The Backward-Forward Method

Unfortunately, little or no time is spent in most math classrooms discussing "heuristics," the art of problem solving. 

This often leaves students grasping at straws, struggling even to know where to begin when staring down an unfriendly, unfamiliar math question.

George Pólya's How to Solve It is a classic on this subject, required reading for all serious math students.

In another classic, How to Read and Do Proofs, author Daniel Solow advances a powerful problem solving approach he calls the “Forward-Backward Method.” 

I’ve found it helpful in my own teaching and mathematical work to reverse the method, first thinking backward from the ultimate goal to various subgoals which, if achieved, would enable direct progress to the original objective.

Whether writing complex proofs or tackling simple algebra problems, this “Backward-Forward” process provides students with a simple yet powerful structure for solving problems.

Just as an archer would prefer to move the target closer, so can a math student make a problem easier by finding a nearer target to shoot at. The next step would be to think further backward, to find another even closer target tied directly to the first, and so on. These subgoals are set by repeatedly asking the same question: “What would I need to know to find that?” And then “What would I need to know to find that?” Subgoals should be written down, to keep the trail clear.

After looking backward as far as possible, it’s time to reason forward from each given fact, with the last subgoal in mind. A different question governs the forward process: “What can I imply from that fact?” And then “What could I imply from that?”

Eventually, forward progress enables us to hit the target. All that’s left is to follow the string of subgoals up the ladder to the desired result.

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Copyright © 2006-present: Christopher R. Borland. All rights reserved.

Winning Focus

Test taking is a competitive activity. 

As is athletics or the performing arts, outstanding achievement on the SAT/ACT depends on maintenance of powerfully sharp, energetic, mindful concentration and “winning focus.” 

In sports, the challenge is the opposing team. In the performing arts, it’s stage fright. In test taking, your adversaries are the test questions. 

Test takers, like athletes and stage performers, need to confront and conquer pressure, stress, fatigue, distractions, and other difficulties with sustained enthusiasm, relentless drive, and total commitment to success. If victory is the object, nothing less will do.

An intense, aggressive, yet controlled state of concentration is critical to performing at one’s best in any competitive activity. “Winning Focus” is so important, in fact, that without it, almost nothing else matters.

By definition, intensity always involves some amount of tension. Undisciplined, raw intensity can lead to varying degrees of frustration, anxiety, and even exhaustion. Athletes, performers, and test takers must learn to thread the needle between two extremes, remaining fully responsive and focused on winning without getting rattled or falling victim to tenseness, tiredness, or negative emotion.

When intelligence is inhibited by inattention, distraction, tiredness, or emotional upset, reduced cognitive bandwidth causes a mental traffic jam, disrupting the efficient flow of ideas.

On the other hand, Winning Focus lights up the brain like a Christmas tree. All kinds of connections, insights, and creative solutions come to mind that would otherwise go unnoticed. Most important of all, careless mistakes are minimized.

Fully half the errors on a typical student's SAT/ACT math test are due to carelessness. If these careless errors were reduced by half, a student scoring 650 on an SAT math section would instead score 720, and one scoring 27 on the ACT would score 31!

These dramatic improvements require neither new math smarts, nor improved testing acumen, nor additional practice – just a 50% cutback in careless mistakes. In fact, math test prep could be restricted entirely to development of Winning Focus, and most students would be well served.

The vast majority of test coaches pay no significant attention to the mental game of test taking. In my work, Winning Focus takes center stage. Using proprietary methods and materials, a natural knack for inspiring and igniting motivation, and a unique ability to train all aspects of effective test prep that only 45+ years in business can bring, I teach my students to track errors, avoid unnecessary mistakes, and generate and sustain powerful, energetic, productive concentration.

The best way to train Winning Focus is to build strength and endurance through gradual exposure to practice tests of increasing length and difficulty, bolstered by professional performance critiquing, feedback, error analysis, and personal support. It boils down to habituating a determined, enthusiastic, mindful concentration on test questions, and training higher levels of focus for longer and longer periods.

Fortunately, most high-performing students already know how to do this. Such students are typically athletes, actors, dancers, and/or musicians, and already know how to generate the state of mind necessary to excel at competitive activities. It’s just a matter of transferring this well-developed ability to the domain of test taking. Although the particulars are more complex, it’s really that simple.

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Copyright © 2006-present: Christopher R. Borland. All rights reserved.

Pick Three: Academics, Sports, Free Time, Sleep

In my day, we somehow managed to get a good education, do required homework, get plenty of sleep, and have lots of time left over for sports, jobs, interests, and all kinds of social activities. Most of my peers did most of it, and quite a few did it all. 

