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.

History of the SAT and ACT

Test nerds and prep professionals already know about this site, which outlines in some detail the history of the SAT and ACT from the late 19th century to the present day. 

Information provided covers the founding of the College Board, the fits and starts and many early and late iterations of the SAT, the inception of the test prep industry in 1946 (Stanley Kaplan), the beginnings of the ACT in 1959, and a great deal more.

It’s a fascinating read for anyone with more than a passing interest in American college entrance tests.

Bibliographic notes are found at the end of the article (though most are not linked).

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Take Professors, Not Courses

In college, you can, with some limitations, choose not only your courses but also your professors. And, arguably, before you choose a major, professors can be more important than courses. 

Using ratemyprofessors.com, students can find the best professors in every department at most colleges and universities in the U.S. Look up your school, and browse the reviews of the most highly rated instructors for things that pique your interest and intuition. Ignore the department. Just find and read about the best professors in the entire college. Even if you’ve never had any interest in a particular field of study, think about taking the professor, not the course. 

Art History? Economics? Astronomy? Shakespeare? Latin-American Studies? Italian? Anthropology? The Mathematics of Gambling? Figure Drawing? Pure Land Buddhism? Botany 101?

The reviews you read about this or that professor may persuade you to take certain classes based on his or her outstanding reputation, particular comments left by other students, and your own instincts.

Great professors change lives. And great schools have great professors. Find them. Work with them. See where it takes you.

You may be surprised – and pleased.

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Bob Books

These zany little offerings for early readers were some of my young daughter’s favorite books when I was teaching her to read at age four. 

Written to be as entertaining as they are simple, Bob Books are as good as it gets in terms of quality phonetic early reading material that’s fun and engaging.

Kids can color-in the pictures to their own liking, which is also cool.

Bob Books come in sets – LOTS of sets!

Click here.

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Assorted Quotes I Can't Add

Unfortunately, Google doesn't seem to be updating the Blogger platform. Apparently, the "Text" gadget is broken.

I've tried hard to find a work around for this particular problem – without any luck, I'm afraid.

I'd intended to add several quotes to that section of this blog's sidebar, but it appears I won't be able to do so.

Rather than let the quotes languish outside the blog, I've decided to write a post listing them. This is that post.

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Bertrand Russell 

No nation was ever so virtuous as each believes itself, and none was ever so wicked as each believes the other.

Righteousness cannot be born until self-righteousness is dead.

It is preoccupation with possessions, more than anything else, that prevents men from living freely and nobly.

The point of philosophy is to start with something so simple as not to seem worth stating, and to end with something so paradoxical that no one will believe it.

The scientific attitude of mind involves a sweeping away of all other desires in the interests of the desire to know.

People seem good while they are oppressed, but they only wish to become oppressors in their turn: life is nothing but a competition to be the criminal rather than the victim.

The infliction of cruelty with a good conscience is a delight to moralists. That is why they invented Hell.  

Ralph Waldo Emerson 

The imitator dooms himself to hopeless mediocrity.

Poetry teaches the enormous force of a few words, and, in proportion to the inspiration, checks loquacity.

Every man I meet is in some way my superior; and in that I can learn of him.

To different minds, the same world is a hell, and a heaven.

You shall have joy, or you shall have power, said God; you shall not have both.

I have been writing & speaking what were once called novelties, for twenty five or thirty years, & have not now one disciple. Why? Not that what I said was not true; not that it has not found intelligent receivers but because it did not go from any wish in me to bring men to me, but to themselves.

Every natural fact is a symbol of some spiritual fact. 

Albert Einstein 

The mass of a body is a measure of its energy content.

The state of mind which enables a man to do work of this kind is akin to that of the religious worshiper or the lover; the daily effort comes from no deliberate intention or program, but straight from the heart.

The supreme task of the physicist is to arrive at those universal elementary laws from which the cosmos can be built up by pure deduction. There is no logical path to these laws; only intuition, resting on sympathetic understanding of experience, can reach them.

If A is success in life, then A = x + y + z. Work is x, play is y and z is keeping your mouth shut.

I believe in intuitions and inspirations. I sometimes feel that I am right. I do not know that I am.

Nationalism is an infantile disease. It is the measles of mankind.

