my team and i first started thinking about intuitions and learning around May 2011, as we were trying to deconstruct with teachers on the Six Learnings programme their observations of students who had gone through our curriculum since 2009.

just a little over three years later, we successfully published our book on Disciplinary Intuitions.

through God’s grace alone, our work has continued to grow and evolve.

another three years have since passed as i write this, and i feel it is a good time to pause and reflect upon what we have learnt thus far.

with the benefit of hindsight, i believe what has driven me all these years has been a commitment to help teachers have a clearer understanding of where their students are coming from.

too often, we as teachers have been guilty of either falling in to the empty jug paradigm, or, of thinking of learner misconceptions as unimportant and something to be over-written as efficaciously as possible, or, of not being cognisant of the differences in how experts and novices frame disciplinary knowledge in the first place (see, for example, Roth & Roychoudhury, 1993).

to some extent, curriculum frameworks such as Teaching for Understanding and Understanding by Design have tried to encourage teachers to address learner misconceptions.

our team feels that more can be done, because we feel that addressing learner misconceptions is only the tip of the iceberg, and - congruent with the Chinese proverb of ba cao chu gen (if you want to pull up the grass, you must take the roots out) - we see learner intuitions as undergirding the conceptions that learners bring to the learning environment.

as a working definition, we see intuitions as the phenomenological bases which influence behaviour and decision-making.

the problem with trying to address intuitions, of course, is that they are - by definition - tacit.

put another way, the difference between magma and lava is that once magma breaches the surface of the earth, it is termed lava.

likewise, it might be argued that once intuitions are surfaced and made ‘explicit’, they cease to be intuitions.

thus, it is difficult or philosophically impossible to interrogate learners as to what their intuitions are :-)

further, at the risk of lapsing in to stereotype, in many learning environments across East Asia, students may be reluctant to share with authority figures what they truly believe or feel, instead preferring to second-guess what their teachers might be wishing them to say.

over the years, as we have dialogued with and reflected with teachers in Singapore and further afield, we would like to believe we have come up with a handful of curriculum designs which give teachers an insight as to learner intuitions, in a variety of disciplinary domains.

our first example is from geography.

the diagram below shows part of a river basin terraformed by a student, within an immersive environment.

in the diagram, it can be seen that the student has terraformed a meandering channel and an ox-bow lake. all looks well, and congruent with content from the textbook.

upon closer inspection, however, it becomes evident that although the student has recalled from the textbook his / her knowledge of ox-bow lakes and has attempted to apply that knowledge by terraforming one here, the student has not fully understood the hydrological processes which lead to the formation of such lakes in the first place. i will not say more lest i give the game away, because it’s good that we each get our thinking caps on :-) suffice to say that it is quite possible for students - be they from East Asia or otherwise - to reproduce word-for-word content (including descriptions of hydrological processes) from the textbook, even under examination conditions, and yet come away with an inaccurate understanding of what they are writing about. such students will of course get tripped up by twists in the questions, but - by that time - it will often be ‘too late’.

best to catch their misconceptions early, by designing environments in which their nascent and emerging intuitions are still malleable.

our second example is from the subject known as ‘design and technology’ in the Singapore syllabus.

one of the problems faced by teachers is how to help students bridge between two-dimensional representations vis-a-vis three-dimensional objects.

in the diagram below, a student is tasked to sketch simple three-dimensional primitives as they are progressively distorted in shape.

it can be seen that from this subsequent diagram that even though the task appeared to be a straightforward reproduction of an on-screen rendition to the sheet of paper, the work of the hand did not quite match up with what the eyes would have been seeing.

darn those pesky intuitions, again :-)

our third example is from analog electrical circuits.

we were approached by a colleague from our university’s School of Electrical and Electronic Engineering to help him address the problem of understanding why his first-year undergraduates could solve circuit diagrams during paper-based assessments, yet were unable to correctly articulate the reasons why.

helping novices understand the principles of electrical current flow has been a perennial bugbear in electrical engineering courses. one of the common ways to approach the problem has been to use metaphors for the flow of current. such methods have been useful but are not without their own conceptual inaccuracies.

after much dialogue with our colleague, we came up with an open-ended learning environment within OpenSim which was deliberately designed not to resemble anything remotely similar to canonical representations.

this was because of our repeated observations that when presented with forms of assessment resembling canonical representations, many novices perform ‘to the test’, with the consequence that their performance does not give teachers accurate understandings of what the novices truly believe or intuit.

teachers are thus unable to design adequate intervention strategies.

the diagram below is a representation of an electrical circuit designed by a student.

the representation is designed as the learner-as-avatar walks around the learning environment, quite literally charting his or her own path. Our Chart-a-Path environment affords the learner latitude in circuit design, while at the same time leveraging Jim Gee’s understandings of projective identity through embodied cognition.

the preceding diagram depicts a simple series circuit. no annotations or colourings were made by the student to demarcate where the resistors would be in this circuit design despite having two ‘troughs’. Though there are visible change in elevation (translated to voltage in this metaphoric activity), it is unclear if the student actually understands the implications of the design, especially given the fact that while the yellow portion of the design suggests an increase in voltage of three units, the tiles are still level.

our final example is from music.

taking a leaf from our preceding case study, we asked ourselves how novices are often introduced to musical composition.

very often - just as is the case in electrical engineering education - the answer was: through canonical representation; greatly simplified - yes - nevertheless still canonical representation.

even so-called ‘gamified’ or playful approaches - such as the use of immersive environments - did not truly seek to acknowledge that novices have very different starting points from experts in canon. for example, although Minecraft has been used in music education, its use has thus far been limited to the creation within the environment of facsimiles of ‘real-world’ instruments, such as keyboards.

with the help of one our interns, we realised that Minecraft - through the affordances of ‘note blocks’ and ‘redstone’ - afforded learners some truly playful ways to approach the creation of tones and simple musical compositions, in ways which bore little resemblance to established canon. we have termed this approach to music composition Redstone Jammin’.

the diagram below is a plan view of a redstone circuit constructed in Redstone Jammin', designed by a student with a formal background in music education.

the student’s construction looks unremarkable, until it is played.

it turns out that what the student has constructed is a circuit for the first few bars of Beethoven’s Für Elise - which, in traditional canonical representation, is depicted thus:

to sum up, it has been a remarkable journey over the years. i am heartened to note that the recent articulation by the Ministry of Education of the Singapore Teaching Practice has - as one of its key components - ‘understanding students and learning’.

through the use of examples from the natural sciences as well as the arts and humanities, i have tried to advance the argument in this treatise that the intuitions that learners bring to their learning environments are important, and that they are myriad in form.

just as significantly, i have tried to suggest ways in which learning environments might be designed to surface such intuitions, for subsequent dialogue among peers and expert others.