Algebra

The LAMP project has developed a sequence of lessons in a hypothetical learning trajectory that targets students’ ability to write viable arguments in algebraic contexts. Most of the lessons encourage students to produce a referent (e.g., variable expression or equation, generic example, diagram) as the foundation of their argument. Students come to the lessons with a predisposition for example production in support of their claims and to augment arguments.

Algebraic habits of mind, at the core of five of the Standards for Mathematical Practice, become both a potent and appealing intervention for at-risk algebra students and a solid prevention-model middle-school course either to accelerate algebra or to ensure success in a later algebra course. The session focuses on the habits of mind in that context, in related professional development work that addresses the Standards for Mathematical Practices, and on assessment of algebraic habits of mind in teachers.

Over a period of five years the SmartGraphs project developed HTML5 software for teaching and learning STEM subjects that make use of line graphs and scatter plots. SmartGraphs activities help students understand the “story” represented by a graph. The project created dozens of activities for algebra, physical science, and other STEM subjects, as well as an authoring system allowing non-computer-programmers to create and disseminate free online activities.

In Assessing Secondary Teachers’ Algebraic Habits of Mind, the project team is developing tools to study the following questions: What are the mathematical habits of mind (MHoM) that secondary teachers use, how do they use them, and how can we measure them?

In this session, presenters share a paper-and-pencil assessment being developed to measure how teachers use MHoM when they do mathematics for themselves. The presenters also share classroom video and a preliminary framework for examining MHoM in teaching practice.