Math for multiple intelligences

by Gretchen Buher with David J. Walbert

Most teachers come out of college knowing they need to have a concise list of rules for their classroom. I have a list of five to seven basic rules: respect adults and students, come prepared, participate appropriately, hold a high level of integrity (no lying, cheating, or stealing), and keep unnecessary items at home. I post them on day one, go over them, and enforce them. But classroom management goes far beyond a list of rules. It’s about setting the stage for learning by building a sense of community and teamwork within the basic structure the rules provide.

Learning to work together

I begin the school year by setting up the expectations for the class. My set of expectations includes rules and guidelines, rewards and consequences. Clearly communicating and implementing these expectations sets the stage for managing a classroom successfully. I have found that when I incorporate group work into my lesson, the success of my students depends on how well I’ve communicated and implemented my foundational expectations of their group work.

On the second day of school, I have the students participate in a team-building activity called "Shipwreck." I split the class into two teams and give each team a garbage bag on the ground. Each team fits every member onto its garbage bag. They can only fit by standing on one foot, so they have to hold each other on the bag. "You’re shipwrecked," I say, "your boat has capsized, and you have to flip your boat — your garbage bag — back over. But no one can get off the boat, because you’re in shark-infested waters, and if anyone steps off the bag, you have to start over."

I let them struggle with this for awhile, trying to figure out how to turn over the bag while everyone is standing on top of it. I’ll see very quickly who the leaders are in the class, who will obstruct others from accomplishing their goal, who works well together — and who not to put in a group together. Then, after ten or fifteen minutes, when they’re getting frustrated, I’ll tell them to freeze and ask them for ideas. We talk about ideas that have or haven’t worked. Most groups still have ideas they want to try, so I give them another five minutes to struggle. Usually, someone will say, "There’s no way we can do this!" Then, I point out that there’s another group right next to you! If the students work together instead of thinking of themselves as two separate teams competing against each other, they can solve the problem. If one team of students jump onto one bag — they have to really hold each other onto the bags, even climbing on each other’s backs sometimes to fit — they can turn over the empty bag, then move to the second bag and turn over the first. Problem solved!

Immediately after the activity, we discuss what we have learned as a group. This discussion is just as important as the activity itself. I ask them some specific questions: What helped your team accomplish its goal? What didn’t help? Who were the leaders in your group? Did they dictate to you, or did they allow you the opportunity to respond? Did one person do all the work? What was uncomfortable about it? How did you come to solve the problem?

Sometimes students will talk about specific people on their teams and what they did or did not do to help, and then we can talk about how to bring people back into the fold and get everyone to participate in a positive way. The discussion raises important issues of group work: is everyone participating, or is one person taking over and doing all the work? Is the group accomplishing it goal, or not? Is the group trying different ideas in order to solve the problem or are they afraid of failing or just unmotivated to work?

I conclude by saying that our approach to math is like being shipwrecked. We have to communicate our knowledge and ideas, and we have to master skills with our team. It’s uncomfortable to struggle, but that discomfort is not something we’re trying to avoid. We deliberately put ourselves in those uncomfortable situations so we can learn to overcome them. I encourage perseverance — creating strategies to solve problems is more important to me than just memorizing a formula for a test! (Memorizing a formula is a strategy, of course, but it’s not the only one.) I also tell them that because our time is so limited, it’s extremely important that we all know how to work together as a team.

Setting up small groups

The third day of school, I set up small groups based on the leadership I saw during the team building activity. For example, I will take five or six of the most vocal leaders and put them in different groups. Depending on the class size, I might not have recognized enough leaders but often I can identify potential leaders. I will also split up the students who seemed most hesitant to initiate so that each group has a mixture of viewpoints in approaching a task. For the most part, I have found groups of three to four students to be the most effective in solving problems. Groups with larger numbers are too easily distracted and it is difficult to give individual attention to each student’s progress within a large group.

As the year progresses, I vary groups by ability or a particular kind of intelligence. To determine how to set up the group, I look at the group of lessons I want them to process. Then, I try to determine which type of grouping would challenge the kids and lead them to being the most productive. In my experience, I have found that it’s important to match the lessons with the makeup of the groups. If I set up a group of visual learners to accomplish a purpose that requires other intelligences, the group can become bogged down and limited in its ability to solve the problem. In general, it seems that the more complex a problem the students have to solve, the more they benefit from diversity within the group.

Starting off slowly

At the beginning of the year, we work in small groups for short periods of time — only ten to fifteen minutes at a time. This pace allows the kids who are still getting a feel for my structure and rules to see how to manage the classroom and reinforce my expectations. It also allows for the students who are afraid of word problems to keep from feeling overwhelmed and unsuccessful. Easing the students into my problem-solving approach helps them find out how I evaluate classroom learning; they realize that independent thinking and evaluating are crucial elements. It is more important to me that a student can prove his answer than that he can simply state the correct answer to get teacher approval.

As I circulate, I’m also building relationships with the kids so they feel more invested in giving me quality work and answers. Not only do I care about them personally, I also value and reward hard work. Students who can show me solid effort, I praise, congratulate, and acknowledge individually and before the class. Other uninterested or unmotivated students receive gentle prodding from me. If this prodding is unsuccessful, I encourage the group to use some positive peer pressure to get them on board. If changes in the behavior still don’t take place, I conference with the student privately to discuss the issue causing the negative behavior and strategies to turn behavior around.

