I personally think dynamic programming approaches are more intuitive due to the step-by-step structure of the dynamic programming. Similar to proofs using induction, the idea of computing the answer for $n - 1$ steps and understanding the relationship between consecutive steps, hence being able to compute the next step makes a lot of sense. I think in general it is just more intuitive to more people. If you understand what you need to compute, then the relationship and transition between states also makes sense.
It just seems to be less abstract and less general. You don't need to understand every case of the problem, you can break it down into few cases and resolve them using the answers for "previous" step. While in greedy ideas, often understanding more general and abstract ideas and structure of the problem play key role. Since you need to understand the problem very well in order to understand the correctness of greedy approaches, it seems harder to come up with.
I personally think, teaching any kind of idea or approach in a simple manner stems from asking the right questions and "teaching" how to ask the right questions. For example, often in dp problems the right question might be, if I know the answer for case $n - 1$, can I compute the answer for $n$? Is there some sort of structure between steps and how can I use it?
For example, in LIS(Longest Increasing Subsequence), if I know the answer for first $n - 1$ elements, I can't easily compute the answer for $n$. However, any LIS among the first $n$ elements either
contains the $n$-th element or
is the LIS of first $n - 1$ elements. So we can understand the connection between consecutive steps. What happens if I remove the $n$-th element from LIS in the first case? Then, it has some last element among $1 \ldots n - 1$. So on and so forth with the right questioning and most of the questions you have listed are resolved with an answer.
I am not a teaching expert, but I believe, if you ask the right questions to the student and let them think for themselves and try to navigate (maybe help a little) their thought process through those questions, it will help them understand the topic more easily.
Finally, just a thought: the issue you are facing might be related more to the student’s lack of interest than to their intuition. I think that when a student is genuinely interested in a topic, intuition often follows naturally. Although I am not confident with my the last claim :)
I personally think dynamic programming approaches are more intuitive due to the step-by-step structure of the dynamic programming. Similar to proofs using induction, the idea of computing the answer for $n - 1$ steps and understanding the relationship between consecutive steps, hence being able to compute the next step makes a lot of sense. I think in general it is just more intuitive to more people. If you understand what you need to compute, then the relationship and transition between states also makes sense.
It just seems to be less abstract and less general. You don't need to understand every case of the problem, you can break it down into few cases and resolve them using the answers for "previous" step. While in greedy ideas, often understanding more general and abstract ideas and structure of the problem play key role. Since you need to understand the problem very well in order to understand the correctness of greedy approaches, it seems harder to come up with.
I personally think, teaching any kind of idea or approach in a simple manner stems from asking the right questions and "teaching" how to ask the right questions. For example, often in dp problems the right question might be, if I know the answer for case $n - 1$, can I compute the answer for $n$? Is there some sort of structure between steps and how can I use it?
For example, in LIS(Longest Increasing Subsequence), if I know the answer for first $n - 1$ elements, I can't easily compute the answer for $n$. However, any LIS among the first $n$ elements either
I am not a teaching expert, but I believe, if you ask the right questions to the student and let them think for themselves and try to navigate (maybe help a little) their thought process through those questions, it will help them understand the topic more easily.
Finally, just a thought: the issue you are facing might be related more to the student’s lack of interest than to their intuition. I think that when a student is genuinely interested in a topic, intuition often follows naturally. Although I am not confident with my the last claim :)