Friday, June 01, 2018

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 their loss into laughs.



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

Thursday, May 31, 2018

2, 800, 44

With regard to the SAT Math Subject Test, the three most important numbers are:

2, 800, 44.



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.



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, and do carefully error analysis and regular review).



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. 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, 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, as long as you get 44 right answers on this test you’ll receive a perfect 800 as your SAT Subject Test score.


You can, quite likely, 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 should probably pick another subject test.

For more SAT2M2 advice and resources, click here.



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

Tuesday, May 01, 2018

Calculator Policies: SAT and ACT

SAT and ACT policies regulate the types and models of calculators allowed for use in solving math problems on standardized tests administered by each organization.

For a while, the SAT had a more or less unrestricted calculator policy whereas the ACT had a tightly controlled one, allowing only those user-installed programs comprising 25 or fewer lines of code. Aside from being unduly onerous, the old ACT policy was obviously unenforceable, and has recently been changed to essentially match the unrestricted SAT rule.

In a nutshell, here is what you need to know:

All features, apps, and user-installed programs are permitted for use, without restriction, on any model of the Ti-84 graphing calculator family (including the powerful Ti-84 Plus CE model) on the SAT, the SAT Math Subject Test (Levels 1, 2), and the ACT.

Below are links to current policies:

SAT Calculator Policy (updated: 2018)

ACT Calculator Policy (updated: 7/1/2017)



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

Sunday, April 01, 2018

How Hard Would You Work for an Extra $1 million?

Although there are no guarantees in life, it's no secret that a top-notch college education generally confers valuable special advantages to those fortunate, talented, and diligent enough to obtain one, including: superior instruction; well-connected networks of alums and professors; preferred access to coveted internship, research, and employment opportunities; etc.

Let's assume that landing a seat at a top school rather than an average school means that you're ultimately able to increase your month salary $1000, on average, over the course of your working lifetime, and that this allows you to save an extra $500 per month, on average, for 40 years at 6% real growth.

That's an extra $1 million in present value purchasing power once you hit retirement. And these numbers are conservative. You could quite easily double them, in the right jobs and fields.

That's a completely different life, not only for you, but for those who come after you.

Now are you motivated?

In general, the best thing you can do to increase the probability of admission to top schools is standardized test prep and college application essay prep. Assuming you're taking the toughest classes you can and are getting the best grades you can, time spent maximizing your SAT/ACT scores and nailing the various common app, personal statement, and supplemental essays you'll write for your college applications will do far more to improve your own College Application Marketability score than anything else you could possibly do with your time.

Once again, there are no guarantees. A hot diploma doesn't mean anything by itself, and students unable to gain entrance to a top 30 school can make up for most/all of that advantage with extra grit, hard work, dedication, and perseverance.

Still, it's worth it to aim high. Go for 100%! Then, celebrate the result, whatever it is. Use failures as feedback to recalibrate the machine.

Life is a summit-less mountain to climb. Every time you reach the top, there's a taller peak off in the distance. Best to learn to love climbing!



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

Thursday, March 01, 2018

Teach Your Child to Read in 100 Easy Lessons

There’s no excuse for illiteracy, and this book proves it:

Teach Your Child to Read in 100 Easy Lessons (by Siegfried Engelmann, et al).

Virtually any educated adult can teach virtually any interested child to read at a comfortable 2nd grade level in just four to six short months (one 20-minute lesson a day, six days a week) using this classic phonics-based home learning tool. If desired, one can take up to a year to complete the 100 lessons (supplementing learning sessions with additional reading materials, extra writing exercises, etc.).

Instructions for the parent-teacher are crystal clear at every stage, and super easy to implement. Students should be able to recognize upper and lower case ABCs before starting, and it helps if to know the main sounds each letter makes, but this is unnecessary.

Using this system our daughter learned to read at age four, the proverbial child with her nose stuck in a book. She went on to be a happy, successful student, and a voracious life-long reader. Precocious children who want to learn to read could start even earlier. Most kids would probably do well to begin at four to five years of age.



