What is ‘longitudinal coherence’?
Liping Ma (2010) describes longitudinal coherence as a teacher’s extensive knowledge of the whole mathematical curriculum and they are able to draw on this to inform their practice. Teaching with longitudinal coherence builds a “conceptual understanding” that connects “new ideas to existing knowledge” that will “build ideas across time” (Krajcik et al., 2009). This allows the basic principles the children have been taught previously by other teachers to be reinforced as the teacher has vertical knowledge of the curriculum. It also allows the teacher to have an excellent knowledge of future stages of the curriculum allowing foundations to be built to support more advanced stages mathematics the children will learn as they progress.
…and the concept knot
Longitudinal coherence therefore builds on the lateral knowledge held by a teacher using connectedness by adding vertical progression to the knowledge package a teacher with PUFM holds. Liping Ma describes this interwoven use of connectedness and longitudinal coherence together as the ‘concept knot’.