Sunday, March 17, 2024

How To Fail A Test With Dignity

Sometimes, you just can't win.

In that case, there's no harm or shame in surrender. So why not have a sense of humor about it?

These students tried and failed, but succeeded in turning loss into laughs.



























































































































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

Friday, March 01, 2024

dSAT Reading and Writing Topics

This is the companion piece to a post I wrote earlier on dSAT Math Topics.

Questions in the Reading/Writing sections of the dSAT cover four broad topic areas: Craft and Structure, Information and Ideas, Standard English Conventions, and Expression of Ideas.

The entire Reading/Writing section is 64 minutes long with 54 multiple-choice questions.

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Modules

Two Reading/Writing modules:

Each module is 32 minutes long, with 27 questions (1:11 per question)

Organized by question type, with similar skills grouped together

Questions within each group are presented in order of increasing difficulty

Each question has its own short passage or pair of passages

Passages are between 20–150 words

Wide range of topics, including literary excerpts and poetry

May contain informational tables and graphs 

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Information and Ideas

12-14 questions, 26% of the section

Use information stated or implied in the passage (may include tables and graphs) to evaluate ideas in the text and draw conclusions.

Tasks:

Determine main idea and central details

Interpret details supporting the main idea

Use evidence from the text, graphs, and tables to support or respond to a claim

Draw reasonable inferences based on the passage

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Craft and Structure

13-15 questions, 28% of the section

Focuses on vocabulary (words in context), text structure and purpose, and cross-text connections.

Tasks:

Determine the primary purpose of the text

Evaluate text structure rhetorically and how the author chose to organize information

Select the best word to complete the text (fill-in the blank)

Compare/contrast two related texts

Make supportable connections between two related texts

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Expression of Ideas

8-12 questions, 20% of the section

Focuses on improving effectiveness of written expression. Test takers are asked to scrutinize topic development, accuracy, logic, cohesion, transitions, and language to improve, refine, and enhance the effectiveness and impact of a text and achieve specific rhetorical goals.

Tasks:

Analyze bullet points and choose the one that best combines information to achieve a certain goal

Identify the flow and structure of a passage

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Standard English Conventions

11-15 questions, 26% of the section

Use editing skills and knowledge to make texts conform to standard conventions of written English, emphasizing proper word usage, sentence structure and form, grammar, and punctuation.

Tasks:

Identify correct punctuation to join and separate sentences and clauses 

Find the best way to complete a sentence so that it follows conventions of standard written English (e.g. proper agreement, verb tense, etc.)

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

Thursday, February 01, 2024

dSAT Math Topics

After trying and failing to find a comprehensive online resource that thoroughly detailed math content covered on the dSAT, I finally decided to put together my own. I've also written a companion piece on dSAT Reading and Writing Topics.

Questions in the Math section of the dSAT cover four broad topic areas: Algebra, Advanced Math, Problem Solving and Data Analysis, and Geometry/Trigonometry.

The entire Math section is 70 minutes long with 44 multiple-choice questions.

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Modules

Two math modules:

Each module is 35 minutes long, with 22 questions (1:35 per question)

75% multiple choice (33 questions), 25% student produced response (11 questions)

30% in-context word problems (≤ 50 words)

Progressive difficulty (easiest first, hardest last)

Calculators are allowed – but don't use a handheld – learn to use Desmos, instead

Questions from each topic area appear in each module
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Algebra

35%: 13-15 questions total

Linear equations in one variable (analyze, solve, create)

Linear equations in two variables (analyze, test, solve, graph, create)

Linear inequalities in one variable (analyze, solve, create)

Linear inequalities in two variables (analyze, test, solve, graph, create)

Linear Functions (analyze, test, evaluate, graph, create)

2D Linear Systems (analyze, test, solve, create)

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Advanced Math

35%: 13-15 questions total

Equivalent expressions

Non-linear equations in one variable (analyze, solve, interpret, create): absolute value, quadratic, polynomial, exponential

Non-linear functions (analyze, solve): absolute value, quadratic, polynomial, exponential

Non-linear systems in two variables (test, solve)

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Problem Solving and Data Analysis

15%: 5-7 questions total

Ratios, rates, proportions, units

Percentages

Analyze and interpret one-variable data: distributions and measures of center and spread (mean, median, mode, range, standard deviation)

Analyze and interpret two-variable data: models and scatter plots

Simple Probability

Conditional Probability

Inference from sample stats and margin of error

Evaluating statistical claims: observational studies and experiments

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Geometry and Trigonometry

15%: 5-7 questions total

Perimeter, area, volume

Lines, angles, triangles

Right triangles

Trigonometry (SOH CAH TOA)

Circles

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Most of this content was paraphrased from the following sources:

What Topics are on the Digital SAT?

