Question: I want to include all students in class discussions, but some of my special education students tune out during meetings. What can I do to make them feel included?
Answer: The Accessible Math Project (NSF HRD--0090070) is working with teachers to learn more about how to successfully include students with special needs in Investigations math classrooms. One of the most common questions discussed by these teachers is how to facilitate meetings in ways that include all students, whatever the range of skills and needs.
Students with special needs or those who are struggling with mathematics need time to practice doing and thinking mathematics at their own level, yet they also need to understand the tasks at hand and listen to what their classmates are thinking. Balancing the needs of the range of students and providing structures to help them learn are challenges in teaching Investigations.
We offer here some of what we have learned from observing and talking with experienced Investigations teachers about facilitating inclusive mathematics meetings. Much of what we describe is appropriate for the whole class; only a few of the teachers' recommendations are specific to students with learning disabilities.
First and foremost, create classroom community
Meetings that are truly inclusive depend on the attitudes and behaviors of the students toward one another. Teachers build inclusive classroom communities from the beginning of the school year, letting students know how they expect them to support one another as learners. Comfortable classroom communities are based on respect and acceptance of differences.
Students with special needs, both those who have difficulty keeping still as well as those who are hesitant to join in, feel safer in classroom communities with clear routines and expectations for behavior. These are classrooms where the teacher spends little time disciplining students, because a reminder is enough. For example, we have heard teachers say "We don't laugh at people in this classroom" or "You can lie down as long as you can pay attention," or "Make sure you listen to Michael. His question may be your question." Humor is a natural part of the classroom and can serve to make a point and acknowledge differences among people without a heavy hand. Mistakes are seen as chances to learn and the teacher, as well as the students, is comfortable not knowing. In a class discussion when a student remarked that the teacher had made a mistake illustrating a fraction, the teacher replied with a smile, "We all have our strengths and weaknesses; you are more organized than I am."
As part of setting guidelines for how students treat one another in your class, prepare students in how they will behave during meeting so that brief reminders are all that is needed for respectful behavior.
Support all students to be actively involved
When asking questions, provide wait time twice. First, allow enough time for all students to form an answer. Write the question as well as saying it. Tell students you are waiting and will not call on the first person with their hand up. Some teachers ask students to show only a thumb up when they are ready to answer a question. Others ask students to jot down their answers for her to see before discussing the problem. When you call on a student, allow enough time for the student to fully explain his or her solution. Expect other students to stay quiet without their hands up.
After you have introduced a game or posed a problem, ask two or three students to explain the game or put the story problem into their own words. Wait to ask a hesitant student until a classmate has rephrased the problem, so that the student has another chance to listen before saying it in his or her own way.
Provide extra support or alternative activity
If you know that the introduction to a new activity will take a long time, plan with a paraprofessional or student teacher to sit near the students who are likely to need extra support.
An even better way to keep students actively part of the group is to teach them the activity or game in advance outside of class time so that these students will be prepared and perhaps ready to help with the introduction to the activity.
If you have no assistant, arrange with students who tend to get restless or have difficulty paying attention a signal that you can give to suggest they move away from the group and start work. Some teachers provide children who have difficulty sitting still and making sense of what the group is doing with other work they can do while the class meets, and then gives them enough of an introduction so they can join in the day's activity.
THE PURPOSES OF MEETINGS
These teachers use meetings for
- introducing an activity
- doing mathematics together
- discussing students' strategies
- whole class reporting/checking work
1. Introducing an activity
The challenge of introducing an activity to the whole class at one time is to make sure that all students understand the task. Present the problem in several different ways. Provide materials for students to work with when useful (such as pattern blocks or cubes or numerals cards). Write problems (and solutions) on chart paper or the blackboard, or use an overhead projector, as well as speaking.
In the following example, the teacher anticipated what her second grade students might need in order to do the day's activity successfully. In this task one student makes a shape with geo-blocks, and then hides it from view. The partner must create a copy of the design by listening to the designer's directions.
Ms. K explains that students will work in partners and take turns making designs with 8 or fewer blocks. Then, their partner will try to reproduce it without looking. She makes a design in front of her on the floor and places a screen so the students cannot see it. She calls on students to ask her questions about her design that can be answered with either "Yes" or "No". After they ask a few questions, she asks the students to remind her of the rules. She writes the rules on the board as students suggest them.
Ms. K also writes words that students mention during the conversation: flat, standing up, looks like, north, above, on top, almost connecting, below, left, right. Ms. K draws two shapes on the board, one above the other. She writes "above" next to the higher one and "below" next to the lower one.
