The College Graduation Crisis: How Remediation Fits In

September 30th, 2011

From 1970 to 2009, undergraduate enrollment in the United States increased by 138%. Over the same time period, however, the college completion rate in the U.S. remained pretty much the same.

What gives?

This is the question at the heart of a comprehensive new report from Complete College America (CCA), “Time is the Enemy: The surprising truth about why today’s college students aren’t graduating… and what needs to change.”

The report trains its eye on how well America’s public colleges and universities are educating students and includes data from full time, part-time, remedial, and transfer students, as well as those earning career certificates.(According to CCA, until this report, “no one has bothered to measure and report the success” of non-traditional students — who make up a whopping 75% of students at public higher-ed institutions.)

“Time is the Enemy” identifies some of the major factors contributing to today’s college completion crisis. Unsurprisingly, “broken approaches to remediation” is one. Currently, remedial students are significantly less likely than non-remedial students to earn a college degree — according to the report, only 35.1% of remedial students earn a 4-year degree within 6 years, compared to 55.7% of all students.

So how do we fix remediation? Here are a few of CCA’s suggestions (read the full report for more):

  • When possible, enroll students into college-level courses instead of remedial courses. “Provide co-requisite and embedded support for those needing extra help.” This way, students can begin earning credits toward their degree right away.
  • If developmental courses are absolutely necessary, make them quick: “intensify instruction.”
  • Revisit developmental course curricula to ensure that what’s being taught is what’s really needed. The report singles out revisiting the format and goals of remedial math in particular: “math should be a gateway, not a gatekeeper, to successful college and everyday life.”
  • Improve placement tests; provide students with prep materials ahead of time to encourage success.

Improving remedial courses is just one of Complete College America’s recommendations for ushering more students into graduation hats and off to broader career opportunities. To read more about CCA’s recommendations and check out detailed state data, read the report.

College Readiness News Roundup: Stagnant College Graduation Rates, Readiness in Rural Schools, and More

September 30th, 2011

A stack of newspapersIn this week’s College Readiness News Roundup, read articles about readiness in rural high schools, No Child Left Behind waivers, and the reasons behind stagnant college graduation rates.

1. Rural Schools Work to Improve Students’ College Readiness

After receiving a federal Investing in Innovation grant, 29 Northeast Tennessee high schools are increasing the effort to make students more college-ready. Read more on Education Week’s “Rural Education” blog.

2. No Child Left Behind: With Waivers, Obama Grants Schools Flexibility

Obama will give schools more flexibility under No Child Left Behind, allowing schools to apply for waivers from specific aspects of the law. The waivers would would allow schools to pursue individual plans for school improvement and improved college and career readiness. Read more in this article from The Christian Science Monitor.

3. Revolution in Education Won’t Be Fast or Easy

“It will look worse before it looks better,” warns Rochelle Riley of Michigan’s sweeping plans for educational reform. Read more about Riley’s predictions, and Michigan’s new definition of “proficient,” in this article from The Detroit Free Press.

4. College Graduation Rates Are Stagnant Even as Enrollment Rises, Study Finds

A report by Complete College America shows that despite growing enrollment, graduation rates aren’t budging — and remedial courses play a large part in the crisis. Read more in this article from the New York Times.

Why Students Don’t Like School, and What Adaptive Learning Can Do About It (Part 2)

September 29th, 2011

Miss Part I of the series? Check it out here.

I recently read Daniel T. Willingham’s Why Don’t Students Like School: A Cognitive Scientist Answers Questions About How the Mind Works and What It Means for the Classroom.

As I was reading Willingham’s investigation, I noticed that most of the real reasons Willingham argues that students don’t like school can be eliminated or reduced through continuous adaptive learning technology. In my first post of this series, I discussed how adaptive learning can improve school by fully engaging students, providing instantaneous or near-instantaneous feedback, establishing a knowledge and hinting scaffold that can guide students in the right direction, and ensuring that each student receives work pitched at just the right level.

