4 Ways to Teach a Growth Mindset

People with a "fixed mindset" think that intelligence is static—that they have a certain amount of it which cannot really be changed. Other people have a "growth mindset." They think intelligence is malleable—that it can be developed and increased through hard work.

Students who have a growth mindset tend to do better in school (especially when they encounter academic difficulties) as well as on the SAT and ACT.  However, cultivating a growth mindset in students is actually much more challenging than it might seem.

Below, are four lessons we have learned about how to cultivate a growth mindset in teenagers. 

  • Do NOT tell students to have a growth mindset

    The first rule of growth mindset is that you do not talk about growth mindset. Teenage students often have a negative reaction to being told how to think. They respond much more positively to being shown that something works with objective evidence. 

    • Do not tell students to "just try harder"

      Most students, especially those who are struggling, have heard "just try harder." This is rarely ever helpful to students. Instead of that old line, explain to students why they should put in extra effort (again, use objective evidence to back all claims) and specifically how to deploy that effort. Sometimes a better strategy is more useful than simply increasing effort.

      • Celebrate mistakes!

        Most students fear making mistakes. They often think mistakes are an indication of a lack of intelligence. But research shows that mistakes are a critical part of learning. Having to work through a difficult problem and try different strategies is the optimum method for learning to improve on standardized exams (and in other areas of life). Encourage your student to embrace mistakes and show them how to learn from them. As one of our students once told us: "Fail...fail better...fail better...succeed."

        • Praise the process, not the person

          Our first impulse is often to praise students for being smart. This sends the wrong message. When students later encounter a setback they conclude: "If my past success meant I was smart, my current struggle means I'm not smart." Instead, praise students for their effort and hard work. This implies that you value hard work and that effort is the root cause of success.


        Are you worried about admission to UCLA, UC Berkeley, and UC San Diego?

        I recently sat down with one of our parents who was extremely anxious over her son's prospects of being admitted to one of several of the University of California's (UC) top campuses. Despite his excellent profile -- he had strong grades (4.1 at a great high school) and had posted an outstanding ACT score (top 5% of the country) -- her perception was that this wouldn't be nearly enough at UCLA, UC Berkeley, or UC San Diego. She wanted to add as many AP courses as possible to her son's upcoming Senior year.

        She went so far as to quote a number of admissions statistics that she had gleaned from the internet, including the following:

        1. UCLA recently saw a 50% increase in admits with 21+ Honors/AP courses
        2. One out of four students who were admitted to UC Berkeley last year scored a 35 or 36 on the ACT
        3. More than two-thirds of UC San Diego's admits last year had a GPA above 4.0

        These were facts. They were true. But...

        ...the critical piece of the puzzle that she was missing was that a student's statistics (GPA, AP courses, SAT/ACT scores) are far from the only factors that are considered in an admissions decision at a selective college.

        The UCs practice holistic admissions -- in short, this means they look at a lot more than just the numbers. In fact, at the majority of selective colleges, it is safe to say that while grades and SAT/ACT scores are obviously quite important, they are far from being the ONLY important factors.

        It often works as follows: once a student is in the competitive range of standardized test scores and GPA at a given school (for instance, 50% of UCLA admits score between 27-33 on the ACT), the actual decision is often made based on qualitative measures. These qualitative measures include essays, outside interests, the student's ability to express a unique point of view, the possession of a unique skill set, or perhaps a track record of intellectual curiosity in an area of study that fits with the school's offerings.

        Naturally, we all want the best for our children. But what the student in this particular story needed to give him the best possible opportunity to gain entrance to one of his top choice schools wasn't necessarily to add more AP classes to his schedule (he had already taken plenty in areas of study that he truly enjoyed). Instead, he needed to take the necessary time to focus his energy on the process of writing unique personal statements, asking the right people for letters of recommendation, and crafting interesting applications.

        I share this story because I know that many parents experience similar levels of anxiety over their child's prospects of gaining admission to one of the "top" UCs. However, it's important to remember that the reality is that selective colleges aren't often wowed by students who only have high GPAs/standardized test scores -- what they are looking for are interesting students.

        To sum up--

        Do SAT/ACT scores and grades matter? Of course they do.

        Are they the only measures that matter? Not by a long shot.

        What always matters? Being an interesting individual.

        So while the scaffolding of an excellent college application requires a solid foundation (GPA, SAT or ACT scores, AP classes, etc.), what really sets top-tier students apart from their peers is a dedication to offering something original and honing their own unique sense of self.