Ms. K: At the end I will ask what words were helpful. Take turns. You are going to need a tub of blocks and a basket for a divider. Today you will work with your blue list partners. (The teacher has made and posted several different arrangements of partners. She tells students which list to use today.)
As children settle with their partners at tables, Ms. K uses one pair to demonstrate to the class how to sit across from your partner and how to place the divider. The paraprofessional sits near a pair of students who she thinks may need extra help. Ms. K moves around the room observing different pairs of students.
Spend only enough time introducing an activity so that most of the students understand what they are to do and can start work. Make yourself available to students who need more help getting started, by inviting them to continue to work with you.
The following is an excerpt from an introduction to subtraction problems for a group of students who have been struggling in Ms. S's first grade class. She knows that these students need extra help interpreting story problems. She has set a task for her other students that they can do independently with a student teacher overseeing their work.
Ms. S: I am telling you a new story today. When I went on vacation I took a bag, and I decided to put in 5 pencils. I thought I might want to write letters. But 3 pencils fell out. Who remembers what happened in the story?
Ms. S. knew that these students had difficulty figuring out the action of the problem and would not have been able to start working on solving word problems independently without a concrete introduction. The students in her group then tried a different pencil problem on their own.
2. Doing mathematics together
Doing some mathematics during a meeting allows the teacher to see how students approach the problem and gives students an immediate way to engage with the mathematics. For some kinds of problems, teachers provide an easier and a harder problem for students to choose between; for others, they write a problem with several steps and expect that all students will be able to complete the first step and some will do more.
What follows is an example of a longer meeting in which students do and discuss some multiplication before going off to work in small groups. On the previous day Ms. G's class worked on the problem 14 x 6 in groups of three, but did not discuss their work in the whole group. Some students were using repeated addition. Others were trying to use the traditional multiplication algorithm, but did not know what number to carry, after starting with 6 x 4. Today Ms. G. poses a different problem for the students to do during the whole group meeting.
On the meeting rug, Ms. G has put out a whiteboard with a marker and a piece of paper towel on it for each student. The students come in from another class, choose one of the boards, and sit on the rug where the board is placed. Three students sit on chairs at the edge of the rug.
3. Discussing students' strategies
When you are planning a meeting for students to discuss their problem-solving procedures, decide what the main ideas are that you would like to focus on, or the main strategies you expect to see or would like to introduce. Instead of calling on volunteers to share strategies, it can be useful to observe students at work and pick out two or three examples of solution strategies that you would like students to discuss.
Some teachers provide whiteboards, clipboards, or student sheets to write on. Students as well as the teacher can look at one another's solutions and point out what they observe. You can ask a few of the students or student groups to write their procedures on the board or on large paper and post them in front of the room before the start the meeting so that everyone can see them.
In this discussion Ms. G's goal is to focus on whether students seem to be making sense of what they are doing and finding the correct answer reasonably efficiently. Because the students have written on whiteboards, they can show their work when she calls on them. She decided to call on Donald because she wanted him to show his strategy of adding the tens and then the ones.
Ms. G: I'm asking Donald to go first because I've never seen that way. When I give you another problem you might want to take a risk and try Donald's way.
To identify certain strategies, it is helpful to give them names (such as "breaking up into tens and ones") and ask who else did the problem in the same way. Here a student volunteered that her strategy was similar.
Corinne: I did the problem that way. Two tens made 20 the other two tens made 40 and 4 times 7 is 28; 40 plus 28 is 68.
Whenever you think any of the students who have difficulty will be able to present their solution, ask them to show it as one of the first because it might be both more accessible and less complex than other methods you want to highlight. Or, instead of calling on the student to explain his or her method, you can summarize what you noticed and, with the student's help, write his or her procedure on chart paper. You might invite a child who has difficulty with the math to demonstrate the solution another child has written or explained.
When Ms. G called on Michael, she had seen on his white board that he had a successful strategy. She did not know he also had then used his answer to do a "number of the day" problem. Michael often does work that is similar to what the class did a day or two previously instead of staying with the work that the class is currently doing. She asks him his solution to 4 x 17.
Ms. G: Do you want to share your method Michael?
By her questioning Ms. G was able to help Michael talk about the strategy he used that connected to the task that the class is working on.
Sometimes it is useful to ask a student to describe a strategy that didn't work very well and discuss what the student might do differently.
Carlos: I did four 17 times. [Had written fewer than 17 fours in a column.] I knew that wasn't the answer so I added 3 more. I counted it, and I knew it wasn't the answer.
Because doing the multiplication and sharing strategies took longer than usual, there is little time left for a work period. Ms. G distributes sheets with two more problems.
