How to generalize your skills to new problems on the GRE: the importance of scaffolded learning

Davis: Hey everybody, this is GRE Bites. My name is Davis, and I’m an educator with over ten years of experience.

Orion: And I’m Orion, the founder of StellarGRE.

Davis: We’re here to bring you your weekly bite-sized episode on GRE prep and grad school admissions. Check out our top-rated GRE self-study program at And don’t forget, you can use the code “BITES” for 10% off any membership.

Let’s get to it. So, in a recent episode, one of the things that was interesting to me, and that stuck out, was this idea of how to transfer your knowledge of how to do one type of question to others. And it just so happens that we’ve been receiving some user responses and listener requests; we got our first listener request.

Orion: That’s right.

Davis: And so we’ll read it, and then we’ll get to the subject at hand. Coming in from Michael, we have the following questions that would be great to hear about: what students are to do when they’ve gone through all the skills, and when they do ETS questions, find almost every one has a new question. He says, “I can’t do the vast majority of the math in the sections. And then when I see the answer, I can follow along. But I’m just not connecting the dots beforehand.” Is this normal? Alright, Orion, what are your expert opinions? What would you say to Michael here?

Orion: Well, first, Michael, thank you for writing in. I’m super stoked that we’re starting to get viewer requests. That’s one of the main points of this channel. So thank you for your participation; it makes me really excited to receive emails from listeners. With respect to this question, “Is this normal?” Yes, it’s unfortunately very normal. It’s a common complaint, especially with respect to the quantitative section. This can date back to high school, where being able to perform a solution to one specific question, then the numbers get changed, the presentation is slightly different, and it’s very hard to generalize from one to the other. This is because, as of yet, the student hasn’t really apprehended the deep structure of the problem.

Math is actually about relationships. Most people don’t understand that; it’s not usually how math is presented. And it’s relationships among quantities as opposed to numbers or values. Apprehending the deep relationships between quantities that are revealed by specific numbers and values is how top performers can effortlessly generalize from a specific problem to other problems with the same essential concept at its core.

That said, that takes a lot of time and a great deal of mastery. And a lot of people just aren’t going to get there in a two-month GRE self-study program, nor should they have to. So that’s one of my big things: if your goal is to kind of learn the math and to apprehend the deep, essential core concepts, which is how a lot of other programs teach for the quantitative section of the GRE, absolutely, you’re going to spend a lot of time, a lot of unnecessary time and energy preparing for the GRE, in my opinion. And that’s because we don’t actually need to know the deep structure, the essential core concepts of a problem in order to solve them.

Davis: So, let me just make sure I’m understanding you correctly. I taught math up through the second year of college and tutored it for a long time. Now, my son, who is 13, is into algebra. This is the exact problem that I’ve come across so many times. But it is what separates students who feel they can just barely get by in math and pass a test, versus those who actually go on to fall in love with math. You’re right, it’s a lifelong pursuit to actually get to that place where you can recognize the relationships and the quantities and see the power that equations can give. But I totally agree with you that GRE prep is not the place where people should be taught to do that. So, tell me more about the diagnostic method that you have. Because that method the GRE offers is a way to bypass this deep knowledge endeavor that you’re talking about, and get to the place you were just mentioning where you can just solve a problem correctly.

Orion: And just for the record, I was one of the students in the former category. I was the one who was just trying his hardest to pass the test and skate by. I was a proud B student in math throughout most of high school. I only really fell in love with math when I was in my 20s, when I think I had enough cognitive maturity to be able to appreciate it at a deeper level. I kind of had to teach it to myself in a way that made sense to me because it was never really taught in an intuitive way by my teachers or the textbooks that I read. So, it is possible.

And it’s a shame that math is taught to young folks in such a way that it’s often alienating and intimidating. Understanding relationships between costs and quantities is a core life skill. And it opens the doors to all kinds of not only professions and practical applications but just a deeper appreciation of reality in the natural world and things like that. It’s really cool. But you’re right, a two-month prep course is not the time and place to fall in love with math, necessarily. It’s probably not going to happen in that short amount of time anyway.

Davis: So, how do we get around this if we’re not going to have the time to really come to that deep apprehension of the core concept?

Orion: Well, we do that through diagnosis, which is a key component of the Stellar method. In my system, there are 50 different diagnostic categories for quantitative problems. This means that I have gone through dozens and dozens of practice tests. I’ve looked at thousands and thousands of problems from ETS and all the major test prep companies. And I can successfully sort all of those problems into one of only 50 buckets.

Davis: This is really good because there are actually only 40 scored quantitative questions on the entire exam. And if you understand that there are really only 50 types of questions on the test, there are only 50 types of questions that you need to prepare for. It significantly simplifies the issue. It’s no longer that there are thousands and thousands of problems. There are really 50 problems in different variations.

So the key component that begins every single chapter in the Stellar system, the Stellar self-study program, is diagnosis. You have to train students how to recognize those 50 individual diagnostic categories.