Here are some more ways that adaptive learning can eliminate or reduce the reasons that students find school distasteful:

1. Lack of self-awareness about learning patterns.

Many students who dislike school feel overwhelmed by the work and do not know where to begin or how to approach the problems they are given. As a result they feel uncomfortable, internalize the idea that school is not for them, fail to seek help, and fall behind.

This feeling of being overwhelmed is caused by what Willingham calls an overload on “working memory” (the capacity to perform cognitive work using stored factual and procedural knowledge as well as information from the environment). This overload is often caused by the presence of one or more of the following: “Multistep instructions, lists of unconnected facts, chains of logic more than two or three steps long, and the application of a just-learned concept or new material.”

There are several ways that adaptive learning can increase the amount of space in “working memory” and ensure that students don’t feel overwhelmed by the complexity of problems they encounter. As I mentioned in the first post in this series, continuous adaptive learning can provide “factual and procedural knowledge” scaffolding and “chunking hints” that guide a student toward the solution while still allowing him to make the discovery for himself.

The benefits afforded by this approach are intertwined by nature; a “scaffold of factual and procedural knowledge” can improve a student’s “chunking” capacity, or ability to break problems down into multiple steps, which can increase both a student’s rate of learning and the overall exposure to knowledge a student receives. These increases can in turn reduce discomfort, aid in “chunking” ability, improve student performance (which generally improves student confidence), and thereby generate a never-ending positive cyclical effect on a student’s relationship with school. In other words, success breeds more success.

All these transformations and moments of insights will also yield greater self-awareness, the invisible ingredient in successful long-term learning. After all, the ultimate goal for school is that students learn how to teach themselves, how to encounter problems in life or on the job and break them down into steps, process the information, deliver solutions, measure results, and iterate. The processes taught in school should thus become so ingrained and automatic that students know exactly what to do when they encounter certain situations. And if they don’t know what to do, they should know what to do to make themselves know what to do–whether that involves defining the problem further, asking the proper questions, or conducting research and evaluating sources.

What adaptive learning can do about it. While developing greater self-awareness is a natural byproduct of learning, adaptive learning can stimulate and speed up the process by inserting “reinforcement” moments into cognitive work–moments that prompt a student to reflect on the problem-solving process, underscore the concept behind the solution, or describe the structure of some body of information. Even if a student happens to correctly guess the answer to a question, he will not be able to complete the lesson without proving his grasp of the underlying concept. This of course increases the chance he will experience repeat success with a similar problem. Any online learning program can achieve these aims in a basic way, but a continuously adaptive system can bring reinforcement to a new level by evaluating how well such moments are working and by providing reflective moments (and even longer exercises) tailored for each learner’s idiosyncratic style.

2. Social Anxiety.

School is quite obviously more than the sum of its parts (homework, testing, grades, etc), in large part because of the opportunity it provides for students to develop an awareness of themselves in relation to others. Unfortunately this social component can sometimes detract from learning instead of enhancing it. Many students are quiet in class for reasons that are more complex than meets the eye; they may not know how to process information delivered to them or orient themselves within the material. They may have preconceived notions about the subject or not understand obscure vocabulary or jargon. They may not have picked up basic skills along the way and may be self-conscious as a result. Whatever the reason, the posturing or mere presence of other students can severely heighten the discomfort and result in total student shutdown.

Anyone who has ever been lost in a class environment knows that it takes a significant amount of grounding or traction in a subject area to even pinpoint a question to ask that might yield a productive response. Thus, those who ask questions are usually the ones who know the most, are the most confident and need help the least.

What can adaptive learning do in this respect? It can provide the appropriate factual and procedural knowledge, so that students feel grounded enough in the material that they can pinpoint the questions they need to ask. For example, imagine a student who is lost in a class session about metamorphic rock: everyone else mentions “sedimentary” and “igneous” rocks and the student can’t figure out what sedimentary and igneous rocks are and what they have to do with metamorphic rocks to begin with. The student can figure out from a scaffolding system (which can be anything from a sophisticated search engine to an online system tailored to individual thinking patterns) that metamorphic rocks are sedimentary or igneous rocks transformed by extreme heat and pressure, and get up to speed with the rest of the class–which is already on to discussing how the foliation on a particular metamorphic rock reflects the pressure and heat it was subjected to. Of course some productive discomfort is necessary in the classroom; but, if designed well, an adaptive learning system will reduce unproductive discomfort and proliferate the opportunity for productive discomfort.

