Remember the Fibonacci sequence? It’s a series of numbers in which each subsequent number is the sum of the previous two: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, and so on. One of the most fundamental concepts in mathematics, it is the basis for the Golden Ratio in architecture and nature, some financial markets, and is seen in the works of great composers such as Debussy and Bartok and in the novels of Dan Brown, Philip K. Dick, and Matt Reilly, among others.
Some students will be astounded to find so many Fibonacci numbers and their applications in their everyday world after just one introductory lesson from you. They will marvel at what was there all along, wondering why they had not seen them before. Other students, however, will not “tune in” so quickly and will need to study many Nautilus sea shells and pine cones before they see the sequence.
The differences between these two groups of students are many-fold: familiarity with the topic and reference points, neural development, language bias, and personal investment in school. Nevertheless, both groups of students are in your 47-minute, fifth period class, and worthy of developmentally appropriate instruction. What’s a middle grades teacher to do?
Effective middle grades teachers know that one group size rarely fits all, so they use flexible grouping based on informed decisions. To guide their decisions about grouping, they can ask themselves the following questions:
- Is this the only way to organize students for this learning? Do I always teach this way, and if so, why?
- Where in the lesson could I create opportunities for students to work in small groups?
- Would this part of the lesson be more effective as an independent or small-group activity?
- Why do I have the whole class involved in the same activity at this point in the lesson?
- Will I be able to meet the needs of all students with this grouping?
- I’ve been using a lot of [insert type of grouping here—whole class, small group, or independent work] lately. Which type of grouping should I add to the mix?
If it’s time for some flexible grouping in our lessons, we can group according to many different factors and structures, including whole class or half class, teams, small groups, partners, triads, quads, one-on-one mentoring with an adult or peer, learning centers, online wiki groups, readiness, interest, and learner profile.
Let’s define those last three, in particular.
Readiness refers to how ready students are for more complexity in their lessons. As students develop proficiency, we move them into more challenging tasks, which may mean moving into differently focused or structured groups. Students struggling to read text appropriate for third graders shouldn’t be asked to learn content by reading text written for eighth graders; students move on to negative exponents only after they understand exponents and reciprocals.
However, more complexity doesn’t mean more workload. We change the nature of the task, not the quantity of the task. We don’t give advanced students two labs to do, for instance, if the rest of the class is only doing one. Instead, we ask the advanced group to investigate something more complex than the rest of the class is investigating.
Interest refers to how we can help students learn the material in meaningful ways.
Learner profile refers to any factor that affects a student’s learning: family situation, learning preferences, specific talents, cultural background, languages spoken in the home, economic stability or instability, access to technology, repeating or skipping a grade level, reading proficiency, and so on.
As we consider grouping students, two important cognitive science principles come to mind: 1) students learn best when information makes sense and is meaningful, and 2) there are two clear steps to every learning experience: accessing the information and processing the information. While these two principles intersect, when we consider flexible grouping, it’s important that we consider them separately.
For example, in the initial “making sense” portion of a lesson, we often present information through lecture, demonstrations, videos, and assigned practice. Some students respond better to lecture than do others; some need to think individually before responding to the larger group; and some need to talk about a topic in order to understand it. Most students can learn through all three strategies but may achieve success sooner via one or more of them. We might form groups to meet these and other learning differences as students first begin to learn content.
To help students process the information into long-term memory, we may have to structure the groups differently—perhaps by interest, such as favorite sport, music group, or author. Students connect with and process the content when we help them see how it manifests in their lives: “I need to learn to read because I need to be able to read video game instruction manuals, posts on my social networking site, World of Warcraft magazines, and the rotating message signs on the front of city buses that I ride to and from school.”
Offering different analogies and cultural references based on students’ personal lives helps them remember the material and apply it in useful situations.
The research sections of the National Middle School Association website (www.nmsa.org) are full of presentations and citations about homogeneous versus heterogeneous grouping, as are the sites for other professional education organizations. In reviewing these sites and reflecting on current classroom practices, we find the wisest course is to keep classroom groups’ membership dynamic, not static. We prefer semi permeable membranes. This means that we rarely maintain the same small group for a whole grading period, let alone a whole year. We’re not afraid of temporary homogeneous grouping.
We are vigilant in our formative assessments, too. If we discover that a student’s assignment to one group is not working for him or the group, we give the student or group the tools to make it work or we move the student to another group. Kay Burke’s What to Do with the Kid Who… (Free Spirit Publishing) has helpful advice regarding these tools.
We are usually thoughtful about students’ group assignments, but sometimes we miss something or a variable doesn’t turn up in the student’s performance until he’s with the group. Revising our decisions in light of the new evidence is better than adhering stubbornly to the original groupings.
If a student believes she has been placed in a group beyond her competence level and asks to be removed, we investigate to determine if we made a mistake in the group assignment or if the student just needs a vote of confidence or an additional tool to tackle the more complex tasks. If, upon investigation, the student’s needs are better served by moving her to a slower paced, less-complex-task group, we move her.
Interestingly, she won’t balk at the re-assignment nor will she feel like she is a slow learner, going to the “dummy” group. Students crave competence, and when they don’t experience it, they shut down, looking for ways to escape. This need to escape is most commonly expressed in middle school with requests to get a drink of water, use the bathroom, or run an errand.
If a teacher has a classroom culture in which a subgroup within the class is considered the “dummy” group, it’s time to suspend the curriculum and address the issue. Every person in the classroom, even the 4.0 students, should experience what it’s like to be a complete beginner at something at least once a marking period. If students are not able to develop coping strategies for complex, difficult tasks in middle school when stakes are not so high, they won’t develop the temperament and neural pathways for handling such demands in high school, college, and the working world where the stakes are much higher. For more on this, see my “Failure Preferred, Actually” column in the February 2009 issue of Middle Ground.
We also want to make sure students do not see differences in learning rate and style as weakness. Instead, students should recognize that all of us learn at different rates and in different ways, despite the fact that most schools are not designed to respond well to those who deviate—higher, lower, laterally—from the exact norm.
Grouping for Goals
Whatever we do, all groups must be doing respectful tasks—tasks that are developmentally appropriate, not busywork. For example, we don’t tell students who can’t identify historical themes in the Constitution to simply draw pictures of what is meant by each of the first 10 Amendments. Instead, we give them the tools to perceive those historical themes. Some of these tools are more concrete, while others are more abstract, but all of them focus on intended curriculum goals.
Even schools with predominantly one culture—social, national, economic, academic—are still abundantly diverse within those cultures. Some of those students need quiet reflection while others need interaction with others; some need more practice time than others; some can see the math applications in music and some will need specific analogies to make those connections clear. With these students, flexible grouping to maximize instruction is too important to receive only occasional attention. Instead, it’s part of our weekly modus operandi.
Just like the Fibonacci sequence, re-grouping for flexible purposes weaves through much of our lives. And just like those numbers, each new learning is the sum of the previous learnings; those pairings and re-pairings matter. Orchestrated by informed, purposeful teachers, these groupings afford opportunities for student learning not to be missed.
Previously published in Middle Ground magazine, April 2010
Rick Wormeli is a long-time teacher, consultant, and author in Herndon, Virginia. E-mail: email@example.com. His latest book, Metaphors & Analogies: Power Tools for Teaching any Subject (Stenhouse), includes many contributions from NMSA’s MiddleTalk listserve.