Liberal Arts - and Montessori

It used to be that the trivium was taught before all else:

• grammar


• logic


• rhetoric

These three (the Trivium) taught the children how to think, preparing their minds to be open to all further learning. These pieces were *foundational*.

Now, unless you are fortunate to attend a truly decent school (whether public or private) or utilize a top-notch homeschool curriculum, these things are just not taught or experienced.

The Trivium paved the way for the remaining foundational studies in the Quadrivium:

• Arithmetic (number in itself)


• Geometry (number in space)


• Music (number in time)


• Astronomy (number in space and time)

I cannot speak for other curricula, since there is nothing I use so fully and completely as the AMI version of Montessori education for primary and elementary. A Montessori education allows me, as mother and teacher, as well as the student, to utilize whatever needed components from SO many other sources. Montessori provides the foundation and the framework, the child's interests and local educational requirements fill in the rest.

I can say that Montessori albums, when followed in laying the educational foundation, both academically and spiritually, CAN and DO provide the liberal arts in their entirety.

So why do we care about the liberal arts? The most concise answer can be found in the article "On the Purpose of  Liberal Arts Education" by Robert Harris (click on the title for the full, long but fascinating article).

I. A liberal arts education teaches you how to think

II. A liberal arts education teaches you how to learn.

III. A liberal arts education allows you to see things whole

IV. A liberal arts education enhances wisdom and faith

V. A liberal arts education makes you a better teacher

VI. A liberal arts education will contribute to your happiness

From The Idea of a University by John Henry Newman

"[The purpose of a liberal arts education is to] open the mind, to correct it, to refine it, to enable it to know, and to digest, master, rule, and use its knowledge, to give it power over its own faculties, application, flexibility, method, critical exactness, sagacity, resource, address, [and] eloquent expression. . . ."

So don't leave out these subjects because there isn't time to fit them in (like astronomy...). These things are the fuel for all other learning. Said another way, other learning isn't worth it without the foundation.

Modern Logic - WFF 'N Proof style!

What is a WFF?????

A Well-Formed Formula of course ;)

Huh? You're asking?

Well here is a Wikipedia article on it, but if you're like me and still saying, "Huh!?" here is a short answer:

In mathematical logic, a well-formed formula, shortly wff, often simply formula, is a word (i.e. a finite sequence of symbols from a given alphabet) which is part of a formal language.

A formal language can be considered to be identical to the set containing all and only its formulas.

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And the better answer is: it's a statement that follows a set of rules. Think of A=B, B=C, therefore A=C. If certain things are true, then other things are true based on sets of given information. Both our language of words and our language of numbers (mathematics) are based on these principles.

We love this game from WFF 'N Proof: Games for Thinkers:

[caption id="" align="aligncenter" width="254" caption="WFF: The Beginners Game of Modern Logic"][/caption]

Details from their website:

WFF includes the first two games from the complete WFF ?N PROOF series. Two engaging speed games allow players to learn to recognize WFF's (Well Formed Formulas) in symbolic logic. Both Shake-a-WFF and Count-a-WFF are fast-paced, exciting games dealing with a unique symbolic system. They are an appealing exercise for all ages.

There are two games within this one (actually a few more if you count the other variations): Shake-a-Wff which is a competition - both players play at the same time and grab a coin in the middle when they have a WFF first. And there is Sequential WFF where the players take turns, so there is no "race."

My 7 year old really, really, really wants to play competition WFF, but he's so into the time-racing component he makes a LOT of mistakes and neither does he proceed nor does anyone else have the opportunity to proceed forward.
So we do a lot of Sequential WFF (players take turns, using as much time as they need to create a Well-Formed-Formula).

If you're looking for a really good LOGIC program or curriculum, this is the way to go. The basic game is $3.50. The next step up is only $35, can be played by a 6 year old and still be challenging for a 60 year old math genius: WFF 'N PROOF: The Game of Modern Logic.

Equations - Mathematics from WFF N Proof

Here is a game we've been playing:

[caption id="attachment_631" align="aligncenter" width="300" caption="EQUATIONS: The Game of Creative Mathematics - From WFF 'N PROOF"][/caption]

You roll the dice, create a "goal" (the answer to the equation); then take turns moving the cubes into either forbidden, possible, and required categories, all the while keeping your equation to reach the goal secret.

When you see someone else make a mistake, you call a flub (there are several types of flubs). Then you have to prove yourself right or the opponent wrong.

It's math, it's strategy... it's logic! Who needs a formal logic curriculum or logic program, when you have games like these from WFF 'n Proof?



From their website:

At home, EQUATIONS lets the whole family share a quality learning experience and have fun too. People of all ages become fascinated by this game. It creates a rich problem-solving interaction filled with complex strategy, bluffing and intrigue. The basic game can be taught to eight-year olds using simple arithmetic. As players develop skill, the game becomes more sophisticated. It ultimately expands to concepts that will challenge any intelligent adult.

EQUATIONS explores a broad range of math topics including elementary arithmetic operations such as addition, subtraction, multiplication, division, exponentiation and root operation as well as logarithms, fractions, decimals, percents, variables, algebra, functions and more.

It sounds complicated - but it is addictive fun!

REQUIRED:  get the DVD to learn how to play - well worth the $5!

Got a Montessori child? They could be ready at late 6 - but only if they've been playing WFF: The Beginner's Game of Modern Logic. I strongly recommend this game for all children, but Montessori children will be especially intrigued by it. It can then be followed up by WFF 'N PROOF: The Game of Modern Logic. More on these in another post ;)