Guidance [of children], however, is difficult, because we ought to take pains neither to develop in them anger nor to blunt their native spirit.
Seneca here warns us of two opposing dangers, two ditches on either side of our right path: either building resentment and anger in our children (how he says this happens might surprise you) or by stifling and smashing their personalities and energy.
But there is only one really liberal study – that which gives a man his liberty. It is the study of wisdom.
In our talk of classical education or a liberal arts education, we must keep our definitions and our aim in view. The liberal arts boil down to studying wisdom. Wisdom comes to us in many forms, and the liberal arts are concerned with wisdom in all its forms – not mere information or raw skills. It is knowledge with purpose, knowledge with application for all of life.
The result of an education in wisdom is a resilient integrity which knows what should be done and has the strength of mind and body to do it.
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Simple Sanity Saver: Math-U-See Tips
Math-U-See begins with the concept of place value and returns to place value to teach every new function. Without place value, you can’t understand why numbers do what they do when you start combining them, so it is important.
Math-U-See has some handy sayings for learning place value – like “Every number has a place” and “place means value.” The numeral 9, for example, means 9 units if it’s in the unit place, but it means 9 tens if it’s in the tens place. It has been quite helpful to have this vocabulary to show my beginning-regroupers that 12 + 8 does not equal 2. Without the zero, that means 2 units, not two tens – you need the zero to put the 2 in the ten place.
Place value is also helpful when they want to work equations from left to right, like reading and writing. No, with math you have to start at the unit place and move up the “street” from there.
Place value brings greater clarity to long division, too. And when you hand your student graph paper on which to do his figuring (highly recommended), you can always remind him, “Keep each number in its right place!” and he might sigh and slump, but he knows what you’re talking about.
So here is my 4th tip for MUS users that is actually applicable regardless of program.
I got this tip from Mr. Demme himself.
Place value in Math-U-See is important. Keeping numbers straight and in their right place is critical, no matter which math program you use.
My older students use graph paper to show their work, but that seems a bit excessive (and also not large enough squares) for the elementary students. Once they get into carrying or borrowing, though, it’s super handy and leads to fewer place-value flubs if you simply turn a lined piece of notebook paper on the side to help you keep the numbers in their right place.