The Penfield (NY) Post
Guest Essay
June 9, 2005
A recent article (D&C, May 10) about the math programs in the Penfield schools characterized the disagreement as if it were a question of style. A box near the main headline was headlined "What's at Stake," and began its answer with "The way the children are taught math." But this is not the issue.
That box goes on to say, "The new curriculum encourages students to develop problem-solving strategies instead of giving them a list of formulas to memorizeä" Well, if you put it that way there is no contest. Goodness, who can prefer "a list of formulas to memorize" to students' "developing strategies"?
But there is a contest. It is not a contest between rote-memorization of meaningless symbols and deep understanding of problem-solving strategies. Those are not the only two choices, even though the National Council of Teachers of Mathematics and the colleges of education are careful to paint it that way. They repeat this sort of misrepresentation so often that even the newspapers have come to believe it.
The real contest in Penfield is between mathematics and non-mathematics, between academic content and childish time-wasting, between what children can learn and what the present Penfield curriculum is pretending to have them "develop".
A good mathematics program takes advantage of the mathematical discoveries of thousands of years of civilized effort, while Penfield has them counting with sticks, starting history all over again.
The systems of decimal and fraction notation are marvels of compressed information, intellectual advances that Euclid did not have available. Arithmetic is not trivial mathematics, and it certainly will not be "discovered" by school children.
It must be taught, and practiced. It is not "a list of formulas to memorize"; its algorithms, such as "long division", are not made obsolete by hand calculators. It is basic to the understanding (not the "memorization") of more advanced mathematics such as is used every day - not just in science, but in the daily work of electricians and machinists - among many, many others.
When teaching is governed by a program that absolutely does not contain needed information, which is the case with the programs at the Penfield schools, there is no "way" of teaching that can overcome the gap. By the time our students get to the fifth grade using the TERC "Investigations" series they are a good two years behind Singapore students of the same age. International surveys (e.g.., the "TIMMS" survey) have shown Singapore at the top and the United States very close to the bottom, in mathematical competence.
And not just "lists of formulas". Consider the comparison (in box) between what children are asked in the TERC "Investigations" used in Penfield and what children of the same age in Singapore schools can do.
Students brought up on the TERC program are simply not prepared to go on to a good middle school program, though it seems to them they are very successful at "math".
And the Penfield "CMP" middle school program compounds the ignorance, and their high school "Core-Plus" series completes the disaster. The trouble is the lack of real math. The style of teaching is not the problem; it is the material.
Ralph Raimi, Department of Mathematics, University of Rochester
Math: Penfield vs Singapore Penfield "Investigations" (Grade 5, "Suitable for Grade 6", too)
Number of students in your class ____________
Suppose you get 6 cents for each bottle you return for recycling. For each problem show how you found your solution.
1. You have collected 149 bottles. How much will you earn?
2. If you share what you earn with one friend, how much will each person get?
3. If you share what you earn with two friends, how much will each person get?
4. Find the fairest way to share what you have earned with everyone in our class, so there is no money left over. How much will each person get?
Singapore (Workbook Grade 5B)
24. Adam bought 8 note pads at $1.45 each and 10 towels. He gave the cashier $100 and received $46 change. Find the cost of a towel.
25. A group of children went swimming. 3/8 of them were girls. If there were 40 boys, how many children were there altogether?
26. Three boys, Juan, Seth and Jared shared a number of stamps in the ratio 3 : 5 : 7. If Seth received 45 stamps, how many more stamps did Jared receive than Juan?
For more about the Penfield, NY, Mathematics curriculum controversy please visit Parents Concerned With Penfield's Math Programs and see the NYC HOLD summary page Controversy over Mathematics in Penfield, NY, Public Schools.
Return to the NYC HOLD main page or to the News page or to the Letters and Testimony page.