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

Thursday, February 01, 2018

White House Fails English

The recent experience of retired English teacher Yvonne Mason echoes the exasperation felt by many of us who spent the entire first two years of high school English doing nothing but arcane grammar exercises out of a workbook.

It may be too much to ask in this age in which English teachers no longer feel the need to teach grammar (and English majors aren't even required to study it), but shouldn't we expect better than this from the office of the highest governmental official in the land?

Argh. [Facepalm.]

I might suggest these English language resources.



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

Monday, January 01, 2018

College Application Marketability (CAM)

The following is a rough approximation of the relative importance college admission committees give to basic elements of a typical application:
  1. Coursework (grades and rigor): 40%
  2. SAT/ACT test scores: 30%
  3. Essays (Common App, personal statements, supplements, etc.): 15%
  4. Everything else (extracurriculars, leadership, legacy, ethnicity, etc.): 15%
Let’s assume that an average honors or AP-level high school course requires about eight hours of work per week (four hours in class, and four hours outside class). Assuming six classes and 36 weeks of school per year, that’s 1728 schoolwork hours per year for the typical college-bound high school student. By the end of junior year, that’s 5184 academic hours. Just to be safe, let’s round down to 4,800 hours. That’s 120 hours per CAM point.

Suppose a student spends an average of two hours per week over the course of 12 months preparing for the SAT. This requires a total investment of 104 hours. To be safe, lets round up to 120 hours. That’s only four hours per CAM point.

Similarly, time invested in planning, drafting, editing, and polishing college application essays is hugely profitable! Let’s assume the average student needs to write one 1000-word Common App essay and eight 500-word supplemental essays and personal statements; that’s nine college application essays totaling 5000 words. To do an outstanding job on these critical pieces of academic work might require 75 hours. That’s only five hours per CAM point.

The takeaway:

Making a serious commitment to long-term standardized test prep and to putting in the time and effort required to write great college essays is highly intelligent!

Yes, of course, you should do all you can to take the toughest courses and get the very best grades possible. You do need to show sincere interest in your favorite schools, committed involvement and initiative in pursuing extracurricular activities for your own enjoyment and in service of others, and accomplishment of notable NTA's ("non-teenage activities").

And, of course, there are only so many hours in the day. Nothing on Earth is more important than maintaining good mental and physical health, properly balancing work and play, and getting enough rest and sleep. You can't do your best work if you're sick, unhappy, or exhausted.

Notwithstanding these important considerations, the fact remains that work on test prep and college essays is up to 30 times more productive than anything else the typical high school student can do to maximize CAM and boost the odds of admission to a top school.

Imagine that you’re taking an additional half-course called “CAM Class” throughout junior year and during the first semester of senior year. The content of this independent study course will consist mainly of your own research into “good fit” colleges, standardized test prep, college essay work, and general college application planning and preparation. You’ll put far less time into CAM Class than you would into any ordinary course – but your devoted participation here has the potential to do far more for your chances of gaining entrance to the college of your dreams than do all the other courses you’re currently taking put together!

This is an incredible opportunity for those committed students willing to step up, embrace the challenge, and make a relatively small sacrifice of time and energy in exchange for the excitement, fulfillment, and future success that only a great college education can provide. It’s smart to commit yourself to building the best college application package you can by working diligently to maximize your score on the SAT or ACT and nail your college application essays.

Make a plan to investigate various colleges and universities that match your goals and fit your personality, prepare thoroughly for the SAT or ACT, write and finely polish your college essays, and complete and fine-tune your college applications well ahead of time. If you can, find a qualified test prep coach and private college counselor to help you along the way. If this isn’t possible, you can do quite well working entirely on your own – without paying for any outside help at all – simply by reading good books on these subjects, researching online, putting in the time, and becoming an test prep wizard and college application expert through self-study.

There’s no better investment than the time and energy required to earn an “A” in CAM Class.



