Learning Trajectories

Written by Kristen Tripet

The idea of ‘learning trajectories’ has gained prominence in the teaching of mathematics over recent years. Trajectories present a progression of expected student development in a specific mathematical domain. While this may sound similar to other approaches, learning trajectories do differ significantly from more traditional forms of instructional design that rely predominantly on hindsight planning—where the expert, for example a teacher or curriculum writer, looks at the endpoint of learning and breaks the content down into small steps. This creates a learning hierarchy that makes sense to the expert, but not necessarily one that makes sense to the learner.

Learning trajectories do the reverse: they plan instruction with insight. Using classroom experimentation, researchers study the development of students’ thinking as they work on a set of instructional tasks focused on a specific learning goal. The documentation of this trajectory forms a framework of reference for teachers to use in their planning of instruction in the classroom.

A learning trajectory consists of:

  1. a clear mathematical goal
  2. a developmental progression highlighting students’ thinking as they work towards the mathematical goal
  3. instructional tasks that support students’ learning.

A key benefit of learning trajectories is that they are student centred. That is, they place students’ mathematical thinking at the forefront. The learning trajectory framework provides teachers with possible student thinking and reasoning that will emerge through tasks, enabling them to plan responses and questioning. The tasks provided illustrate the types of representations, questions and activity that support students to build deep understanding. Teachers can modify tasks to meet the needs of the learners in their classroom.

reSolve: Maths by Inquiry will be using research-based learning trajectories to inform the next phase of developing classroom resources. Using these trajectories, the team will work with teachers and academics across Australia to create lessons that support the development of students’ thinking in particular mathematical topics. The tasks in each topic will provide support for teachers in key ‘hot-spots’, whether these are areas of difficulty for students or where limited resources are currently available. Each topic will have lessons that span a number of year levels.

We are greatly looking forward to accessing the expertise of Australian researchers and harnessing the creativity and experience of teachers from all states and territories across the country.