3-day Landscape of Learning Intermediate Series

Day One: Examining children at work

This institute begins by examining children at work on a series of investigations and during minilessons. The NSF-funded digital materials are used to examine a multitude of strategies as real children work on given problems, to discuss developmental differences in the strategies and the big ideas underlying them, as a way to construct a developmental trajectory that can be used as a framework for designing investigations and for documenting and assessing student progress over time. Emphasis is placed with participants on the search for evidence of mathematical understanding in contrast to general (more superficial) quick interpretations. The role of teacher questioning and discourse is also examined.

Day Two: The importance of models

On the second day, attention turns to an examination of the important models related to the mathematical topic at hand. For example, if the institute is on multiplication and division, grades 3-5, the focus would be on the use of the open number line as a way to represent and support regrouping of repeated additions, the ratio table model as a way to support proportional reasoning, and the use of the array to examine the commutative, distributive, and associative properties (as well as to connect a geometric representation) for multiplication. The perspective is taken however, that the math is not in the model to be seen, but instead is only in the mind of the learner who must interpret and use the model. After examining the benefits of models, the digital environments are used to explore the emergence of them, from models of situations initially, to models used by teachers to represent students strategies in minilessons, to the eventual use of them by learners as mathematical tools for thinking. Contexts used to support the development of modeling are also examined.

Day Three: Putting it all together

On the third day participants work to complete the landscape on the topic and grade span that was the focus of the institute. Precursor ideas to other ideas and strategies are discussed and debated to determine where to place the landmark ideas, strategies and models. Sample pieces of children's work and video clips are attached as a full trajectory is completed. The trajectory is then used to examine a variety of contexts and minilessons and determine what mathematics they would support and where they would go on the trajectory. The trajectory is also used as an assessment tool. A few children in the data base on the digital environments are examined and the landscape is used to map out their developmental pathways.

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