        Math Formulas We Wish Every Student Had Memorized


        Want to score higher on SAT and ACT math sections? Memorize these formulas before you begin prepping. 


        1. Average or mean = Sum of values / Number of values

        Ex: (10 + 12 + 14 + 16) / 4 = 13


        2. Probability = Target outcomes / Total outcomes

        Used to calculate the chances of something occurring from a set of possible outcomes.

        Ex: A jar contains five blue marbles, five red marbles, and ten white marbles. What is the probability of picking a red marble at random?

        5 / 20 = .25 or 25%


        3. Quadratic Formula: x = −b ± √b²-4ac/2a

        Used for determining the x-intercepts of a quadratic (parabolic) equation.

        Ex: A = 1, B = -4, C = 4

        • x = -4 ± √4² – 4 (1)(4) / 2(1)
        • x = -4 ± √ 16 – 4(4) / 2
        • x = -4 ± √16 – 16 / 2
        • x = -4 ± √ 0 / 2
        • x = -4 / 2
        • x = -2


        4. Distance Formula: d=√(x₁ – x₂)² + (y₁ – y₂)²

        Ex. Find the distance between points (6, 6) and (2, 3)

        • d=√(6 – 2)² + (6 – 3)²
        • d=√(4)² + (3)²
        • d=√16 + 3
        • d=√25
        • d = 5


        5. Slope Formula: Slope = y₂ – y₁ /  x₂ – x₁

        Calculate the slope (angle) of a line that connects two points on a plane.

        Ex: Coordinates = (-2, -1) (4, 3)

        • s = 3 – (-1) / 4 – (-2)
        • s = 4 / 6
        • s = 2 / 3


        6. Slope Intercept: y=mx+b

        Formula the defines a line on a plane, given a known slope and y-intercept.

        Ex: Slope = 2, Intercept point (0,3)

        • y = 2x+3


        7. Midpoint Formula: (x₁+x₂) / 2, (y₁+y₂) / 2

        Calculates the midpoint between to points on a plane.

        Ex: Find the midpoint between (-1, 2) and (3, -6)

        • (-1 + 3) / 2, (2 + -6) / 2
        • 2 / 2, -4 / 2
        • Midpoint (1, -2)


        8. Area of Triangle: area = (1/2) (base) (height)

        Calculate the total area within a triangle based on the lengths of the sides.

        Ex: Base = 5, Height = 8

        • a = 1/2 (5)(8)
        • a = 1/2 (40)
        • a = 20


        9. Pythagorean Theorem: a²+b²=c²

        Used to calculate the length of an unknown side of a right triangle, given two sides are known.

        Ex: a = 3, b = 4

        • c² = 3² + 4²
        • c² = 9 + 16
        • c² = 25
        • c = √25
        • c = 5


        10. Area of Rectangle: area = length x width

        Calculates the total area within a rectangle shape.

        Ex: length = 5, width = 2

        • a = 5 x 2
        • a = 10


        11. Area of Parallelogram: area = base x height

        Calculates the total area within a parallelogram.

        Ex: base = 6, height = 12

        • a = 6 x 12
        • a = 72


        12. Area of Circle: π * r²

        Calculates the total area within a circle.

        Ex: radius = 4

        • a = π x 4²
        • a = π x 16
        • a = 50.24


        13. Circumference of Circle: circumference = 2π *  r

        Calculate the length of the outline of a circle.

        Ex: radius = 7

        • c = 2π x 7
        • c = 43.98


        14. Sine (SOH): Sine = opposite / hypotenuse

        A trigonometric identity that represents the relative sizes of the sides of a triangle and can be used to calculate unknown sides or angles of the triangle.

        Ex: opposite = 2.8, hypotenuse = 4.9

        • s = 2.8 / 4.9
        • s = 0.57


        15. Cosine (CAH): Cosine = adjacent / hypotenuse

        A trigonometric identity that represents the relative sizes of the sides of a triangle and can be used to calculate unknown sides or angles of the triangle.

        Ex: adjacent = 11, hypotenuse = 13

        • c = 11 / 13
        • c = 0.85


        16. Tangent (TOA): Tangent = opposite / adjacent

        A trigonometric identity that represents the relative sizes of the sides of a triangle and can be used to calculate unknown sides or angles of the triangle.

        Ex: opposite = 15, adjacent = 8

        • t = 15 / 8
        • t = 1.87

        Do Excellent Grades = High SAT & ACT Scores?