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

Friday, December 01, 2017

MOOCs are Coming of Age

At their inception several short years ago, MOOCs (Massive Open Online Courses) were an unproven concept with passionate advocates and doubters on opposite sides of a great debate. MOOCs were going to revolutionize higher ed, or destroy it. No one could tell which it would be.

A decade later, top MOOC providers like Coursera and EdX have grown and prospered. Top-notch course offerings by the best universities in the world have attracted millions of students world-wide. Legions of online pupils of all ages have completed courses, some earning coveted professional certificates and even fully-accredited graduate degrees online. Low cost has made high quality higher ed available to a much wider, world-wide audience.

Though forms are still evolving and the precise roles to be played by MOOCs are still uncertain, both the radically new concept and the traditional educational landscape have survived and even thrived as a result of the introduction and mainstreaming of MOOCs.

Today, MOOCs and associated certificates/degrees are legitimate educational alternatives.

See links below for further info:

Massive Open Online Course (WikiPedia)

By the Numbers: MOOCs in 2017

The Future of MOOCs


Coursera Professional Certificates

Coursera Undergrad and Grad Degrees


EdX MicroMasters Certificates

EdX Professional Certificates

EdX Series Programs

MIT Open Courseware

Stanford Online



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

Wednesday, November 01, 2017

Take College Classes While in High School

There are many reasons to take college classes while in high school:

1. A's in college-level work look good on college applications.

2. Advance placement could save you valuable time and money in college (students may earn enough extra units to earn their undergrad degree in just three years, allowing them to begin careers or grad school well ahead of schedule).

3. You can get pesky general education requirements out of the way while trying out various ideas for majors, so that once you're at your dream school you can make the most your tuition dollars by taking upper-division courses freshman year and exploring or developing majors early.

4. Advanced high schoolers may be feeling like they've had enough of high school, and will be invigorated by dipping their toes into a more intellectual environment, interacting with college professors and students, etc.

5. Your academic work does double-duty this way, earning both high school credits and college units at the same time, so you can take fewer high school classes senior year (you might even be able to leave campus at lunchtime).

If you have a junior college near home, chances are you can take courses there as a junior or senior in high school. Local four-year colleges may also allow you to take courses for college and high school credit simultaneously. 


Colleges and departments often place arcane restrictions on the transfer of college credit earned before matriculation. Be sure to check with your high school counselor, the registrar at your local college, and relevant departments at the schools to which you'll be applying for admission – to be absolutely sure of the credits you'll be earning – before enrolling in college courses while still in high school.

After graduating high school in 2011, our daughter took a gap year before attending Wesleyan University, and took two semesters of junior college calculus during that year off. Before enrolling in the JC courses, she called the Wesleyan registrar and confirmed that yes, the two JC calculus would, in fact, be counted for credit at Wesleyan. Once she got to Wesleyan, however, and decided to major in mathematics, the math department head refused to count her "A" grade in JC multi-variable calculus toward her math major at Wes! The JC course would be counted for graduation, but not toward the requirements for the math major. So, she had to retake the course at Wesleyan. As it turns out, the Wesleyan math department would have accepted for full credit within the major any upper division math courses taken at a four-year college. Had our daughter known this ahead of time, she could easily have taken the 3D calculus course at Sonoma State University, just 15 minutes from home, rather than at the local JC.

I had a student several years ago who a similar experience at Amherst. He earned a 5 in AP calculus AB in high school, but nevertheless had to retake the course at Amherst, due to restrictions on college credit earned at other schools.

With proper forethought and requisite caution, taking college courses while in high school can be a wonderful opportunity to stretch intellectual boundaries, boost applications, fulfill requirements, save money, and investigate prospective majors ahead of time.

Do your due diligence, check early with all parties involved (including heads of relevant departments), get promises of credit in writing (via email), and you should have no unhappy surprises.



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

Sunday, October 01, 2017

Children's Books for Teaching Math

Great story books abound, and children love them ... but there are also plenty of fun, well-crafted nonfiction books for kids, and these are just as important to include during family reading time.