I don’t know exactly what happened, but that’s certainly not the norm for college bound high school students, anymore.

Nowadays, with all the time it seems to take to be competitive for a seat at a good college, it’s normal for serious students to be sleep-deprived.

Studying is important. But there’s a point at which more time spent studying hurts your GPA more than it helps. Lack of sleep will eventually become harmful to memory, creativity, thinking, reading, writing, and other mental and physical processes necessary to do good academic work.

Growing teenagers need a good nine hours of sleep per night. When I ask students how much sleep they’re getting, the answer is generally in the neighborhood of six to seven hours per night. That’s not enough. And it matters. Adding just one hour of sleep per night could significantly improve your energy levels, cognitive functioning, mood, and academic performance. 

[First of all, it's worth asking if you're pursuing the right goal. A top college should be only your goal for the right reasons. Your reasons. There are other good options. You really do not have to do this, if you don't want to. Only you can decide if the path to a top college is right for you. Having said that, I'll assume you've rationally chosen that path, for yourself, for the right reasons, and are looking for ways to make the trip as productive and frictionless as possible.]

Under-disciplined but otherwise ambitious students today can pick three of the following four desirables: academic success, sports, free time, and sleep. All may seem essential. How do you pick just three?

First, choose reasonable sleep time on a regular basis, and some downtime to go with it. Without your health, nothing else matters, and little else can be accomplished. This should be non-negotiable.

That leaves academic success, and sports/extracurriculars. Academic success is the whole purpose of the undertaking, so pick that.

Now what? No sports or extracurriculars? 

Maybe not. Is baseball really that important? Band? Volunteering? Sometimes the answer will be “No, not that important.” Other times it might be “HELL YES, that’s extremely important.”

So, what’s the answer, then? Can't I have it all? 

The answer is a qualified "yes, you can" and the not-so-secret ingredient is self discipline. 

To have it all you’ll need to become very good at making tough choices and sacrificing the small stuff. ALL the small stuff.

The word “No” will become a very close friend. You must learn to say “no” to just about anything and everything unimportant. Sometimes a nap may be a good idea; other times, not. You may want to do two sports simultaneously, but is it worth the hit to your academics?

You’ll need to become a master planner. You’ll need to be motivated and organized. Deliberately set things up so you’ll get things done and get enough sleep. No slouching. No this, no that. That's a lot of no.

Luckily, the things you'll need to refuse are probably things you don't want to do anyway, if you think about it in light of what's important and valuable and rewarding to you.

It’s time to grow up. That’s really all it is. Childhood is basically over. No free lunch. Go out there and pay your dues.

Chances are quite good the effort will be well worth it.

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Copyright © 2006-present: Christopher R. Borland. All rights reserved.

Surest Way to Destroy Your Score

It never ceases to amaze me that students will spend time and effort prepping for a test like the ACT or SAT and then go out and stay out late with friends the night before the big test. 

Please … promise me you won’t do that.

The best way to ruin your SAT/ACT score – by far – is to not have enough sleep the night before you take the test.

In fact, one good night’s sleep isn’t really enough. You should get plenty of sleep on each of the two nights immediately before test day. Three nights would be best.

Plan your week so that you’ll be able to go to bed early and get plenty of sleep the last two or three nights before taking your test. Get ahead on any papers or presentations due and study in advance for upcoming tests or other assessments.

You’ve put in a lot of hard work in preparation for this. Whatever you do, get good sleep, and be well-rested when you take the exam.

P.S. The next best way to destroy your score is to be dehydrated. Make sure to drink a lot of water each of the last two days before test day, and a full glass that morning. Don't forget to use the bathroom before leaving for the test site.

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Copyright © 2006-present: Christopher R. Borland. All rights reserved.

Slow Down to Go Faster

High-stakes timed tests like the SAT and ACT are inherently stressful experiences, and reducing stress is a primary goal. A chief driver of this stress is time pressure.

Paradoxically, sometimes the best thing one can do to improve speed on timed tests is to do untimed practice.

In untimed testing, students take all the time they need to fully understand questions and find correct answers. Without the pressure of the clock, it's much easier to master various question types and discover the best ways to find right answers most quickly and easily.

It's also ironic that getting stuck on super-hard questions during untimed practice is actually a good thing. By spending way too much time on impossibly difficult questions, students learn to quickly recognize "nightmare questions" they can't answer and just going to waste their time on test day (the strategy: eliminate, guess, move on).

After gaining everything possible from untimed testing, students then return to timed practice, and work on speeding things up. Now they know what to do – they just need to do it faster.