        No, they don't. Students with excellent grades are more likely to score higher on the SAT and ACT.  But many students with high GPAs do not score as high on standardized exams as they presumed they would. 

        It may surprise you to know that the material on the SAT and ACT exams often does not align with what students learn in school (for example, students are rarely asked to write, edit, and submit an entire essay in under forty minutes). ACT and College Board work quite hard to align their assessments with what is taught in high school. But as you might imagine, it is extraordinarily difficult to create one standardized exam that assesses what millions of students across the country (and the world) learn in high school.

        The key is that students should not fear the disconnect between the material they learn in school and the questions they'll face on the ACT and SAT. Instead, they should recognize the exams for what they are -- stepping stones on the path to their goals for the future.The SAT and ACT reward students' hard work and dedication. With the right instructors, the right system, and a little bit of elbow grease, students can improve their scores dramatically. 

        Viewed in this context, the SAT and ACT are no longer assessments -- they are opportunities. 


        Would you like to schedule a free practice exam for the ACT, SAT, HSPT, SSAT, or ISEE?

        Contact us here.


        Test Prep: 8 reasons why 1-on-1 is more effective than a class

        We are often asked why 1-on-1 instruction for the SAT or ACT is superior to classroom instruction. Here are just few of the reasons: 

        1. Students will have the full attention of their instructors to maximize specific strengths and address areas of improvement,

        2. Instructors take time to articulate and understand the student’s short and long term goals and personalize instruction to reach those goals,

        3. The instruction is customized to the student’s particular character, personality, strengths, weaknesses, needs, and goals,

        4. Students are paired with instructors based on their particular needs and personalities,

        5. Students work more efficiently and effectively at their own pace,

        6. The test prep schedule can be tailored to students’ busy lives,

        7. Students receive mental and emotional support to ameliorate testing anxiety and stress,

        8. By monitoring a student’s progress every step of the way, the instructors are able to help students achieve unparalleled success.

        Contact us today to learn more about 1-on-1 preperation

        College Admissions as an Experience, Not a Possession

        We’re all familiar with the adage that “money can’t buy happiness.”  However, research suggests that some purchases yield more happiness than others – namely, experiences make us happier than material possessions.[1] [2]  

        We can apply this same idea to the college admissions process. Families often pursue admission to a highly ranked university as though such prestige is a commodity that can be possessed.  However, we would encourage families to view the college admissions process as an experience of self-exploration; an opportunity to identify long term goals and search for a suitable environment to help achieve said goals. Like the research regarding discretionary spending reveals, adopting this approach helps families to enjoy the overall admissions process and enables them to be more successful at choosing a college that is the right fit for each student's individual aims and aspirations. 

        The same idea applies to standardized test preparation. We tend to treat our desired test score on the ACT or SAT as though it were a possession. However, a standardized score has little inherent value by itself. ACT and SAT scores often help students gain admission to selective colleges or earn merit-based scholarships, but even those ends are only valuable insofar as they lead to the life experiences from which students can learn from, grow, and enjoy.  Moreover, the reality is that a standardized score is never evaluated in a vacuum. Rather, it is assessed among our other achievements such as grades, extracurricular activities, and leadership roles.  Thus, when students view the process of preparing for the SAT and ACT exams as an experience of growth rather than as a pursuit of a commodity, they transform the process into an opportunity to learn valuable skills including, but not limited to, growth-mindset, learned optimism, resiliency in the face of setbacks, overcoming anxiety in high-pressure situations, and successfully achieving long-term goals. 

        To sum up, treating college admissions and test prep as experiences for growth rather than possessions to be obtained will achieve two ends: it will benefit students’ and parents’ overall well-being and life satisfaction, and it will help them to be more effective in their pursuit higher ACT and SAT test scores and admittance to selective colleges.


        [1] Van Boven and Gilovich, “To Do or to Have? That Is the Question” (Journal of Personality and Social Psychology, Dec. 2003)

        [2] Gilovich et al., “A Wonderful Life” (Journal of Consumer Psychology, Jan. 2015)

        How Colleges Can Admit Better Students

        This thought-provoking article from the New York Times, How Colleges Can Admit Better Students was published by the New York Times on 18 March 2017.

        Among other interesting observations, the researchers conclude that:

        • ACT composite scores do correlate with a student’s success in college, but Math and English section scores are much better predictors of success.
        • Students whose overall G.P.A. is a result of better grades during their junior and senior years are much more likely to succeed in college than students with the same overall G.P.A. who did better during their freshman and sophomore years.


