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Carol Dweck is one of the most famous learning theorists alive today. Though she has been studying mindsets for decades, she is perhaps best known for her (appropriately-titled) book, Mindset Her ideas have directly helped hundreds of thousands of readers learn and teach more effectively, and they have indirectly helped millions more by influencing the way we think about learning and intelligence today. When it comes to intelligence there have always essentially been two schools of thought. One claims intelligence is a relatively fixed quantity that is stable throughout our lifespan, while the other argues it is a malleable quality that can change depending on experience (i.e. a variation of the infamous Nature versus Nurture debate). Adherents to the first school often adopt "entity" theories of intelligence and pursue "performance goals," in which they are concerned with gaining favorable judgments of their competence, whereas adherents to the... read more

No one likes to mess up, but going to great lengths to avoid errors - even when the consequences of making an error are benign - is unlikely to help you learn. In fact, in her review of the literature, Janet Metcalfe makes a compelling argument that making errors while learning - so long as you receive corrective feedback - results in better outcomes than making no errors at all. Her findings are somewhat counterintuitive. If the goal is to perform flawlessly in high-stakes situations, shouldn't we pursue perfection in order to prepare for them? Early theorists feared that the commission of errors would make it harder to learn the correct response later on. One of the most famous psychologists of the 20th century, Albert Bandura, believed that only correct responses should be rewarded; errors, if they occurred, should be ignored. However, what Metcalfe's review of the literature suggests is that errors should be encouraged as part of an active exploratory learning process,... read more

The journal Science has recently published a meta-analysis of numerous long-term studies examining the correlation between high GRE scores and the quality of work done by graduate students once they are enrolled in doctoral (and in some cases) master degree programs. The researchers--professors of Education at several universities have included there is no evidence that there is a relationship between a high GRE score and "successful" work in grad school; in this case, successful means contributing meaningful, thoughtful, and original work in response to assignments, whether they be short research projects or doctoral dissertations. Another study, in fact, has found a correlation between receiving high scores on the GRE and doing poorly in certain fields of study. This may seem counter-intuitive, but then, so many things are.  I'm not including a link for time limitation reasons, but the study would be easy to track down and read if you insert the appropriate descriptors... read more

It's not controversial to aver that procrastination is bad. Most would agree without giving it a second thought. But what about procrastination is so harmful, and why do we procrastinate when we readily agree we shouldn't? When I talk about procrastination, I'm talking about delaying an important task despite knowing we will suffer as a result. Why would we do this? The problem seems to have its roots in an inability to manage emotions, and from an overweighting of short-term benefits over long-term costs. In a landmark 1997 study, Dianne Tice and Roy Baumeister rated college students on an established scale of procrastination, then tracked their academic performance, stress, and general health throughout the semester. Initially the procrastinators reported lower levels of stress, presumably because they were enjoying more pleasurable activities in lieu of the work they should have been doing. By the end of the semester, however, the procrastinators earned lower... read more

It's fairly likely that you've heard someone talk about "mindfulness." It's less likely that you know exactly what mindfulness entails, and even less likely that you've heard of Ellen Langer, the "mother of mindfulness" in Western academia. In fact, even if you Googled mindfulness you'd find credit for its popularity in the West given to a man named Jon Kabat-Zinn. Langer's name doesn't appear anywhere on the first page of Google's results, so you probably wouldn't learn that she earned her PhD and began her line of research around the same time as Kabat-Zinn, and that the groundbreaking nature of her work led her to become the first woman tenured in the Psychology Department at Harvard in 1981. Her research has had profound effects on how we think about everything from aging and mental health to decision-making and learning. So even if you don't know her name, it is likely that in one way or another you are familiar with some of her research. The focus of this... read more

Marshaling the cognitive resources and committing the amount of time required to earn good grades and high test scores takes effort. The rewards from these achievements are often delayed, while the rewards from having fun with your friends, playing video games, interacting on social media, watching tv, etc. are more immediate. What strategies can you use to help overcome this mismatch? In the framework explored in this paper, the authors propose that the decision to delay gratification is mediated by two systems: a "cool" cognitive system, and a "hot" emotional system. The more the hot system dominates, the more likely you are to succumb to temptation. Thankfully, as we get older, the cool system matures and thus makes it easier for many of us to delay gratification. We are most vulnerable to the hot system when we are young. You’ve probably seen the marshmallow experiment in which young children are placed in front of a table with a marshmallow... read more

You might wonder what emotion has to do with learning, and why I am writing a blog about sleep and emotion. If you think about it, though, how you to react challenging situations - the emotions you feel, and the cognitions, physiology, and behaviors that accompany them - can have a profound impact on how you learn. Indeed, emotional reactivity can have a profound impact in multiple domains, but in this blog we will focus on its impact on learning. Modern neuroscience is not necessary to understand that sleep is fundamentally important. However, it increasingly allows us to understand why that is the case. Andrea Goldstein and Matt Walker reviewed the literature on sleep and emotion and make a compelling case for the causal role of sleep in optimal affective brain function. For our purposes, I want to focus on the overarching theme of how sleep deprivation diminishes effective emotional reactivity. When people are sleep deprived for even one night, functional... read more

