving problems, students gain a deeper understanding of these math concepts and how they are intertwined, which also expands their future possibilities in math and STEM fields.
What Integrated Math Looks (and Sounds) Like
So what does this look like in the classroom? In the Lower School (kindergarten through 5th grade), students are assigned a group activity at the beginning of class. The teachers ask students thought-provoking questions throughout these exercises about what they are noticing, why it is important and how it relates to math. Multiplication tables are still memorized, but it’s made fun by incorporating music. In a recent third grade class, the students sang the multiples of four in their best “opera” and “squeaky” voices. Students are also encouraged to share their thoughts with their classmates. Throughout it all, they are learning important math concepts including prime and composite numbers, values and equations, and they are having a blast doing it. Listen to a group of 5th graders work through a math problem:
The 6th and 7th graders follow a student-centered, problem-based learning curriculum with rich investigations and problems that mesh well with Lower School program and prepare them for the next curriculum they will start in 8th grade. Students work in small groups or independently on investigations that introduce big questions and key mathematical concepts that build upon each other. The teacher facilitates the learning process and students collaborate with each other to solve real-life problems, which keeps them engaged and enthusiastic throughout class.
In grades 8 through 11, there are no textbooks. Everyone works from spiral-bound books filled with word problems. And instead of students sitting at separate desks facing the front of the class and the teacher, the desks are all arranged in a big square or oval to face each other and the teacher sits with the students. This is known as the Harkness method, which was established at the private boarding school Phillips Exeter Academy in the 1930s to encourage collaboration and respect for all voices in the classroom.
Throughout class, the students take on the role as leaders, sometimes in teams, to write their homework problems on large white boards throughout the room and explain the reasoning they used to solve them. Then the class and teacher discuss the methods and key concepts used and challenge each other to think about the answer from different perspectives.
Much of the work throughout every grade is visual with students sharing their work on white boards and projectors throughout the classroom. Students are often encouraged to draw pictures that will help them solve problems and often, the questions posed have a visual component. Throughout class, there are many “a ha!” moments and gasps, lots of excited chatter and teamwork among students and the teacher before and during class. In a recent fourth grade class, every hand shot up to answer a question. Students are not expected to always get the right answer. Making mistakes is encouraged and best effort is expected. Teachers are also available outside of class to help students, as needed.
The Struggle is Real
Make no mistake, this math program is rigorous. At every level, the teachers encourage the students to think more deeply about what they are learning, explain their reasoning and consider other possible approaches. In one recent ninth grade honors math class at RPCS, they covered everything from the Pythagorean theorem (geometry) to quadratic formulas (algebra) in just 70 minutes. One honors student explained, “I can’t imagine going back to a regular math program, but in the beginning, I really struggled and didn’t like it at all. With my teacher’s help, I have become very confident in math and my grades have improved a lot.”
This ability to persist even when something is difficult is a crucial part of integrated math and a fundamental principle at Roland Park Country School. “A productive struggle is the goal,” explains Carla Spawn-van Berkum, Assistant Head of School for Academics. “The very best learning happens when things are hard.”
Research backs this up. A few RPCS teachers have taken classes with Jo Boaler, a professor of mathematics education at Stanford University and a pioneer in the field. Boaler is also the faculty director of youcubed, a program that offers teachers, parents and students resources to excite students about math. According to Boaler, researchers who studied high achievers found that their brains aren’t any different. Instead, “People who achieved the most were those who were always pushing at the edge of their understanding,” she explained on youcubed.com. “Making mistakes, correcting them, making more mistakes. They weren’t getting work correct all the time, they were always struggling.” By setting high targets and trying different ways to reach them shows that there are no limits to what people can learn.
And Michael Giardi, a middle school math teacher in Los Angeles, California and creator of MathHooks.com, a tool for math teachers to encourage rigorous thinking among their students, has a similar philosophy. When students grapple with math, they gain a deeper understanding of the problem, which helps the mathematical concepts click and results in more enjoyable learning. “Allowing students the opportunity to practice inquiry before instruction makes math come alive,” Giardi wrote in a recent article, “Promoting Productive Struggle in Math.”
Preparing the Next Generation of STEM Leaders
At Roland Park Country School, the faculty has seen firsthand how well the students respond to this type of learning. By facing and overcoming their struggles, this curriculum empowers the students to feel increasingly confident about their mathematical abilities. “My favorite class is math because there are so many different ways to solve problems,” said a 5th grader at a recent visiting day.
An integrated math curriculum encourages students to have a growth mindset, become risk takers as they dive into problems, be creative and persistent and revel in the challenge of not knowing how to solve a problem, but figuring out a path to an answer. And most importantly, it helps girls believe in their own abilities to excel in math. Plus…it’s fun!
This article was written by Abbey Pulcinella and is sponsored by Roland Park Country School as part of our Cool School Partners series. Read more about the Roland Park Country School in our Independent Schools Directory or call them at 410-323-5500. Photos provided by Roland Park Country School.