        How Colleges Can Admit Better Students

        By DEVIN G. POPE MARCH 18, 2017

        As colleges nationwide prepare to announce this month which applicants they have decided to accept, it’s worth asking why so many admissions offices pass up easy opportunities to admit higher-quality students.

        Nearly all colleges, for example, make use of two metrics to gauge student quality: cumulative high school grade point average and composite score on the ACT (the most widely taken college admissions exam). But research has shown that these metrics are imperfect: They are less predictive of student success than alternative measures that are equally simple to calculate and whose use would lead to a better incoming class.

        Consider grade point average. Students whose overall G.P.A. is a result of doing better later in high school (say, junior and senior years) are much more likely to succeed in college than students with the same overall G.P.A. who did better early in high school (say, freshman and sophomore years).

        A paper in The Journal of Public Economics by the economist George Bulman provides evidence for this claim, using data from Florida. He shows that an additional G.P.A. point in 11th grade makes a student 16 percentage points more likely to graduate from college, whereas an additional G.P.A. point in ninth grade makes a student only five percentage points more likely to graduate from college. Later high school G.P.A. is approximately five times more predictive of whether a student drops out of college within two years, and two times more predictive of eventual labor market earnings.

        Something similar is true of ACT composite scores. These are the rounded average of scores on four individual sections of the ACT (math, English, reading and science). By using the ACT composite score, college admissions offices are giving equal weight to each of the four subtests. But in a 2013 paper I wrote with the education researchers Eric Bettinger and Brent Evans, using data from public college students in Ohio, we provide evidence that the math and English subject tests are far more predictive of college success than the reading and science tests.

        For example, a student who achieves an ACT composite score of 24 by getting a 26 on the reading and science tests and a 22 on the math and English tests is 10.4 percentage points more likely to drop out of college by the third year than a student who achieved a composite score of 24 in the opposite manner.

        Don’t get me wrong: Cumulative high school G.P.A. and ACT composite scores do correlate with a student’s success in college; there is no great harm in having admissions offices use them when considering student applications. But there is also no point in using them when these better metrics are just as easily available.

        So why are colleges sticking to the old approach?

        Admissions officers may be worried that reweighting high school G.P.A.s or ACT scores will affect the diversity of the student body they admit. Both the papers discussed above, however, find reweighting does not adversely affect minority students (if anything, it helps them).

        Colleges may also be reluctant to adopt these more predictive metrics because popular college rankings, such as those produced by U.S. News & World Report, use the old metrics in their calculations. While it is possible that schools using the more predictive metrics would see a small initial drop in rank (because of the mistaken appearance of admitting a student body of lower quality), most schools would more than make up for this drop by improving their graduation rate four years later. (Ideally, U.S. News & World Report and others would adjust their methodology to reflect the most recent research on what predicts student success.)

        Admissions officers may also lack the proper incentives or feedback necessary for change. Whether or not a student does well in college is not something you can typically determine until a few years after the admissions decision, and thus admissions officers may not feel that they are blamed or rewarded for student success. University officials need to actively encourage admissions offices to take a long-term perspective.

        The two examples above — G.P.A. and ACT — provide just a glimpse into the growing field of data and analysis relating to college admissions. Some colleges, such as West Virginia University and Houston Baptist University, are already using sophisticated statistical methods to predict which students are most likely, if accepted, to matriculate and, therefore, where recruiting efforts should be focused. Other colleges, such as Georgia State University and the University of Arizona, are trying to predict which of their current students are most at risk of dropping out, and how best to help these students with additional support.

        But most colleges have yet to take advantage of even simple improvements that a more data-driven process suggests. These schools are missing out.


        Devin G. Pope is a professor of behavioral science at the Booth School of Business at the University of Chicago.

        This article was published by the New York Times on 18 March 2017

        Parent Question: "Why is the PSAT capped at 1520???"

        We received this question from a parent:

        Hi Nick,

        I have a PSAT/SAT question and I am sure you have a very logical answer!

        So from my understanding, the PSAT is out of 1520. If that is true, then why does it say that if a student took the SAT on that same day, they would receive the same score? How can that be, if the PSAT is out of 1520 and the SAT is out of 1600?

        Hope you are well! 

        -From a concerned parent whose named has been removed for privacy reasons



        Hi concerned parent whose named has been removed for privacy reasons, 

        That is a great question as this is confusing to a lot of people (and the PSAT 8/9 only goes up to 1440, just to complicate things further!)

        But the answer is pretty straight forward... 

