That’s why we run Knewton Open House, a free online seminar, Q&A session, and all-around SAT prep get together.

Next session: Monday, March 15 @ 8pm
Register now.

• Each free open house includes:

• An SAT orientation that breaks down the test section by section

• A detailed walkthrough of the layout, features, and reporting tools that are built into the Knewton course

• A half hour of Q&A—just chat your questions for instant feedback

Want to host an open house in your home?

If you get a small group of five or more parents together for the seminar, we’ll throw in for pizza (plus some Knewton gear). Register now.

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Kristen is one of our bestest teachers, helping students across the country with their SAT prep. She’ll be leading the webinar.

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Prime Factorization: My single favorite topic on the GMAT. It’s not even a contest.

My passionate (some would say evangelical!) advocacy of prime factorization results not only from my finding prime numbers so inherently fascinating in and of themselves, but also from the plain and simple truth that prime factorization proves surprisingly useful on questions on which prime numbers aren’t even mentioned.

For example, any time you’re given a question asking about multiples and factors, you can bet that prime factorization will help you get to the answer quicker.

Case in point — this Data Sufficiency question from the Official GMAT Guide:

If positive integer x is a multiple of 6 and positive integer y is a multiple of 14, is xy a multiple of 105?

(1) x is a multiple of 9

(2) x is a multiple of 25

Notice, no mention of prime numbers at all. But take any other approach to this problem, and you’re likely to get pretty frustrated and lost rather quickly. You could certainly test numbers, but good luck taking only two minutes finding values that work for every case!

Now, I’m going to re-write the question and statements using only prime factorizations:

If positive integer x is a multiple of 2*3 and positive integer y is a multiple of 2*7, is xy a multiple of 3*5*7?

(1) x is a multiple of 3*3

(2) x is a multiple of 5*5

All of a sudden, the question becomes much more manageable. We know from the prompt that x carries at least one 2 and one 3 as factors. We also know that y carries at least one 2 and one 7 as factors. Therefore, the product xy must carry at least two 2s, one 3, and one 7. We are asked if xy carries at least one 3, one 5, and one 7 as factors. After reading the prompt, we know xy has one 3 and one 7, so all that’s missing is the one 5.

Notice what we’ve just done: We’ve shown that in order to establish sufficiency, all we need to do is determine whether there’s a factor of 5 somewhere in x or y (or both).

Statement 1 lets us know that x has two 3s and mentions nothing of 5s. But that doesn’t necessarily mean there isn’t a 5 there. There also might be a factor of 5 in y. Because we cannot determine the presence or absence of factors of 5, this statement is insufficient.

Statement 2, on the other hand, lets us know that x definitely has a factor of 5. And again, we already know from the prompt that x has a factor of 3 and y has a factor of 7. Therefore, the product xy has at least one 3, one 5, and one 7 as factors, and we can conclude unequivocally that xy is a multiple of 3*5*7 = 105. Sufficient.

Final answer: B

Even on questions that do explicitly mention prime numbers, things can get really ugly really quickly if you don’t use prime factorization.

For example, take this Problem Solving question, also from the Official Guide (answer choices not included):

In a certain game, a large container is filled with red, yellow, green, and blue beads worth, respectively, 7, 5, 3, and 2 points each. A number of beads are then removed from the container. If the product of the point values of the removed beads is 147,000, how many red beads were removed?

The use of 2, 3, 5, and 7 is a prime clue (pun very much intended). You might look at 147,000 and panic because the number is so large. But let’s break down 147,000 into it’s prime factorization:

147,000

= 147 * 1000

= (7 * 21) * 10 * 10 * 10

= (7 * 7 * 3) * (2*5) * (2*5) * (2*5)

Now, the question asks us how many red beads were removed. Red beads are associated with a point value of 7.

We know that the final point total was 147,000, and when we broke that number down, we found that there were only two factors of 7. Therefore, the only way we could get that score is if we removed 2 red beads. That’s it! 2 is our final answer!

