Does not compute

Posted on December 22, 2011 by

Forget reading, check out what used to pass for 8th grade math. This was the curriculum used by the majority of public schools in the late 1800s and early 1900s called Ray’s Higher Arithmetic.

Typical word problems:

Howard M. Holden sold $21600 U. S. 4’s, 1907, registered at 99 3/8%, and immediately invested a certain amount of the proceeds in Illinois Central Railroad stock, at 80%, which pays an annual dividend of 6%; he receives $840 from the railroad investment; with the remainder of his money he bought a farm at $30 an acre: required the amount invested in railroad stock, and the number of acres in the farm?

A lady had a grass-plot 20 meters long and 15 meters wide; after reserving two plots, one 2 meters square and the other 3 meters square, she paid 51 cents a square meter to have it paved with stones: what did the paving cost?

The difference of time between two places is 4 hr. 18 min. 26 sec.: what is their difference of longitude?

A bought a farm of government land, at $1.25 an acre; it cost him 160% to fence it, 160% to break it up, 80% for seed, 100% to plant it, 100% to harvest it, 112% for threshing, 100% for transportation; each acre produced 35 bu. of wheat, which he sold at 70 ct. a bushel: how much did he gain on every acre above all expenses the first year?

Received on commission 25 hhd. sugar (36547 lb.), of which I sold 10 hhd. (16875 lb.), at 6 ct. a lb., and 6 hhd. (8246 lb.) at 5 ct. a lb., and the rest at 5.J- ct. a lb.: what is my commission, at 3%?

I took a risk of $45000; re-insured at the same rate, $10000 each, in three offices, and $5000 in another; my share of the premium was $262.50: what was the rate?

What is a broker’s gain in 1 yr., on $100, deposited at 6%, and loaned 11 times for 33 da., at the rate of 2% a month?

Without peeking, can you answer those problems? I can barely even understand what they’re asking for!

Children “skipping ahead in math” today aren’t actually as smart as they think. It’s just that the material is so much easier that they breeze through it. Then they get to college, after acing what passes for calculus (go back and read Leibniz or Newton’s original works, for a taste of real calculus), and hit a mental wall.

Slogging through a 10-page mathematical proof generally requires that you can do quick mental computation. Applying math generally requires that you can evaluate all manner of word problems. This is why hardly anyone studies math anymore, even if they get excellent grades in high school math. The gulf between school and university math is absolutely enormous, and when you go back to the older school texts, it’s pretty obvious why that is. And even university-level math is a joke when you see what they used to study at that level.

Just like with reading, we study middle school math in high school and high school math in college. A parallel four-year delay. So we are, on average, 4 years behind our grandparent’s generation.

Update on Using Ray’s Arithmetic

We are now using Ray’s curriculum in our homeschool, and we are very satisfied with it. It’s well-structured, simple, challenging, and thorough. It does require more from the teacher and it isn’t split by grade, but it is flexible enough to fit to any student’s abilities. You just repeat each lesson until they’ve mastered it, and then move on to the next. As one homeschooler noted:

Also, Ray’s can be used with bright children or slower children, it matters not. A bright child might master the the content of the lesson in a day or two. He is then free to go on to the next. He isn’t held back. The slower child might master the content in two weeks. He is then free to go on to the next. He isn’t made to feel as if he isn’t “caught up” to where he is supposed to be, because Ray’s is set up as a series of content to be mastered, not as 3rd grade math, 4th grade math, etc. The bright child who “gets it” isn’t forced to do two weeks of lessons teaching the same content as in modern math, and so avoids boredom, and the slower child isn’t rushed through two weeks of lessons teaching the same content if he really needs to spend four weeks on it, and so he avoids labeling himself in his own mind as no good at math.

Because Ray’s is ungraded, the lessons are not keyed to 1st grade, 2nd grade and so on, anyone can begin where they are and not feel as if they are doing “baby” work.

You don’t complete “one book per year”, as there are four books and they cover all of the math including pre-algebra. Just plan it out so that it fits the pace your child learns at, whether it takes 6 years or 10. After this we plan on using our old college math texts (algebra, geometry, and trigonometry), as we won’t need to bother with “high school math” after this curriculum.

Our son is a math whiz, but even he is struggling to master the addition section of the primary book, so we will probably only get through addition and subtraction this year. These books are essentially designed to turn your child into a human calculator.

The addition section, which is aimed at first graders, contains oral exercises like:

A farmer sold a barrel of apples for three dollars a tub of butter for nine dollars and a load of wood for seven dollars. How much did he receive for all?

Although the section focuses on addition, all of the sections include addition, subtraction, multiplication, and division questions. This is simple to do with counters, as you just shift and group them as needed. For instance (Lesson IX, which we completed today):

1. How many are 8 and 1? How many are 7 and 2? How many are 6 and 3? How many are 5 and 4? How many are 4 and 5? How many are 3 and 6? How many are 2 and 7?

2. How many are nine times 1? How many are three times 3?

3. One from 9 leaves how many? Two from 9? Three from 9? Four from 9? Five from 9? Six from 9? Seven from 9? Eight from 9?

4. How many ones in 9? How many threes in 9?

5. How many are 9 and 1? How many are 8 and 2? How many are 7 and 3? How many are 6 and 4? How many are 5 and 5?

6. How many are 2 and 8? How many are 3 and 7? How many are 4 and 6?

7. How many are ten times 1? How many are five times 2? How many are two times 5?

8. One from 10 leaves how many? Two from 10? Three from 10? Four from 10? Five from 10? Six from 10? Seven from 10? Eight from 10? Nine from 10?

9. How many ones in 10? How many twos in 10? How many fives in 10?

The set is non-consumable and therefore an incredibly good value. It contains lots of mental math and drill, which is our weakness, as we’re all better at concepts than computation. Drill, baby, drill. It covers all of the essential topics and is complete in itself, but we combine it with logic puzzles and the Math Worksheet Site.

Posted in: Education