When you're studying before a test, the question of how to allocate your study time inevitably arises. What should you study first? Where should you spend the most time? Janet Metcalfe and Nate Kornell designed three clever experiments to find out. In the first experiment, participants were allowed to choose how to allocate their study time. They were tasked with learning English-Spanish word pairs of varying difficulty (easy, medium, and difficult), under three different timing conditions (5s, 15s, or 60s). In each trial, one pair from each category appeared and participants could choose where to spend their study time. The most important takeaway from this experiment was that, under tight timing conditions, allocating study time to the easiest items was the most effective strategy. However, Metcalfe suspected that advantage would shift to medium items if participants were forced to spend the bulk of their study time on them. So, in Experiment 2, participants... read more

We all know we do better when we're well-rested than when we're not. Modern sleep research has started to uncover exactly why that's the case. In terms of memory, there are at least two important reasons to make sure you're getting enough sleep. First, we better remember what we learned the day before. This is because sleep plays an essential role in the conversion of short-term memory to long-term memory. Short-term memory relies heavily on a brain region known as the hippocampus (named after the Greek word for seahorse, given its shape), while long-term memory relies on a broad network of cortical association areas. When we learn new information, the hippocampus is very active, and when we sleep, it turns out that the activity of our hippocampus predicts how well we will remember what we learned when we wake up. Researchers have even found interesting ways to manipulate and improve this process. For example, in one study, experimenters paired the scent of a rose with a spatial... read more

When I worked for Kaplan, they required all private tutoring lessons to be two hours. That surprised me because I thought of lessons as one-hour affairs. However, I soon discovered that we could get through a lot more in one two-hour lesson than we could in two one-hour lessons.  Why? For starters, each lesson always starts with a few pleasantries and takes a couple of minutes to get going. Furthermore, it usually takes 15 minutes or so for students' minds to warm up and perform at their best. So by the time we are at our best flow, if the lesson is only one hour, we have often used a quarter to a third of our lesson time.  In my experience, I've found that 90 minutes works well for many students. With 90 minute lessons, we can go through the warm up period and spend more than an hour at our most productive level. An hour is generally too short and delivers less value per dollar than a longer lesson.  Exceptionally motivated students can often... read more

Sometimes I work with students who perform well during our lessons, but who struggle when it comes to actually taking the test. It turns out the reason for this might be genetic.    When we experience stress, our prefrontal cortex is flooded with dopamine. Some of us are coded with a gene that slowly removes the dopamine, while others have a variant that rapidly removes it. The prefrontal cortex is critical for planning and decision-making, and it performs best when an optimal level of dopamine is maintained. Normally, on many cognitive tests, people with the slow variant of the gene perform better. But in stressful, high-stakes situations the opposite happens: those with the fast variant do better. Thus people with the slow variant have been dubbed Worriers, and those with the fast variant, Warriors.    However, being a Worrier does not mean you will inevitably be a victim of chronic underperformance in stressful situations. In one of the studies... read more

The Economist recently published an article with some surprising research findings about stress. Contrary to popular belief, stress is not always bad, nor is it the amount of stress that matters. Rather, the key determinant of its impact on performance and health is largely psychological.    In one study, researchers divided a set of GRE test takers into two groups. Saliva samples were taken to establish baseline stress levels for all participants. Then one group was told that stress during practice exams is natural and can improve performance, while the other group just took the test. Saliva samples were taken at the end of the exam, and the results from both groups indicated similar levels of stress. BUT, the group that had learned stress can be helpful scored higher on the practice test (and, several months later, on the actual GRE) than those who just took the test.    Even more impressively, in 2012 a group of researchers scoured through... read more

Over the years, I have noticed that many students do not like to take their practice test scores at face value. When students get scores below their goal, the temptation to rationalize is strong. "On Test Day, I will take it much more seriously, so I'm sure my result will be higher." "I was distracted during XYZ sections, so my score on those isn't as accurate as it could be." "I only really focused on the Math sections, that's why I didn't do as well on the others." "I made a lot of careless mistakes." I'm not saying these are excuses - it's possible they are accurate explanations - but even still, thinking this way will not serve you well. For starters, if you're not taking your practice tests as seriously as you would the actual test, that's a problem. The whole point of practice tests is to prepare you for the real thing, so you should treat them as if they are the actual test. Furthermore,... read more

I can't speak for every tutor, but I know that if you work with me I have certain expectations of you in order to ensure that you will see the greatest possible improvement in your score. Luckily, they are really quite simple, and adhering to them makes a huge difference. I've attached a PDF version to summarize my Top 5 Test Prep Essentials that you can download, but I will review each of them below too.    For starters, I may be stating the obvious, but you absolutely must complete all homework assignments. All my assignments are tailored to your current performance and designed to help you achieve your goal score. Many students aspire to achieve dramatic improvements, and I fully believe such improvements are possible. BUT, in order to achieve such goals, it is imperative that you complete every homework assignment. If there is a notable gap between your current score and your goal score, that is perfectly ok, but it makes the homework that much more important... read more

