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Math's Affect On Self-Esteem

“I am just stupid in math,” a student from Stonington High School in Stonington, CT recently said while explaining her algebra woes. In comparison, we almost never hear a student say “I am stupid in English.” Poor math performance affects self-confidence. We have worked with many students from New Haven, CTwho seem to link their math performance with IQ more than other subjects. The objective nature of math is the likely reason. Other students demonstrate with certainty that they have better math skill in a way that reading, for example, is not overtly illustrated. In class, when students raise their hand to answer: “47”, there is something different conceptually than when other students discuss literature.

We recently were working with a student from Guilford High School in Guilford, CT. We’ll call her Andrea. She had convinced herself that she was “stupid in math” and was now in the process of convincing herself that she was “stupid in everything”. Math was really the only subject where she was floundering but it provided evidence, in her mind, that, in her words, “I’m just not smart.”

That’s tough for us to hear as teachers but this is heart-breaking for parents. Andrea’s mom had called us, in part, because she felt that she was failing as a parent. “More than anything, I want my kids to feel good about themselves. I always tell she is smart. But, it doesn’t seem to work anymore.”

Our philosophy centers around mastery and, in relation to self-esteem, we have preached that mastery is what creates self-esteem. We, too, could tell Andrea that she’s smart and try to convince her through other motivational strategies that her abilities in other areas illustrate her brainpower. But, in the face of getting Ds in math, and suffering on a daily basis in math class with evidence – in her view – of her lack of intelligence, our words would only serve as a temporary band-aid.

We had to prove to her to Andrea that she could do better. In doing so, we would demonstrate that she was not stupid. We started with the basics. It became clear that she had never mastered the basics of algebra. She had likely crammed enough to pass the class. But, she struggled to recall the most basic structure of how to solve simple equations. For example, we would show her 2x = 10 and she would say the correct answer: “5” but when we showed her 2x = 73, she did not understand that she needed to, in math terms, “multiply each side by the reciprocal” or “divide by the coefficient” and in layman’s terms for this problem, divide by 2. She had been doing problems in her head and estimating answers but had not mastered the mechanics of equations.

Of course, Andrea felt stupid when she had to do more complex algebraic operations such as foiling.

We dove in to both master the basics and build her confidence. Andrea gradually mastered our systems for mastering math. She could see that if she followed procedure – she was good at straight line direction following – she could move forward in problems. Soon enough, two things happened. She began to do better in math. Her D became a B-. More importantly, the facts proved to her that she was not stupid.

Andrea’s mom actually cried when she heard her daughter say “I am not dumb. I just need to learn more stuff.” So true, for all of us.


The Mastery Process: Getting Through the Plateau

When we use the term, “mastery”, we are generally describing a process. Although we use the term “mastered”, it is only the rare individual who can master complex skills.

What we try to do is help our students on the road to mastery as students and in all their core areas of skill development.

The road to mastery, however, is complex.

Here’s how it often goes:

The student starts at the beginning and progresses until the first roadblock. The student hits a roadblock and then feels frustrated. Here’s where some students get stuck. They have a hard time moving through the roadblock.

This is the plateau that causes great struggle for many students.

They start to feel like they “can’t get it”.

But, that’s usually not the case. We work with students to move through the plateau. Many times internal processing takes some time and ideas begin to click only after the mind has a while to work through the complexity of the idea.

Soon enough, we get them to move upward on the learning curve.

The Importance of the LSAT in Law School Admissions:

We recently came across this article written by Bill Henderson, a Professor of Law at Indiana University:

The Drift Toward Pure Numbers Admissions [by Bill Henderson, cross-posted to ELS Blog]

Law schools are part of a production function for entry level lawyers. Therefore, if law schools alter their admissions practices, the character and complexion of the law school applicant pool can shift in significant ways. On the input side, the data are crystal clear: over the last 15 years, the rankings arms race has pushed U.S. law schools toward a pure numbers approach to admissions. The more interesting question, however, is whether prestige-conscious law firms are now, inadvertently, experiencing any fallout. First the data.

Law schools operate in an environment of supply and demand and are famously counter-cyclical. When Silicon Valley was booming in the late 90s, law school applicants plummeted. When the economy faltered in the early 90s or after 9/11, applicants spiked. Therefore, to examine how admissions practices have changed over time, it is important to pay attention to the underlying applicant pool. Below are trend lines for median LSAT scores by USNWR rank for 1994 and 2007, which reflect classes that entered in the fall of 1993 and 2006 respectively. During those two admissions cycles, the number of applicants was virtually identical: 89,600 (class entering fall 1993) and 88,700 (class entering fall 2006).