Adaptive learning can identify social possibilities that build student confidence and make students more likely to participate in large discussions. By aggregating and analyzing data, an adaptive system can create situations in which students assist and mentor each other online. Depending on the aim of the class, teachers can use data regarding performance, learning style, and preferences, to create cohorts of students who complement each other academically. In an English class, for instance, you might be able to create mini workshops of 4 people each, with each workshop composed of an “organization” master, a “style” master, a “grammar” master and a “clarity of purpose” master. Teachers can also create opportunities for peer evaluation that allow students to grapple further with the material at hand (it’s an age-old principle that you don’t truly learn something until you teach it yourself). Using data culled from assessment and surveys following these activities, teachers can then determine the efficacy of these strategies.

3. Need for appropriate pacing.

When observing classrooms, it is always fascinating to chart the wax and wane of student energy and focus. One second, everyone is riveted; the next, everyone is distracted by a bee or a lawnmower, and momentum is lost entirely. The amount of debate surrounding something like block scheduling points to the underlying difference in student needs. Some students function better if they’re working on one project for an extended period and have ample opportunity for reflection, while others need a constant change-up or enjoy a rapid succession of drills.

Adaptive learning can help us out in several ways here. As described in the previous post, any continuous adaptive learning system is built on opportunities for students to “show what they know.” Such opportunities, in addition to engaging students more fully, also break up instruction and order activities in a natural way, ensuring that precious class or study time is not wasted.

An advanced system can also help educators discover the precise way that lectures, assessments, activities, and peer evaluation opportunities should be combined to produce maximum learning benefits for each individual student. One student, for example, might learn best in the sciences if she absorbs a lecture, is tested on it immediately, and then engages in group work. In English class, by contrast, that student might see the most gains if she engages in an activity, absorbs some instruction, then reinforces her understanding by evaluating someone else’s paper. Or for that student, the adaptive system might determine that it’s not the kind of classroom activity that matters but rather the kind of cognitive work she is doing. Maybe she needs rigorously analytical work (think logic games) before introspective creative work. Maybe her ideal “learning day” consists of math drills, nonfiction reading, then creative writing.

The data generated by an adaptive system can also help determine the ideal amount of time each student should spend doing each type of activity. The system might discover, for example, that one student functions best if he learns in 20 minute spurts for 3 hours at a time with approximately 5 very short breaks thrown in, while another student works best in 1 hour segments with two 10-minute breaks built in.

In summary, adaptive learning can help educators serve up academic material in a way that is tailored to each student’s unique learning style.

Stay tuned for more reasons why students don’t like school — and how adaptive learning can help!

The EdTweet Show: Gamification, Mobile Learning, and More [VIDEO]

September 29th, 2011

You’ve seen our EdTech Tweets You May Have Missed series… now check out our brand new video series: “The EdTweet Show.” Watch as star anchors Dave and Jess give a 2-minute or less rundown of interesting edtech articles that popped up in our Twitter feed this week.

This week, Jess and Dave cover news about game-based and mobile learning, Google Hangouts, and more. Watch the show, then check out the full list of EdTech tweets below!

Here’s the full list of tweets!

EDUCAUSE 2011: New Session with U.S. CTO Added — Tweet Your Requests

September 28th, 2011

EDUCAUSE just announced a new featured speaker for its 2011 Annual Meeting: Aneesh Chopra, U.S. Chief Technology Officer. Chopra will be leading a session on Thursday with James H. Shelton, III (Assistant Deputy Secretary for Innovation and Improvement) about the importance of innovation in education.

Attending EDUCAUSE? Chopra has requested that conference attendees tweet him (@aneeshchopra), telling him what you’d be interested in hearing him speak about during the session. Whether you want to hear about cybersecurity, digital literacy, or just what it’s like to go to meetings with President Obama, be sure to let your ideas be heard. Use the hashtag #EDU11 #EDUAneesh when you tweet.

