Living Math part 2

More ideas about math from Charlotte Mason (and my interpretations):

Mason believed that after a child could add and subtract numbers up to 20, it was time for multiplication.  (Multiplication was an objective in 2nd and 3rd grade, therefore adding and subtracting numbers up to 20 would have been an objective in 1st grade.)

In Form II (4th through 6th grade), after a child had mastered multiplication, he or she would demonstrate division with manipulatives.  Mason's approach was always manipulatives before facts.

Based on original exams from Charlotte Mason schools, students did not work with numbers in the hundreds until 4th grade.

In first through third grade:

"Let him have a heap of pennies."  Mason advocated using money to teach math.  In the U.S., we can use pennies and dimes to teach the base ten system.

When a child can understand that the number in the left column is how many dimes there are, and the number in the right column is how many pennies there are, she suggested teaching place value.  After the child mastered tens, move to hundreds.  (Do not give the child who is at this stage a page of problems to solve.)  After the child had mastered working with hundreds, move to thousands, and so on.

When regrouping (which Mason called "carrying"), Mason wrote that students should say 2 tens instead of 2, or 3 hundreds instead of 3.  I was taught to "carry" and "borrow," but when I became a teacher, I was told that the concept had been renamed "regrouping."  Frankly, I don't think it makes one bit of difference what you call it, so long as you do it.  Students are now taught to "regroup" because when you are doing a problem like 53 - 39, you take 1 set of ten from 5 tens (leaving 4 tens), and group that 1 set of tens with the 3 ones (giving you 13, so you can calculate 13 - 9).

According to Mason's sequence for math, she thought students should weigh and measure everything before beginning fractions.  This is not at all what happens in public school.  In fact, my students' textbook is ordered so that fractions are taught several months before measurement.

Carefully graduated teaching and daily mental effort on the child's part at this early stage may be the means of developing real mathematical power, and will certainly promote the habits of concentration and effort of mind.  - Charlotte Mason, Vol. 3

...

Mathematics depend upon the teacher rather than upon the text-book and few subjects are worse taught; chiefly because teachers have seldom time to give the inspiring ideas, what Coleridge calls, the 'Captain' ideas, which should quicken imagination.

How living would Geometry become in the light of the discoveries of Euclid as he made them!
-Charlotte Mason, Vol. 6 (page 232)

Math instruction needs to include stories about famous mathematicians.  A few of my favorite books:
-Mathematicians are People Too
-Mathematicians are People Too, Volume 2
-Historical Connections in Mathematics, Volumes 1-3 (This series was beautifully illustrated by my mom!)