Elyse Mycroft at has compiled an excellent list of wonderful books to use in introducing the panoramic world of mathematics to children:

Children's Books for Teaching Math

Early math topics from numbers and counting to patterns and sorting, fractions, measurement, time, basic operations, and financial literacy are introduced and explored.



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

Friday, September 01, 2017

Math Worksheets and Drills

Overuse breeds contempt, as evidenced by how unfashionable it's become in most American schools to utilize worksheets and drills in teaching math to kids.

Actually, it's important to attend to both sides of the pedagogic coin teaching and learning mathematics: discovery and memorization. Anything less, and ... trouble ensues.

Currently, the discovery side of the coin is in vogue and generally gets adequate attention.

For the foreseeable future, it may be up to parents to supply the drill and worksheet components that lead to memorization of basic math facts and mastery of essential processes.

Below are some good resources:

Super Teacher Worksheets



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

Tuesday, August 01, 2017

5 Rules for Marketing a Private Educational Practice

When I began teaching privately in the 1970's, tutoring wasn't yet a thing. It wouldn't become a thing till the late 1980's. By the turn of the century, the academic coaching market had long been a billion dollar industry. In 2018, it will surpass $100 billion.

In the old days, it was simply a matter of contacting college admission consultants and academic deans at local private schools, arranging meetings, asking for referrals, and then doing stellar work. Nowadays, with the educational landscape awash in tutors of all stripes, it can be hard to get a foot in the door.

Nevertheless, the basic template for running a successful private educational practice remains the same today as it's always been.

It boils down to five basic rules.


Rule 1: Be Excellent

Excellent work is the sine qua non of successful private practicing educational businesses. You solve problems for parents who hire you and create good will for colleagues who refer to you. These are your two top priorities, and must always remain so.


Rule 2: The Three Marketing Tasks

Marketing a private educational practice successfully involves three key tasks:

A. Identify what you're good at.

B. Find people that care about that.

C. Show them how good you are.

[Attribution: Justin Sigars, BodSAT Prep.]

The first task is arguably the most important. Most private teachers over-generalize, and would do well to pare down their offerings to those few at which they're most expert and feel most confident.

By limiting one's offerings to only those market niches virtually no one else can serve as well as you can, you increase the number of raving fan clients you have and boost the velocity with which word of mouth spreads the message of your fabulous service.

Precisely identifying what you're great at doing sets the direction and scope of your practice and clarifies the targets and content of your marketing efforts.


Rule 3: The goal is ... Raving Fan Clients.

[Not clients, nor satisfied clients, not even happy clients ... Raving Fan Clients!]

In end, it's all about generating great word of mouth from clients who RAVE about you, and for that you need to do excellent work, go well beyond the call of duty, and give more value than the money you charge (and if you're good, you can and should charge a high fee).

Raving fan clients can't stop talking about you and the stupendous value and level of service you provide. They spread your name far and wide, propagating a buzz about you that takes on a life of it's own. Because people only ever hear wonderful things about you, contacts who've never met you begin sending you referrals based solely on the strength of your reputation.


Rule 4: People will only refer to you if you make them look good.

Your job, therefore, is to make your referral source look good by exceeding expectations, giving true service, and producing fantastic results.

It's a good practice to thank referral sources for referrals, and to get back to them at least once with a progress report on how great your student is doing.

Make sure your referral sources hear about it whenever a client they've referred expresses great pleasure with your work.


Rule 5: Always quickly follow up enthusiastic praise of your work with a request for positive feedback.

When a student who's been failing algebra suddenly gets an A- and then an A on two consecutive tests, I guarantee you'll get an email message from a new Raving Fan Client praising your skills and expressing gratitude for the wonderful work you're doing.

At that moment, ask for positive feedback.

Such feedback could take the form of an email to the person who referred you, singing your praises. It could be a 5-star Yelp review. At the very least, ask the client if he would please share your contact info with other parents if/when he gets the chance. You can also ask the student involved to give your name to classmates who may be looking for tutoring.