These are just two examples of a large number of questions made easier by prime-factor prowess. Practice making those factor trees! And notice how prime numbers help you answer questions about other topics like Greatest Common Factor and Least Common Multiple.

Photo by Tim Alamenciak

Kalyan is a top teacher at Knewton, where he guides students through their LSAT prep.

Lecture based classes are common largely because they are easier to implement from an organizational standpoint, thus helping keep tuition costs lower than they would otherwise be. But there is a tradeoff – they are also far less optimal from a pedagogical standpoint than smaller, more interactive classes because the single-paced nature of the lecture just isn’t appropriate for the needs of a large number of students.

I encountered this problem rather frequently at the undergraduate level. For the better part of three hours every Tuesday evening, I would fight to avoid falling asleep in a packed auditorium, while the professor would lecture and write scarcely legible chemical reactions on a chalkboard that happened to be much too small for the room. The conundrum I found myself in was that I could learn the material covered in three hours of class if I spent 45 minutes alone with my textbook. I didn’t need to be an economist to figure out that spending three hours in that suffocating and dimly lit auditorium was an incredibly inefficient allocation of my time.

Ten years later, I am finishing up my third Masters degree (in Economics of all things) and am confronted with yet another iteration of the same problem, except I now have additional commuting time to deal with. It now takes me a total of 4.5 hours to assimilate the information I could in 60 minutes on my own. Attendance is compulsory, as a result of which I estimate that I will waste 42 hours in class this semester.

But I am not the only type of student whose needs aren’t being met. Consider the predicament of a student who pays attention for 3 hours in class and for one reason or another, still doesn’t quite get it. This student might be better served by spending 5 hours on the same material. This brings me to my central point- given the technology available, it seems absurd to put the two of us in the same lecture and settle on a mean duration of 3 hours which would neither address my needs nor hers/his.

We typically assume that “student ability” is normally distributed i.e. the student described above and I would fall on the periphery of this distribution with most students clustered around the mean. While that might appear to mitigate the severity of the problem, I have yet to see any concrete measurement of “student ability” or, more pertinently, evidence of its application on a group by group basis. I am, of course, talking about learning, and not grading, which tends to be more accommodating, if dangerously so.

The detrimental effects of compulsory attendance requirements coupled with ineffective teaching are understandably more amplified for students with non-traditional learning styles and/or other constraints.

My security guard, for example, works full-time to fund his college degree, and is also taking a full load of classes. It is inevitable that he will not be able to attend every session, and it is quite likely that his grades will suffer even if he does a stellar job on all the assigned exams and homework material. This is a consequence of the fact that in far too many cases, in addition to a student’s academic performance, attendance is treated as a mandatory requirement. This is most frequently manifested in the form of “If you miss more than x number of classes, you will drop one (half/full) letter grade”.

There is something fundamentally wrong with this premise. Learning styles can be quite diverse and it is dangerous to assume that learning is well correlated with attendance, particularly in large classes. In an ideal world, this would be the case, but in a system riddled with inefficiencies – one in which it is the norm to judge professors on the basis of their research prowess instead of their merits as teachers, this connection may well prove tenuous.

Such a grading scheme also doesn’t account for how long an individual spends on the material outside class, which could, at least for some students, be a better determinant of performance. In the case of the aforementioned security guard, most of his learning happens while he is sitting at the guard’s desk, in between pushing buttons to let people into the building. Should he be penalized for where he chooses to study?

His case is made stronger by the fact that unlike days past, teachers aren’t the only resource that students have. The advent of search engines, online journals, online encyclopedias etc. have meant that the proactive student will never suffer a dearth of resources.

It is also worth considering the evolution of the intellectual toolbox that educational institutions aim to impart to students. This toolbox certainly shouldn’t be the same as it used to be. The collection of tools and skills required to thrive today isn’t the same as it was in the 1960’s or even the 1980’s. For example, with ready access to search engines, recalling arcane details is no longer as vital. What is more important, however, is being able to make sense of the endless reservoir of information that is the internet, and being able to separate reliable, well-founded information from inadequately supported, misleading and/or downright false information. This necessarily means that students need to receive more training in elementary logic and critical reasoning in order to avoid these pitfalls of unsupervised learning. Existing curricula need to place a far greater emphasis on this fundamental skill than they currently do.

