Empirically-based hypothetical learning trajectories for fraction concepts: Products of the Learning Through Activity research program

The Measurement Approach to Rational Number (MARN) Project, a project of the ongoing Learning Through Activity (LTA) research program, produced eleven hypothetical learning trajectories (HLTs) for promoting fraction concepts. Four of these HLTs are the subject of research reports. In this article, we present the other seven HLTs We judged that the data and analyses of these seven would not separately make sufficient contributions to merit individual research reports. However, presenting these seven HLTs together was intended to meet the following goals: 1. To give a broad set of examples of HLTs developed based on the LTA theoretical framework. 2. To complete a set of HLTs that provide a comprehensive example of HLTs built on prior HLTs. 3. To make available for future research and development the full set of HLTs generated by the MARN Project. LTA researchers have focused on how learners abstract a concept through their mathematical activity and how the abstractions can be promoted. The MARN Project continued this inquiry with rigorous single-subject teaching experiments.