Davis: Help me out here a little bit because I went through the StellarGRE program. I don’t remember that there were 50. I thought it was broken down – are those 50 broken down into even fewer categories in terms of being able to diagnose quickly and move forward?

Orion: Yes, there are sub-variations within the different 50. For example, one of the 50 diagnostic categories is combinatorics. And there are combinations and permutations. Within combinations, there are multi-group combinations, and there are also multi-level combinations.

Davis: So, that was five different problem types that you could diagnose with one diagnosis. And this is a combinatorial problem.

Orion: Yes. But you can see that it’s almost like this, the solar system is a fractal.

Davis: Yeah.

Orion: Where you can zoom in and zoom out at all different levels of granularity and still have a high-resolution vision of what you’re supposed to do. The point is that, whether we’re talking about those 50 high-level categories or even the subtypes of the subtypes within each category, there are always diagnostic signs that students can be trained to reliably recognize that will orient them to the type of problem they’re dealing with.

These diagnostic signs are always English words, mathematical symbols, or geometric figures. It’s one of those three things. And the top of every chapter begins with Visa, the diagnostic signs associated with this general category. These are the diagnostic signs associated with this subcategory. This is how you discriminate between the two varieties of this question. And the idea is that most of success on the GRE is recognition. Because again, there’s just 50 problems that they do over and over and over again. And if you can recognize the type of problem you’re dealing with, hopefully, within the first 10 seconds of encountering a new problem, well, then you can shuffle forward in your working memory, all the content, all the strategies and techniques associated with that diagnostic category, or that sub-variation.

You can remember what the strategy or the technique you used on 10 previous problems, if it worked on those 10 previous problems is probably going to work on this 11th problem that you’re encountering.

Davis: So we’re talking about a different way to train your recognition in your brain when you’re approaching problems, taking it rather than in practice, training the specific mechanics of each individual practice question and trying to somehow glean general concepts out of that to take to the test. Stellar GRE and the self-study program, and Orion, your program takes those generalizations already done for you, teaches you what to look for, in terms of like you said, the English words or the mathematical symbols or the images associated with a problem, and it’ll help you queue up what you need just for that.

Orion: Yeah, I think that’s a good summary. And this requires some degree of repetition. But the point is in the Stellar system, you should know what to do on every step of every problem for the entire four hours, like, I break it down on that minute of a level, like even where to put your eyes when you first encounter a problem, and the sequence of thoughts that are most conducive to you solving that question within 90 seconds or less. And I’m able to do this at such a fine resolution, because again, the test is standardized. It’s the same test over and over and over again, it just looks different to students. Because they don’t yet have that, you know, they haven’t seen 10,000 versions of it.

Davis: So, again, can you give us like you said, where to put your eyes when you first look at a question to help understand this diagnostic test? I know it won’t make sense without the full context of the entire, you know, diagnostic method. But where do you look, when you first see a question to help you understand what type of question?

Orion: It’s a great question. So, regarding diagnosis, we should probably do a whole episode on this. But because it’s a really good question and a core component, it’s my second Quantitative Efficiency Strategy. I have three primary quantitative variances. Number two, once you’ve decided to tackle a problem in the first place, you should look at the answer choices. Because 85% of the questions in the quantitative section can be sorted into one of only four different what I call “structural diagnoses,” which are revealed by what’s going on in the answer choices. That’s what I’m remembering.

Davis: Yeah.

Orion: And on a very high level, when you look at the answer choices, you’re going to look for two different things. The choices are going to have real numbers or they’re going to have variables. And the answer choices are either going to be a ‘choose one’ or ‘choose many’. And that suggests that there are four different primary combinations of structural diagnosis: variables choose one, variables choose many, real numbers choose one, real numbers choose many. And this should take all of half a second to perceive, right.

And this is important because each one of those four structural diagnoses is associated with a general problem-solving strategy that works every time for that type of problem. It’s not always the most efficient route to the solution, but it will always work for that type of problem. And if you know that route, and even though it might not always be the most efficient, if it’s trained and practiced, it’s definitely within the efficiency margins needed to get a perfect score on the GRE. Sure, if I can look at the answer choices, and within two seconds determine a flexible, general problem-solving technique that will work on this problem.

It’s like I already have oriented in the direction of the solution, functionally immediately upon seeing the question. Now, that’s a huge game changer.

Davis: That’s powerful.

Orion: So diagnosis is super important. The sooner you can recognize the type of problem you’re dealing with, then the diagnosis, the treatment, the solution should follow naturally, organically from that recognition. That’s the whole point of diagnosis from a medical perspective. And that’s the key in order to generalizing solutions to problems on the quant section, right? It’s the power of diagnosis.

Davis: Well, thank you, Michael, for your question. It’s provided a really fruitful discussion, and left a few more questions, I’m sure.

Thanks, everybody, for tuning in. We’ll be back next week with another bite-sized episode of GRE Bites. If you have a topic you’d like discussed on a future episode, let us know at And if you’re ready to take your prep to the next level, check out our top-rated GRE self-study program at You can use the code “BITES” for 10% off all memberships there. Talk to you soon.

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