This will also need to be accompanied by the evolution of the role of a teacher from “sole information provider” to “learning facilitator”. Persisting with the “sole information provider” strategy in this day and age may be dangerous because it engenders an approach to learning that revolves solely around attending class and not putting in much effort outside of it, which can be a serious handicap to overcome once students are outside the academic establishment.

From the perspective of a graduate student, there may not be a better substitute to face-to-face interaction with exceptionally accomplished researchers. Research institutions are a place where experts aggregate and great minds often collide. The benefit to society from these activities certainly cannot be overstated. Graduate students are typically better off than their undergraduate brethren because class sizes in graduate programs tend to be much smaller, with students being more rigorously selected, thereby allowing for an environment in which every individual’s needs can be addressed (most of the time).

Undergraduate students, however, are vastly different beasts and are not normally given the privilege of the intimate class setting (the rare individuals that are pay dearly for it). The typical introductory undergraduate course has at least 40 students and consequently takes the form of passive learning from lectures designed to meet the needs of the amorphous “average student.”

Compounding these problems is the fact that the tenure system, despite its benefits, has made it possible for lazy researchers to impart little or no useful knowledge to their students in the classroom, particularly in schools that cater to disadvantaged demographics. Considered a bad influence on graduate students, such teachers are often relegated to teaching- you guessed it- undergraduate courses, where they are free to be as lazy and pointlessly tyrannical as they please.

From a pedagogical standpoint, any system that aims to provide a single solution for a diverse variety of learning needs is necessarily bound to be inefficient. The tools provided by technology offer solutions, however.

If evidence were required that an online learning platform can be as effective as a physical one, the success of Knewton’s model provides an excellent example. With our team-teaching approach we are able to utilize the benefits of a lecture environment while simultaneously being able to address individual student concerns and questions that may have otherwise prevented them from fully understanding the material that followed.

Importantly, we offer a variety of algorithm based learning tools. With a web-based approach, it is possible to identify individual student weaknesses on the basis of their performance in well characterized areas of a test. Further, we are able to give students the opportunity to hone those skills in a focused manner (e.g. with Create a Quiz on the LSAT course).

This list, however, is merely a humble beginning. We have only recently begun to really delve into the wealth of student performance data we generate on a daily basis and are working furiously to produce practical tools that will help students generate a customized self-study program which will be complemented by the live lessons and archives that are currently available.

While our product offerings are currently limited to standardized tests that we have developed curricula for, there is no reason why this model cannot be applied to high-school and college-level courses. Since online learning platforms are massively scalable, a greater number of students could realistically be taught by the best instructors in the field. Perhaps even more importantly, they will have a wealth of learning tools as well as virtual resources to help them diagnose the specific concepts they are having trouble with and to develop custom learning programs that cater to their individual strengths and weaknesses rather than abstractions like “mean student ability.”

Next time: How standardized testing can (contrary to public perception) help level the playing field for everyone.

• VentureBeat wrote about the launch of our SAT course. Read the great article here.

• To celebrate the launch, we’re giving away 5 FREE SAT courses to deserving students.

• Knewton is now also on Tumblr. Bookmark it and come back for updates on, among other phenomena, the standing desk craze in our office.

• Our team is growing quickly and we’re hiring for several positions. Keep checking in at our the Knewton jobs page.

• Our CEO Jose is tweeting. Follow him; he’s says interesting things very often (I sit near him and hear).

No two students are the same. So it’s not a surprise that traditional prep courses don’t work for everyone. If you’ve been burned by a prep course that wasn’t a match for you, we feel your pain. And we’re here to help.

If you took a classroom prep course in the past year and weren’t happy with your results, we’ll give you 50% off a Knewton GMAT course or LSAT course.