Ready for a little riddle? Sure you are! I'm going to list seven phrases, three words each. Without looking it up, I want you to tell me what all twenty-one (7 times 3) of these words have in common. There is only one right answer. Ready? Piff! Paff! Puff! Knisper! Knasper! Knusper! Pim! Pam! Pum! Riks! Raks! Poks! Cric! Crac! Croc! Pif! Paf! Pof! Knap! Knetter! Knak! So what do you think? Any ideas? I'll give you a minute to think it over. You're giving up? Already? Wait, let me give you a hint. I left out one of the phrases: Snap! Crackle! Pop! Starting to get where I'm going with this? As it turns out, those phrases are the onomatopoetic sounds RICE KRISPIES cereal produces, according to its marketing in other countries, from Germany to Mexico to Finland. That's right, in Germany, pour some milk over your RICE KRISPIES and you hear "Knisper... read more

Standardized test math doesn't behave like normal math. On a normal math test, your knowledge of the concepts and material is being tested, using (hopefully) fair test questions. On a standardized test, though, they're looking for you to think outside the box, to apply math concepts and algorithms to unusual situations, and to really understand what they're looking for and find the quickest way to go about it. Let's take a question from a recent GRE student's lesson: If 4x – 5y = 10 and 6y – 3x = 22, then what is x + y? Now, this is a set of two equations with two variables each, so it looks to me like a perfect candidate for solving as a system. If I were solving this one on a regular math test, I'd start off trying the substitution method, since I'm more comfortable with that one. So let's explore that one first: I'll start by solving the first equation for y: 4x – 5y = 10 - 5y = 10 – 4x y = (-10/5) – (4/-5)x y = -2 + (4/5)x Then... read more

Alas! You have to take the GRE in order to get into the program of your choice. Keep in mind that if you do not prepare well, you may have to take the test again, which will cost you probably around $200 or more. If you do not prepare well and it sets your studies back a year, that could cost you a year of earning potential in your lifetime. That's not a fun math problem. Maybe you need that extra year to prepare, but if you are ready, why go at the GRE in a less than 100% manner?   Let's say you already have your fall date set and you have two months or less to prepare for the exam. Here is what I recommend. Research the GRE stats of the university you are considering. Contact your POI (person of interest) and find out how well you need to perform on the GRE. If you need to score in the 90th percentile in the quantitative portion, that's something you need to know. Your POI may say that you need to score in the 60th, but if everyone who was admitted in the previous... read more

Normally, an equation has a single solution when it contains only one undefined variable.  For example, take the equation 3x + 7 = 19.   3x + 7 = 19     [original equation] 3x = 12     [subtracted 7 from both sides] x = 4     [divided both sides by 3]   This is one case of a larger trend in algebra.  As I've already said, you can solve an equation for one answer when it contains a single variable.  However, this is derived from the larger rule that you can solve a set of equations where there are as many distinct equations as there are variables.  These are called simultaneous equations, and occur any time that two equations are both true over a certain domain.  In the more practical sense, this is what you should do if an exam asks you to solve for a value and gives you two different equations to use.   To solve simultaneous equations, we can use three strategies. Addition... read more

The general form for a box-and-whisker plot is really easy. Let's take a simple data set.   8.2, 15.9, 12.8, 7.4, 24.7, 23.2, 9.6, 7.9, 8.3, 10.2   First, we need to take those data and put them in numerical order.  When we do that, this is what the data set looks like: 7.4, 7.9, 8.2, 8.3, 9.6, 10.2, 12.8, 15.9, 23.2, 24.7   [Note: Any computer program that runs spreadsheets or statistical analysis will probably accept the data in any sequence.  Ordering the data is only necessary when doing this process by hand.] Once ordered, we need to find the median of the set. The median means the "middle" value. In this case, the set has 10 values, so there's no singular "middle" value of the set when ordered least to greatest. To create one, we'll take the two middle values and average them. (9.6 + 10.2)/2 = 9.9 [The only reason we took an average is because there is not "middle"... read more

Summer is the best time to start studying for college/career entrance exams. Since there is no school and homework, you will not feel overwhelmed when it is time to study. Studying for just an hour a day, 5 days a week, will increase your chances of getting a higher score and you will still have time to enjoy the summer. Alternate subjects weekly. Familiarize yourself with all the subjects on the test. Purchase a test preparation book to get question examples. By the end of the summer, you should have done every problem in the book, including the practice exams. If you need additional help, ask your tutor. Study with others. You will be more motivated to study this summer if you are involved in a study group. Find students that are taking the same exam. Ask your tutor to for a group study session. Knowing that there are other students with the same goal as you can help your study sessions be less stressful. Know your calculator. If a calculator is permitted... read more

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