I am not an Atheist. I do not know if I can define myself as a Pantheist. The problem involved is too vast for our limited minds. The human mind, no matter how highly trained, cannot grasp the universe. We are in the position of a little child, entering a huge library whose walls are covered to the ceiling with books in many different tongues. The child knows that someone must have written those books. It does not know who or how. It does not understand the languages in which they are written. The child notes a definite plan in the arrangement of the books, a mysterious order, which it does not comprehend, but only dimly suspects. That, it seems to me, is the attitude of the human mind, even the greatest and most cultured, toward God. 

George Pólya 

The teacher should not discourage his students from using trial and error – on the contrary, he should encourage the intelligent use of the fundamental method of successive approximations. Yet he should convincingly show that, for many situations, straightforward algebra is more efficient than successive approximations.

We wish to see the typical attitude of the scientist who uses mathematics to understand the world around us. In the solution of a problem there are typically three phases. The first phase is entirely or almost entirely a matter of physics; the third, a matter of mathematics; and the intermediate phase, a transition from physics to mathematics. The first phase is the formulation of the physical hypothesis or conjecture; the second, its translation into equations; the third, the solution of the equations. Each phase calls for a different kind of work and demands a different attitude.

In plausible reasoning the principal thing is to distinguish a more reasonable guess from a less reasonable guess. The efficient use of plausible reasoning is a practical skill … and it is learned by imitation and practice. What I can offer are only examples for imitation and opportunity for practice.

Even if without the Scott's proverbial thrift, the difficulty of solving differential equations is an incentive to using them parsimoniously.

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The Mighty Khan

Khan Academy is the apotheosis of K-12 distance learning and one of the chief miracles of the information age.

Nowhere can one find a larger variety of excellent educational offerings, from Pre-K curricula and grade school standards to AP Art History, APUSH, Differential Equations, and Organic Chemistry.

Khan's educational offerings, available in 42 languages, are used in diverse ways in public, private, and homeschool classrooms all over the world. Total views are in the billions, and growing.

And no wonder. The courses are rigorous, well-organized, and expertly taught, and a pleasure to use. Founder Sal Kahn is a genius, a visionary, and probably the world’s best private tutor.

There’s no excuse for boredom.

Click here.

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The Centimeter Grid

Use of a "Centimeter Grid" is a wonderful, multi-sensory way to teach basic math facts: addition, subtraction, multiplication, division.

Using the grid, students color-in squares to represent numbers, and then count the end result.

For instance, to learn 2 + 6: 

The student first colors two squares the same color, labeling them with a "2," and then six more in the same line using a different color, labeling these with a six, and finally, after counting up all the colored squares, labeling the entire set of colored squares with an "8." By this demonstration, it's clear that 2 + 6 = 8. [It's also clear that 6 + 2 = 8, 8 – 6 =2, and 8 – 2 = 6, thus completing a "fact family" cementing the  addition/subtraction relationship of the numbers 2, 6, and 8].

After discovery of each math fact, students "collect" the facts by writing each one on a flash card for later games of "flip the card" to help with memorization (Triangle Cards can speed up the process considerably by emphasizing fact family relationships).

But memorization should only be attempted after discovery. Students must first discover the math fact experientially, preferably physically, in multiple ways, by repeatedly demonstrating the fact for themselves. Then they record the fact for purposes of memorization. 

The order here is critical: discovery first, then recording, and finally memorization.

Consistent with the Scientific Method, it's best if students use more than one method, and repeat the experiment several times, to confirm results before recording them (e.g. first using a Centimeter Grid, then a Hundred Numbers Chart, and then counting pennies). This helps ensure the development of "number sense," a core mathematical capacity without which memorization is an empty exercise, at best. Memorization of math facts without corroborating discovery robs students of the intuitive "feel" for numbers they'll need to be successful in advanced courses later on.

Only if the student knows, experientially, by his own experimentation and record keeping, that 2 + 6 does in fact make 8, will he be able to make "sense" of that fact and integrate it with other ideas. This is a crucial distinction: the difference between mere belief and actual experience; between mastery and connectable knowledge on the one hand, and isolated, disassociated, meaningless memorization on the other.

Download your own copy of a Centimeter Grid here.

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Math and the Master

The phrase "Renaissance Man" is epitomoized by Leonardo da Vinci, the master of masters, founder of the High Renaissance. Geometry infused Leonardo's work, and was a particular obsession of his (e.g. The Golden Ratio, perspective, knots, fractals).

An article published by The Mona Lisa Foundation goes into some detail about the geometric underpinnings of Leonardo's design thinking.

