Learning Trajectory
When planning what to do in a lesson, do you take into account how the learning will take place?
Then term hypothetical learning trajectory has been used by Marti Simon (1995) and other authors to describe the assumptions made by a teacher when planning a sequence of lessons.
Main Section
Although different learners are likely to develop in different ways, when planning a lesson it is necessary to consider a sequence of tasks. The question then arises as to what an appropriate order for those tasks might be. A hypothetical learning trajectory is the sequential development and enrichment offered to learners as a result of working on the sequence of tasks and interacting with their teacher. It is an anticipated possible path of concept development and technique improvement.
One of the positive features of this construct is that it reminds you when planning that the whole point is that learners actually develop. Each choice made, each task offered to learners is subject to a “so-what?” or a then-what? question to which the hypothetical learning trajectory is a response.
It is important to remember that the imagined trajectory is hypothetical, and that many learners will not follow it. Research by Brenda Denvir & Margaret Brown (1986, 1986a) and showed that learners often come away from a lesson having learned something quite different to what the teacher thought the lesson was about. Learners are will-possessing organisms, not mechanical robots, so what they make of their experiences and activity is highly idiosyncratic. [see also teaching takes place in time].
Any attempt to describe a hypothetical learning trajectory is likely to involve some use of Vygotsky’s notion of a zone of proximal development.
Probes & Prompts
What developments do you expect learners to make during work on the next topic?
Taking Action
When working with colleagues on planning a sequence of lessons, try to articluate to each other some of the possible hypothetical learning trajectories you anticipate. This could provide a focus for further discussion arising from observations of what happens.
Case Studies
Research Sources
Simon, M. A. (1995). Reconstructing Mathematics Pedagogy from a Constructivist Perspective. Journal for Research in Mathematics Education, 26(2),p114-145.
Simon, M. A., & Tzur, R. (1999). Explicating the Teacher's Perspective From the Researcher's Perspectives: Generating Accounts of mathematics teachers' practice. Journal for Research in Mathematics Education, 30(3), p252-264.
Denvir, B. and Brown, M. 1986. Understanding number concepts in low attaining 7–9 year-olds. Educational Studies in Mathematics, 17 (1), p15–36.
Denvir, B. and Brown, M. 1986a. Understanding number concepts in low attaining 7–9 year-olds: Part II. Educational Studies in Mathematics, 17 (2), p143–64.
See Also
Categories
Constructs, Curriculum, Obstacles, Professional Development