Engaging the range of learners in understanding mathematics is one of six goals that guided the development of the curriculum. In order to achieve this goal, Investigations was based on experience from research and practice, including field-testing that involved documentation of thousands of hours in classrooms, observations of students, input from teachers, and analysis of student work. As a result, the curriculum addresses the learning needs of real students in a wide range of classrooms and communities. The investigations are carefully designed to invite all students into mathematics—girls and boys; members of diverse cultural, ethnic, and language groups; and students with a wide variety of strengths, needs, and interests.* However, the curriculum alone can only do so much. Only the teacher can understand and support the particular learning needs of a particular class of students in a particular school year.
Mathematics teaching and learning at its best is a collaboration among teachers, students, and the curriculum. Both the teacher and the curriculum contribute to this partnership in important ways. The curriculum materials provide a coherent, carefully sequenced core of mathematics content for students and supportive professional development material for teachers. Teachers are active partners in learning the curriculum well, understanding how each mathematical focus is developed, and implementing the curriculum in a way that accommodates the needs of their particular students.
In other words, modifying the curriculum with integrity requires that teachers:
- Know the curriculum. This means taking the time to understand the mathematics focus of each lesson and how the mathematical ideas build over many lessons. Learning the curriculum well means holding back the urge to change activities because they seem too easy or too difficult before trying them or seeing students’ work.
- Know the mathematics. This requires content knowledge and an understanding of the ways in which students typically interact with that content. Therefore, Investigations was designed to be a professional development tool that provides opportunities for learning about mathematics content, how students learn, and effective pedagogy. The design of the curriculum focuses on the teacher as learner as well as on the student as learner.
- Know the students. This involves observing students’ work, listening to their discourse, and developing an understanding of their mathematical ideas by analyzing what they say and do. In mathematics, as in any subject, teachers continually assess students' strengths and needs and think through how best to accommodate differences to involve all students in substantive and challenging work.
The curriculum supports teachers in using this knowledge to modify the curriculum and support the range of learners in their classroom. See Components: Range of Learners for a description of the various features aimed at helping teachers support all of the learners in her/his classroom.
One of these features – classroom cases – offers illustrations of teachers using what they know about the curriculum, the math, and their students to engage the range of learners in understanding and doing mathematics. These teacher-written cases present situations from Investigations classrooms and invite readers to grapple with what it means to support the range of learners. They focus on one of three themes—community, accommodations, or language and representation—and end with questions to consider and discuss. An example from each grade level is available for download below.
* This essay is based in large part on text found in the curriculum. See page 6 of any unit, and pages 1-2 of any Implementing Investigations.
- Kindergarten Case (Accommodations for Learning) PDF
- First Grade Case (Accommodations for Learning) PDF
- Second Grade Case (Language and Representation) PDF
- Third Grade Case (Language and Representation) PDF
- Fourth Grade Case (Language and Representation) PDF
- Fifth Grade Case (Setting Up the Math Community) PDF