        A student's score on the PSAT is estimated to be what they would score on the actual SAT. So, a 900 on the PSAT is estimated to be a 900 on the SAT... 1150 is 1150...1350 is 1350...and so on, all the way up to 1510.  

        The exception is with students who get every question on the PSAT correct. These kids are capped at 1520.  The PSAT does not contain the highest level difficulty questions that are found on the SAT. The College Board caps these students at 1520 because they don't know if these students would answer the highest difficulty level questions correctly or not.

        So to recap, the PSAT and SAT are on the same scale for all scores...students just can't score higher than 1520. 




        Do you have specific questions about your PSAT score report?  

        Practice testing protects memory against stress

        (MEDFORD/SOMERVILLE, Mass., Nov. 24, 2016)—Learning by taking practice tests, a strategy known as retrieval practice, can protect memory against the negative effects of stress, report scientists from Tufts University in a new study published in Science on Nov. 25.

        In experiments involving 120 student participants, individuals who learned a series of words and images by retrieval practice showed no impairment in memory after experiencing acute stress. Participants who used study practice, the conventional method of re-reading material to memorize it, remembered fewer items overall, particularly after stress.

        Ayanna Thomas, PhD, associate professor of psychology, “Typically, people under stress are less effective at retrieving information from memory. We now show for the first time that the right learning strategy, in this case retrieval practice or taking practice tests, results in such strong memory representations that even under high levels of stress, subjects are still able to access their memories,” said senior study author Ayanna Thomas, Ph.D., associate professor and director of the graduate program in psychology at Tufts.

        “Our results suggest that it is not necessarily a matter of how much or how long someone studies, but how they study,” said Amy Smith, graduate student in psychology at Tufts and corresponding author on the study.

        The research team asked participants to learn a set of 30 words and 30 images. These were introduced through a computer program, which displayed one item at a time for a few seconds each. To simulate note taking, participants were given 10 seconds to type a sentence using the item immediately after seeing it.

        One group of participants then studied using retrieval practice, and took timed practice tests in which they freely recalled as many items as they could remember. The other group used study practice. For these participants, items were re-displayed on the computer screen, one at a time, for a few seconds each. Participants were given multiple timed periods to study.

        After a 24-hour break, half of each group was placed into a stress-inducing scenario. These participants were required to give an unexpected, impromptu speech and solve math problems in front of two judges, three peers and a video camera. Participants took two memory tests, in which they recalled the words or images they studied the previous day. These tests were taken during the stress scenario and twenty minutes after, to examine memory under immediate and delayed stress responses. The remaining study participants took their memory tests during and after a time-matched, non-stressful task.

        Stressed individuals who learned through retrieval practice remembered an average of around 11 items out of each set of 30 words and images, compared to 10 items for their non-stressed counterparts. Participants who learned through study practice remembered fewer words overall, with an average of 7 items for stressed individuals and an average of a little under 9 items for those who were not stressed.

        Amy Smith, graduate student in psychology“Even though previous research has shown that retrieval practice is one of the best learning strategies available, we were still surprised at how effective it was for individuals under stress. It was as if stress had no effect on their memory,” Smith said. “Learning by taking tests and being forced to retrieve information over and over has a strong effect on long-term memory retention, and appears to continue to have great benefits in high-stakes, stressful situations.”

        While a robust body of evidence has previously shown that stress impairs memory, few studies have examined whether this relationship can be affected by different learning strategies. The current results now suggest that learning information in an effective manner, such as through retrieval practice, can protect memory against the adverse effects of stress.

        Although the research team used an experimentally verified stress-inducing scenario (Trier Social Stress Test) and measured participant stress responses through heart-rate monitors and standardized self-reported questionnaires, they note that stress effects are variable between individuals and additional work is needed to expand on their results. The team is now engaged in studies to replicate and extend their findings, including whether retrieval practice can benefit complex situations such as learning a foreign language or stressful scenarios outside of a testing environment.

        “Our one study is certainly not the final say on how retrieval practice influences memory under stress, but I can see this being applicable to any individual who has to retrieve complex information under high stakes,” said Thomas, who is also director of Tufts Cognitive Aging and Memory Lab. “Especially for educators, where big exams can put a great deal of pressure on students, I really encourage employing more frequent more low-stakes testing in context of their instruction.


        Would you like to schedule a free practice exam for the ACT, SAT, HSPT, SSAT, or ISEE?

        Contact us here.




        Article Originally posted: http://now.tufts.edu/news-releases/practice-testing-protects-memory-against-stress