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[quote=Anonymous][quote=Anonymous][quote=Anonymous][quote=Anonymous][quote=Anonymous]Both PISA and NAEP results have reported poor math results for the US for many years.

Various forms of "new math" curricula have been tried without improvement. What we do not do is teach math effectively. Many students, probably most students, do not get enough math practice. If we were good at teaching then the after school math centers would not be spread from coast to coast.

Other countries with high math scores in PISA teach students math methods that always work and [b]only teach one method per topic (e.g., Multiplication, division, algebra) so the students get enough practice to memorize that one method.[/quote][/b]

This times 1000. Bright students can handle being taught multiple methods to solve problems. Slower kids need to be taught one way until they master it. Imagine if your new neighbor asked you directions for how to get to Target and knowing that they were new to the area, you told them the simplest, most direct way. After time and many trips using that way, they might start trying other ways or not but they would know how to get to Target. Instead we teach kids all of the ways to get to Target in fairly quick succession. The result is some kids getting most or all of the ways correct and many kids having no idea how to get there. That's math education in public schools. 
-a teacher[/quote]

+ 1 million. I have a friend whose kid was way behind in math. Pulled that kid to homeschool and used a drill-and-kill math curriculum where there was just one way to do it that was drilled to death, and the kid caught up.

My very fast-at-math kid hated the multiple methods because it slowed down learning the easy and efficient way to do it (whatever the standard algorithm is). She easily intuited what all the other methods were trying to teach and didn't need it. The "math workshop" model is just as bad as the "readers and writer's workshop" (aka Lucy Calkins) for kids on all ends of the math spectrum.[/quote]
Which one?[/quote]

A lot of homeschool families use Saxon Math as a traditional spiral math program. Here is a sample lesson for 4th grade. 
Warm UP
Math facts Fluency -Power Up B

Count aloud - Count by fours from 4 to 60 and then back down to 4.

Mental math
Count by fours from 4 to 60 and then back down to 4.

Problem Solving
In problems a–c, practice splitting the second number to add.
a. Number Sense: 57 + 8
b. Number Sense: 78 + 6
c. Number Sense: 49 + 4
d. Number Sense: 63 + 19 + 200
e. Time: The Johnsons are driving to Yosemite National Park. They expect that the drive will take 6 hours. If the Johnsons left their house at 6:50 a.m., at what time would they expect to arrive at the park?
f. Measurement: Many adults are about 2 yards tall. Two yards is how many feet?
g. Geometry: True or False: Parallel lines intersect.
h. Estimation: Madison has $18.47. Round this amount to the
nearest 25 cents.
Choose an appropriate problem-solving strategy to solve this problem. Here we show four squares. The first is made up of
1 small square. The second, third, and fourth squares are made up of 4, 9, and 16 small squares. Describe the pattern that you see. How many small squares would make up the sixth square of the pattern? Explain how you arrived at your answer.
1 4 9 16 [picture is given of the squares]

Introduce New Concept
There are 43 apples in the large basket. There are 19 apples in the small basket.
[Picture of baskets are shown]

The difference tells us “how many more” and “how many fewer.” There are 24 more apples in the large basket than in the small basket. There are 24 fewer apples in the small basket than in the large basket.
When we compare the number of apples in the two baskets, we see that 43 is greater than 19. To find how much greater 43 is than 19, we subtract.

Larger amount − Smaller amount = Difference
43 − 19 24

Reading Math
We translate the problem using
a larger-smaller = difference formula.
Larger: 43 apples - Smaller: 19 apples =  Difference:24 apples

As we think about this story, we realize that it is not a “some went away” story because nothing went away. This is a different kind of story. In this story we are comparing two numbers. One way to compare two numbers is to subtract to find their difference. We subtract the smaller number from the larger number.

Here we show two ways to write the formula:
the Formula is shown in a graphic but the formatting doesn't work so I didn't include it. 
A diagram can help us understand a larger-smaller-difference plot. In the following diagram, we have used the numbers from the apple problem. There are two towers, a “larger” tower and a “smaller” tower. The “difference” is the difference in the heights of the two towers.
[graphic shown]

Three worked examples are shown, then 3 practice problems are given

Then students complete 30 mixed problems, some with new concept and many from previous chapters so the material is retained. Subtraction and addition with borrowing, square roots,

Example:

Multiply:
12.  a.  5 × 8 b. 2 × 8 c. 5 × 9

13. a. How many quarters equal one dollar?
b. A quarter is what fraction of a dollar?
c. Three quarters are what fraction of a dollar?

14. Represent Use digits and symbols to write this comparison: Three hundred nine is less than three hundred ninety.

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