We compute the set of naive pointed homotopy classes of endomorphisms of the
projective line P^1 over the spectrum of a field. Our computation compares well
with Fabien Morel's one of the motivic pointed homotopy classes of
endomorphisms of P^1: there is an a priori monoid structure on the set of naive
homotopy classes and the group completion of this monoid is isomorphic to the
group of motivic homotopy classes.