For more EDUCAUSE-related posts, click here.

MBA News Roundup: Lunch with Dean of HBS, Evolution of the MBA Infographic, Stanford Leads in Green MBAs

September 28th, 2011

Welcome to another installment of Knewton’s MBA News Roundup! This week, check out articles on the HBS Dean’s take on changing business education, an illustrated history of the MBA program, and another list of b-school rankings, this time the theme is “greenest.”

1. Dose of Humility with a Harvard MBA

Dean of HBS Nitin Nohria sits down with some Wall Street Journal reporters to discuss his curriculum overhaul and character-building in the context of business school.

2. Evolution of the MBA [Infographic]

Did you know that in 1950 the University of Western Ontario became the first school in Canada to offer an MBA program, almost a full century after the University of Pennsylvania became the first American school to do so in 1881?

3. The Pros and Cons of Going Abroad for your MBA

Considering a business education with a more global slant? Check out these veritable overseas instituations for an MBA with more international zest. Ole!

4. Aspen Institute Releases List of Top Green MBAs

Stanford students deemed the most concerned with both types of green.

MBA Admissions Tip: MBA Application Data Form

September 28th, 2011

This MBA admissions tip comes to us from our friends at Clear Admit. For more expert MBA admission advice, check out their blog.

With MBA programs’ Round One deadlines just around the corner, we wanted to offer some words of advice about an often overlooked element of one’s file: the application data forms. All too often, we see candidates leave these online application forms for the last minute, even rushing to enter all the required information from work on “deadline day.” The truth is that a weak effort on these forms can do serious harm to one’s candidacy, as it might reflect poorly on the applicant’s professional polish or commitment to the application process. This being the case, here are a few tips for those who are in the midst of completing this component of the application:

1) Don’t be lazy. We know that many applicants feel “burned out” from their essays and that it’s tempting to zip through the application forms and provide a bare minimum of information. While it’s fine to use your resume as a starting point, make sure that you think beyond this ready-made content and consider other information that might be of interest. In many cases, the forms are a great opportunity for you to list outside activities in depth, offer a quick explanation of a bad semester, share the significance of some professional awards you’ve received, and so on. In fact, your application forms will often be the starting point for the admissions officer’s review of your file, so it’s important to put your best foot forward.

2) Follow instructions. If a school asks you to list activities in order of importance to you, then do not list them chronologically (as you may have done for another school). If the school asks for a contact person, title or the number of hours/week, do not leave these fields blank. As attention to detail is very important, spell checking another important step in this process. In fact, many admissions officers have stated that they use the application forms as a way to see whether or not candidates have the ability to follow instructions and show attention to detail.

3) Make everything clear. The last thing you want is for your reader to have to play detective in understanding your career progression, making sense of gaps in employment, or evaluating your undergraduate performance. If your listings are not clear, the reader may assume you are hiding something – a conclusion that could seriously damage your chances. By the same token, you should avoid using industry jargon and be sure that all of your statements will make sense to a reader who is not familiar with your industry or function. Given the level of competition in the applicant pool, the admissions office can afford to dismiss files that are confusing or difficult to follow.

4) Don’t go overboard. Admissions officers typically review several files in a sitting – devoting much less time than you might imagine to each file. With this in mind, avoid listing 18 activities, 22 awards and 17 publications – especially if some of those items date back to high school (or are more than 10 years old). Stay focused on the elements of your background that are most relevant, while following the instructions that have been outlined. Remember that the application process is an exercise in marketing, and that the schools appreciate applicants who are discerning about what details to share and know how to present themselves most effectively.

As always, best of luck to those of you who are applying!

More on the Integrated Reasoning Section

September 26th, 2011

Last time I blogged about what I learned at the GMAC Test Prep Summit and I briefly mentioned the new Integrated Reasoning section that will begin to appear on the GMAT in June 2012. On its website GMAC has made available some sample questions that you can find here.

