I often see or hear “backwards” where “backward” is required.

Problem:
These two words are not always interchangeable.

Explanation:
The word “backward” may be used as an adjective or as an adverb.

The word “backwards” may be used only as an adverb in standard English.

These rules give us these examples of valid and invalid usage:

• “He took a backward approach.” — valid as adjective
• “He drove ten feet backward.” — valid as adverb
• “He took a backwards approach.” — invalid as adjective!
• “He drove ten feet backwards.” — valid as adverb

Solution:
Use “backward” for everything. This obviates the need to remember that “backwards” may be used only as an adverb.