Step 1: Know the goal.
Wrought iron is the purest form of iron. It is made by removing carbon, sulfur and phosphorus from cast iron in a reverberatory furnace (the puddling process).
Step 2: Find the lining.
The furnace is lined with haematite, which is iron(III) oxide $Fe_2O_3$.
Step 3: Understand its job.
Haematite acts as an oxidising agent. It feeds oxygen to burn away the impurities.
Step 4: Write the idea.
Carbon and other impurities are oxidised, for example $Fe_2O_3+3C\rightarrow 2Fe+3CO$. The impurities leave as gases.
Step 5: Name the process.
Because impurities are removed by adding oxygen, the chemical change is oxidation.
Step 6: State the answer.
\[ \boxed{\text{Haematite, oxidation}} \]