When we develop curriculum in schools, we’re saying “scope and sequence,” to mean the progression of learning experiences we design for our students. The term “scope and sequence” suggests that learning is a linear progression from a beginning point, through a series of points, ending at a particular point.
This linear model might have evolved from the industrial model of education so well illustrated by Sir Ken Robinson’s TEDtalk, animated by RSA. Because students are processed in batches through schooling, it might have happened that educators developing programmes of learning sequenced learning in a linear manner associated with grade levels.
But what if learning were not linear? What if each student has different times of readiness for different skills regardless of when he or she was born, which Sir Ken Robinson calls their “date of manufacture”?
This was the problem with the previous misunderstanding that the Approaches to Learning document in schools had to follow the format of a complicated matrix, wherein skills were mapped out as introduced and various points of proficiency and mastery indicated throughout the chart. The question still remains, if approaches to learning skills are mapped out in a linear fashion much like many of our ATL SLE charts in the past did, how do we account for students’ different times of readiness for different skills? Do we build a three- or four-dimensional matrix?
Kath Murdoch, writing about the inquiry learning approach, suggests that when students learn through the recursive inquiry cycles, we take into account each student’s thinking and learning process as their pathways to understanding. Inquiry approaches allow each learner entry points to understanding, and the teacher is able to facilitate how each student can follow individual pathways to understanding and skill acquisition in the learning process. The inquiry approach allows us to orchestrate learning; everyone has their preferred instrument to play, and they all come in to the song at different times, but together they play towards a collaborative harmony.
The inquiry approach allows us to follow a recursive, rather than a linear model for learning. This pedagogical construct is an underpinning approach to teaching and learning in the IB.
If learning is constructed through recursive inquiries, how do we address this non-linear curriculum?
Consider our curriculum framework for the continuum. The continuum framework involves a spiraling through concepts, from large macro-concepts in the PYP, into more specific concepts in the MYP, involving both interdisciplinary key concepts and disciplinary related concepts. As students spiral through the conceptual curriculum, they gain depth through the threads of macro-concepts, and they gain breadth by exploring relationships between the interdisciplinary key concepts through the disciplinary related concepts. See the example in the illustration below.
Similarly, there is a recursive spiral of approaches to learning skills in the continuum. If we take just one skill: analyse, we are able to see the spiral of this skill in the continuum’s programme of inquiry.
The curriculum might not be linear after all. Learning in the continuum follows this recursive inquiry cycle.
The suggestion here is that there are mini-curriculum cycles in the units we teach, and we use the inquiry cycles to spiral through conceptual understanding and skill acquisition and rehearsal in the unit.
As we move into the subject overview, we might find that the units spiral learning through the conceptual and skills framework in tandem, through the use of a learning cycle in the subject.
If we connect all the subject overviews and tease out the conceptual threads and skills development threads out of these, we may find ourselves creating a spiraling curriculum, delivered through inquiry and constructivist approaches, inclusive of and providing multiple pathways to understanding and mastery for all learners.
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The Learner's Toolbox 
Dear Aloha, your post made me think of the way Hegel used the term ‘Aufheben’ when describing how when arriving at a different plateau, we have an opportunity to look back, evaluate and generate strategies on how we will move up, for in this ascending process “Nothing is lost or destroyed but raised up and preserved as in a spiral”. The way you placed competencies and skills in the spiral got me thinking of a way in which this spiral can go through the different degrees of challenge and complexity in Marzano’s cube.