Your textbook is correct. I believe you are confusing an increase in demand and a shift in the demand curve and conflating the quantity demanded with the demand curve.
The quantity demanded is just how much of the good the consumers want in one particular case (e.g. for one given price). The demand curve tells you the quantity that would be demanded in all cases (for any given price).
Demand can increase without a shift in the curve, as there can be a movement along the original curve itself.
A shift in the demand curve, would mean that there is a different (in your case higher) demand at all prices. For example, if the income of the consumers increases, you might expect there to be more demand for the good at any given price. Concretely, a shift would mean that previously there were two pairs of shoes being demanded at a price of 50\$ and after the shift there are three pairs of shoes being demanded at a price of 50\$.
The sale on shoes in your example does not cause such an effect. The sale lowers prices, which increases demand (the quantity demanded). It is equivalent to a movement along the demand curve. Before there were e.g. two pairs of shoes being demanded at 50\$ and now the price is e.g. 25\$ so the demanded quantity equals 4 pairs of shoes.
In other words, take a demand curve and use any point on the curve as the situation before the sale. After the sale you have a lower price. Finding the quantity that corresponds to that price on that same curve will yield a higher demand, without shifting the curve.