My teaching philosophy is that everybody has a different style of learning, and the job of the instructor is to work with the student to figure out what that style might be to ensure the highest quality learning and understanding.

Get to know the student a little bit, talk about how they typically learn best (verbally, visually, hands-on, etc.). Go over specific subjects they are focused on, find out what concepts they aren't understanding as well as others, and determine how we can go about tackling those concepts.

I think an independent learner is someone who is able to form their own understanding of a concept based on their own knowledge and style of thinking. So I would focus on helping the student to understand the material by putting it in their own words, forming their own unique visualization and understanding of the problem at hand. That way, when they need to use that skill later on in a new concept, it will be that much easier for them to grasp it.

Focus on their progress and successes rather than when they fail to understand a concept right away. Students are much more eager to participate when they are confident, rather than hesitant.

Tackle the skill a different way. I would try several different ways of looking at the problem and explaining it to see what sticks. If the student is still struggling, I would note to take extra care and time coming back to that concept later in the lesson.