 Have you ever noticed how your engineering professors often assign practice problems for a course, but do not provide full written solutions for you to check your work? What's the deal with that? Do they hate you so much that they try to make your life so difficult? I mean, it's possible your professor hates you. I don't really know them or their relationship with you. But I'm willing to bet that they don't. So let's examine what real constructive motives could be behind this behavior. I am Dr. Rands, an aerospace engineering professor with a passion for helping students navigate their way through academia. On my YouTube channel, I share videos related to technical engineering content, as well as on student skills and behavior. Learning is tough, like really tough. It takes time, practice, success and failure for skills and concepts to really be absorbed and mastered. Your professor certainly understands this. Or at least they should understand it as it is literally their job to generate and disseminate knowledge through research and teaching. So how can not providing full written solutions actually benefit the learning process? Wouldn't doing so simply provide students with a resource they can use to learn from their mistakes? If we idealize the behavior of a student, the answer to this is, of course, yes. But as every engineer will learn in their career, idealized solutions can often depart from reality. Let's take a look at this from one of my own personal learning struggles, trying to learn the Dutch language while I am living in the Netherlands. I will be the first to admit I'm a bit lazy about studying my Dutch grammar and exercise books. So I encounter a lot of things in Dutch that I simply do not understand. And unfortunately my process for figuring out what I do not understand is to simply pull out my mobile phone, consult Google Translate and magically get the answer to my misunderstanding. But do I really learn from that? Well, I might manage to memorize a few phrases and pick up a few words here and there, but I will not really make good progress in learning the language. And I can certainly attest to that since I have been doing this for the past eight years, I have lived here and I would still find it a challenge to read and understand anything without consulting my phone for some help from Google. So what am I doing wrong? Learning is rooted in adversity and finding your own way to overcome that adversity. Now that might seem like a statement you would find on a motivational poster, but the sentiment is true. Perhaps not stated in a way that is immediately helpful, but true nonetheless. I like to break down this sentiment into three necessary steps. The first step is that you need to be prepared to be wrong. What do I mean by this? Simply put, if you're not solving problems that you might get wrong, you're not challenging yourself. You are simply hovering in your comfort zone of existing capability and knowledge. Remembering this is important in order to eliminate the stigma of failure and making mistakes in learning. This is as true in learning a language as it is in learning any other skill or ability. I like to remind myself of this fact by thinking of the word fail as an acronym for first attempt in learning. I truly believe that universities are and should be a safe space to make mistakes and encounter failures, as long as you're prepared to use them as an opportunity to learn, which brings us to our next step. Step two is to critically reflect on and identify potential weaknesses in your solution. This is where most students would believe that having access to the full solutions to the problem they got wrong would be useful. I mean, how else are you supposed to identify what you possibly did wrong? Of course, the full solution would help you solve that particular problem, but what if you encounter a similar problem where a critical detail has changed? You know, the type of problem professors like to put on exams to test your real understanding. The situation would be analogous to having looked up and memorized the solution to one mechanical puzzle, and expecting that will directly help you in solving another different mechanical puzzle. In this puzzle example, there must be certain concepts and skills behind solving the puzzle that you can identify and resources you can use to develop them. Lucky for you, when taking a course in a university, these concepts are laid out for you in the form of learning objectives for the course. So when you solve a problem, you should reflect back on your solution and give yourself some feedback in relation to these learning objectives. Do you understand what concepts are necessary to solve it? How confident are you in your understanding of those concepts? Are certain skills such as algebra and calculus holding you back? You know, the type of feedback your professor tries to give you on assignments that you tend to want to use to argue for grades rather than take as constructive criticism. How would this look in practice? Let's return to the simple Dutch language example we had earlier. Without using Google Translate, I would not know the direct translation of the statement, but I would actually know the context of the statement. I can also see that vocabulary knowledge is also important and can look at how many of the individual words I understand. Next, we have general concepts of grammar and how sentences are arranged in Dutch. Identifying these, I can do a personal assessment of what I am least confident in and where there are likely misunderstandings. The final step requires you to act upon the identification from the previous step. You have identified areas that you feel you are weak in, so now you have to address those weaknesses. Again, here a written solution is of minimal value. It will tell you what you might have actually done wrong, but it doesn't address the underlying weakness. Luckily, your professor has provided you with a wealth of additional resources aimed to accomplish this. You have textbooks and readers, lecture notes and lecture slides, perhaps some example problems that have been worked out in class, or even these days, some teaching videos that have been posted on YouTube. In the case of our language example, I can consult a Dutch to English dictionary to help with the deficiencies in vocabulary understanding. I can consult a grammar textbook for Dutch grammar, and I may talk to a Dutch friend to see if they can explain the nuances of how time is communicated in the Dutch language. The important thing is that none of these strategies is looking at the particular problem at hand as the ultimate goal to overcome. Instead, they are aimed at addressing the underlying weaknesses you have identified so that you can repair your learning. Once that is done, you can attempt your original problem and even tackle new problems. At this point, I often have students argue that they prefer an alternative approach. If they are simply provided with enough example problems with full solutions, they can simply study those problems and their solutions and learn the underlying patterns within them. Although this strategy can yield some success in passing some exams, there are two significant problems with this approach. First, this strategy of memorizing solutions and detecting patterns in them is the root of many approaches to artificial intelligence. The problem with us adopting the same learning strategy is that computers will always be able to store more data. They'll always be much more quick at searching and accessing that data, and they'll be able to identify more patterns more quickly compared to any human. So rather than trying to be artificially intelligent, we should focus on leveraging the real intelligence of humans. Secondly, learning solutions can be useful for solving that particular problem or a simple variation of it, but it does not prepare you for solving new problems that have never been solved before. This is a big limitation of artificial intelligence at the moment. If you train an algorithm to tell the difference between an image of a tree and an image with the letter B in it, it might fail the task the first time it encounters, say, a rotated image of a tree or a lower case B. Of course, you can address this by providing even more solutions containing such variations, but then you limit yourself to only solving problems that have already been solved before. So, does your professor hate you by not posting full solutions to all the practice problems? Actually, not in the slightest. They're actually trying to help you develop the critical reflection and diagnostic skills needed to effectively learn from the mistakes that you may make.