Here’s a quick breakdown of the new section:

The Table Analysis prompt requires you to analyze and sort data in a spreadsheet-like document. The Graphics Interpretation prompt requires that you understand concepts like slope and lines of regression (otherwise known as “lines of best fit”). I wouldn’t be surprised if other kinds of graphic representation, such as pie charts and Venn diagrams, will appear as well.

The Multi-Source Reasoning prompt is like a Critical Reasoning inference question with three distinct but related passages. Finally, the Two-Part Analysis Prompt gives you two components to a solution and requires you to provide your answer in a table format. Both the Multi-Source Reasoning and Two-Part Analysis prompt involve some simple math, and the Multi-Source question requires some basic knowledge of probability. Full disclosure: at first I found the Two-Part Analysis prompt very difficult, because I foolishly assumed that the third column referred to a percentage, and not just to the actual increase of members per year. I constructed a complicated exponential equation when all that was really required was a simple linear equation!

Once I realized my mistake, my impression of these problems was that they were pretty easy. I’m not sure if the math will get much harder; how very nice of the GMAT to provide a calculator for the easiest math problems and then take it away for the Quant section!

But remember, you will see 12 of these prompts, and have to answer one or more questions about each in 30 minutes. In April 2012, GMAC will release new GMAT Prep software (which, by the way, will be Mac-compatible!), as well as the 13th Edition of the Official Guide. Once we see more sample questions, we will have a better sense of how difficult the section is and how it will be scored.

EDUCAUSE 2011 Speaker Spotlight: John Foliot, Manager of the Stanford Online Accessibility Program

September 26th, 2011

As a lead-up to this year’s EDUCAUSE conference, we’re interviewing some of the speakers who will be sharing their knowledge and experience at the conference. It’s our hope that these interviews will spark conference and give conference attendees a better sense of this year’s speakers.

For this installment, we spoke to John Foliot, Manager of the Stanford Online Accessibility Program. John is speaking on a panel at EDUCAUSE 2011 entitled “Developers View of Accessibility: Pitfalls, Gotchas, and Solutions.” John was gracious enough to speak to us via email about the ins and outs of online accessibility and EDUCAUSE.

For more EDUCAUSE-related blog posts, click here.

1. What do you see as the greatest challenge to improving online accessibility?

In many ways, the answer to that question today is the same answer we had five and even ten years ago: education. Due to the decentralized publishing environment that seems to thrive in higher education, getting to the actual content authors is often the biggest hurdle. It’s not that these authors are deliberately creating inaccessible content, but rather often they are unaware that doing “this” (whatever “this” might be) is inadvertently introducing access issues. In my experience, most content creators, when informed of an issue, are both apologetic and willing to correct or modify their work, which is gratifying. Only rarely do I hear “I don’t have any disabled students in my course” or “what about academic freedom?” – again these issues are often addressed with educating that person on the advantages that ensuring accessible content brings to them, often due to increased search-ability (SEO), or simply a better user experience for all users.

2. What guiding principles inform your work with SOAP? How, if at all, have these principles changed or evolved in your 5 years leading the program at Stanford?

Education and Outreach has been a significant part of my efforts to date, along with evaluation and reporting. I’ve worked hard at establishing myself as a credible technologist on campus, one with a goal (for sure), but also one who also understands the complexities of a rapidly evolving and changing user-base and requirements. I like to joke that I am more like the fireman (racing to fires when needed, but more focused on fire-prevention), rather than the “accessibility police” chasing after developers and slapping them into hand-cuffs.

I’ve found that grass-roots initiatives on campus tend to see the most adoption, as real people have a real and vested interest in seeing their favorite solutions thrive; I’ve striven to be part of those activities on campus since I first arrived. The Drupal CMS adoption at Stanford is a classic example of that, and Drupal has now become the CMS of choice by most of the tech folk on campus – to the point that a new division within our IT Services department is being established this September to both provide robust on-campus support to Drupal, as well as to steer and enhance the Drupal eco-system at Stanford.  Drupal is succeeding because the technologists on campus believed in it early on, and grew support organically, via peer-to-peer support using tools such as a campus-wide Drupaler’s mailing list, volunteer “drop-in days” (where the gurus helped the newbies), and organizing an on-campus Drupal conference and other developer initiatives. It’s been exciting to see Drupal take root, and I’m pleased to have been part of that effort since it first began.

