What is the best grouping method that teachers can use if students have different abilities?

Imagine you have a group of 30 children who want to play soccer. You would like to divide them into two teams, so they can practice their skills and learn from their coaches to become better players.

But what is the most effective way for them to improve: Should you group the children according to skill level, with all of the most skilled players in one group and the rest of the players in the other group? Or, should you divide them into two equal teams by talent and skill?

For a fresh approach to this age-old question in grouping theory, a researcher from the University of Rochester, along with his childhood friend, an education professor at the University of Nevada, Las Vegas, turned to math.

“The selection and grouping of individuals for training purposes is extremely common in our society,” says Chad Heatwole, a professor of neurology at the University of Rochester Medical Center and the director of Rochester’s Center for Health + Technology (CHeT). “There is a historic and ongoing rigorous debate regarding the best way to group students for the purpose of instruction.”

In a paper published in the journal Educational Practice and Theory, the research team—which also includes Peter Wiens, an associate professor of teaching and learning at the University of Nevada, Las Vegas, and Christine Zizzi, a director at CHeT—developed, for the first time, a mathematical approach to grouping. The approach compares different grouping methods, selecting the optimal way to group individuals for teacher-led instruction. The research has broad implications in education, as well as in economics, music, medicine, and sports.

“Our solution was to look at this through a purely mathematical lens, evaluating for the greatest good of the entire sample,” Heatwole says. “To our knowledge, this novel mathematical approach has never been described or utilized in this way.”

Two approaches in grouping theory

According to global grouping theory—the study of how the selection of individuals into groups affects group members’ learning and performance—there are two common ways to group individuals:

• A like-skill tiered grouping strategy where individuals of similar aptitude are grouped together; one group has considerably more skill than the other group. Picture classroom reading groups, where the more advanced readers are placed in one group and the less advanced readers in another group.
• A cross-sectional grouping strategy where equal groups are formed, composed of individuals of varied aptitudes; all groups have near-equal skill. Think of two soccer teams, each equally composed of individuals who have played soccer before and individuals who have never played.

To evaluate these two common grouping methods, the researchers used mathematical principles and equations. For their analysis, they began with a number of assumptions, including: multiple groups would be formed; the individuals involved would have different skill levels; an optimal teaching environment would be one in which a student is taught at a level that matches his or her skill level; and the optimal grouping system would maximize the collective benefit for all students.

Using this novel approach, they found that like-skilled tiered grouping is better than cross-sectional or random grouping, when the end goal is improving learning for all individuals.

“We showed that, mathematically speaking, grouping individuals with similar skill levels maximizes the total learning of all individuals collectively,” Heatwole says. “If one puts like-skilled students together, instructors can teach at a level that is not too advanced or trivial for the students and optimize the overall learning of all students collectively regardless of the group.”

Economics is at the core of the approach, which also confirms that small groups, with a higher teacher-to-student ratio, are the most beneficial for optimal learning.

‘This is what the math shows’

There are, of course, caveats to the rule. The researchers’ approach assumes that the end goal is to obtain the most collective benefit for everyone. If the end goal was different—for instance, if the goal was to generate one Olympic athlete at the cost of all other athletic trainees—the conclusion and optimal approach may be different.

“In this latter case, you would design the coaching and train the other players for the benefit or growth of one player,” Heatwole says. “It might mean no one else benefits, while one person benefits to the highest degree. But that’s not how our approach was designed.”

Instead, the approach takes a “how do we raise everyone” view, he says. “How can we set up a teaching situation where all of the students benefit the most?”

Heatwole recognizes the researchers’ conclusion may be controversial, but he says the approach illustrates how math can offer an unbiased way to solve everyday problems.

“That’s the beautiful part of this,” he says. “We’re just laying down the facts and saying these are the assumptions, this is the mathematical approach, and this is what the math shows. This is a practical example of how math and science can help solve age-old questions and facilitate the learning, growth, and potential of all parties.”

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Tags: Center for Health and Technology, Chad Heatwole, Department of Neurology, featured-post, medical center, research finding

Category: Society & Culture

When it comes to addressing a wide range of skills and abilities in your classroom, there is no one-size-fits-all solution. As a teacher, you have to tailor your lesson plan to different learning styles, student backgrounds and a variety of other factors.  

If this sounds like a daunting challenge, Eugenia Mora-Flores, EdD, has some reassuring guidance for you. Mora-Flores is the chair of the Master of Arts in Teaching (MAT) program at USC Rossier.  

(Prepare to make a difference in the classroom.)

As a Professor of Clinical Education, former K–12 teacher, author and consultant to K–12 schools across the country, here is her expert advice on how to educate students of varying skills and abilities in your classroom.

Use differentiation  

Differentiation is the process of making education accessible for all students. It’s a personalized approach to teaching that addresses individual learning needs rather than using one strategy to address everyone.  

