The temporal evolution of a wave packet ψ(x,t) confined to an infinite square well (occupying the region 0 ≤ x ≤ L), as manifested by fractional revivals of the probability density P(x,t) ≡ | ψ(x,t) |2 and the time-dependence of the expectation values of position, momentum and force (X(t) ≡ ⟨x⟩t, Π(t) ≡ ⟨ p̂ ⟩t and Φ(t) ≡ ⟨F̂⟩t, respectively) are studied, using wave packets for which Π(0) = 0. In the region accessible to the wave packet (0 < x < L), p̂ and the Hamiltonian Ĥ commute; still, p̂ is, in general, not a constant of the motion, and the three expectation values are all time-dependent, except when the initial packet has a definite parity, that is ψ(x,0) = ±ψ(L - x, 0), which implies X(t) = L/2 and Π(t) = 0 = Φ(t). For a packet with no definite parity, Y(t) ≡ X(t) - L/2 stays, if the packet is sufficiently narrow at t = 0 close to zero nearly all the time, but executes large excursions in the neighbourhood of instants at which the probability density experiences a mirror revival or a revival. This behaviour, with no classical counterpart, can be understood by paying attention to the presence of infinite potential barriers (at x = 0 and x = L) and taking account of the net force felt by an initially off-centred wave packet. It is shown that though plots (against time) of expectation values catch a glimpse of the revival structure of a wave packet, such plots fail to reveal some fractional revivals.