As time goes on, I increase the amount of time we spend in small groups, I increase the complexity of the tasks, and I give students less guidance. In doing this, they are encouraged to become independent thinkers, learners and workers, and they gain confidence.

Like a family

In Dream Keepers, Gloria Ladson-Billings argues that ethnic groups that succeed educationally tend to study in groups. She suggests that African American students would learn more effectively in a community environment in which everyone is responsible for the success of the group and of its members. The model is the family. If one person fails, it makes the whole family look bad, so every member of the group is responsible for making sure that every other member understands everything, participates, and gets help when they need it. Setting up this kind of family situation fosters unity in a group even when the students are working with someone they don’t particularly want to work with; they know that they’ll be held partly responsible for the success of the group.

If I start the year with a team-building exercise, the students almost always buy in to the idea of group work. Occasionally, though, a few students are reluctant to participate. If we have problems with one group, I’ll point out to them that it doesn’t seem like everyone in the group is working, and I’ll ask what they might do to involve them. Are they not being listened to, or are they choosing not to participate? For my unmotivated students, I have had to occasionally "punish" them by giving them lunch detention where the students must complete the class work on their own. Usually in this case, the students would rather not struggle by themselves and turn the behavior around. Other times, I’ve found that personality conflicts within the group were to blame. In this case, we have a "family therapy" session with me acting as mediator. We sit down to determine how to work more effectively as a group. In my experience, the threat of "family therapy" — especially when it’s during their lunch time — is unbelievably effective in correcting the problem. However, if problems still arise, small group adjustments can be made.

Sometimes, the students in the group lack confidence or are embarrassed by doing well. When this situation occurs, I pull a student aside and explain, "Here are the strengths you bring to this group. I put you in this group because you have these positive qualities, and you can be a tremendous asset." I try to build her up and give her reason to believe in herself. Then, I’ll meet with the group members to help that person participate; I’ll encourage them to see what the student has to offer and ask them to make sure to bring her into the discussion.

Constant assessment

I set up the class activities so that they are highly structured. Students have a paragraph to read and a couple of questions to answer, or a problem to interpret and solve (what do I know, what do I want to know?), not simply a list of things to compute but a variety of activities. I want to be actively involved in the student’s learning processes. So I constantly access their work by going to each group and asking them how they solved the problem. My goal is to ask each child within the group a different question. For example, I might ask one student a summary question, another student an inference question, and a question that will lead students to state the solution. If a student is unable to answer one of my questions, I give the group time to discuss possible answers before returning to conclude my verbal assessments of the group.

When I started out doing group work, I found that I could easily get stuck working exclusively with one or two groups that particularly needed help. Then, my time verbally assessing the other groups seemed rushed. I ended up setting a time limit for myself of three to four minutes per group. I’ll start with the groups that I expect will need the most help getting started. I’ll ask them, "What’s our goal?" "What am I trying to figure out?" Often the group can work more independently once they’ve gotten started. Then, I can circulate and evaluate the progress of other groups.

In three to four minutes I can ask each student in a group guided questions that I have predetermined and have a good sense of whether he or she understands. If everyone in a group can answer the questions, I make a check mark or star in my notes for each member of the group. If they don’t understand, I’ll give them a hint to try a different approach, or I’ll guide them with questions like "What do we know? Where have we heard that before?" If a student gets the wrong answer, I’ll ask if the group agrees. If they don’t, I ‘ll ask them to explain their thinking to that student, and I’ll come back a few minutes later. This way, I’m able to assess every group in a class period, usually two or three times each. Over the course of a class period, the groups may have eight to twelve problems that get progressively harder, so that different levels of students are still being challenged. I try to assess questions in chunks of three or four problems to keep students moving.

If I carry a clipboard around with me, I can keep track of every student’s progress — yes, she understands this, or no, she doesn’t, for each question — and if I need to give them grades or explain why a child receive a specific grade, I have data to refer back to as a reference. I also don’t need to collect class work every day. Daily verbal assessment reduces my paper load and also tells me how well the students are able to verbally communicate what they know. (For more about how I assess group work, see my article "Assessing the Learning Process.")

The value of group assessment

Each group decides for itself how to work, whether to tackle the problems individually and then discuss their different ideas or to work on each step as a group. But however they decide to work, I assess them as a group. Every member of the group must have an understanding of the concepts before I’ll check off on the group as a whole. I assess students this way because I feel it’s just as important to be able to communicate what you know as it is to know it. There are times when mastery of the entire skill set is an unrealistic expectation. However, it is essential that we make progress in understanding the concepts. I keep two mental expectations of mastery — one is the expectation of what will be mastered during the course of a lesson, the other what will be mastered after a skill set is revisited.

Sometimes, an advanced student will want to work alone and let the rest of the group work together, especially when he or she is not grouped by ability. While I appreciate these students’ quick-mindedness, I often require them to bring the rest of the group along with them in order to get the credit. In the process, advanced students will sometimes discover that they’re not very good at explaining what they know. They have the opportunity to develop that skill, and they’re challenged in an area where they need help. In addition, having to slow down and explain their thinking step by step can help them learn; by clarifying their thoughts for others, they come to understand them better themselves.

Wrapping up

At the end of each class period, I pull the students back together and focus on what we have learned, pulling out the major points I want them to remember from the lesson. I try to help each group master the lesson’s skills within a class period, but sometimes it is necessary to finish a second day in order for all groups to reach a common goal. Getting each group to a determined mastery point allows each group to participate in this wrap-up discussion, and everyone gains confidence because they’ve had a chance to get the problems right within the group.