  We discuss the precanonical quantization of fields which is based on the De
Donder--Weyl (DW) Hamiltonian formulation and treats the space and time
variables on an equal footing. Classical field equations in DW Hamiltonian form
are derived as the equations for the expectation values of precanonical quantum
operators. This field-theoretic generalization of the Ehrenfest theorem
demonstrates the consistency of three aspects of precanonical field
quantization: (i) the precanonical representation of operators in terms of the
Clifford (Dirac) algebra valued partial differential operators, (ii) the
Dirac-like precanonical generalization of the Schr\"odinger equation without
the distinguished time dimension, and (iii) the definition of the scalar
product for calculation of expectation values of operators using the
Clifford-valued precanonical wave functions.
