Borland Educational News and Views

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

Arithmetic Wiz (iOS)

Zapzapmath: K-6 Math Games (iOS)

Math Facts Flash (Android)

Zapzapmath: K-6 Math Games (Android)

Mental Math (iPhone)

Math Brain Booster Games (iPhone)

-

Mental Calculation

Mathemagics (iOS)

Mencal (iOS)

Mental Math Quick Speed (Android)

-

Training Sites

Varsity Tutors Flashcards

Math Trainer

Winhoff.net

Arithmetic Game

-

Other

Mad Minute

Wikipedia: Mental Calculation

Wikipedia: Mental Abacus

-----

Contact Chris

borlandeducational.com

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:

STEAM Kids

Exploralab

Exploratopia

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!

-----

Contact Chris

borlandeducational.com

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.

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. YouTube instructional videos here.

-----

Contact Chris

borlandeducational.com

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:

1" Grid Tablet 24 x 32 Inches

Quadrille Paper Grid Pad 17 x 22 Inches

Canson Foundation Series Quadrille Graph Paper Pad 11 x 17 Inches

-----

Contact Chris

borlandeducational.com

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:

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

-----

Contact Chris

borlandeducational.com