I thought that since the topic of fractions, decimals and percents has come up, and it is the major "Big Idea" in math for fourth grade I would like to give some examples of how the teaching of this topic has changed from the BS period (Before Standards) to the AS period (After Standards).
In the BS period of math instruction our text book would introduce adding fractions with like denominators and then unlike denominators. The student book looked something like this;
1/3 + 1/3 = (several of this type of problem) There were two pages - about 60 problems of this type. Then on to the 'big stuff'. 2/6 + 1/3 = (several problems of this type)
My job as a teacher was to teach how to do these calculations. (the adding fractions recipe,the adding fractions with unlike denominators recipe) About 1/3 of the class would go on to 5th grade still adding 1/3 + 1/3 and getting 2/6, or saying "I just don't get it Mrs. A. Why isn't it 2/6?"
In the AS classroom students might build rectangles with tiles and make 1/5 blue and 4/5 red. Solve problems such as - 1/5 of 50 beans are how many beans, 1/2 of 20 beans are how many beans, 1/3 of 30 are how many beans? Explain why 1/5 of 50, 1/2 of 20 and 1/3 of 30 are the same number if 1/5, 1/2, and 1/3 are not equivalent fractions.
Build a rectangle that is 1/2 red, 1/5 blue and 3/10 green. What are the dimensions of the rectangle? (2x5) How many total tiles? How many green tiles? Use the same fractional parts to build a rectangle with 20 total tiles. How many are green? How many are blue? How many are red? Build a rectange with 30 total tiles etc.
Predict how many green there would be in a rectangle of 40 total tiles. Explain you reasoning. Check to see if you were correct. If not see if you can find the error in your reasoning.
These types of activities would go on for about a month.
Which type of learning experiences would you prefer for your own child? The AS or the BS method of instruction?
With all of the theoretical discussions on the list lately about how the standards are, or are not, destroying math education in the US, I thought it was about time we begin to speak in the specific. How exactly do the standards look when put into practice. There is a definite difference. Personally I consider it a change for the better. I would NEVER go back to "the basics", as they looked BS.