Understanding trajectories

Thinking about the start and the finish

The first thing you’ll notice when you begin trying to make the descriptions of the entry and exit levels is that you’re not just talking about one thing.  A mechanical engineer will advance their mathematics, mechanics, communication, design skills and more during their study: that is, their education is made of more than one thread of development, more than one type of skill.  In Compass, we call these threads trajectories, and they’re one of the fundamental parts of our method of curriculum design.

Trajectories are themes, threads, specific developments of ability which change throughout a programme of study.  They do not necessarily represent a theme of subject matter, but may have contributions throughout many of the papers taken in a programme.  Trajectories are characterised by a beginning point (the students’ abilities at entry to the programme) and an end point (the students’ abilities at graduation), and this development is contributed to in a meaningful way by the papers in the programme.

Actions for programme planners: 1 Make a list of the broadest and most important skills and abilities you want students to develop through the programme.  These are the big buckets, the broad brushes, the generalities.  These define your trajectories.

The second thing you’ll notice about your trajectories is that after defining the big bucket above, they probably describe quite different kinds of development and quite different kinds of skills from one another.  For example, there are two important trajectories in Engineering Science: programming or computation and mathematics and modelling.  I’ll explain these below.

The first difference is in the starting points themselves: When students come into an engineering programme they must have a certain level of maths ability already – after all, they’ve seen maths every year of their schooling up until this point!  But we don’t assume anything about their programming abilities.  Some students may have done some prior to entry, but since it’s not a requirement, we have no choice but to start from scratch when teaching it.  In maths, students can already apply their skills to problems, and perhaps even analyse situations using them.  In programming, they have as yet no reliable knowledge or understanding at all.

The second difference is in the kind of development which happens:  In programming students start by learning the basics of syntax and logic and gaining basic knowledge and understanding.  Later on, they will apply their skills and eventually use them to create new simple computer programs.  In maths, they will probably still be required to analyse situations, it’s just that as they advance, the situations will become more complicated and the analyses more difficult.  At this point we realise that we need two different ways of describing the progress of the students, and for this we introduce two different learning taxonomies, Bloom’s and STRIP, explained below.

Bloom’s taxonomy* [1. A substantial revision from 2001 is presented in Anderson, L. W. & Krathwohl, D.R., et al (2001) A taxonomy for learning, teaching and assessing: A revision of Bloom’s taxonomy of educational objectives. New York: Longman.] describes six different kinds of cognitive ability ranked according to their sophistication.  These levels are:

  1. Knowledge: students can remember or recite information
  2. Comprehension: students can understand and explain what they know
  3. Application: students can apply what they have learnt to new situations
  4. Analysis: students can make meaningful conclusions or connections from what they have learnt
  5. Synthesis: students can design and create new works
  6. Evaluation: students can critique, justify, and redesign new and existing works

* Bloom’s Taxonomy really has three domains: cognitive, affective, and psycho-motor.  We’ll concentrate here on the cognitive domain only, but still call it “Bloom’s” for short. 

In the maths example above, students remain in the same Bloom’s level throughout their studies.  They do not design or create new mathematics, it just gets harder and more complicated.  Our second taxonomy represents the addition of this complexity and relationship.

The SOLO Taxonomy (Structure of Observed Learning Outcomes) [2. Evaluating the Quality of Learning: The SOLO Taxonomy (New York: Academic Press, 1982] was designed by John Biggs and Kevin Collis and was first used to analyse student writing output.  We have taken the basic principle, but have adapted it to describe the kinds of tasks students will encounter (as opposed to the outcomes they will display).  It is not so much the Structure of Observed Learning Outcomes as the STructure and Relationships in Problem Solving, or STRIP.

The SOLO Taxonomy is reinterpreted into the STRIP taxonomy thus:

  1. Pre-structural: There is no understanding needed, only disconnected information
  2. Uni-structural: There is one relevant aspect to be considered at a time
  3. Multi-structural: More than one relevant aspect must be taken into account
  4. Relational: The connections or relationships between the many variables or aspects of the problem become more important than any aspect in isolation
  5. Extended abstract: The student must take a step into the unknown by predicting or hypothesising based on their previous analyses and understanding.

We can now use our two taxonomies to draw the diagram below, which shows development of sophistication (Bloom’s taxonomy) on the horizontal axis, and development of complexity (STRIP taxonomy) on the vertical. Our two example trajectories of maths and programming have been plotted too, and we can see straight away that the kinds of underlying cognitive development required to successfully navigate each is quite different from the other.

bloom strip

Of course, the maths and programming trajectories were chosen to make this point.  In reality you may have much more parallel trajectories, and it should be remembered that this is not an exact science – we’re only looking for general trends at this stage.

Actions for programme planners: 2 
For each of your trajectories, estimate the position on the diagram in which the entry and graduation points sit, and sketch them.
Now you’re ready to enter your trajectories into Compass, should you so choose.  Please see the guides for help with creating a new programme or creating new trajectories.

Our next step is to make our trajectories a bit more manageable by creating some milestones along the way.