Every time you produce a particularly noteworthy result – as indicated by receipt of high praise – turn it into positive public feedback of some kind.


And yes, all this takes copious amounts of energy. Which means, if you're successful, you'll eventually have to limit the amount of work you do.

But that doesn't have to mean putting the brakes on your income. As of 2018, the best private practice educators in the San Francisco Bay Area consistently earn multiple six figure incomes.



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

Saturday, July 01, 2017

Math Fact Cards, Apps, Calculation Training Sites

Technology has utterly changed nearly every aspect of modern society. Nowhere is this more evident than in the realm of teaching and learning.

One of the most important early learning goals is the attainment of "numeracy:" a visceral sense of what numbers are together with basic utilitarian mastery of what they do.

After learning to count, compare, and estimate numbers, a child's next goal in the study of arithmetic is to understand addition and subtraction (joining and separating) and multiplication and division (repeated addition and repeated subtraction).

Once these definitions are demonstrably clear, addition and multiplication facts are collected through experimentation with real objects and memorialized in tables. After addition and multiplication tables are memorized, subtraction and division facts are easily learned as "reverse addition" and "reverse multiplication." Related math facts are then grouped four-at-a-time in "fact families" and recorded permanently in memory as gestalts (2+3=5, 3+2=5, 5-3=2, 5-2=3). The goal is instant recall of each and every single-digit math fact.

Thus attained, basic numeracy opens up the world of mathematics as both tool and tableau, powerful and beautiful beyond imagining.

Engaging, efficient tablet and smartphone apps have replaced the venerable flash card stack as the method of choice for learning basic math facts (though flash cards can still be used productively in assessment and to add variety).

Ultimately, kids and adults so inclined can train as mental mathletes performing astounding feats of human calculation.

Below are math fact apps and training sites I recommend:


Flash Cards

3-Corner Addition Subtraction Fact Family Cards

3-Corner Multiplication Division Fact Family Cards

Addition Subtraction Multiplication Divison Flash Cards (with Word Problems)


Math Fact Apps

Math Fact Flash (iOS)

Arithmetic Wiz (iOS)

Zapzapmath: K-6 Math Games (iOS)

Math Facts Flash (Android)

Flashcard Math Free (Android)

Zapzapmath: K-6 Math Games (Android)


Mental Calculation

Mathemagics (iOS)

Mencal (iOS)

Math Facts Plus (Android)

Mental Math Games (Android)


Training Sites

APlus Math Flashcards

Math Trainer

Arithmetic Game



Wikipedia: Mental Calculation

Wikipedia: Mental Abacus



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

Thursday, June 01, 2017

Guidebooks: Science Experiments and Projects

Scientific inquiry, invention, experimentation, and discovery are all possible at quite sophisticated levels using ordinary materials found in every home or easily purchased online.

Parents without scientific degrees, however, will normally draw a blank stare at the thought of setting up and operating a "family lab" at home.

Fretting is unnecessary, however. By setting aside a dedicated science space in the home (even just a small table and bookcase in the family room), and using a few good books as guides, the task needn't be unduly burdensome.

To get things going, below are listed some great activity books for young scientists and their parents:




The Science Explorer

The Curious Kid's Science Book

Big Science for Little People

The 101 Coolest Simple Science Experiments

The Big Book of Makerspace Projects

Tinkerlab: A Hands-On Guide for Little Inventors

Electronics for Kids: Play with Simple Circuits and Experiment with Electricity!



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

Monday, May 01, 2017

Early Data Visualization

The rise of computing in the last century changed the course of the mighty river of mathematics.

Discrete methods of solution came to supersede analog ones as "on-off" digital technology replaced the continuous. Analytical methods and number-crunching overtook the elegant formality of logical solutions and symbol manipulation, lending to the latter a strangely passé and almost quaint air.

Yesterday, algebra and calculus were king and queen. Today, its statistics and data analysis.

Students will likely continue to study the traditional arithmetic-algebra-trig-calculus sequence we've all been used to, at least for a another decade or two.