This approach has been useful to a great many students of mine over the years, particularly on the ACT science section, which is famous for being a time-burner. Unfortunately, its counter-intuitive nature can make this miraculous study tactic uncomfortable to use at first. Once regularly employed in practice, however, improved results generally dispel any initial doubts or fears.

Building muscles slowly in the early stages of any strength-building process just makes sense. The same goes for building test-taking muscles.

It's a maxim that applies to disciplines as widely varied as musical performance, athletics, academics, and more. At all stages of the learning process – and especially at the beginning – deliberately sacrificing speed for the sake of developing concentration, accuracy, and control is the best way to optimize progress.

Slow down, to go faster!

ratemyprofessors.com

Until you declare a major, take highly-rated professors, not classes!

Think of ratemyprofessors.com as Yelp for college professors. Search for your school (or prospective schools), and get reviews and ratings by real students of instructors in all departments. Use the site to find life-changing teachers and avoid duds.

Some reviews are more helpful than others, and as is the case with other review sites, ratemyprofessors.com doesn’t tell the whole story. But with quantified measures like "Overall Quality" and "Level of Difficulty" (among other indicators) it’s a whole lot better than having no idea at all as to which teachers are likely to be golden and which should probably be avoided like the plague.

Most/all established professors at are listed at each institution, and university-wide averages give you some idea as to the quality and collective personality of various faculties.

Schools are rated by students according to other important factors, as well (e.g. reputation, happiness, food, facilities, location, social life, etc.), providing useful comparative data.

As an example, click here to see data for Wesleyan University.

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Copyright © 2006-present: Christopher R. Borland. All rights reserved.

101 Things to Do Before You Graduate

Life Coach Julian Gordon has published an indispensable book for college freshman:

101 Things to Do Before You Graduate.

Listing 101 truly useful and important academic and personal goals to fulfill as an undergrad, Gordon gives callow freshmen a roadmap to follow to make the most of their college years.

Those four undergraduate years will be over before you know it, and with them will disappear once-in-a-lifetime opportunities. Don’t waste some of the most important and potentially profitable and enjoyable years of your life! 

This book makes a great gift. Should be required reading for every college-bound high school senior. Slightly out-of-date, but still a fantastic font of fabulous ideas for undergrads. 

UPDATE: Great TED talk given by Jullien on the 4.0 GPA That Really Matters.

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Copyright © 2006-present: Christopher R. Borland. All rights reserved.

2, 800, 44

Concerning the SAT Math Subject Test, the three most important numbers are:

2, 800, 44.

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2:

You should take the SAT Math Subject Test, Level 2 (SAT2M2). There’s virtually no reason for anyone to take Level 1.

Here’s why:

SAT Subject Tests allow students to pick the two subjects at which they most excel and then show off by getting very high scores on those tests. A very high score on Level 1 of the SAT Math Subject Test is meaningless, because it begs the question: “If this student is so good at math, why didn’t she take the SAT2M2?”

And that would be a good question. If you’re so good at math that you’ve chosen mathematics as one of your two subject test areas, you should certainly be taking the most advanced level of the math subject test, which is Level 2.

Opting for Level 1 of this particular test defeats the purpose of choosing this particular subject area in the first place.

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800:

A perfect 800 is the score you want on the SAT2M2. Fully 20% of students who take the test get this score. A much lower score, once again, kind of defeats the purpose of electing this subject in the first place.

By choosing math as one of your two subject test areas, you’re declaring yourself to be a hotshot math student. You should therefore be able to score in the top 20%, which means you want an 800 on this test, or darn close to it.

The good news is that this isn't that hard to do, as long as you’re truly good at math, make the best possible use of your calculator, and work hard to prepare (i.e. take lots of practice tests, assiduously critique the results, do careful error analysis, and review regularly).

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44:

This is the number of right answers you need out of the 50 questions presented on the SAT2M2.

Notice that you don’t need a perfect score to get a perfect score. Not even close. On average, you only need an 88% (44/50) to score a perfect 800. No one can tell the difference between someone who gets 88% of the answers right and someone who gets 100% of the answers right; on the SAT2M2, both students receive the same scaled score: 800. So you’re shooting for 44. Anything above that is nice, but superfluous.

What about the other six questions?

You get a pass on these six. You can skip them all, get them all wrong, or skip some and get some wrong. It doesn't matter.

Here’s why:

According to the most recently released official SAT2M2 practice tests, on average, you actually only need a raw score (correct answers – .25 * incorrect answers) of 43 to get a perfect 800 scaled score. If you skip all six questions, your raw score is 44. If you answer all six incorrectly, your score is 42.5, which rounds up to 43. If you skip three and get three wrong, your raw score is 43.25, which rounds down to 43.

