He sits at his desk, hands over his head, a sheet of paper in front of him. On the sheet are math problems unlike anything he’s done in class, leaving him unsure and frustrated on how to continue.

This student isn’t alone. Nationwide, math scores plummeted after the pandemic, dropping 7 percent in 2022. Studies done by the National Assessment of Educational Progress and the Education Recovery Scorecard show that math continues to stay at lower levels compared to pre-pandemic numbers in the majority of the US. However, they also show that there is progress being made in many districts towards reaching higher math proficiency.

The progress is in large part due to the adoption of different teaching methods — ones that focus on conceptualization rather than memorization. Teachers promote tools such as manipulatives, like multiplication blocks or fake money, to help visualize math and to learn how to solve problems.  These new methods are a part of a movement emphasizing understanding in math education that initially spiked in the 90s. However, a key difference between the current movement and the movement that stretched from the 80s to 90s is the research behind it.

“(These methods now) have their own set of research findings on how how to best foster learning for students confronting complex problems, them collaborating with each other, them using authentic kind of modeling meaningful to them, to their communities, to their lives, them creating products that they can showcase and revise,” Chair and Professor in the Department of Teaching and Learning at Southern Methodist University Candace Walkington said.

According to Walkington, another difference comes from what the courses aim to prepare the students for. The traditional teaching, focused on memorization and following the basics, is geared towards preparing students to be efficient workers in their future. The methods focused on concept understanding, however, are more poised to be creative thinkers and entrepreneurs.

Though there are many benefits to the new methods, there are also several obstacles in implementing them into existing curriculums, often causing educators to stay away from the unfamiliar. 

“People will try the conceptual understanding approach and get frustrated with it after a short time, and then they fall back to traditional instruction. You know what their memorization, what they’re familiar with, what they perceive has always worked, even though, if you look at the evidence, it hasn’t really always worked,” Walkington said.

In the Dallas Independent School District, a new system of math teaching, called Eureka Math, was implemented in 2023 as a part of a state-wide effort to improve math testing scores. Eureka aims to help students better understand math concepts through collaborative work, exploration of concepts, and modeling problems by connecting to real life. 

The goal of math teachers in the Lower School is to give their students a strong education. Like the Eureka math curriculum and other initiatives to improve math proficiency, the lower school teachers focus on getting the students to truly understand mathematical concepts instead of memorizing them, and tools like manipulatives are used in the classroom to help with this understanding.

“We take (the students) through lots of different ways to do the same problem, and I emphasize that we can be flexible in our thinking and we have different methods and I just am building their toolkit so that they can see the math,” fourth grade math teacher Lee-Ann Graham said. “A lot of that is using manipulatives and using models.”

Math teachers in the lower school teach from a set of books called GO Math!, a K-6 math curriculum aligned with Common Core standards. These textbooks were adopted into the lower school math curriculum in 2012, and as they continue to be improved, students at St. Mark’s learn from the most updated ones. To ensure academic rigor, students are taught from the books marked for one grade level higher. One of the biggest reasons these textbooks are used is because teachers find that they are structured in a way that is very conducive to learning.

“In our GO Math! textbook, each day we start with an essential question (regarding) what they should be able to do by the time that lesson is done, and then we review a tiny bit, then we do a model and draw,” first grade math teacher Teri Broom said. “None of what we do in our lessons ever is rote.”

By combining unique teaching methods with a strong learning structure provided by a rigorous curriculum, the teachers help lower school students build a strong foundation in math that not only helps them perform well now but also prepares them for higher level mathematics later on.

“I would have loved to have been taught this way when I was growing up because when I was growing up, it was just ‘Do this,’” Graham said. “There was no understanding about why you were doing anything. And so now as a teacher teaching the Common Core and the different, deeper ways to get a conceptual understanding, I would have understood this a ton better. It is really wonderful the way that math is taught these days.”

However, not everything is based on the textbook. The math teachers often go beyond the book and enrich the learning experience of the students by offering special activities, like deriving the value of pi on Pi Day, March 14, or an after school “math club” to help  students with more specialized instruction. To give the students a challenge, the math teachers sometimes give the students puzzles or tests like the Continental Mathematics League (CML) test.

In order to create an environment conducive to learning, lower school math teachers try to make the classroom a place where students are comfortable with making mistakes. For teachers like Graham, one of the most valuable things students can learn from her class is the lesson of not being afraid to make mistakes.

“I also want (my students) to learn that this is a safe place to take a risk and make a mistake,” Graham said. “That’s the culture that I’m trying to build here because I want their confidence in their math abilities to go sky high and for them to be able to try different things, and sometimes students can be very subdued if they don’t feel like they have a safe place to ask questions.”

Ultimately, the goal of lower school math teachers and the math program as a whole is to help already talented students attain a high level of mathematics mastery based on a strong understanding of fundamental concepts.