The Advantages of Heterogeneous Student Groups in Math

It’s just two months into the school year, and students in my class are working in their student-led, heterogeneous learning communities. Students know these as just “learning communities.” In distress, “Leilani” stormed out of her learning community and walked up to me to ask, “Mr. Manfre, can I switch groups?” When I asked why, she proclaim​​ed, “Well, they just don’t get it!” At that moment, I realized Leilani was exactly where she was supposed to be.

Leilani had always been a high-performing student in mathematics. In previous years, she would correctly complete her assigned work, and then the teacher would “differentiate” by providing new material to accelerate her learning and avoid “holding her back.”

That approach fed into the misconception that high performance correlates to greater mathematical ability, when in fact, it’s actually just quick processing. Quick processors like Leilani thrive in an inequitable educational system bounded by tight time constraints of a class period, school day, and school year.

Providing Leilani with this sort of accelerated differentiation feeds into the fixed (and incorrect) mindset that she is smarter than her peers. In fact, the more I accelerate her learning, the more isolated her learning experiences become, narrowing her perspectives of mathematics and decreasing opportunities for her to develop conceptual understanding through discourse.

For every Leilani, there’s a “Keala,” a “low-performing” student who is only perceived this way because she’s not a quick processor. Keala needs to understand the intricacies of the whys and hows of mathematics in order to fully process it. She may also need more visuals, as it is harder for her to grasp abstract concepts. Keala’s needs would be seen as an inconvenience in a classroom that valued fluency above all.

Typical Differentiation

In many math classrooms, teachers work hard trying to meet the different needs of their students. You may see typical differentiated classrooms working with three isolated stations: (1) the Leilanis working by themselves or collaboratively on accelerated material, (2) the Kealas receiving small group differentiated instruction, and (3) the rest of the class working individually, in pairs, or in small groups on grade-level content.

The problem is, when high-performing students are placed in these homogeneous groupings, nobody has to ask (or answer) the depth questions of  “why” and “how” for multiple reasons:

• Mistakes are at a minimum, so even when there is discourse, there is much agreement over the most likely correct answer.
• Since there are fewer mistakes, students develop math anxiety, or fear of being wrong, and are less likely to ask questions that would show they don’t know.
• The teacher is often spending most of their time with the struggling low performers and not able to ask questions to challenge and extend the conceptual understanding of the high performers. This also leads to lower-performing students being conditioned as passive recipients of learning instead of active contributors to their learning environment.

What if isolated differentiation was not the solution? What if there was a way to have “differentiation through inclusivity” where students at different mathematical performance levels got their individual needs met, not through isolation, but by working together? There is.

In order to receive differentiation through inclusivity, there is an overarching core belief and three key components that must be addressed.

Core belief: All students are capable of learning mathematics through different processing times and mechanisms. Some need more time, others need alternative approaches or additional scaffolds, but all can learn math.

If we embrace this core belief, then we truly understand that people aren’t good or bad at math, just unique in how they bridge surface to deep to transfer learning. Archaic math classrooms honor and reward the quick processors and their speed in fluency over the rest; whereas contemporary math classrooms are grounded in research that values and prioritizes deep conceptual understanding, which comes from embracing the knowledge that mathematics can be learned and executed in multiple ways through many different representations.

3 Components of Differentiation Through Inclusivity

1. Heterogeneous grouping. Intentionally created heterogeneous learning environments allow students to serve as a part of the curriculum for their peers. These heterogeneous environments shift the focus from typical differentiation by product to differentiation by process with students at the center.

Productive struggle comes from the wide range of levels of learners working together on a common task and learning with and from one another. Students in heterogeneous grouping ensure diversity of ideas and opportunities for discourse around such ideas, leading to greater conceptual understanding.

2. Communicated value of heterogeneous grouping. Students need to see value in engaging in such higher-order discourse around diversity of understanding. I use “tiers of understanding” to create the personalized value for the mixed levels of learners to work together.

Students of different levels seek to work with each other for their mutual and individual benefit. It also creates a mathematics classroom culture that invites mistakes as an essential contributor to the learning experience, minimizing math anxiety.

3. Equitable scaffolds, roles, or protocols to support students in achieving excellence in heterogeneous groupings. In this case, my students were supplied with scribe protocol, learning community responsibilities, and a protocol for empathetic explanation, which helped them with the productive discourse required to navigate diversity of understanding.

Students in my class are intentionally placed in heterogeneous learning communities to provide the productive struggle that Leilani experienced when she approached me asking to switch groups.

Through months of working with her learning community, Leilani improved her communication ability to not only provide meticulous explanations but also ask inquisitive questions for her peers to articulate their thought processes, allowing her peers to serve as elements of the curriculum. As a result, conversations contained higher-order discourse, leading to a greater depth of conceptual understanding for all members of her learning community.