No matter what you do with the other six questions, as long as you get 44 right answers on this test you’ll likely receive a perfect 800 as your SAT Subject Test score.

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You can probably do this.

Anyone who could score 700 on their own just sitting down and taking the test with no prep at all (requiring a raw score around 33: e.g. 35 right answers, five skips, ten wrong) can score 800 with strong preparation, plenty of practice, good calculator skills, and the right calculator programs.

And once again, if after a year of high school precalculus you can’t just sit down and get a 70% on this assessment (35/50), you might want to pick another subject test.

For more SAT2M2 advice and resources, click here.

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Copyright © 2006-present: Christopher R. Borland. All rights reserved.

Two Dynamite Questions

Dave Denman, an expert educational consultant and long-time colleague, gave me a tip many years ago that was one of the best study nuggets I’d ever heard.

During or after completing your homework in a given class (say, history), think of two "dynamite questions" to ask your teacher the following day, about the general topic you’re currently discussing in class. Make these questions interesting, not run of the mill, but as thought provoking as possible. Jot these questions down in your notes.

Then, at an appropriate time during class the next day, be sure to ask your teacher these two questions!

Asking thoughtful questions is one of the best ways to make the class more relevant and interesting to other students, and doing so will certainly get you noticed by your instructor. In addition, coming up with these questions in the first place gets you thinking more deeply about the material you’re learning in class and therefore tends to make it more interesting and memorable to you. Teachers always greatly appreciate and respect students who ask great questions, especially those who make a habit of doing so on a regular basis. These students are obviously taking a special interest in the class, and nothing makes a teacher’s day like students who consistently put forth the effort to ask insightful, probing questions.

Although it only takes a couple of extra minutes to do so, recording and then asking dynamite questions really livens up class time, makes your teacher’s job a whole lot easier and more enjoyable, and goes a long way to making any class more fun and interesting for you and your fellow classmates.

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Copyright © 2006-present: Christopher R. Borland. All rights reserved.

Memorize The Quadratic Formula ... In Seconds

Ah ... the venerable Quadratic Formula. Algebra students everywhere have to memorize this well known formula for solving quadratic equations of the form: ax² + bx + c = 0.

Many students in early algebra courses lose critical test and quiz points just because they haven't yet fully committed the Quadratic Formula to memory.

I recently came across a brilliant way to do so almost effortlessly ... a memory trick so sublimely ridiculous I couldn't help but think of the famous line: "This is so crazy ... it just might work."

(Sung slowly to the tune of "Pop Goes the Weasel")

"X is equal to negative B

Plus or minus the square root

Of B squared minus 4AC

ALL

Over 2A."

Silly.

Effective.

Try it!

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Copyright © 2006-present: Christopher R. Borland. All rights reserved.

Get The Solutions Manual

While textbooks required for demanding math and physical science courses generally provide explanations and examples designed to help students review covered material or make better sense of teachers' lectures, the sample exercises included are often too limited or few in number to paint a complete picture of the topics presented. Answers are usually given for odd-numbered homework problems, but oftentimes this just isn't enough.

The issue for many students in these tough classes is how to get those particular answers.

Wouldn't it be nice if there was a companion book that would actually list the step-by-step solutions for each odd-numbered problem in a given math or physical science textbook ... not just the answers?

In most cases, there is such a book. It's called the "solutions manual," and possession of one of these miracle volumes can sometimes make all the difference between ease and stress, progress and frustration, success and failure.

The solutions manual is the perfect compliment to the required text for any important math or science course. When stuck in the mud on a particular homework exercise, students can simple appeal to the solution shown in the manual, allowing them to answer their own questions and continue their forward progress with the assignment. Instead of pulling out their hair over a particularly vexing problem, students can use the solutions manual to quickly figure out what they've been doing wrong, and then apply the techniques illustrated in the manual's solution to other similar exercises, saving valuable time and energy (e.g. solutions to even-numbered exercises can typically be inferred from those given in the manual for corresponding odd-numbered problems). In this way, the solutions manual acts as a virtual tutor, enabling students to make much more efficient and effective use of time spent doing homework or studying for exams.

I always recommend that students about to take a difficult math or science class invest in a copy of the solutions manual for the textbook required for that class. The best way to find a copy is to visit the publisher's web site or do a Google search using the full name of the text followed by the author's name and preceded by the phrase "solution manual" or "solutions manual" (without quotes). Once you have an ISBN number for the appropriate solutions manual, you may be able to find a less expensive copy by searching for it on amazon or eBay. 

