These resources describe a method for teaching recursion and/or induction that can make it easier for students to get past the difficulty of “wishful thinking.” Anecdotally, they’ve helped a lot of struggling students have ‘aha’ moments about how recursion works, because an intermediate result is an extra-verbose version of the final solution that includes a lot of intermediate steps spelled out explicitly. For a quick overview, read the slides or watch the video. The worked examples page goes into more depth.