What's on the digital SAT Math Test?

Educator's Guide to the Digital SAT

The New Digital SAT Format

(New) Digital SAT Test Format

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

Monday, January 01, 2024

Desmos

The online Desmos graphing calculator is fast taking over from the venerable Ti-84 series of handheld calculators as the default calculator tool in secondary education. Now that Desmos is included as an integral part of the digital SAT, acquiring intermediate-level Desmos skills is fundamental to maximizing math scores on this important assessment.

[Familiarity with the Ti-84 Plus CE handheld graphing calculator is still crucial to optimizing math scores on the ACT.]

I'm not aware of any succinct, comprehensive exposition of Desmos skills required for use on the dSAT (I'm working on it).

At this point, the best one can do is to peruse the various official materials linked in the "Desmos First Steps" and "Desmos Graphing Calculator" sections below. 

Check out each link, read the information provided, and do the sample exercises until you've covered all topics presented (search Google for additional help with particular topics).

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Desmos First Steps

User Guide

Quick Start Guide

Getting Started: Desmos Graphing Calculator

Getting Started: Creating Your First Graph

Getting Started Articles

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Desmos Graphing Calculator

Graphing Calculator

Graphing Calculator: Essential Skills

Graphing

FAQ: Graph

FAQ: Student Graphing

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Desmos Geometry

Geometry

Geometry Tool

Transformations

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Other Desmos Calculators

Scientific Calculator

Matrix Calculator

3-D Calculator

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Desmos Miscellaneous

Tutorials

Desmos YouTube Channel

Keyboard Shortcuts

Help

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

Friday, December 01, 2023

Look Inside the Digital SAT

The digital SAT has arrived, 

In the meantime, much has been written about all aspects of this latest incarnation of the SAT. All along, The College Board has offered limited information concerning what we who care should expect.

But the private analyses of those whose businesses and livelihoods hinge on gaining an early, accurate, and comprehensive view of this strange new beast are also well worth noting.

In addition to those featured on the SAT/dSAT resource page of my business site, below are several more such reports.

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

Wednesday, November 01, 2023

Bring a Mouse to the SAT

Most people find use of a mouse to be a time saver, especially if you’re accustomed to employing one. 

On the digital SAT, every second counts, and a mouse is one of your best friends on this important assessment.

The College Board allows use of a mouse on the digital SAT. Practice with your favorite mouse at home. Then bring the same usb mouse with you on test date, plug it in, and go.

This seems like a minor detail, but there’s almost no such thing when it comes to high-stakes testing.

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

Sunday, October 01, 2023

The Official Digital SAT Study Guide

The Official Digital SAT Study Guide by The College Board has been the sine qua non of SAT work for decades. 

But with the SAT's switch to a new digital format, just how useful is this latest incarnation of the venerable test prep tome? Why buy a book printed on paper when the test is now taken on-screen?

These are good questions.

The new edition contains four non-adaptive paper versions of the digital SAT – the very same "linear" tests made available as free downloads to students everywhere – which are roughly 70% identical to the four official adaptive on-screen tests contained in the College Board's BlueBook app (the only official tests available in on-screen adaptive form).

So that's even less reason to buy the book, right?

Right. Except for one thing.

Currently, there's a severe scarcity of official SAT practice materials (this happens each time the College Board decides to overhaul the test). Every new official SAT question made available to the public for practice gives valuable clues as to what to expect on the test, and is therefore worth gold.

As it happens, the new College Board Official Guide to the SAT contains 192 printed practice questions different from those provided anywhere else. That's nearly the equivalent of two additional full-length digital SAT tests.

So yes, at this point, you should buy the new edition – if only to gain additional practice with those 192 precious questions.

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

Friday, September 01, 2023

Commercial Test Prep

Needless to say, when I graduated high school in 1975, it was an entirely different world.

With plenty of well-paying blue collar jobs available in the U.S., a college education was seen as an optional luxury, not at all a requirement to live a good middle-class life. I remember befriending a Golden Gate Bridge worker in the late-1980’s who was paid an annual salary of nearly $60,000 – $150,000 today – taking tolls!

Not many students used any kind of prep, though. I took the PSAT in high school, cold, no prep or pre-test studying at all, as a lark (and hit 98th percentile). But I never told the SAT (didn’t feel like wasting a Saturday morning). Most of my friends acted similarly. College just wasn’t a must-do, at the time.