(Note: the term "solutions manual" usually refers to the "student solutions manual" containing solutions to odd-numbered problems; the "instructors solutions manual" shows solutions to all problems in the text, but is available only to course instructors).

Don't pound the table, become discouraged, or fall behind ... just get the solutions manual!

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Copyright © 2006-present: Christopher R. Borland. All rights reserved.

Study Buddies!

One of the best things you can do to improve your chances of success in a given class is also one of the most fun.

"Study Buddies" are people you meet and with whom you agree to form informal academic partnerships in each course you're currently taking. Not only will these relationships help you make sure you make it through the course successfully, they can also add to your social life!

As a new semester begins, find two people in each class, fellow students you like who seem to share your particular standards and interests, and exchange contact info (phone, email, etc.) with them. Now, if you miss class and need information about homework, an upcoming test, lecture notes, etc., you have two people you can call (if one isn't available, the other probably will be).

Study Buddies may even choose to go beyond occasional contact to form more formal study groups that meet before important tests to go over course material and help answer each others' questions, work together on group projects, etc.

Forging and utilizing these alliances can result in better grades, reduced stress, and enhanced involvement and participation in class, while providing a safe and productive way to make contact with other students you'd like to meet and get to know better.

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Copyright © 2006-present: Christopher R. Borland. All rights reserved.

Don't Let Your Studies Put You To Sleep

Once students enter high school, and certainly after starting college, late night study sessions become at least an occasional necessity. As a red-eye session grows longer and the body and mind increasingly tire, the law of diminishing returns eventually sets in, reducing the benefit of additional study. Before fatigue and stress combine to turn your brain to cardboard, it's good to learn a few key tips about how to avoid falling victim to "sudden brain shutdown syndrome."

In essence, the rule is to do that which is most likely to put you to sleep as early as possible in the day. If you've got a lot of boring reading to get out of the way, or need to complete some hideous math homework that makes you want to do almost anything else instead, be sure to do these things while you're fresh and wide awake, resisting the temptation to put these off until the wee hours of the evening when you can barely keep your eyelids up as it is. Uninteresting, yawn-inducing activities most likely to put you to sleep should be done as far from sleep time as possible, saving more engaging or physical activities like lab experiments, model-building, or group collaboration for later in the evening when extra interaction or increased interest will help you stay awake.

If there's just no way to avoid dull, passive activities late at night, consider moving your studies temporarily to a coffee shop or similar gathering place where the buzz of people around you will help keep your eyes open and prevent "zombie brain" without so distracting you that you can't hear yourself think.

It's a good maxim to live by, anyway: do the stuff you don't like first, then reward yourself with the cool stuff afterward. The willingness to delay gratification yields even greater benefit for busy, semi-exhausted students who must find a way to get an impossible amount of work done and yet remain conscious and functional while doing it all.

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Copyright © 2006-present: Christopher R. Borland. All rights reserved.

Follow a Daily Study Schedule

One of the most important study habits for students to establish and maintain is that of following a daily study schedule.

Without setting aside regular times each day to get homework, project work, and test prep done on time, it's just too easy to procrastinate and not get the job done. Many students study only haphazardly, in fits and starts and at odd times, often waiting till "crunch time" to frantically complete work in a mad rush just before deadlines pass. Quality suffers as stress and pressure increase, and as a consequence, grades diminish (to say nothing of students' enjoyment of the learning process).

By contrast, forming the habit of "clocking in" and "clocking out" at particular times in a well-planned daily study schedule helps ensure that homework and projects will be completed consistently and on time, and will meet or exceed acceptable standards of quality. Eliminating the feeling of "overwhelm" that comes from being chronically late is just one of the many benefits associated with adhering to a strict daily study routine. In addition, maintaining regular study hours often makes it possible to get important long-term work done early, allowing extra time to improve quality and polish the final product.

As soon as children are given homework on a regular basis parents should provide them with a daily study schedule to follow to make sure they're able to get their school work done as soon as possible after coming home from school. After a suitable break to unwind after a long day at school, three consecutive periods of study should begin, roughly equal in length, with a short break in between: "Homework Time," "Project Time," and "Extra Time."

Homework Time is for completing short-term assignments due the next day (i.e. homework), with the most important or difficult assignments done first. Project Time is for long-range assignments, projects, or papers generally due more than one day in advance (including upcoming tests and quizzes). Extra Time is to complete any work not finished during the first two daily study periods, or to review or polish work already completed.