Just complete this form and tell us about your experience with others. Once we’ve confirmed your old enrollment, we’ll send you a promo code for the discount.

Check out our free trial of GMAT prep or LSAT prep to see the ways Knewton works for you, and see what our customers say.

Get your second chance

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If you’re a recent or soon-to-be college grad (or maybe you realized your undergrad degree in Art History ain’t gonna pay the bills) and you are passionate about computers and computer programming, here are my tips for becoming a successful practicing software engineer. Many of these things probably aren’t the things they taught you in your college programming classes, but all of these are important.

Read more after the jump.

1. Practice! Practice! Practice!

You learn to code by, um, reading and writing code! If you don’t have much experience and want to get started, find an open source project you care about and contribute a patch or two.  The “View Source” feature of Web Browsers and the open source movement are 2 of your greatest assets when learning to code.  Use them! As someone who started his career copying BASIC programs from Compute! and Byte magazines, I can’t tell you how great it was to discover the magical “View Source” menu item in Netscape.  Open Source projects will teach you about packaging, style guidelines, automated testing, bug tracking, and version control — while also giving you much needed practice. Don’t forget, your code doesn’t *work* until someone else uses it.  If you can’t work at a startup and need to get code into the hands of users quickly, open source projects are a great way to go.  I still recommend going with the startup, though.  At Knewton, everyone from summer interns to new full-time engineers ship code (that customers actually use) in their first couple weeks of starting.  I’d like to get this down to the first day.In your early practicing, make sure to develop really strong habits.  I learned the most of my habits from Steve McConnell’s Code Complete and Kent Beck’s eXtreme programming.  Write code others can support if they need to, but try to make it so they don’t need to support it I’d also recommend checking out PragDave’s Code Kata site to work on solving problem:

http://www.codekata.com

2. Work at a startup!

You will learn more in your first month at a startup than you will in your first year in any other company.  The first company I worked for was a 3-person shop in Syracuse, NY.  I learned everything from how to become a practicing software engineer, to how to be a customer support person, estimate and bid consulting jobs, write requirements, QA, write user manuals, configure SQL Servers, configure IIS Servers, configure linux firewalls … If your first job entails you being handed requirements that you then write code for and hand “over the wall” to QA – run!Don’t just take my word for it.  Here’s what one of our former interns who recently graduated and landed a sweet job in CO had to say:

“I had NO experience as a coder.  You guys gave me a LOT.  In fact, more skillz than you can really understand. Things that transferred over beyond Ruby, RUnit, Rails, MySQL unix commands (I’m loving that I actually understand how to use the CLI in my Ubuntu set up btw…), etc – more the ability to take a bunch of instructions I barely understood and google my way/solve my way to a solution.”

Joining a startup is less risky than you think.

3. More specifically, work for my startup

4. Don’t be afraid to make mistakes! or Perfection is for popes and Chinese emperors.

In 1999, I got my first big job at an online brokerage (Datek) in NYC.  This was back when everyone, probably including you, traded online and doubled their money daily – basic fundamental laws of economics changed… until they didn’t.  The day of my first big release, I took down the ability to login to the production site at market open.  This was, as my CTO at the time reminded me, “reeeeaaaaaaalllllly baaaaaddddd.”  However, we talked through the problems and took the appropriate steps to ensure I couldn’t make the same mistake again (it involved improper DB connection handling, lack of performance testing, deployment timing and rollback procedures).  If he fired me, maybe I’d feel differently about making mistakes.  Fortunately, for me, he understood these types of mistakes will happen — as long as you’re willing to grow from the mistakes and not repeat the same mistake twice.Don’t forget that coding is a creative endeavor; typically, there is no one correct solution.  Be prepared to try several.

