Parents' views on failure (and not intelligence) are important in cultivating a growth mindset.
Adam Rifkin stashed this in Growth Mindset
Children’s intelligence mind-sets (i.e., their beliefs about whether intelligence is fixed or malleable) robustly influence their motivation and learning.
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The basic gist of this paper is that how parents talk about intelligence and failure matter. There's decades of research showing that if you praise intelligence over trying, it teaches the child that you're either good or bad at things and there's nothing you can do a bout it. When you praise effort, they tend to persevere more. In short, if children think intelligence is fixed, they see no reason to try.
What this study adds is saying is that these messages aren't being sent by parents views on intelligence but by their parents views on failure. They find " Overall, parents who see failure as debilitating focus on their children’s performance and ability rather than on their children’s learning, and their children, in turn, tend to believe that intelligence is fixed rather than malleable."
For those interested in learning more Carol Dweck (the co-author and really the biggest name in this area) has a heap of resources available including a few books. She also has a lot of talks on the topic. Here is her TED talk and here is a longer talk she gave about the "Growth Mindset":