Each period should be of a reasonable fixed length (e.g. one hour for high school students, 45 minutes for middle school students, and proportionally less for younger children). Students should habitually "switch gears" at the end of the allotted time and move on to the next period of study (even if work remains from the previous period), but not before. On particularly light days, it's permissible to finish the first two periods early, if all work has been accomplished, but not the last; Extra Time should always last the full time allotted, if only to do extra review, focused reading, skills practice, or similar study. If sports or other after school activities prevent commencing the study schedule just after the school day ends, it should begin as soon as possible after these other activities have concluded.

Here's a sample schedule for a high school student who gets home at 3:30 P.M., with no after school activities during the week:

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Monday-Friday

Homework Time: 4-5pm; Project Time: 5-6pm; Dinner and relaxation: 6-7pm; Extra Study Time: 8-9pm.

Saturday-Sunday

Additional time as needed to keep academic skills, assignments, and projects on track (i.e. ahead of schedule), and to be prepared for upcoming tests and quizzes.

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Making a habit of working on both homework and long-term projects and/or upcoming tests and quizzes each and every day makes it difficult for too much unfinished work to pile up. Nevertheless, pile-ups can occur, and should be dealt with as quickly as possible over the weekend to prevent them from dragging on or growing worse. Likewise, it's a very good idea to occasionally use free time on weekends to get out in front of especially difficult or complex projects before they can turn into problems; investing extra hours to get ahead in this way is like "saving money in the bank," and is an extremely profitable and wise use of one's time.

It really is by far the best approach, if possible, for children to make a habit of completing all school work each day right after getting home from school. Nothing should be allowed to interfere with a student's work during study periods (no phone calls, television, music, internet, etc.). But under NO circumstances should a student's study schedule be allowed to interfere with adequate sleep; all study periods MUST be completed before bedtime, preferably well before (nothing ruins health and wrecks academic performance like sleep deprivation).

Committing to a regular study schedule is a sacrifice – but a far less painful and much more profitable one than defaulting to the helter-skelter "study when I feel like it" method adopted by so many unfortunate young people. Parents interested in the academic progress and happiness of their children should insist they follow a daily study schedule to maximize the probability of their success in school.

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Copyright © 2006-present: Christopher R. Borland. All rights reserved.

Elephant's Memory

Hypercard was a simple but ingenious software development program included free with every early Mac computer that single-handedly ushered in the hypertext revolution responsible for the internet and modern computing as we know them today.

10 years ago, one HyperCard stack called "Elephant's Memory" made quite a profound impression on me. Essentially, Elephant's Memory taught simple techniques that allowed readers to unlock a phenomenal ability to memorize and recall information. By taking the user through a few simple exercises, it showed that anyone can have a truly amazing memory by learning to employ basic memory association techniques that act as "hooks" on which to hang information.

Mnemonics (pronounced "new-MAWN-iks") are clever semantic associations that help a person remember something by linking it mentally to something else that's already in his permanent memory, or to a wild, humorous, "off the wall" (i.e. memorable) new image created specially for the occasion. Like using training wheels on a bike or crutches while a broken leg heals, memory devices like mnemonics act as a bridge between short and long term memory, a way to "get by" until true, permanent memory has been achieved. Often amazingly simple and yet unbelievably effective, these methods offer a welcome alternative to the slow, painful "brute force" memorization technique most people use to memorize uninteresting things like lists, formulas, etc.

For example:

Suppose you wanted to memorize the countries in Central America. You could do this by brute force, that is, by sitting down and repeating over and over again the names of these countries until you finally succeed in remembering them. Or, you could create and use a mnemonic, like this:

"Great Big Elephants Have Never Conned Pennsylvanians."

Now, with such a zany, unforgettable image in one's mind, it's easy to remember that the countries of Central America are (more or less north to south):

Guatemala, Belize, El Salvador, Honduras, Nicaragua, Costa Rica, and Panama.

Being from California, I always had a hard time remembering how to correctly place the states of New England on a map ... until I created the following mnemonic to help me get them straight once and for all:

"Most Newborn Vampires March in Correct Rows."

By conjuring up such an outlandish sentence that gives rise to an indelible mental picture (who could forget newly born vampire babies marching in neat, tidy little rows), it's easy to recall that these states are, (north to south):

Maine, New Hampshire, Vermont, Massachusetts, Connecticut, and Rhode Island.

You can forever remember the first twenty digits of pi by using a "weird and silly story" as a memory device (similar to mnemonics, weird and silly stories make it fantastically easy to remember even very long lists of otherwise dissociated items):

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"THREE days ago, ONE panda bear went to make a phone call with FOUR giraffes. Each giraffe wore FIFTEEN scarves having NINETY-TWO stripes and SIXTY-FIVE polka dots. After THIRTY-FIVE minutes, EIGHT HUNDRED NINETY-SEVEN drops of lemonade rain fell and NINETY-THREE fairies flew out of the phone. TWENTY-THREE of them proceeded to sing the Star Spangled Banner EIGHT times, until FOUR of the fairies collapsed from exhaustion."