It begins:

The important relationship of mathematics to art cannot be [overstated] when discussing Leonardo’s later work, and in numerous documents, letters and notes, the relevance of this is well documented. At times, he seems obsessed with these issues: while working on Mona Lisa for example, Leonardo is reported by Fra’ da Novellara to be concentrating intensely on geometry.

“Non mi legga chi non e matematico.”

“Let no one read me who is not a mathematician.”

-- Leonardo da Vinci

[Continue reading here.]

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Episodic Memory vs. Semantic Memory

Memory is mysterious.

Why do we recall some facts and not others? These event but not those?

How does human memory work?

What can we do to optimize memory in various situations and settings?

30-year primary teacher Clare Sealy has written a fascinating acting article in Education Next contrasting Episodic Memory with Semantic Memory and discussing the implications in educational settings.

The article begins:

When we look back on our own school days, our strongest memories are probably a mix of big occasions—field trips, plays, and sports days alongside more personal events tinged with strong emotion. Things that happened that were really funny or sad, or that made us feel excited, interested, exhilarated, or angry. We don’t tend to remember vividly, if at all, actually learning the substance of math or English or design technology. We might remember amusing anecdotes from lessons gone awry, or still bristle at past injustices — “but I wasn’t talking” — or have a vague impression of sitting in the science lab, with fleeting snippets of memories of this or that experiment. All of which leads to us making the entirely reasonable hypothesis that if we want students to remember what we teach them, then we need to make our lessons more like the spectacular one-off special events, or, at the very least, involve something specially selected because it’s exciting and possibly unusual. Memorable events, in this view, should form the template for creating memorable lessons.

As reasonable as this seems, this is a myth. It is a myth because human memory works in two different ways, both equally valid but one of which is much better at enabling us to transfer what we have learnt to new contexts. This transfer is an essential prerequisite for creativity and critical thinking.

The two forms of memory are known as episodic and semantic memory. Episodic memory is the memory of the ‘episodes’ of our life—our autobiographical memory. This takes no effort on our part, it simply happens. We don’t have to try consciously to remember what happened yesterday. Those memories just happen automatically. But there is a downside. Episodic memory is “easy come, easy go.” If you try to remember what you had for lunch yesterday, you will probably remember. If you try to remember what you had for lunch a year ago today—unless that happened to be some very significant date and some particularly noteworthy lunch—you will have no idea.

Semantic memory, on the other hand, involves much harder work. We have to expend effort to create semantic memories. This is the kind of memory we use when we consciously study something because we want to remember it. Unlike episodic memory, it does not just happen. The upside, however, is that the effort involved results in a long lasting memory.

Have you ever been in a course where you have really enjoyed listening to the speaker, found the subject matter interesting and the presenter amusing and engaging. Yet when you try to explain to someone the next day what the course was about, all that is really left is a vague impression of your emotions during the day, tinged with the odd snippet of content? You know the course was really good yet can’t really explain what it was actually about beyond the most general of assertions.

[Continue reading here.]

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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.

39 Top Tips for Taking Standardized Tests

After devoting multiple decades and 25,000 hours to any discipline, one learns a few things. Such is certainly the case with teaching in general, and test prep coaching in particular. 

An expert's "Rules of Thumb" represent the distillation of his esoteric knowledge. Gaining access to these fundamental principles and practices is one of the best ways to leap forward and save time and trouble on the road to mastery.

Linked below are my own bedrock test-taking do's and don't's – core tips, tricks, and bits of advice to help maximize your results on standardized tests. The notes apply to most multiple-choice tests.

If you find just a handful of things you can apply to your own plan of attack, it will have been well worth the read.

i hope you'll find the list helpful. Click here to download it.

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Take a Professor to Lunch

One of the smartest things you can do as an undergrad is to cultivate close working relationships with favorite professors.

Instructors can provide useful extra instruction, put students on the inside track for special research and internship opportunities, open doors to helpful career connections, and give invaluable tips and advice of all kinds to those who go the extra mile to show a sincere interest in their courses and chosen field.

This is a good idea even before you decide on a major. The fact that you've taken the initiative to arrange an informal one-on-one meeting outside of class says much about your maturity and intentionality, and teachers will usually return the interest and bend over backwards to help you.