Obviously the blue line (2007) is higher than the orange line (1994). In fact, despite slightly fewer law school applicants, the average median LSAT increased by 2.18 points (std. dev. of 1.99). For the record, only three schools fell out of Tier 1 between 1994 and 2007. And it cannot be explained by the ABA policy shift that instructs law schools to no longer average LSAT scores when reporting 25th, 50th, and 75th percentile figures, thus slightly pumping up the volume of high LSAT scores. That change was not enacted until the summer of 2006.

Here is the same analysis for UGPA (1994 data came from the Princeton Review, 2007 from the ABA):

Although we might chock some of the higher UPGAs (avg. of +.17, std. dev. of +.12) on grade inflation between 1994 and 2007, it is likely that schools were also trying to maximize this number. More after the jump ... .

When admissions officers are under constant pressure to beat last year's numbers, something has to give. I suspect it is students who took challenging majors but have LSAT scores slightly under the target. Or applicants with impressive work experience, evidence of leadership, or a history of overcoming major obstacles. Although LSAT and UGPA scores are strongly correlated within the applicant pool, they tend to be very weakly correlated (or sometimes negatively correlated) at individual law schools. Why? Because applicants who are above both medians tend to have admissions offers at higher ranked schools. After a school locks down its target LSAT and UGPA medians, the modest overlap between the two groups means there are precious few spots left. And often those spots are used to improve a school's diversity profile.

Over the years I have talked with many admissions officers. They corroborate the sea change. Further, many of the old hands argue that the current fixation on maximizing numbers is misguided--that, based on their experience, great candidates are being passed over for nondescript or unadventurous students with high numbers. In other words, a large portion of candidates with compelling resumes and personal statements are being systematically pushed down to lower ranked law schools.

At a law firm level, there is a certain irony at work. Many partners could not get admitted to their alma mater; yet, between 2005 and 2007, as NLJ 250 hiring increased rapidly, 53% of the new jobs went to students at USN Top 20 schools. Rigid adherence to the elite law school model drove the starting salary cost structure from $125,000 to $145,000 to $160,000--a legacy that is hard to swallow in a down market. But were these intangibles--now less prevalent at most law elite law schools--part of the firms' secret sauce? To my mind, this is an interesting question. Further, a recent Moneyball study by Kerma Partners suggests that the answer may be yes.

The Importance of Grades and the New Economy

To paraphrase Thomas Friedman, author of The World Is Flat who paraphrased Bill Gates:

Twenty years ago, from a purely career-financial perspective, if you had the choice of being a “B” student from Brooklyn or an “A” student from Bombay, you would choose the former because America’s economic domination was so thorough that opportunities were abundant for even our average students.

Today, however, many would choose to be the “A” student from Bombay.

Why?

The Internet’s power has created an interconnected world that outsources many knowledge based jobs.

In the 80s, many manufacturing economies did not see the challenge of outsourcing until their cities started shutting down.

Many children of manufacturing workers were “educated” that they would be working at the local plant when they reached adulthood. Consequently, many parents did not put much emphasis on getting a college education. Their now grown-up kids subsequently suffered as there were fewer jobs awaiting unskilled laborers.

There is a similar phenomenon taking place in the lower to mid-range level white collar world.

Those who have jobs that can be done at a fraction of the cost by an English-speaking worker from a different country (India as the most notable) are losing their jobs at a rapid rate.

To give but one example, H&R Bloch, the noted tax preparation firm no longer hires thousands of American accountants to prepare basic tax returns. Instead, most of the work is done by Indian accountants who work cheaper (and many would say harder and better) than the average new accountant from an average US college.

Metaphorically, those called on to do the work on the higher end (where jobs are secure) will be the “A” students, not necessarily the “B” students and probably not the “C” students.

Many of the high school students we meet in Southeastern, CT do not fully understand that getting better grades will have a direct impact on their college choices and that their college will have a direct impact on their job prospects.

Indeed, many parents are still in the 1980s-1990s mentality of US world economic domination where jobs were plenty for any student from any college.

We recently worked with a student from Essex, CT. He had a problem turning in his homework on time.

Yet, he had grand ambitions for his career. He wanted to make a “ton of money on Wall St.”.

His grades, however, were consistently doomed by his attitude toward homework.

We met him when he was a senior at a prep school in Southeastern, CT. It was too late to shift his college admissions opportunities (a 2.5 G.P.A. would not impress many admissions’ officials!). He was admitted to a non-prestigious college in New England with no history of sending its graduates to Wall St. or other top financial entry ways.

We are still working with him in a virtual tutoring capacity as he hopes to attain top grades in order to transfer. It would have been far better, however, had he understood the connection between grades and potential college choices years ago.


The Learning Consultants
(860) 510-0410
dcapuano@learningconsultantsgroup.com