5. Reality… zen and the art of “boring” tasks.

You studied sexy problems in school, you know how to solve nine-queens efficiently, find shortest path in a graph, compute Chebyshev distance in a metric space…the large part of your day as a software developer will not be spent working on such problems. More than likely you will spend a day on a far wider range of tasks that are comparatively less interesting in an engineering/problem-solving sense. These lower-level tasks are generally more simple and yet each decision that is made in their execution can be evaluated and perhaps improved upon. Design details as small as method signatures, naming conventions, loop constructs or recursion, tail-recursion or not (maybe even that’s too sexy!), are both extremely important and regularly overlooked. A large program is built on many lines of code. Each line contains required prior decisions to produce. An appreciation for these small details will contribute a lot not only to the quality of the program as a whole, but to the education of the coder.If you’re not already in a coding-related field, look for ways to make your current job more efficient through automation.  This can be as simple as creating access databases, word mail merges and batch files to automate tasks that used to take you hours or days to complete.  This is actually how I got my start coding professionally, by building MS Access database apps that made week-long tasks takes hours (mass mailings to customers at an HVAC rep and students at the SU Masters of Public Administration program).

6. Finish!

You don’t get any points for effort.  You need to finish what you start.  Half-written, incomplete code atrophies very, very quickly.  If you find yourself starting more than you finish, you need to revisit the scope of your problems.  Code against smaller problems, but finish the code!

The tour will feature 24 startups doing exciting work, and—you guessed it— not doing it in Silicon Valley. This summer, Bob, his family, and a TV camera crew will travel the country in their 1996 Winnebago motor home, filming the finalists as part of a reality show for a major cable channel.

Help Knewton be one of those startups!

Visit here and search for Knewton. Rank us with five stars and comment on our nomination to help ensure that we make it to the top 24. Thanks!

Affordable, Interactive Test Prep Course with Advanced Capabilities Provides Students Around the World with the Resources They Need to Ace the SAT

New York, N.Y. — March 2, 2010 — Knewton, a leading online educational company, today announced the launch of its new SAT prep course. The course is the first in the industry to use adaptive learning technology to ensure that students raise their test scores. By hiring only the best teachers in the country and broadcasting classes online, Knewton offers a course far superior to any other, for a fraction of the price. With an introductory offer of $290 per course (regular price only $490) and the industry’s top money-back guarantee—at least a 150-point gain or a full refund—Knewton is offering the smartest test prep at an affordable price to aspiring college students.

Read more here.

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Data Sufficiency questions are often difficult to get used to, because they require an adjustment in your approach to math problems.  When you went through math classes growing up, the end goal was always “Find the value of x” or “Find the area of this circle.”  You were asked to give hard responses to these questions, and nothing mattered more than finding a definite value.

With Data Sufficiency, answering the question does not matter as much as the ability to answer the question.  You are not primarily concerned with the final answer, but rather whether you have enough information to get you to that answer.  For example, if you’re asked to find the value of x, and a statement tells you that 300x + 257 = 1345, you know that this statement is sufficient, because you can perform arithmetic on that equation to isolate x.  Are you going to perform it?  No, because it’s too complicated and you don’t need to!  All you’re concerned with is whether you can find the answer.

It might strike you as odd, but because of this principle, you can tackle some supposedly difficult DS questions without writing down a single equation or calculation!  Sounds too good to be true, but in actuality, it makes a lot of sense.  Remember, in business school you’ll be given data in case studies, and you’ll be expected to determine relatively quickly what information is relevant.  DS questions are perfect for testing this ability because you have to look at the information given to you and cut to the heart of what is most important about that information.

As an example, let’s look at this rather wordy DS problem:

Martha bought an armchair and a coffee table at an auction and sold both items at her store.  Her gross profit from the purchase and sale of the armchair was what percent greater than her gross profit from the purchase and sale of the coffee table?

(1)  Martha paid 10 percent more for the armchair than for the coffee table.

(2)  Martha sold the armchair for 20 percent more than she sold the coffee table.