Nevertheless, stats and datasci are coming up awfully fast in the rear view mirror, and it's just a matter of time before we watch them zoom by.

What does this mean for modern day parent-teachers?

Teach your child to enjoy measurement, recording data, and making pretty graphs!

Families can track chores done using points hand-recorded on a refrigerator door chart in bar-graph form. Weather data taken from a home weather station can be tabulated and line graphs generated. Personal goals can be set and progress memorialized using large presentation pad graph paper for all so see.

Finding ways to make creating, recording, analyzing, and visualizing data fun and rewarding will go a long way toward developing "data sense" in your growing children.

Start as soon as they can count and "color inside the lines."

Large format graph paper:

School Smart 1" Grid Tablet 24 x 32 Inches

Alvin Quadrille Paper Grid Pad 17 x 22 Inches

Canson Foundation Series Quadrille Graph Paper Pad 11 x 17 Inches



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

Saturday, April 01, 2017

Mathematics Methodologies

The rise of pay-to-play extra-curricular educational options in recent decades has transformed the landscape of traditional education.

Private tutoring, for example, is no longer regarded as a mark of shame; in fact, it's often a source of pride ("My tutor is Joe Hotshot ... who's yours?").

In tandem with the explosive birth and rapid growth of the private tutoring industry in the U.S., a multitude of companies now offer group math tutoring in various styles and flavors. Some of these champion distinctive pedagogic approaches and programs with almost evangelical passion.

Below are some of the better-known, with notes on each:

Russian School of Mathematics
RSM posits that kids can and should be taught abstract thinking and higher-order reasoning skills (e.g. algebra) from a very early age. Results are impressive.

Singapore Math
Successful national mastery learning model emphasizing a three-step pedagogic approach (concrete, pictoral, abstract) and fewer concepts more deeply learned.

Kumon Method
Worksheet-based math and reading systems. Though currently out of fashion, the "drill and kill" mastery learning approach reintroduced by Kumon works. Quite well.

Aloha (Abacus Learning of Higher Arithmetic)
Malaysian learning programs emphasizing brain development science and left-right hemispheric integration. Math programs teach mental abacus calculation.

Vedic Math
Indian system of mental calculation based on Vedic Mathematics by Swami Bharati Krishna Tirtha. Udemy courses here and here. YouTube instructional videos here.

Proprietary IXL technology is used by one out of nine American children and over 200,000 teachers (2018). Originally math only, now multi-subject. Details here.



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

Wednesday, March 01, 2017

Early Puzzles, Problem Solving, Math Games

Lots of fun family activities expose children to logical problem solving and exercise mathematical thinking muscles without adding columns of numbers or solving equations.

Games and puzzles that develop cognitive abilities, reasoning, and heuristic skills are great ways to get better at math without really trying, and provide alternative content for productive family learning times.

Below are just a few ideas:



Puzzle Barron's Logic Puzzles


Q-BitzQ-Bitz SoloQ-Bitz Junior (Ages 3+)

SET Visual Perception Game


Math Dice

Balance Beans

Press Here Game

24 Game: Integers






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

Wednesday, February 01, 2017

The Miracle of Human Anatomy

The study of human anatomy has fascinated humankind's greatest thinkers since antiquity.

No machine rivals the breathtaking complexity of the human body and its myriad systems and organs, and nothing in art or nature surpasses it's dazzling, intricate beauty and harmonious melding of form and function.

Anatomical models, drawings, and texts reveal many of the tantalizing secrets lying under our own skins, and the study of human anatomy should be part of every home science curriculum.

Following is a list of recommended resources:

Walter Products Tabletop Human Torso Model

4D Vision Human Anatomy Torso Model

Smart Lab Toys Squishy Human Body

Smart Lab Human Body Model

Melissa & Doug Magnetic Human Body Anatomy Play Set

Gray's Anatomy for Students: With Student Consult Online Access, 3e

Anatomica's Body Atlas

The Anatomy Coloring Book



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

Sunday, January 01, 2017

Family Science

As essential academic skills, the "3 R's" (Reading, Writing, 'Rithmetic) dominate primary and secondary education at nearly every phase. This is as it should be.