Additionally, differentiation is a useful tool for promoting equity in the classroom. It not only accounts for different learning styles, but student backgrounds and experiences as well.

Use differentiation to accommodate visual, aural and verbal learners, gifted students and students with moderate disabilities—all while acknowledging the unique cultural perspectives of historically marginalized students.

Differentiate at every phase of the lesson plan

Differentiated instruction means using “a range of strategies to communicate the same information in a lesson,” said Mora-Flores.

Lesson plans are typically structured in phases. “In each phase of the lesson, there may be opportunities to accommodate [different] needs. [But we don’t want] teachers to think they need to create 15 different lessons.”

Here are some common phases with examples of accompanying differentiation strategies:  

The introductory phase

In the introductory phase of a lesson, you may want to use visuals to recap the previous lesson, while asking a higher-level question to engage gifted learners. You can also break students into groups to discuss prior learning.  

The research/Inquiry phase

In the research phase of the lesson, you can offer a variety of resources for students to learn more about a subject. By providing different modalities such as articles, podcasts, videos, models, experimentation opportunities etc., you ensure that everyone is able to connect with the topic.  

The demonstration phase

Use think-alouds (i.e. ask questions and discuss how to understand the content that you’re reading) to demonstrate how to acquire comprehension skills.

The practice/application phase

As students work on their own, you can address them individually. Support them by prompting their thinking and guiding them through challenges.

Explore other instructional strategies

Differentiation is a broad term that encompasses many different instructional strategies. In order to address a wide range of skills and abilities in your classroom, explore different tactics under the umbrella of differentiation to find out what works for you and your students.

Creating peer interaction groups for students can be effective. Whether it’s partnerships, small or large groups, each has its own unique benefits. Switching partners or groups within group discussions can also help keep perspectives fresh.  

For students who require support developing their academic language, teachers can use language tools such as sentence frames and key academic vocabulary words, as well as providing opportunities to talk to their neighbors or table mates to rehearse the language.

“We also have strategies that help students organize their thinking,” Mora-Flores added. “Graphic organizers [help students] figure out just how to organize the range of information that’s coming in.”  

Consider intentional grouping  

Intentional grouping is when teachers organize students by common interests, backgrounds, or other criteria.  

For example, students who demonstrate an interest in pursuing a topic at an advanced level or perhaps students with varying academic ability, can work together to tackle a specific question from your lesson plan. Through collaboration, they use their shared interests or attributes to better engage with the material as individuals.

Take a holistic view of students’ needs

It’s important to consider a wide variety of factors that affect students’ ability to learn. Mora-Flores adds that teachers should “look beyond formal identifications of students in our classrooms to really think about students as individuals.”

Here are a few important formal (and less formal) categories of students whose needs you should plan to accommodate:

• English language learners.
• Students with special needs. (This is a broad term—make sure you identify the particular need and plan accordingly.)
• Gifted and advanced learners.
• Students who prefer collaborative spaces.
• Independent workers.
• Home and family backgrounds.

Addressing diversity requires thorough planning

All students bring a range of cultural and social experiences and assets to build upon at school. To ensure that your classroom is equitable for everyone, first reflect on class subject matter as a whole.  

For example, if you’re tasked with teaching American history, compare the range of diversity in the United States versus the European perspective of your textbook. Does it represent the experiences and history of the students in your class?

Then, once you’re organizing your lesson plan, determine how to engage students about equity and diversity. Allow them to have critical dialogue with each other so that they can understand different perspectives.

Collaboration enhances learning for everyone

Collaboration is a key tool to addressing a wide range of skills and abilities in the classroom. “The opportunity to hear something from a different perspective helps us understand the bigger picture of what we’re studying,” said Mora-Flores.

Additionally, collaboration can have the following benefits for students with varying needs:

• Self-reflection. Hearing about others’ experiences can motivate them to refine their point of view.
• Exchange of language. Hearing peers articulate their ideas can help students develop their academic language, and ability to share their own thoughts with a range of audiences.
• Students feel valued. Collaboration makes students feel like they belong to a community of learners.
• Increased empathy. Understanding different experiences helps students empathize with their peers.

A Master of Arts in Teaching empowers you to support more students  

While there are other paths to earning your teaching credential, aspiring teachers can build an enhanced set of skills at an accelerated pace through a master of arts in teaching program.  

For example, USC Rossier’s MAT program prepares you to meet teaching profession standards, as well as standards for supplemental certifications. You acquire the knowledge to teach in a general education classroom, and can choose to pursue an Education Specialist Credential, California Bilingual Authorization for Spanish, or Gifted Education Certificate.

With your enhanced preparation, you’ll be equipped to address more student needs in your classroom once you start teaching.

Ready to help all students succeed?  

Become a Teacher