Ms. G: Some of you shared ways. Now I want you to work in groups to work on another problem. Teach each other your ways. We don't have a lot of time. You have about 15 minutes to do the problem and share.
4. Whole class reporting/checking work
It is not necessary to always end an activity with sharing strategies. Many days it is valuable to use the whole math period for students to work and end the work period without a concluding discussion. At other times, use a shorter form of whole class reporting, where everyone checks his or her own work. Here are some examples:
"Everyone look at their multiple tower to see what the tenth number is. Read some out. Notice that it ends with 0. Does anyone have an earlier number that ends in zero? What did you multiply to get that number?"
"We have discussed different ways to do subtraction problems. Who used a 100 chart today? Who counted up? Who counted backwards from the larger number? Did anyone use an open number line? Did anyone try a method that is new for them?"
You might ask students who worked together to check with another group that they agree on a list of solutions (e.g. for problems such as all the fractions less than one half or the percent equivalents for the eighths or all the ways to take a total of 8 peas or carrots).
TIPS FOR RUNNING SUCCESSFUL MEETINGS:
The advice teachers we work with give most consistently is to focus each meeting on learning mathematics or preparing to do a mathematics activity.
1. Keep meetings short and focused.
Keep the important mathematics in the lesson in mind when planning meetings. This can focus the discussions to meet the needs of the class as a whole as well as the needs of the students who are struggling with mathematics.
2. Set specific guidelines and expectations for behavior during meetings.
In many primary grade classrooms, students gather on a rug for the class meeting and then return to their places or choose places for work-time. In fourth and fifth grade classrooms, students often stay at their own desks for meetings. Some teachers vary the setting, with children staying at their desks when the meeting will be short, and gathering together when a longer time is needed.
To facilitate a smooth transition to meeting on the rug, some teachers assign students places to sit on the rug, changing them every month or so. Others place circles, mats, or white boards to clearly mark the places available for students to sit. Others allow students to sit wherever they want in a circle as long they can see the teacher and all of the other students. They might remind students to make a good choice about sitting where they will be able to pay attention. Some students will sit, others kneel, and others may find they are able to sit more quietly in a chair. The teacher might remind students about "listening behavior" during the course of a meeting.
3. Prepare materials and working groups ahead of time.
Establish routines so that students can get right to work independently at the end of meetings Then you can then work with a small group instead of taking time to help the class settle in and get started.
Have all materials easily accessible to students. In some classrooms, students keep generic materials such as pencils, crayons, erasers, scissors, rulers, and paste in baskets in the middle of each table or group of desks. Materials particular to one activity or subject can be prepared and placed in boxes or trays for each group of students who will work together to fetch as they begin work. If math materials are stored in a particular area of the room, it is easy for students to readily access what they need when they need it. With student help, teachers can distribute student books or papers quickly. It is useful to provide a few extra copies in case a student wants to start over and to make some copies of additional work for students to do quietly when they have extra time. One folder might hold work to provide practice and review, and another to provide more challenging problems.
Establish procedures for choosing or assigning partners in advance so that you don't take time away from doing mathematics. Some teachers keep students with the same partner for a period of time; some alternate the way they pair students, according to the type of activity; others let students choose partners with some adult "guidance" about what makes a suitable partner.
4. Provide Extra Help
Students with learning disabilities need to be included in the regular class meetings and activities in ways that they will be successful. They also need time to work in a small group with a teacher. In an example above, we saw how Ms. S. worked with a group of first grade students during class time. Teachers of older students may let students decide to work with her to get started on an activity, limiting this help to 3 to 5 students each day so that it becomes a privilege.
In the best of circumstances, a special education teacher or paraprofessional skilled in working with Investigations math can work with the teacher during classes and also offer extra help to students outside of class. Teachers can use these extra sessions to
- make the mathematics more explicit to the students;
- provide guided practice and suggest practice students can do at home;
- introduce an activity or game before it is introduced to the whole class;
- rehearse with students how they can write out and explain their methods during class meetings.
Because class discussions are an important part of building a mathematical community, the range of learners in a classroom needs to be taken into account in planning these meetings and sharing sessions, and encouraging participation. However, students who have difficulty listening to instruction in a large group are not likely to learn new mathematics through these discussions. Often students who are struggling with mathematics need extra time to practice mathematics instead of participating in whole group activities.
Keeping the discussions brief and focused and the students actively engaged will result in more time spent on building mathematical understanding and developing efficient ways to solve problems for all learners.
Cornelia Tierney and Judy Storeygard,
Accessible Mathematics Project, TERC