Using Investigations in a Multiage Classroom

This month's spotlight article summarizes a discussion on multi-age classrooms held at the Investigations User's Conference in Fitchburg, Massachusetts on October 21, 2000. This discussion was led by Karen Schweitzer of Williamsburg Public Schools (MA), Katie Bloomfield of Shutesbury Elementary School (MA) and TERC, and Lucy Wittenberg, formerly of Fayerweather Street School (Cambridge, MA) and now of TERC. Among the three of us, we represent nearly 30 years of experience in teaching multi-age classrooms, ranging from Kindergarten to 4th grade. We are also all long-time users of Investigations.

Our aim in this conversation was to talk about some of the challenges faced by a teacher who is trying to implement a math curriculum that is essentially designed for single grades in a classroom which has more than one grade. (Although this usually means two consecutive grades, in this particular group, several 3-grade spans were represented.) We also wanted to share ideas and suggestions for how to make it work, agreeing that in spite of the challenges, it seems important to do so. In the course of the discussion, three key issues emerged:

  1. How do you use the Investigations curriculum to structure a yearlong sequence of units and activities that have coherence?
  2. How do you organize and manage a multi-age classroom to make the best use of the curriculum?
  3. How do you keep track of what students are learning when there is a wide range of mathematical abilities and understanding, as well as a variety of activities taking place in the classroom? In conjunction with that, how do you meet the needs of all students?

To address the first issue, a number of models and structures were discussed. Some examples were:

  • To organize the year around content strands, and to match units from both grades that address the same strand, choosing comparable activities from each
  • To use Choice Time regularly, so that children can be working on activities at their own level simultaneously
  • To use Ten Minute Math activities as a regular classroom routine that can involve students at a variety of levels
  • To make use of other personnel (classroom aides, interns, special needs teachers) to run more than one group in the classroom, making it more possible to use the curriculum intact
  • To make different decisions about structures based on the mathematical content -- this came up when many of us agreed that it seems hardest to combine two grades during number units, but easier during data and geometry units

A key point in this part of the discussion was that regardless of the content, the unit, or the structure, it's essential that we as teachers begin with having clear mathematical goals for all of our students. In order to be able to choose activities and investigations that will move each child along in developing important mathematical ideas and skills, we need to be able to articulate what those ideas and skills are.

We spent the most time brainstorming and sharing ways to accomplish what was laid out in the first structure mentioned above, that of matching units around carefully selected content strands. One example was offered from a small multi-age private school that is focusing on this issue this year; their plan for the year is presented below.

Content Strands for the Village School, Royalston, Massachusetts (A work in progress!)

Measurement (September/October)

Focus on:

  • Length (Gr. 1-6)
  • Weight (Gr. 1/2/3)
  • Volume (Gr. 4/5/6)

Units:

  • Bigger, Taller, Heavier, Smaller (Gr. 1)
  • How Long? How Far? (Gr. 2)
  • From Paces to Feet (Gr. 3)
  • Measurement Benchmarks (Gr. 5)

Number Sense and the Number System (November/December)

Focus on:

Gr. 1/2/3:

  • Visual images of number
  • Counting and grouping
  • Tens
  • One hundred
  • Addition and subtraction: combining and comparing numbers

Units:

  • Building Number Sense (Gr. 1)
  • Coins, Coupons, & Combinations (Gr. 2)
  • Mathematical Thinking at Grade 3 (Gr. 3)
  • Things That Come in Groups (Gr. 3)

Gr. 4/5/6:

  • Numbers in the hundreds
  • 1000 and 10,000
  • Factors and multiples
  • Addition and subtraction with landmarks

Units:

  • Arrays and Shares (Gr. 4)
  • Landmarks in the Thousands (Gr. 4)
  • Mathematical Thinking at Grade 5 (Gr. 5)

Data (January)

Computation and Operations (February/March)

Geometry and Fractions (April/May/June)

The second issue we discussed, which was about organizational and management practices, centered on Choice Time. One teacher offered that she limits the number of choices so that she can get to more groups of students while they're working without having her own focus be too scattered. Another teacher shared a Choice Time "menu" that she uses, which helps her not only keep track of the activities students are choosing, but allows for quick note-taking about how each child is handling the activity. She included the following indicators that could be commented on:

  • Task completed
  • Student followed directions
  • Work is accurate
  • Student demonstrated understanding of the concept
  • Student was able to take the activity further

Several teachers make use of math logs or journals, so that there is a record of children's work on Choice Time activities to collect and look back on.

On the last issue, about keeping track of students' learning, a number of teachers felt that "gathering evidence" in some way is essential. Having student work to look at becomes especially important when it is not always possible to observe every child during work time. In terms of observing and interacting with children while they're working, we talked about how to "get to kids in meaningful ways." One suggestion was to choose one or two things to focus on and look for while circulating, and to plan what those will be ahead of time based on the mathematical goals.

Finally, it should be noted that throughout this conversation, we kept returning to the idea of what it means to build a mathematical community in our classrooms, where math is both integrated and whole in much the same way that we strive to have language arts be. This was clearly a group of teachers that both believe in the benefits of a multi-age setting for children, and want the best mathematics for their students.

Katie Bloomfield, Shutesbury Elementary School, MA, and TERC
December 2000

This information was reprinted with permission of CESAME, Northeastern Univ., and the Educational Alliance, Brown University.