My personal strategy has also been to be part of the larger technology discussions on campus, where I bring the “accessibility perspective” to the table; however I have taken pains to ensure that I keep up with all the emerging technologies, so that I am not seen by others on campus as a one-tune fiddle. Web accessibility is important, but cannot live inside its own little bubble – it needs to be part of the larger whole, and so being involved in the bigger tech discussions has helped keep me relevant and related to most initiatives on campus.

Of course the POUR principle (Perceivable, Operable, Understandable and Robust), which is at the heart of the W3C’s WCAG2, is also a core mantra for me: helping developers and content producers understand what POUR means to them helps them understand what real accessibility entails.

Finally, I believe in what I call the Path of Least Resistance – which translates to: “Make things easier for people to do the right thing, and they will do the right thing”. Campus life is busy and moves quicker than many believe, and there is a constant struggle to get things done in time for yesterday. Ensuring that tools, processes and other forms of support exists so that “accessible” development is as easy – or easier – than inaccessible development is important for success. Our in-house captioning system for videos is an example of that philosophy at work, and we are proud that other higher-ed institutions have shown interest in our system since we launched it.

3. In what ways do you think web accessibility will improve in the next 5, 10, 50 years? Who or what do you foresee being the driver(s) of these changes?

I think that the web moves way too fast to try and predict where we will be in 5 years, let alone 10 or 50 years. Less than 4 years ago, “mobile” development was barely, if even, on the radar of many higher education institutions, and now it is *the* hot topic. Even institutions that jumped in early by developing dedicated mobile apps are now looking at “web apps” as a more sustainable and cost effective way of reaching their student body, and with advances in the technologies, even “off limit” mobile tools such as the camera and phone accelerometers will soon be available to HTML5 developers. I am watching and participating in that space quite actively, as it will continue to be a growth area for a number of years to come. Interestingly, many accessibility best practices also have real and tangible benefits on the mobile platform, as the confines and restrictions that mobile brings to web development force content creators to focus in on the key issues: scalable text, good structured documents, brevity of text, abandoning distracting “sidebar” content, clear navigation (and hopefully the demise of “flyout navbars”), etc. As an example, mobile phone users will have a hard time if a website’s navigation requires the use of a mouse because they typically only have an alphanumeric keypad or a small touch screen.

Of course, HTML5 is now emerging as the new standard for web development, and with that comes better integration of ARIA (Accessible Rich Internet Applications), a slew of new form inputs and landmark elements, and new advances in multimedia (with the <audio> and <video> tags) that will make the next generation of web content leaner, more robust, and significantly more accessible – at least that’s the vision. Having been involved with some of that emergent Standards work at the W3C, I believe we will succeed – all-in-all HTML5 will make creating accessible web content that much easier as it too is using the “path of least resistance” principle. I am watching with particular interest the continued emergence of video on the web as being an exciting new frontier: I don’t think we’re anywhere near where that technology will take us in just a few more years, and with it will be new challenges with regard to accessibility, and new solutions too. So watch that closely.

4. Are there any sessions or events you’re particularly looking forward at this year’s Educause conference? If you’ve attended Educause before, do you have any recommendations for first-time attendees?

There are a number of interesting accessibility-related sessions coming up this year at EDUCAUSE 2011. I am looking forward to Tuesday’s Preconference session on “IT Accessibility Law, Policy, and Implementation”, “Beyond Compliance: Strategies to Increase Online Accessibility and Engagement for Students with Disabilities” on Wednesday, and Thursday’s “IT Accessibility in Higher Education, Present and Future”.

