Themes
Multiage Thematic
Instruction: Interdependence
| Management | Flexible Groups |
| Developmentally Appropriate Practices | Problem Solving Activities |
| Student-Centered Classroom | Other Math Programs |
The underlying issues which I faced when I implemented my own math instruction within a multi-age context are numerous. When I discuss the flexible groupings that occur in my multi-age classroom and how concepts are introduced to the whole group, I am often asked to explain what I mean. At one time I was able to produce a flow chart explaining my method of "grouping" or flexible grouping strategies.
FIRST:
I begin a new concept within a strand (whole numbers, rational numbers, probability, measurement etc.) with one or two weeks of concrete experiences, building understanding, and informal assessment to gauge students ability to learn, understand, and transfer. I assess their ability to move from the concrete to the abstract. Manipulatives tend to confuse the students who think abstractly, but they need them in order to understand the mathematical concept. These students help the students who are developing understanding at any given time.
I cover all concepts I will teach within the strand before I teach the students in small groups. I also determine the MENU activities at this time.
SECOND:
I then give a pretest which also helps them to focus on what they are going to learn. This pretest addresses the skills and concepts in the Curriculum. After doing this, my groups are formed. Groups are flexible so a student can work in cooperative groups on open-ended problem solving activities from the menu, or they can work with me in a heterogeneous group to hear how other students solved the same problem. The students may also work on a specific skill with students who need the same skill.
The menu contains skills and concepts relating to the strand and other strands we have studied. I level the activities in the menu from initial, to developing, and extending. The first menu item is Problem of the Day. The entire class works in cooperative groups to solve the problem. Nine items follow. The first three are initial concepts that all students can do. The next three items are developing concepts and become a little more challenging. The last three items are EXTENDING ACTIVITIES which build on the first six. I use this type of menu when I am facilitating the learning or working with small heterogeneous groups of students on specific concepts or skills.
I use an initial menu when I address the specific needs of the older students and the skills within the district's mandated curriculum. The initial menu contains the initial understandings of a concept. The rest of the students can work through the menu independently. When I meet the needs of the younger students, a developing menu is posted for the rest of the students. The developing menu contains skills and concepts which build upon each other and develop the student's understanding of the concept.
Each menu lasts about two weeks and I keep a continuum to reinforce and review concepts within each. I created a very basic math continuum which coincides with the district's curriculum. The continuum starts with initial mathematical understandings.
The menu is a classroom learning environment where children have a number of activities or investigations to complete by a given date. Usually tasks are posted around the room, but I post them on a long sheet of lined tag board. The students choose their partners, for their small groups, and work on activities. Some students choose to work alone. Students keep their work in a folder. The students and I developed a rubric together. When they finish the menu they attach the rubric to their work and turn it in to me. Students also like to post their problem solving activities on the bulletin board in the hallway.
Explaining my groups is difficult because I don't have rotating groups. They are flexible and constantly changing. I sometimes call small homogeneous groups to work on specific skills, or I may go to them while they are working on an open-ended problem solving activity. Sometimes students form their own groups and want me to teach a specific skill because they believe they are ready to learn it. My groups depend on what I am teaching and what the students want to learn.
CLASSROOM GROUPING (COOPERATIVE GROUPS FOR WHOLE GROUP LESSONS)
My tables are numbered 1-8. Every two weeks students choose a number and sit at the corresponding table. These are their cooperative groups for whole group lessons and problem of the day.
Whole group Assessment--Pretests, observations, interviews, journals and open-ended problems.
BEGINNING A STRAND/CONCEPT: PLACE VALUE, MULTIPLICATION, ETC.
I teach whole group (cooperative groups) with a concrete, manipulative approach, to build understanding and assess informally. I notice students who can think abstractly and students who need more concrete materials to solve the problems. All concepts in the strand are covered and I do not focus on individual skills in the curriculum at this time. I take one to two weeks for this assessment depending on the strand.
Concept development Concrete (Object-Mental Image-Sound-Symbol )
For a different perspective see Debbie Hackett's Math Program.
An Eclectic Math Program Bob Goodwin
Carmi Scheller Planning for Intermediate Level Math
Mathematics in the Multi-age Classroom by Janet Caudill Banks
Mathematics in the Primary Classroom by Kitty Ward