Saturday, September 08, 2012

CM and Math

The past few years, math and writing have been bees stuck in my bonnet.  I'm parking a few math links here for my own help.  Perhaps they will help others too.

Miss Mason:
There is no one subject in which good teaching effects more, as there is none in which slovenly teaching has more mischievous results...a child who does not know what rule to apply to a simple problem within his grasp, has been ill taught from the first, although he may produce slatefuls of quite right sums in multiplication or long division...Care must be taken to give the child such problems as he can work, but yet which are difficult enough to cause him some little mental effort.
(Give the child problems which are difficult enough to cause him some effort.  This is key in understanding so many of CM's recommendations.  CM is gentle, yet rigorous.  CM respects the child, yet challenges the child.)

More from CM on arithmetic:
The copying, prompting, telling, helping over difficulties, working with an eye to the answer which he knows, that are allowed in the arithmetic lesson, under an inferior teacher, are enough to vitiate any child; and quite as bad as these is the habit of allowing that a sum is nearly right, two figures wrong, and so on, and letting the child work it over again. Pronounce a sum wrong, or right––it cannot be something between the two.
On the beauty of mathematics: 
 We take strong ground when we appeal to the beauty and truth of Mathematics; that, as Ruskin points out, two and two make four and cannot conceivably make five, is an inevitable law. It is a great thing to be brought into the presence of a law, of a whole system of laws, that exist without our concurrence,––that two straight lines cannot enclose a space is a fact which we can perceive, state, and act upon but cannot in any wise alter, should give to children the sense of limitation which is wholesome for all of us, and inspire that sursum corda which we should hear in all natural law.
On examination-driven teaching of math:
Arithmetic, Mathematics, are exceedingly easy to examine upon and so long as education is regulated by examinations so long shall we have teaching, directed not to awaken a sense of awe in contemplating a self-existing science, but rather to secure exactness and ingenuity in the treatment of problems.
(I want to awaken a sense of awe in my students.  Math was created by God.  It cannot be denied that mathematical laws exist outside of man-made laws.)

On math and success:
...why should a boy's success in life depend upon drudgery in Mathematics? That is the tendency at the present moment to close the Universities and consequently the Professions to boys and girls who, because they have little natural aptitude for mathematics, must acquire a mechanical knowledge by such heavy all-engrossing labour as must needs shut out such knowledge of the 'humanities' say, as is implied in the phrase 'a liberal education.'... [Mathematics] may not engross the time and attention of the scholar in such wise as to shut out any of the score of 'subjects,' a knowledge of which is his natural right.
(Lord, please help me remember this!  Awaken awe, challenge the student, keep math focus in perspective relative to other subjects.)


lindafay said...

Hi Katie,

I just read these passages this week. I have a math 'weak' child and she will probably not go on to college, so I've been debating how high she should go in math...

Katie said...

I am in the same situation. That is why I posted these quotes this week! :) I'd love to hear your ideas on the subject.

Katie said...

Actually, my student does plan to go to college, so I am wondering how quickly I need to get her to algebra.

Lisa said...

Thanks for these excellent quotes about Math from Miss Mason, Katie. A great reminder..and timely for me right now as 3 of my children really struggle with Math; not the lessons, but when I put a test in front of them, they fall apart and rarely get even half of them right. So a ? for you, if you don't mind: should I drop the Math tests altogether?

Katie said...

How old are your children?

Katie said...

Another question to ask is what are your (or your children's) long-term plans regarding math.

If your student is quite young, you may want to forgo tests altogether for awhile. If your student is upper elementary or middle school, you may want to begin acclimating him to math tests, especially if there is standardized testing in his future.

If your student is older AND wishes to go into a field like chemistry, physics or engineering, I think learning to take math tests is pretty important. If you have an older student that is planning to become a horse trainer and at this point has no plans for college, testing is not as important. A student heading into a liberal arts major at a college will not need as much math as a science/engineering major, but will still need to take math tests, so some prep there is necessary, but not as much as in other scenarios.

I think what CM is saying here is not to let it eat up too much time. For instance, my oldest has taken both the SAT and ACT in preparation for college, and has taken two math classes at the community college. However, her preparation for this did not consume her life. She did not engage in weeks or months of SAT math prep. The amount of time she spent on math increased as she got older, but never went too far above an hour per day, even during her college math classes.

Katie said...

Let me say it a different way-- respecting the personhood of the child means while we expect hard work and discipline from the student, we also respect his or her bent. If a student is not bent toward math, we respect that. The student still needs math for practical, mental and spiritual reasons. However, I would not expect one of my other children (that perhaps does not have a bent toward math) to take the same course my oldest took.

Katie said...

One more comment... I am responding to your question in between helping my 11yodd with her math, lol, so I'm having trouble being coherent. ;o)

The point I am trying to make is that you will have to sort of feel your way through on this. You know your students, their situations, their dreams, their gifts and talents, their weaknesses.

It would be so easy if we could just follow some rule such as 'forget math tests if a student struggles with them' or 'always include math tests', wouldn't it? ;o) But how bland life would be if everyone were the same!

Lisa said...


My 3 middle children are 8 yrs. old, 10 yrs. old and 11 years old. One son loves inventions and electrical things, one son loves art, writing, and drawing. And my 8 year old daughter wants to be a wife and mama. :)

All of them are one level ahead for their ages. I'm wondering if that's the problem. (My 13 year old is in Algebra 2 and is doing fine.)

We are using Saxon math. It's what my 2 older children used and did well with it - but hated it!. (That was in the "text-book" days of our homeschool.) A whole new math curriculum isn't a financial possibility for us right now.

I have asked other AO/CM moms for advice and I always get the same answer: "try shorter lessons". I do that, but it's still absolute drudgery to do Math every day. Sometimes my children even cry when they're having a hard time with a math problem.

What am I doing wrong?

Katie said...

That is a tough question!

Some lessons just aren't as pleasant as others but we still have to do them. If a student is crying at a lesson, then I can think of two possible reasons:

1) The student is overwhelmed and discouraged (perhaps the challenge is too steep or perhaps the student is not feeling well or perhaps the curriculum is not a fit)

2) The student does not wish to do hard things (perhaps math has been easy in the past, or perhaps he is very intelligent and used to things being easy in general, or perhaps he is testing your authority)

One of these is a curriculum/approach issue, and the other is a character issue. I would be praying and thinking hard about which applies to my situation, and when I figured it out, I would look through CM's writings for her wise instruction on the issue.

Hope this helps. :)

Lisa said...

Thanks so much, Katie. I will be praying about it and asking the Lord for wisdom about what to do. And I will also be re-reading some of Miss Mason's writings for insight.

Hope you're having a blessed day. :)

Lisa said...

one more thing, katie...IF i decide to eventually switch math curriculum to maybe MEP (on the ambleside website) would i know which level to put them?

Katie said...

Thanks, Lisa! I thought I was having kind of a rough day-- our dryer has been out of commission for three weeks and we just found out it won't be fixed for another week. That made me grumpy. Then I thought about all the real trouble in the world and found that I was very blessed even without a working dryer. ;o)

I hope you had a blessed day too.

Katie said...

There is an MEP homeschool yahoo group that helps with placement questions, etc. MEP is a different approach from many other curricula, so if your students are pretty young you might start them at the beginning. After Year 6, students that finish strong can head straight into algebra. The folks at the Yahoo group know much more about it than me, though.