So, naturally:

π = 3.1415926535897932384...

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It would only take a bit more work to create five different stories such as the one above (or, five "chapters" of the same story) to easily enable the average person to repeat from memory the first 100 digits of π in just a short while, something most people would ordinarily consider impossible. By reviewing the linked stories, and practicing this feat several times, one could then permanently establish the ability to recall at will the first 100 digits of π (in general, memory devices like these need only be rehearsed successfully a handful of times to produce the desired result). Quite impressive at parties.

Mnemonics and memory stories are easy to make up on the fly, as you need them. Just remember to make them as outrageous, funny, and visually bizarre as possible.

Now ... go memorize something.

Have fun!

(For a short summary of simple memorization techniques, click here.)

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Contact Chris

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Copyright © 2006-present: Christopher R. Borland. All rights reserved.

Easy Bibliographies

Ever had trouble figuring out how to put together a proper bibliography for a research paper? 

Want to make the chore less difficult, onerous, and time consuming?

You need is an automated bibliography composer!

A detailed bibliography, with complete and correctly cited entries, is an essential part of any good work of academic research. Without one, the reader cannot easily assess the credibility of your work or the thoroughness of your research, and even after taking the time to read your paper is left at a very unsatisfying kind of "dead end."

The following free online service makes the process of organizing, properly formatting, and printing a polished MLA or APA bibliography fast and easy:

http://www.easybib.com/

A premium bibliography service on the same site ("MyBib Pro") costs $8 per year, and offers online storage of bibliographies (making them available from any computer), MLA footnotes, parenthetical citations, etc.

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Contact Chris

borlandeducational.com

Copyright © 2006-present: Christopher R. Borland. All rights reserved.

Front And Center

Your classroom seat matters.

When teachers don’t assign seating but rather allow students to take their own seats in class, where is the best place to sit?

The answer is clear and simple: the front row, center seat!

Students who sit in front near the center see better, hear better, are better seen and heard by the teacher, are less distracted, and generally have a more focused, higher quality academic experience than those sitting in the back rows. Furthermore, teachers automatically give extra notice and respect to those students interested enough in what they are teaching to choose to sit up front day after day. Students who sit in front generally care more about the class they’re in (or soon begin to), and this extra measure of commitment adds to all the other benefits to produce a real and distinct advantage for these students.

Although sitting in the back of the room may be more fun, socially, it’s the worst place to be if your main goal is to succeed in school.

A lot more extraneous talking goes on in back of the room. It’s a lot easier to be distracted. It’s harder for the teacher to see your hand raised to ask an important question. You can’t see or hear as well. It’s harder to “get into” and feel interest in the class. And, unconsciously, by sitting in the back of the room you’re telling yourself and your teacher that you don’t care much about this particular course, that you’re not really “going for it.”

Make an effort to sit in one of the front rows (the very front row, if possible), at or near the center, in every session of every class in which you can choose your own seat.

It makes a big difference!

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Contact Chris

borlandeducational.com

Copyright © 2006-present: Christopher R. Borland. All rights reserved.

Can a Beautiful Hand Improve Grades?

Doctors aren't the only ones with indecipherable handwriting.

Many of us, myself included, have fallen prey to the temptation to neglect the art of penmanship in favor of barely legible scratch that most other people cannot easily read. This is easier and easier to do, of course, given how much of our writing we now do on keyboards of various types.

Using a keyboard, without the need to consciously form individual letters, we can write much, much faster, it's true. But is there a cost to ignoring the art of proper handwriting?

The administrators, teachers, and students of the Mary Erskine and Stewart's Melville Junior School in Edinburgh, Scotland would say yes, absolutely, there is a severe cost to be paid for ignoring the ancient art of penmanship.

The real cost is not in developing the embarrassing scrawl that passes so often these days as handwriting, but rather in missing out on the boosted levels of effort and intention forced by the use of the traditional fountain pen itself. Apparently, the mechanics of the implement require one to enter a higher state of focus and concentration which then transfers over to the information one is writing about, producing a habit of greater commitment and energy that directly translates into better learning of course content, as well.

At these two Scottish schools, all students and teachers are required to take special handwriting instruction, and do most of their work utilizing modern fountain pens.

It all really seems to work rather well.

Once you've gotten the feel of the classic writing implement, a task made much easier by modern improvements in fountain pens, it's something you'd never want to give up, they say.