Stanley Kaplan invented the modern test prep industry in 1939, and between 1940 and 1980 his company’s courses and books were essentially the only ones available to help interested students maximize scores on the standardized tests like the SAT.

Then along came the Princeton Review in the mid-1980’s, upending the entire educational testing scene. Despite protestations from the College Board and others, PR showed everyone just how easy it was to game these tests and quickly raise scores without doing much to improve nominal academic ability.

When I began tutoring professionally in the late 1970’s, test coaching wasn’t yet a thing. Following the huge success of PR, the test prep industry as we know it today was born. 

The test prep universe is vast. Companies old and new seem infinite in number. With the advent of distance learning on a mass scale during the Covid epidemic, this number has grown further.

It’s not easy to make a choice, nowadays, given the multitude of options. To aid in your search, listed below are my current favorites, based on my own long experience and most recent research on the subject:


Tuesday, August 01, 2023

Mock dSAT Practice Tests

It’s always the same.

Whenever the College Board trots out a new version of the SAT, years elapse before we have enough official practice material to adequately prepare students for the test.

True to form, to date, the College Board has only made released four official computer-based adaptive SAT tests to the public. To do a good job preparing for the SAT, students need 3-4 times that number.

As always, we’re left to evaluate the various mock SAT practice test offerings currently available. Luckily, most companies offer a free sample test.

In fact, you could pay nothing (or almost nothing) for multiple mock dSAT practice tests simply by signing up for free trials from the list of providers below.

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Princeton Review

Saturday, July 01, 2023

Cracking BlueBook Second Modules

With only six available official digital adaptive SATs and PSATs, it’s critical that students get access to all questions contained in the “second modules” of each section of each test in the BlueBook app. 

There’s no way to do so directly, but an easy workaround gets the job done: 

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1. After completing your practice test, save the answer page.  

2. Retake the same practice test. 

3. To access the harder second module, enter only correct answers when you retake the test; to access the easier module, enter only incorrect answers. 

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Click here to view and download (File > Download) correct answers to first modules from BlueBook SAT Tests 1, 2, 3, and 4.
 
You may also want to screenshot important questions as you practice (hardest problems, any you’ve answered wrongly, etc.) and keep these in a folder for further study.

These few official tests are best used sparingly to assess progress in your prep work or as “dress rehearsals” before test dates.

They're the only ones you’ve got. Don’t waste them!

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

Thursday, June 01, 2023

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 PĆ³lya 

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

Monday, May 01, 2023

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

Saturday, April 01, 2023

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

Wednesday, March 01, 2023

Coaching v. Tutoring

Academic Coaching is a specialty in the field of private practice education.

How has academic coaching evolved? What's the difference between ordinary tutoring and professional academic coaching? When is it wise to hire an expert, despite the higher cost?

The purpose of this article is to clarify the distinction between ordinary tutoring and academic coaching and help answer these salient questions.

Historically, private tutoring was the way most education happened, the primary means by which critical knowledge and skills were passed from one generation to the next.

Whether the subject matter is hunting mammoths, learning Latin, sewing a dress, playing piano, passing the bar exam, or mastering basic algebra, nothing beats one-on-one private instruction with an engaging, expert private teacher. Indeed, it's been said that the best possible educational setting is "yourself, Aristotle, and a log."

[Continue reading here.]

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

Wednesday, February 01, 2023

I ❤︎ TurboScan

Scanning apps are nothing new, but when TurboScan came out more than 10 years ago, they were. TurboScan was a breakthrough, and quickly became a mission-critical app for busy professionals everywhere, and it remains so today.

I use TurboScan practically everyday, in my professional and personal lives. Making perfect color or black/white scans of important hard-copy receipts and documents (and then mailing them as pdf documents to myself or others) has become a crucial part of my workflow. In fact, I'm still discovering new features. Even without having bothered to teach myself the full range of its usefulness, Turboscan has radically changed and fundamentally improved the way I, and others I know, conduct business and teach online.

I've been thoroughly dependent on TurboScan nearly since its inception, and I'd be lost without it. I can't recommend it more highly.

You can find TurboScan in the Apple or Android App Stores. Both free and pro versions are excellent.

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

Sunday, January 01, 2023

Mathematical Logic

The trunk of the tree of mathematics divides into two main branches: applied mathematics, and pure mathematics.

Applied mathematics is concerned with calculation. Getting the right answers. Building things. Making sure the probe lands safely on Mars, that the bridge can withstand high winds, that revenue will exceed expenses. Utilitarian math.

