Disproportionation reactions are those in which an
element is simultaneously
oxidized and
reduced.
One example is the decomposition of hydrogen peroxide:
2H2O2 -----> 2H2O + O2
In hydrogen peroxide, oxygen has an oxidation number of -1. In water it is -2, while in elemental oxygen it is 0. Thus, of the four Os with a charge of -1, two have increased to 0, and two have decreased to -2.
Another example is the reaction between halogens and alkalis. For example, chlorine with sodium hydroxide:
Cl2 + 2NaOH -----> NaCl + NaClO + H2O.
Chlorine started with an oxidation number of 0; in NaCl (common salt) it has an oxidation number of -1, while in NaClO (sodium chlorate (I)) its oxidation number is +1.