How do we encourage referent-based mathematical argumentation without encouraging students to request that examples accompany otherwise viable arguments? Assessment concerns are explored and discussed.
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. First-year data indicate that the LAMP lessons, with the emphasis on foundations with referents, may inadvertently encourage students to critique otherwise viable arguments for not including a referent, such as an example(s). This session provides an overview of the LAMP lessons and assessments and a summary of the task-based interview and assessment data collected as the project progressed. A summary of the outcome data is presented to illustrate some favorable and unintentional outcomes, such as students critiquing otherwise viable arguments for not having a referent. This data is presented in the form of student written work and videos of students writing and critiquing arguments. Participants are asked to review select LAMP materials and student data, including videos of students constructing and critiquing arguments, and offer suggestions for improving lessons or assessments, or both. The goal is to improve students’ abilities to critique arguments and to improve the LAMP project’s ability to distinguish between naïve empiricism and personal preferences, which may include desires for an example alongside any argument, including those that are already viable.