The article is a very interesting read:

School shuns tech, teaches fountain pen

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Contact Chris

borlandeducational.com

Copyright © 2006-present: Christopher R. Borland. All rights reserved.

Cite It Right

Properly formatting the information one presents in an academic work is important. Doing so is probably required, and in any case, it's easy ... with a little help!

To the unprepared, however, conforming to particular writing and formatting styles in high school and college research papers can be a real hassle, and many students find this requirement irritating, time consuming, and distracting. APA, MLA, and Chicago styles all have different requirements for presenting and citing information. Strict and correct adherence to the style favored by the instructor is absolutely necessary, and even minor deviations may result in a lowered grade for the project you're working on.

Dealing properly with headings, tables of content, page numbering, bibliographies, footnotes, etc. can be troublesome. But full compliance with standards of correct formatting is non-negotiable to many teachers, and patient submission to rigorous formatting requirements gives your work a professional look and feel that noticeably and significantly improves its value.

Luckily, software that interfaces with popular word processors to easily produce correctly formatted written projects with a minimum of fuss and bother is available for both Mac and PC platforms!

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Reference Point Software Templates cost only $28, work with both Mac and PC operating systems, and allow the user to compose properly formatted works in APA or MLA style using Microsoft Word, Microsoft Works, or Corel WordPerfect (although I don't have personal experience with this product, numerous customer testimonials tout it's effectiveness and ease of use.

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Various online sites exist to help students with proper formatting and citation. The following are two you might like to visit:

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Dr. Scribe's Guide to Research Style:

http://www.docstyles.com/;

and an excellent writing help site produced by Purdue University:

http://owl.english.purdue.edu/owl/.

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Various, now you have no excuse.

Cite it right!

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Contact Chris

borlandeducational.com

Copyright © 2006-present: Christopher R. Borland. All rights reserved.

Distance Learning for High Schoolers

Truly, many roads lead to Rome ... and to successful receipt of a diploma.

I myself am no stranger to "distance learning," a popular buzz-phrase signifying the earning of full academic credit for structured, supervised independent study work done outside the physical walls of a major educational institution. In fact, I earned my undergraduate degree back in the early 1980's from the State University of New York at Albany while enrolled in the Regents External Degrees Program, which was at the time one of only two fully accredited external degree programs in the United States. I remember with fondness teaching myself calculus and studying the history of mathematics though college-level correspondence courses administered by the University of California at Berkeley (UCB) and Brigham Young University (BYU).

In the old days, this meant learning on one's own from an approved textbook, completing assignments on paper, mailing them to the instructor for grading and comments, and then ultimately taking a proctored final exam to receive credit for the course. Nowadays, distance learning courses are typically conducted online, since the miracle of the internet makes possible a much richer and more efficient flow of educational content and course work between student and instructor. But the idea is essentially the same: independent study, followed by submission of course work, followed by assessment and finally the granting of credit.

Over the course of my 29 year career as a professional academic coach, tutor, and mentor, I've occasionally been hired to help high school students raise an unacceptable grade or earn additional course credits by completed various accredited distance learning courses offered through prestigious institutions such as UCB and BYU. These courses offer many advantages over typical high school classes taken during the academic year at school (e.g. being able to work at one's own pace, polish and perfect one's course work before submission and grading, study subjects outside the standard high school curriculum, etc.), and generally grant full academic credit to students completing them. Nevertheless, it's very important to first obtain written approval from your school before enrolling for credit in any distance learning course, to be sure that credits and grades earned will be fully accepted by your school.

Serious independent study work such as this both demands and fosters greater than average self-discipline, motivation, and organization, and requires real commitment of the part of all concerned ... but can be an excellent way to supplement or improve one's academic resume and develop qualities of independence, pro-activity, and responsibility so critical to success in college and beyond. Nevertheless, it may still be a good idea to secure the services of an academic coach or other capable adult to supervise distance learning courses to make sure that timely progress is being made and important deadlines are met. You've got to be committed and follow through ... but if you're a motivated, self-starter who reads well and wants or needs extra academic credit or stimulation, online or other distance learning courses may be just what you're looking for!

Below are links to accredited distance learning opportunities offered to high school students by UCB and BYU:

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UC Berkeley Extension Online

http://explore.ucxonline.berkeley.edu/highschool/body_hscourses.html

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BYU Independent Study

http://ce.byu.edu/is/site/courses/select.cfm?&TYPE=hs&SUBJECT=75

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Contact Chris

borlandeducational.com

Copyright © 2006-present: Christopher R. Borland. All rights reserved.