I've always been interested in pure mathematics: the study of numbers, purely, for no other reason. Useless math, in other words. Math for the sake of math, only. Utterly non-utilitarian math.

The purest of pure math is logic, the foundation of mathematics. Mathematical logic is "meta-mathematics," the software running the machine, the engine under the hood.

One my favorite undergrad courses was an upper-division class in mathematical logic. Not long ago, I decided to take out some old textbooks, and summarize what I'd learned decades ago. The result was a set of simple notes for doing "Truth-Tree" proofs, one my favorite class activities.

You'll find those notes here.

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

Thursday, December 01, 2022

Secret Sauce

Standardized testing is an inescapable fact of academic life.

Unfortunately, many students receive low scores simply because they lack the necessary test-taking know-how, preparation tools, practice habits, or skilled instruction required to maximize scores on tests like the SAT and ACT.

Nowhere is this more evident than on the math sections of such tests.

Of course, mathematical ability is the best predictor of success on any math test, and many tutors use an entirely content-based approach in an attempt to quickly increase standardized test math scores. In most cases, however, this is a fool’s errand.

[Continue reading here.]

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

Tuesday, November 01, 2022

The Most Fun You Can Have With $100

Micro-financing makes seed capital available to poor people who want to start their own business but simply cannot afford to get the started. 

The opportunity to rely on themselves, to think realistically of a day when poverty will be a thing of the past for themselves, their families, and possibly their communities, as well, is an enormous blessing for all concerned.

None of this happens easily, of course. Much hard work and dogged determination will be required to make these micro-businesses into growing, thriving, profitable success stories.

But most of these dreams do, in fact, come true.

As the business owners get to work, and start seeing their labors bear fruit, beliefs in scarcity and the inevitability of poverty start evaporating. These outcomes would be impossible without the initial loan of seed capital by small-scale venture capitalists like you and me.

That's where micro-lending site Kiva comes in.
Kiva brings together low-income would-be business owners in 70+ countries with small-scale funders to help make dreams real.

As a Kiva member, you deposit a fixed sum (say, $100) into your Kiva account, and then lend it out to one or more applicants applying for financial seed money to start their businesses. Would-be business owners post info about their themselves and their business aspirations to make it easy for funders to decided where to loan their money (country, type of business, picture of themselves, etc.).

Once the money you've loaned is repaid, it returns to your account, so you can lend it out again ... and again ... and again and again and again! Kiva boasts a 96% repayment rate (!), so your original investment of x dollars can easily have the impact of 5x or 10x or more!

Becoming an active Kiva lender is certainly one of the best ways to spend $100 and a half our every few months (and one of the most fun.)

Kiva is given the highest rating (for stars, 90%) by Charity Navigator:

Check out Kiva for yourself.

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

Saturday, October 01, 2022

ACT Mini-Tests

Mini-testing helps students discover the high levels of energy, focus, and discipline (pacing) required to maximize scores on the English, Math, Reading, and Science sections of the ACT. 

For each test section, students take shorter timed “mini-tests” containing a representative sample of questions in a fraction of the time proportional to the number of questions in the mini-test.

This exercise is a sprint! The goal is to push oneself, in short bursts to the very high level of focus and energy required to achieve a perfect score. Through trial, error, and increasing application of personal will, students learn to enter and eventually habituate the state of mind necessary to maximize their scores.

For example, an ACT math mini-test is created as follows:

From an official ACT test, the math section is printed. The student attempts to answer 1/4 of the questions in this section in 1/4 of the time allowed. Instead of completing an entire ACT Math section – which would require 60 minutes to answer 60 questions – the student has 15 minutes to answer every fourth question in this section: #1, 5, 9, 13, etc.

A bubble sheet is not used, but the standard marking system is observed (circling letters, writing large capitals under question numbers, adding “?” or “X” for guesses, etc.). The student uses an analog watch reset to exactly 12 o’clock to mark time

At the conclusion of each mini-test, students check their answers, critique their performance, and record insights. This material is then studied and reviewed thoroughly (reviewing notes and reworking incorrectly answered questions) before repeating the process. "Practice, critique, review, repeat!"

Below are standard time limits recommended for various ACT mini-tests:



English

One passage, 15 questions: 9 minutes

Math

Every 4th question, 15 questions (#1, 5, 9, 13, etc.): 15 minutes

Reading

One passage, 10 questions: 8 minutes 45 seconds

Science

One passage, 6-7 questions: 5 minutes 50 seconds

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