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 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 courses 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.

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

Children's Books for Teaching Math


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 when 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 goal is ... Raving Fan Clients.

[Not clients, not satisfied clients, nor 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 great work, go well beyond the call of duty, and give more value than the money you charge (and if you're very 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 3: 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. 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.

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.


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

One of your primary goals with each client 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 clients they refer express 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 transformed many aspects of modern society, and nowhere is this more evident than in the realm of teaching and learning. Nevertheless, the need to commit to memory all basic facts of arithmetic remains one of the great pedagogical constants.

It's not all down to rote memorization, however. One of the most important modern early learning goals is the attainment of "numeracy:" a visceral sense of what numbers are together with utilitarian mastery of what they do and how they do it.

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



Mad Minute

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

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.

Saturday, April 01, 2017

Early Data Visualization

The explosive increase in computing power in the last half of 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 notions replaced the continuous. Analytical techniques 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, calculus and algebra were king and queen. Today, its statistics and data science.

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.

Thursday, March 02, 2017

The Miracle of Human Anatomy

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

No machine rivals the awesome complexity of the human body and its myriad systems and organs. 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.

Wednesday, February 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.

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.