What is it with Harvard Business Review that it publishes lots of beginner-level articles these days? The feature in the March issue of HBR on "Learning to Learn" is a very basic feature advocating for aspiration (wanting to learn), self-awareness (understanding your level in the skill you want to learn), curiosity (trying something until we succeed) and vulnerability (accepting you may be bad at something for months). This is the sort of cutting-edge thinking that get you published in HBR these days.
Here is what I would've added to it, taking a manager's or would-be manager's perspective, since after all this is HBR's target audience. First, do you really need to learn the skill or are you reacting like the employee you were in your previous role? Maybe you did a lot of data analysis before you were promoted to manager, and now your direct reports are talking about R and Python. Do you actually need to learn the software, or are you just a little nostalgic for your old job? Let's assume you actually need to learn a new skill for your new job. There will be two types of skills you have to learn: (a) skills you know you don't have or have a lack of, and (b) skills you don't realize you don't have, like those people who think they have amazing interpersonal skills because they ask their employees how they're doing once every six months.
Obviously, identifying (b) skills is tricky. So you should make a list of the top skills you (and anyone you use as sounding board - mentors, advisors, former colleagues, new boss, new colleagues) think you will most need in the new job, and evaluate your blind spots. Why did the person who used to have your job (in case of a promotion) succeed, or fail? What are the skills you didn't need as much in your previous job? We often develop skills to the level we need to function in our current role, and not much above. (Unused skills tend to atrophy.) Where will you need to stretch? Are you really that good? What stories are you telling yourself that may no longer serve you? For instance, you may work in Division A, where the one thing you know for sure is that Division B is full of the people no other division wants and everything wrong in the company is their fault. If you're promoted to leading Division A and the role calls for a close interaction with Division B's manager, you will achieve whatever goals you have a lot more easily if you change the story you tell yourself about Division B to something more empowering.
As you move up the ranks, learning shifts away from technical to personal/interpersonal content, from tactical to strategic issues, from direct contributor to delegator, from one-way communication (to one's immediate supervisor) to matrix collaborations with one's team and other units. If you can't think of a skill you need to learn, think about situations in your work life that keep repeating themselves. That will probably give you a clue.
For instance, if you were very successful early on when you took the helm of a company in trouble, but have been struggling with getting your team to follow you now that the company is on surer footing, maybe you have a "savior" leadership style that works well in times of crisis but not as well in less troubled times, where employees seek more autonomy. (This also begs the question: do you need to learn more consensus-based leadership styles, or do you need to find another company in trouble?)
When were you last wrong? If you can't remember when you were last wrong, then you have the issue you need to learn served to you on a platter, because no one is never wrong, and being convinced you're never wrong will only stifle dissent and discourage your colleagues or direct reports to be honest with you. If you've had even a moderate amount of success in your career so far and been promoted at least once (or been put on the fast track to promotion), it is also worth thinking about who might be wanting you to fail. People have the most irrational reasons for wanting others to fail, and people who succeed have such a different outlook (focusing on improving themselves, seeking role models, etc) than people who try to make others fail (obsessed with pulling others down to their level) that you might not identify potential troublemakers by reasoning alone. Yet, those people leave clues - they badmouth you to others, or make subtle digs at you. Lyndon Johnson is famous for saying that you don't belong in politics if you can't walk into a room and say immediately who is for you and who is against you. Once you start moving up the ranks, this is true of the business world too.
Finally, you need a learning plan. What will the outcome look like when you have achieved your learning objective? Say you want to learn a new language because you're being transferred overseas. Do you want to have a basic conversation around the water-cooler on Monday morning, speak enough to go and buy groceries, be fluent enough to understand your new colleagues when they speak in their mother tongue? What are reasonable time commitment and timeline to achieve your objective? Has someone done something like this before? Who will you enlist to achieve your goals? What are your intermediary milestones and your weekly goals?
An issue with academia is that new Assistant Professors get hired at research universities on the basis of their research but are expected to also teach. Quite a few, at least in engineering, have not taught during their doctoral studies and were only Teaching Assistants. These professors have to be "good enough" teachers to get tenure, but not exceptional. Hence, some of them don't see the value in learning how to be a great teacher given the time pressure to produce enough high-caliber research by the time they come up for tenure. They make the calculation, unconscious or not, that on-the-fly teaching (the "let's get the slides from my colleague and hope for the best" approach to teaching) will be good enough. They have few role models beyond the professors they remember from their early years in graduate school (later years are usually devoted to research), since professors rarely attend each other's lectures.
Learning to be a good teacher then is something that only professors genuinely interested in how to make their students best learn the material (whether for the good of their students or as an intellectual challenge but not primarily out of desire to gain tenure at a research university) learn how to do. This doesn't mean that professors who aren't good teachers don't want to be good teachers, but they may not find the time to become good ones - or they may be delusional about their abilities, as the HBR article suggests, in the one interesting stat the author quotes: in a Cornell study, "94% of college professors reported that they were doing above average work." (We will note that median and mean aren't the same thing, which the HBR article doesn't point out, and that the stat isn't solely about teaching-related work.)
For my readers serious about developing their leadership skills, I recommend the unfortunately titled Primal Intelligence: Unleashing the Power of Emotional Intelligence, which is a must-read. I also highly recommend The 21 Irrefutable Laws of Leadership, where I first read the LBJ quote.