complete and balance the following semi-reactions and indicate if it is oxidation or reduction:
tio2 (s) → ti2 + (aq) (acid medium)

mn2 + (aq) → mno2 (basic medium)

For the first eqn:
Mn2+(aq) -> MnO2(s) [basic sln]
Step 1: Balance elements other than O and H. Mn is already balanced.
Mn2+(aq) -> MnO2(s)
Step 2: Add H2O to balance O.
2H2O(l) + Mn2+(aq) -> MnO2(s)
Step 3: Add H+ ions to balance out H.
2H2O(l) + Mn2+(aq) -> MnO2(s) + 4H+
Step 4: Add OH- as it is a basic solution. Must do it to both side to balance.
2H2O(l) + Mn2+(aq) + 4OH- -> MnO2(s) + 4H+ + 4OH-
Simplified to
2H2O(l) + Mn2+(aq) + 4OH- -> MnO2(s) + 4H2O(l)
Step 5: Balance the charges by adding electrons.
2H2O(l) + Mn2+(aq) + 4OH- -> MnO2(s) + 4H2O(l) + 2e-
Step 6: Check that all element and charges are balanced.
For the Second :
TiO2(s) → Ti2+(aq) [Acidic Sln]
Step 1) TiO2(s) -> Ti2+(aq)
Step 2) TiO2(s) -> Ti2+(aq) + 2H2O(l)
Step 3) TiO2(s) + 4H+ -> Ti2+(aq) + 2H2O(l)
Step 4) Omit as it is an acidic solution so you do not have to add OH- to neutralise the H+ ions.
Step 5) TiO2(s) + 4H+ + 2e- -> Ti2+(aq) + 2H2O(l)
Hope that helps you to see where you went wrong.
Note: I'm not sure whether you need to put states for H+ and OH- ions. But they would both be (aq).

Yes you are correct use the scientific method