Prior to sister chromatid separation during cell division, bundles of 12–24 microtubules (MTs) assemble into kinetochore (K-) fibres and, through pushing and pulling forces, cause the chromosomes to oscillate between opposite poles. Although poleward and anti-poleward movements are typically associated with depolymerising or growing MTs, respectively, the dynamics of individual MTs within the K-fibre has so far remained elusive. Here (p. 1991), Andrew McAinsh, Nigel Burroughs and colleagues developed a live-cell imaging assay to simultaneously track kinetochore position and quantify MT polarisation. Using the EB3 polarisation protein as a marker, they found that, although EB3 intensity was higher on kinetochores that move away from the pole (i.e. anti-poleward) than on those moving towards it, this bias was only limited, strongly suggesting that K-fibres are not coherent and contain a mixture of polymerising and depolymerising MTs. The authors also discovered EB3 bursts, which they found to occur more often on anti-poleward-moving kinetochores. Their estimate of the number of polymerising MTs suggested that EB3 bursts represent instances of transient, near complete coherent MT polymerisation within the K-fibre. In addition, knockdown of the kinesin motors MCAK and KIF18A modulated EB3 bursts and polymerisation bias. Taken together, this study correlates the dynamics of MT polymerisation with the oscillations of kinetochore movements and, thus, reveals important new insights into the mechanism of cell division.