Once you've decided on your field of study, fostering close, productive, professional relationships with key professors is no longer optional – it's absolutely essential and expected. Formal and informal mentorship can be the result, and nothing is more important in making a mark in your department and advancing career prospects.

Considering all there is to gain, you'd be surprised how underclassmen do this. All the better for you, since their indolence makes you stand out even more as a self-motivated go-getter.

Taking a professor to lunch is one of an annotated list of suggestions in 101 Things to Do Before You Graduate, a wonderful book by author and performance coach Julien Gordon. Although the book is a bit dated, I still recommend it to every rising college freshman. Those about to go off to college are almost certain to find several ideas in the book that will pique their interest and help them derive the most benefit from their precious college years.

Why not take a professor to lunch?

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Early Math Materials and Pedagogy

For several years, when I was a young father, my daughter and I took an enormous amount of pleasure in working together on early math.

In the process, I used and developed a series of graduated activities to enable her to learn increasingly advanced concepts at her own pace. 

The primary goal was always to develop "number sense," an intuitive feel for numbers and how they behave. Efforts at memorization came only after concepts made "sense" and were fully internalized.

Now that I'm a proud grandfather of another little girl, I recently reviewed early outlines of these activities, principally for my own recollection, but also so that I could recreate these happy experiences with my daughters daughter.

Interested parents or grandparents are welcome to download my rough notes here and here for their own use in beginning or supplementing early math education within their own families.

I hope you and your young ones have as much fun exploring early math as we did.

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Flatland

This late 19th century science fiction work about single and multi-dimensional worlds was penned by actor, minister, and headmaster Edwin Abbott to interest his students in geometry – and also to mock some of the many vagaries of Victorian society.

Written in inimitable 19th century British style, the book is a classic novel that brings to life core concepts of mathematics and physics that would be otherwise inaccessible to most mere humans.

An active imagination is all that's required to absorb the core concepts presented. It's easy to enter Abbott's 1-D, 2-D, and 3-D worlds, and, by extension, into those of even higher dimension. 

After all, the book was written with a middle school audience in mind!

Middle school 150 years ago was a different animal than it is today. Nevertheless, Flatland remains both an accessible recreational math primer and marvelous short work of fiction and satire. Less than 100 pages long, Flatland can easily be read in a single sitting.

I used to buy this book by the dozen, and give them away as gifts to my most curious math students.

You can read others' impressions of Flatland and order you own copy here (or get the ultra-inexpensive edition here).

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Fox, Chicken, Grain

"Fox, Chicken, Grain" is one of my favorite logic puzzles for younger students.

Here are the rules.

A farmer wants to successfully ferry a fox, chicken, and sack of grain across a river. He can take several trips back and forth, drop things off, and pick things up on each side of the river between trips. But he can carry only two things in his small boat, other than himself, at one time.
Unfortunately, the farmer has a few problems.

If left alone together on the same side of the river, the fox will eat the chicken, and likewise, the chicken will eat the grain. But the fox will not eat the grain (and, of course, the chicken will not eat the fox).

How to get everything safely across the river?

I usually use coins of different sizes to represent the fox, chicken and grain, and a small torn piece of paper as the boat (rowed by the farmer).

It helps to use a sheet of paper with a "river" drawn on it to simulate the situation. You an download a printout here.

Similarly, there's a puzzle called "Cannibals and Missionaries," in which three missionaries are trying to get themselves across a river filled with man-eating fish. They have to contend with three cannibals, as well, who also must get across the same river in the same canoe at the same time.

Here are the conditions:

Only two people can occupy the boat, and multiple trips can be taken in either direction. People can get  off the boat, once it gets to one side of the river or the other, and can re-enter the boat, at will. Unfortunately, if the cannibals outnumber the missionaries at any time on either side of the river, they will eat the missionaries. If this happens, the games ends unsuccessfully.

Complicating matters, only one missionary knows how to paddle the canoe, although all the cannibals know how to do so.

How to get all six people across the river in one piece?

In this case, I use three coins of one type to represent the missionaries (only one of which is heads up, indicating he can paddle the canoe), and three of another type as the cannibals.

Likewise, it helps to have the piranha-infested river drawn on a sheet of paper as a backdrop for the game, and a small piece of torn paper to use as the boat. Click here to download the backdrop.

In both games, the analogy to mathematics is found in the fact that, at each and every stage of the game, only one move makes sense and isn't obviously problematic. Patient, mindful examination of each potential move at each decision point leads one inevitably in the right direction – just as it does in solving math problems.