First, let’s approach this algebraically to show how cumbersome it ends up being:

In general, Gross Profit (P) is the Selling Price (S) minus the Buying Price (B):

P = S – B

We want to know what percent greater the profit of the armchair (P_armchair) is than the profit of the coffeetable (P_coffeetable).  If we represent the missing percent as x, then the equation would be

P_coffeetable*(1 + x/100) = P_armchair

Rearranging, we would get:

x = 100*(P_armchair / P_coffeetable – 1)

We know that P = S – B, so we can substitute:

x = 100*[(S_armchair - B_armchair/ (S_coffeetable - S_coffeetable) - 1]

Confused yet??  I sure am!!

But try to look at things from a sufficiency point of view.  Notice that you need absolute values for the gross profits in order to solve for x.  You could also find the ratio between the two gross profits.

Now that we’ve seen how ugly this looks when all the algebra is written out, let’s take a more common-sense approach.

The prompt:

Martha bought an armchair and a coffee table at an auction and sold both items at her store.  Her gross profit from the purchase and sale of the armchair was what percent greater than her gross profit from the purchase and sale of the coffee table?

What we need in order to determine sufficiency:

In essence, this question asks you to compare the values of two profits.  You need the value of each profit OR the ratio between the two profits.  Notice that you can figure out what information you will need without writing down a single number or algebraic expression.

What each statement tells us:

(1)  Martha paid 10 percent more for the armchair than for the coffee table.

Without writing any math, you can deduce that this is insufficient, because buying prices are mentioned, but no selling prices.  And with no selling prices, we certainly can’t determine anything about profit.

(2)  Martha sold the armchair for 20 percent more than she sold the coffee table.

Now, we’ve got information about selling prices, but nothing about buying prices.  Again, Insufficient because there is no way to determine profits.

So far, nothing too difficult.  It’s pretty simple to narrow this down to C and E.  But how do we determine whether the statements together are sufficient?

You could test numbers here, but really all you need to do is realize that the statements only give you percentages to work with.  For the sake of illustration, let’s pick numbers to see what this means:

According to Statement 1, Marta could have spent $100 on the coffee table and $110 on the armchair, or it could have been $10 on the coffee table and $11 on the armchair.  (Unlikely prices, maybe, but remember, the real world doesn’t apply here!)  There are infinite possibilities for what the buying prices could have been.

Likewise, Statement 2 tells us that Martha could have sold the coffee table for $100 and the armchair for $120.  Or it could have been $10 for the coffee table, $12 for the armchair.

You’ll notice that because the absolute numbers for selling and buying prices vary so much, so too do the gross profits!  And if the gross profits can fluctuate that drastically, there is no way on Earth you can nail down one specific percentage increase from one profit to the next!

And thus, without writing a single equation, you can determine that the answer must be E.

It’s very very tricky to get your mind to think this way, especially since you’ve been trained all your life to hack away at a problem until you come up with a definite answer.  But it is absolutely imperative that you begin to look past the math of DS questions and ask yourself what information is necessary to solve the problem.

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The two portions of the Writing section on the SAT test the same rules. At Knewton, we break them down into a list called the Freshman 15. Your ticket to a sweet score on this section is to learn these rules. Think about it this way; if someone could give you a list of every vocabulary word that could possibly be tested on your exam and you could ace the sentence completion section by memorizing a list of about 15 words, you’d be ecstatic, right?

What’s even more exciting is that the simplest rules, the ones that are the most easily memorizable, are the ones that are tested on the “hardest” questions. Why is that?

Well, none of us, in everyday speech, would use, let alone recognize an error in a sentence like: “I am at once delighted with the contents of your speech but annoyed with your tone.” The correct version of this sentence is: “I am at once impressed by the contents of your speech and annoyed with your tone.” But once I tell you that “at once…and” must come as a pair, I bet you’d never miss a question testing this concept. Knowing this rule — and the fact that other connector buddies like “neither…nor,” “between…and,” and “just as…so” go together — will get you a hard question right on the Improving Sentences section every time.

The same 15 or so simple and digestible rules come up again and again. Learn them and you’ll be at once eager to tell everyone about your score increase and ready to apply to better colleges.