"Mathematics teaching and learning at its best is a collaboration among teachers, students, and the curriculum. … [Teachers] are … active partner[s] in this … partnership, and the curriculum must support [their] complex job by providing information about mathematics content and student learning. From the beginning, our intention in developing Investigations has been to create a professional development tool for teachers—a tool that provides opportunities for learning about mathematics content, how students learn, and effective pedagogy. Our design focuses as much on the teacher as learner as on the student as learner." (Implementing Investigations, pp. 1-2.)
The Investigations curriculum was designed to be a tool for professional development. Below are several broadly sketched examples of professional development, along with suggestions of features of the curriculum to highlight.
A Unit Workshop. Teacherscome together as a grade to plan to teach a particular unit. They get an overview of the mathematical ideas and expectations of the unit. They work through several of the critical activities, games, and discussions in the unit, and consider how selected features highlight the mathematics and help teachers support the range of learners in their classrooms.
- Mathematics in This Unit
- Assessment in This Unit
- The text of a session/activity/discussion
- Teacher Notes/Dialogue Boxes
An Assessment Workshop. Teachers at one (or more) grades explore the features that support teachers in assessing and supporting students’ learning.
- Assessment in This Unit
- Observing Students at Work (a section that appears in each Session)
- Sessions that contain formal assessments
- Assessment Checklists
- Assessment Teacher Notes (which include analysis of student work in relation to the benchmark/s)
Participants then use these features to analyze a set of student work.
A Workshop on a Particular Strand or Topic. Teachers come together to think about a specific strand (e.g. 2D geometry or fractions) or topic or issue (e.g. facilitating class discussions, differentiation, making Math Workshop work, fluency, or review and practice).
- Implementing Investigations includes K-5 Teacher Notes (e.g. "Discussing Mathematical Ideas" or "Computational Fluency and Place Value") and classroom cases about teaching the range of learners.
- Curriculum Features describes how the curriculum supports the range of learners, provides review and practice, and emphasizes early algebra.
- Curriculum in the Classroom includes essays about making such features work (e.g. class discussions, differentiation, Math Workshop, review and practice).
- Curriculum by Math Content provides documents that lay out the big ideas in each strand, K through 5.
Working with Individuals or Small Groups. The curriculum is a powerful tool for a leader who is working with indivudal teachers, or with a grade level during their common planning time. Looking closely at a Session before teaching it can help teachers: think about the mathematical focus of the lesson and of any discussions in it; prepare any needed materials and plan for any logistical challenges; consider the questions to be thinking about while observing students at work; and predict how the range of learners are likely to respond to the Session and plan accordingly. The unit also supports reflection after the lesson. Teachers can compare student ideas/work samples with those in the text; they can read more about a particular idea some students are struggling with and get ideas about how to work with those students. Consider a story from a math staff developer:
"I arrived to facilitate a grade level meeting, ready to discuss recent happenings in teachers' classrooms. It turned out that no one had done the activity in the unit that asked students to write the numbers as high as they could on adding machine tape; they all thought it was too easy and unnecessary. We looked at the Session to see the mathematics the activity focused on (the math focus points) and what it might tell them about their students (the Observing Students at Work), and they all agreed to try it before the next meeting. When they did they were astounded at how engaged students were, and at how much they were able to learn about what students did (and did not yet) understand about the counting sequence."
Working with a Whole Staff. Some schools use part of staff meetings to discuss Teacher Notes, to look at a piece of student work, or to do some math together. Because of concerns about review and practice, one principal set aside 10 mintues of each staff meeting to highlight the Classroom Routines and Ten-Minute Math Activities—a critical but often overlooked component of the curriculum. Teachers rotated the responsibility of leading the math activity with their colleagues, and discussion focused on the review and practice embedded in the activity, and how it could be tailored to specific content.
"The use of curriculum materials as a core for professional development provides a direct link between teacher enhancement and what actually happens in the classroom. Professional development of this sort has two advantages: (a) the teachers leave the professional development experience with a concrete unit (or units) of instruction -- a way to begin implementing what they have learned, and (b) the materials themselves continue to provide information and support to teachers as they teach. They serve as a catalyst for engaging teachers in thinking about children's mathematical thinking -- a way of continuing the professional development experience." (Russell, 1997.)