However, a close second place should be assigned to STEAM subjects: Science, Technology, Engineering, Art, Mathematics.

Family science study can be a rewarding and fascinating family activity. Investing a relatively small amount of money in a scientific instruments of reasonable quality can open up entirely new worlds to impressionable and curious young minds. For example, keeping a good compound microscope at ready disposal in the family kitchen avails kids and adults alike of the opportunity to do real spur-of-the-moment science. Having a serious entry-level telescope standing by in the garage for use on those clear, dark, moonless nights when star gazing is most rewarding is a simple way to reify the infinite for youngsters and adults alike.

At all stages, the scientific method can be taught, utilized, and reinforced: Ask a good question, make a sensible guess about the answer, test that guess experimentally (or search the internet for information), confirm or adjust the guess based on what's learned, then repeat.

Having popular scientific magazines prominently displayed at home – and making sure your kids catch you reading and discussing them frequently – is another fun and engaging way to bring science into the home.

Why is it that so many scientists are amateur artists, musicians, painters, video programmers?

The arts are, of course, inextricably linked to the sciences. Affinity for one generally predicts affinity for the other. Music, dance, acting, visual arts, sculpture, architecture, and other diverse artistic disciplines intersect in fascinating ways with scientific fields ranging from physics and chemistry to anatomy and psychology.

Moreover, the dedication, sharply-focused thinking, and keen observational ability required to become a competent stage performer or fine artist are precisely the same "soft skills" central to advancement in STEM fields (but that's another post ...).

Parents can thoroughly enjoy home science along with their kids. The excitement of discovery is every bit as tangible and real when an adult first witnesses an oozing protozoa gobble up a bacterium as it is for a first grader or high schooler.

Full STEAM ahead!

For more ideas, see the following:

Science Tools and Manipulatives

Scratch Coding Resources

Robotics Toys, Aids, and Activities

The Miracle of Human Anatomy

Guidebooks: Science Experiments and Projects

Five Books Guaranteed to Make Kids Love Science

100 Best Science Books for Kids

Great Science Books for the Little Ones

Amazon's Best Selling Science Books for Children



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

Thursday, December 01, 2016

Daily Math Time

In addition to daily Reading Time and Writing/Drawing Time, parents should spend a small amount of structured fun time each day with each child on math.

From the earliest age, children can be taught to say "one, two, three" as they're lifted into the air or as they touch their index finger to each of three similar objects. Counting objects to ten, twenty, and more naturally follows, as the child gains facility and understanding.

Math has been called the science of pattern, and patterns are everywhere we look. Simple binary patterns like on and off, sitting and standing, quiet and noisy are all easy to point out and ask your child about. Later on, more complex patters like colors in kitchen tiles or lines on the floor can be explored.

Geometry is everywhere also. Various shapes from dots to lines to triangles to circles can be identified in the surrounding environment ("Can you find a green rectangle on the road up ahead?"A red octagon?"

Basic numerical concepts such as more, less, and equal are easy to discuss with young tykes (short, long, longest, etc.).

Eventually, the two basic algebraic operations – addition and subtraction – can be explained as putting things together to form one larger group or separating large groups into smaller ones.

Once basic math facts are memorized, simple story problems can be created and solved on the fly, and positive/negative numbers (and operations with them) can be introduced.

Math manipulatives can play a central role is making Daily Math Time interesting, engaging, and productive for all concerned.

As always, the focus is on fun, lots of hugs and high-fives, taking things slowly and at the child's own pace, and quitting structured time early to keep them wanting more.

Additional resources and ideas follow:

Math is Everywhere ... and it's Fun!

Math Fact Cards, Apps, Calculation Training Sites

Scratch Coding Resources

Early Math Toys, Aids, and Activities

Early Puzzles, Problem Solving, Math Games

Math Exploration Station

Math Worksheets and Drills

Children's Books for Teaching Math



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