Introductory 2-day Institutes

Day One: Experiencing Math Workshop and Examining the Practice in the Elementary Classroom

In order to deepen their understanding of mathematics, teachers are asked to be learners in a mathematics environment where math is seen as the posing and solving of problems, the searching for patterns, and the construction of formulae, models, and strategies. We usually spend about an hour, to an hour and a half, doing a fun mathematics investigation that warms the group up and helps them see firsthand what an active math workshop is like. They also participate in a "math congress" where they share their strategies with the group. "Math congress" is an important part of "math workshop" and is much more than a "share". We model careful scaffolding to help build connections across solutions and to ensure that discussion occurs on the important mathematical ideas. The whole experience is then used for analysis and reflection and a backburner for the day is started with a list of participants' insights, questions, ponderings about the teaching and learning of mathematics.

Next we use our NSF-funded interactive CD-Rom materials showing video of exemplary MitC classrooms allowing us to "transport" participants digitally into examining math workshop in the elementary classroom. The footage is used in a very interactive way to involve participants in examining teachers and children at work. With the technology we do several pieces. One piece is on "kid watching." We analyze a group at work and discuss the mathematical strategies being used. We revisit the clip several times each time going a level deeper in order to develop participants' abilities to notice and understand the "big ideas" of mathematics that the children are struggling to develop. A second piece is on the teacher's decision-making in designing a context. A third is on planning and structuring a math congress. Participants are given sample pieces of children's work and asked to plan a congress. After discussing and debating their choices and reasons why, they examine the choice of the teacher in the digital environment and observe the congress in action.

Day Two: Developing Efficient Computation Strategies with Mini-lessons

This second day begins with an overview of what it means to calculate with number sense-how mathematicians look to the numbers first to decide on a clever strategy. We take the approach that efficient computation should be the goal of computation work, meaning that children should develop a deep sense of number, landmarks, and operations resulting in a repertoire of strategies, rather than the employment of the standard algorithm across all problems. The focus is on understanding, not simply procedures. We do several mini-lessons with participants as examples of ways to develop number sense and by way of doing this also deepen their own repertoire of strategies for computation. We also explore with them various models like the open number line, the open array, the ratio table, and the double number line, all of which can be used as tools to think with. Afterwards we analyze the choice of numbers used and how strategies were represented with these models. Once again, using the digital classroom materials with classroom footage we explore very interactively how teachers at various grade levels are doing mini-lessons. In the afternoon participants design their own mini-lessons and try them out with each other. The day ends with a general presentation on how to help parents understand these new goals.

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