The description below shows an evolution of adaptation. Initially my former teaching partner and I were fairly free to create a math program for our classroom based on our professional judgement. However, our district (along with our state) has been in the process of renewing the math curriculum. This has helped our district with some much needed changes, as it moves us from a focus on computation to a mathematical orientation.
At my building this has meant a change from the 1985 version of Addison-Wesley to the 1998 version of Everyday Math with firmer expectations as to its implementation. Unfortunately, Everyday Math is structured in such a way that it is nearly impossible to use in a multiage setting without splitting the students into grade level groups for math. Because of this, the intermediate multiage teachers at our school are implementing a math program using the ideas of Janet Banks with the Investigations math materials. Below is a short history of our math program and a description of how I am currently using the Investigations math materials.
During the 1995-1996 school year, our district used Addison-Wesley for math instruction and it was fairly easy to modify for our program. What my former teaching partner and I did was look closely at the scope and sequence, pretest the kids, place them in rough ability groups without regard to age, and then teach math to the small groups. We had one hour of math each day and six different groups with two teachers. We split these groups in two so that each of us was in charge of three groups. We were able to meet with each of our groups for half an hour on a rotating schedule. For instance: I had three groups which named themselves the Hexagons, The Polygons, and The Math Minds. On Mondays I met with the Hexagons for the first half an hour and the Polygons for the second half an hour. On Tuesdays I met with the Math Minds the first half an hour and the Hexagons the second. On Wednesdays, the Polygons first, Math Minds second. Thursdays, Hexagons first, Polygons second. On Fridays we had a slightly different schedule and I met only with the Math Minds. Thus we met with each group three times per week.
When a group was not meeting with either teacher they would be completing assignments, working on a self-paced math concepts and facts program we purchased from Joyful Noise Publications, or occasionally working on an independent learning project. Students would move back and forth between groups throughout the year as they showed mastery or the need for more practice.
During the 1996-1997 school year our district was in the process of finding/creating a new math curriculum that would be in line with the Washington State Essential Academic Learning Requirements. In our classroom we tried out the Everyday Math materials. We liked it mathematically but couldn't see an easy way to "multiage it." So for that year Heidi and I split the class by grade level. Our hope was that once we better understood the program we would be able to modify it to better fit our multiage structure.
In the spring of 1997 our building adopted the Everyday Math curriculum materials. We used it, as was our obligation, but although we tried to modify it to meet the structure of our classroom, we couldn't seem to do it without upsetting the integrity of the program. During our 1997 Summer Institute our school was able to spend three full days orientating ourselves to and working with the program. During that time Heidi and I found that the explorations, projects, and games portions of Everyday Math were easily multiagable. The lessons however seemed to be much more difficult to modify. So our plan for the following year was to teach the Everyday Math lessons by grade level for three to four days per week, set up the explorations and games (which we also used in conjunction with the lessons) as centers to be worked on once a week, and incoporate the Everyday Math projects into our project time on Fridays. This turned out to be harder than we thought and it wasn't long before we abandoned this plan and simply taught the program as it was meant to be used, in a single grade fashion.
Shortly after this we learned that I would be teaching a self-contained intermediate multiage class (grades 3, 4, and 5). At this point I decided to work with my administrators to get permission to use the Investigations math materials in conjunction with Janet Banks' plan for implementing math in a multiage setting (the Investigations materials had been adopted by our building to supplement Everyday Math). During the summer of 1998, after numerous committee and teacher meetings, we received approval from our school board for the multiage classrooms in our district to use the Investigations math materials as our primary source for math instruction.
I now group math instruction in units by math strands (ie., mathematical thinking, the number system, operations, fractions/decimals, geometry, data and statistics, measurement, and chance and probability). Math continuums have been put together for each strand that are based on the Investigations scope and sequence and reflect our district's scope and sequence (which is based on the Washington State Essential Academic Learning Requirements). Pretests are created for each of these strands that reflect those continuums. I teach a particular math strand during a set time period to everyone in my class. For instance all of the 3/4/5 students will be working on the number system during September, in October and November they will be working with operations. At the start of each unit all of the students will take the pretest for that strand. Based on their test results and where they fall along the continuum for that strand, they are put into small instructional groups which I meet with on a regular basis. While I am meeting with these small somewhat homogeneous groups (ability, not age), students who are not meeting with me are working on strand-related activities and assignments at an assigned table. Ideally these tables have students from each age and will represent a heterogeneous grouping of students based on the math strand's continuum. In that way they will be able to discuss, model, and help each other with their individual math work. Of course these different groups will change each time we change strands. Each year I will teach the same strands at about the same times. Students who were with me the previous year will be given a pretest for the strand and will hopefully be at a different place along the continuum.
The table below shows which Investigations units I use for each strand.
Continuums and Pretests
Note: In addition to Investigations, I use materials from Everyday Mathematics, Marilyn Burns, Joyful Noise, and Addison-Wesley to supplement.
Below are some math links you may wish to explore.