Of course, I am also looking forward to being a panelist at “Developers View of Web Accessibility: Pitfalls, Gotchas, and Solutions” on Wednesday, and I invite anyone interested in web accessibility at Higher Ed to stop by for one of our “Ten-Minute Tune-ups”, offered by myself or one of my EDUCAUSE Accessibility Constituent Group colleagues in the CG Lounge  (Wednesday afternoon from 3:30-4:20pm, or by chance at other times during the conference).

As for tips to first-time attendees? Network, network, network. Ask lots of questions (remember, there is no such thing as a dumb question), and pace yourself.  EDUCAUSE is a huge event, and there is a lot to see and learn. Trying to cram it all in is understandable, but I find that focusing on a few key topics proves to be more useful than running from session to session to session, seeing lots but retaining little. Spend the time in hallway chats, they have the most value (at least for me), as they are true dialogs and not just “info-dumps” – and if you see me, stop me and say hi, I love to meet new people.

Intuition and Common Sense on Geometry DS Questions

September 23rd, 2011

“Who cares?”  That should be the operative question on your mind as you tackle Data Sufficiency problems.

Here’s what I mean:  Suppose I ask you the question “What is x?”  I then give you a statement that says “2,346.456 x + 87,234 = 912,347π”.  Is the statement sufficient?

“Yes,” you’d say (hopefully!).

“But do you know what x is?” I’d respond back.

And what would you say?  Yup, you got it:  ”Who cares?!”

All we care about is the ability to find x.  We don’t care what x actually is.  Because the statement gives us a simple linear equation with only one variable, we have the ability to find the value of that variable, and that’s all that matters.

This seems a pretty elementary point in and of itself, but it’s one that many students often forget when out in the field tackling tough DS problems.  Specifically on Geometry DS problems, the temptation can be to plug numbers into formulas and tackle the problem as if it were a PS question.  But often times, this is completely unnecessary and a tremendous waste of time.  Many times, you can solve Geometry DS problems intuitively using common sense and simple logic.  But it all hinges on the ability to identify exactly what information you need.

Let’s take a look at the following official DS problem:


A circular tub has a band painted around its circumference, as shown above.  What is the surface area of this painted band?

(1)  x = 0.5

(2)  The height of the tub is 1 meter

Stop!  Don’t write any formulas!  It’s great if you know the formula for the volume of a right circular cylinder, and that might come in handy on PS problems and maybe a more intricate DS problem.  But let’s take a moment to think about what information is really necessary here.  We want to know what the surface area of that band is.  Ask yourself:  What’s keeping us from knowing that?  What’s missing?

Well, we can’t very well know the surface area if we don’t know how wide the cylinder is.  What determines how wide it is?  Radius!  And if we know radius, we also know circumference.  But is that enough?  Nope.  We also don’t know how high x is.  So the two missing pieces of info can be boiled down to:  ”x = ?  and r = ?”

This makes perfect sense when you think about it.  How can you know the surface area of something if you don’t know its dimensions?  In this case, the two dimensions are the circumference around the cylinder (which can be determined by radius) and the height of the band, and we need both to get the surface area.

Now that we’ve figured out intuitively what information we need, let’s look at the statements:

Statement (1) gives us the value of x.  Great…nothing about the radius, though.  Insufficient.

Statement (2) gives us the height of the entire cylinder.  Great…nothing about either the radius or the value of x.  Insufficient.

Statements (1) and (2) together give us the height of the entire cylinder and the value of x.  Awesome….where’s the value of the radius?  Still nowhere to be found.  Answer:  E.

We didn’t write down a single equation, and yet we still got out of the problem quickly and with the correct answer.

Now, try your intuitive skills on this other official DS geometry problem.  Remember, try to do it without equations!  Use your common sense!  And post your step-by-step intuitive solutions in the comments!

The inside of a rectangular carton is 48 centimeters long, 32 centimeters wide, and 15 centimeters high.  The carton is filled to capacity with k identical cylindrical cans of fruit that stand upright in rows and columns, as indicated in the figure above.  If the cans are 15 centimeters high what is the value of k?

(1) Each of the cans has a radius of 4 centimeters.

(2) Six of the cans fit exactly along the length of the carton.