In a recent article published in the Journal of Urban Mathematics Education, Myers, Sztajn, Wilson, and Edgington seek to address a common criticism of the Learning Trajectories (LT) perspective, particularly as it pertains to mathematics education.
In contrast to a perspective that would see concepts discretely, and that would assess student mastery according to the extent that they either got them right or got them wrong, the LT perspective views concepts sequentially, and in such a way that the mastery of one builds upon prior knowledge with the aim of achieving some clearly defined objective. LT approach views teaching as involving goals, sequences of topics that are necessary to go through in order to achieve those goals, and activities that effectively facilitate topic mastery.
A criticism of the LT perspective, however, is that (as the metaphor itself anticipates) the process it describes if far too linear, and that it tends to ignore other important factors that contribute to successful learning. By reducing learning strictly to sequences of concepts to be mastered, the LT perspective ignores other socio-cultural factors that function as preconditions to learning. In short, Learning Trajectories Based Instruction (LTBI) may be viewed as reductive in so far as it ignores fundamental inequalities that differentially encourage or impede the learning process.
Myers et al. argue that LTBI is not incompatible with a more equity-conscious approach to pedagogy. They argue that a sensitivity to issues of diversity is in fact latent within their existing model, and use Gutiérrez’s equity framework (2007) as an opportunity to identify several ways in which LTBI in mathematics education might also be sensitive to questions of social justice. It is obvious that students cannot learn unless they have access to the right resources, but Myers et al. embrace a wider notion of access that acknowledges that social and cultural factors, in addition to economic and geographical ones, are constitutive of a student’s learning environment. They argue that, in viewing students, not as ’empty vessels,’ but as people who enter into a learning situation with a preexisting wealth of knowledge and values, teachers are better able to facilitate learning along mathematical trajectories to the extend that those trajectories are located with respect to other larger life trajectories. This perspective resonates very strongly with that of John Dewey, who famously viewed learning as only possible to the extent that it could be connected with a person’s history (what they already know and value), present needs, and goals for the future. It also resonates strongly with what we know from rhetoric in general, that people will only listen if they think that what is being said is important to them.