Can you do it? Give these a try!

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Test Your Mindfulness

How strong are your mindfulness muscles?

To find out, try your hand at these deceptive, simple-looking tasks.

In the first case, you job is to simply read the sentence contained within the triangle. As you read the sentence, write it down on a piece of paper. With luck, you'll see what's going on, here.

In the second case, try to say the COLORS of the words written, NOT the words themselves, in order, while reading at a normal pace. If you mess up, start again. Do not slow down to a snails pace in order to succeed in getting to the end of the list (although even that might not work).

Mindful, attentive concentration is a critical prerequisite for success in mathematics, and for quite a number of other activities, as well. Mindfulness is a capacity that can be trained, and just like any other training regimen, one begins with weakness but gets gradually stronger with practice and determination.

To find more puzzles for practice, search the internet.

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Hundred Numbers Chart

A 10x10 grid of numbers written from left to right, top to bottom, starting in the upper-right corner with 1 and ending with 100, is called a "Hundred Numbers Chart." 

It's a highly effective tool to teach eager youngsters how to add and subtract two digit numbers, instinctively, using the chart as an aid. Eventually, the chart becomes internalized, and students can do the calculations rapidly and accurately entirely in their heads.

To begin using the chart:

First, make sure the child can already count by 10s. Then have the child learn from experience that the numbers in the chart simply represent counting, and that counting forward 10 squares can be done more easily by starting on any square and moving straight down to the square immediately below.

To demonstrate 23 + 35 = 58:

Start with your finger on 23. Move straight down three rows (each move represents adding 10, so three such moves represents adding 30). Now, count right five spaces. The answer, clearly, is 58. A similar process can be employed to carry out subtraction. Borrowing and carrying is handled by wrapping around the ends of rows as one executes the process.

Parents should give this a try themselves, first, and become masters at utilizing the tool before attempting to use it to instruct their children. After a very short while, using the chart becomes second nature for adults.

Children will take more time to achieve the same level of skill, of course. But with patience, practice, and plenty of good energy, encouragement, and hand clapping, they'll soon be performing difficult mental calculation with ease and accuracy.

A Hundred Numbers Chart is also useful in teaching young kids to count by twos, fives, tens, threes, and fours (a precursor to learning multiplication). 

For example, to learn to count by threes:

Have your student start on three, circle that number, then count spaces three at a time, circling the number in colorful crayon each time they land on a new square, and saying each new number out loud. Verbalization is critical as an aid to memory. The colored numbers will form a clear geometric pattern that will eventually make memorizing the sequence easier. After a while, counting by twos, three's fours, etc. will become second nature.

Learning to count by threes, for instance, is a great way to introduce multiplication. One 3 is 3; 2 threes are 6; 3 threes are 9, etc. Again, doing this activity out loud and with colored crayon is super important. Before you know it, your child will have mastered the threes.

Click here to download a Hundred Numbers Chart to print and use at home.

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Basic Math Concepts: ACT and SAT

First produced a number of years ago, Kaplan's 100 Key Math Concepts for the ACT still has relevance for ACT test takers today.

Each core math concepts presented is elemental and should be easily understandable to any high schooler signed up to take the test. Nevertheless, a great many will have trouble with at least several of those listed.

Students should use the document as a checklist, as follows:

Beginning with the first item, grade each concept A, B, or C depending on your current level of understanding. If the topic is completely understood, give the item an "A" grade. If the item is not at all understood, give the item a "C" grade. Somewhere in between? Give the item a "B" grade.

Your task, of course, is first to master any concepts graded "C," and then all those graded "B." The best way to accomplish this is to use a friend, tutor, or Google to help you learn to handle each concept and/or skill presented.

The list is a bit dated, however, and the ACT writers have since updated the content of the test's math section to include more advanced concepts.

Click here for the original document and here for a list of the most recently added ACT math topics.

Click here for the Kaplan document corresponding to the pre-2016 SAT

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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!

Cosmic Eye

This epic science video takes viewers from the realm of everyday human experience to macrocosm, microcosm, and back, by the power and magic of exponential growth. 

It's a brief 2:29 excursion that could make your day.

Powers of 10 was one of the first such "logarithmic zooming" films, released in 1977 by ground breaking mid-century designers Charles and Ray Eames (see Wiki article here). Orders of Magnitude is an excellent recent variation on the same theme.

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