Suzy Ronfeldt is avoiding the standard complaint that NCLB and standardized tests remove all creativity and enjoyment from the reading and writing process. She claims, instead, that standardized tests are the reason so many children are bad at math:
In addition to days and days of testing, No Child Left Behind advances the idea of teaching through textbooks and workbooks -- not discussion and discovery. It emphasizes a curriculum that is a mile wide and an inch deep...Educators must speak up about the value of a different sort of curriculum, one that honors children's wonderful ideas and builds a dynamic dialogue between teacher and child, and between child and child -- especially in mathematics....
If there were no evidence that those days of dynamic dialogue have been producing kids whose knowledge of basic mathematical skills is pretty shaky, we wouldn't be having this discussion.
Let me explain. In my math class, we take time for children to write their own story problems as they make sense of 38 minus 19. One child writes a take-away problem: "There are 38 birds in a tree, and 19 flew away. How many are left?" Another writes a comparison subtraction problem: "There are 38 books on the shelf and 19 on the table. How many more books are on the shelf?"
No problem there - I don't know that it necessarily contributes anything to the concept of subtraction of two-digit numbers, but it might.
First, the children share their problems, and we discuss whether they make sense for 38 minus 19. Then the children share their various strategies for solving these problems. One child breaks 19 into "friendly numbers" such as 10 and 9 before she begins subtracting. Another "counts up" from 19 to 38, and another decides to "round" the numbers, subtract them and then compensate for the rounding. All the while, the children are sharing their thinking and reasoning with one another. You won't find this kind of "math talk" in a workbook or a standardized test.
Probably because the "friendly number" and "counting" concepts, while amusing, are the kinds of things that (a) are not required for mastery of the subject, and (b) should be left behind as the child masters ever more sophisticated mathematical skills. And why should kids be required to decide, as a group, whether they've come up with something that makes sense for 38-19? I'm all for creative teaching techniques with younger kids, but after a certain point, you're just reinventing the wheel.
The National Council of Teachers of Mathematics, in its landmark 2000 book, "Principles and Standards for School Mathematics," writes: "When students are challenged to think and reason, they learn to be clear and convincing. ... But if their learning becomes a process of simply mimicking and memorizing, they soon begin to lose interest."
Ahhh, the real basis for this complaint; Ms. Ronfeldt is upset that memorization has once again been made a part of the mathematics curriculum, as she is convinced that memorization is incompatible with the "real" learning of mathematics. To her, group discussion and creative reasoning are more important, although she might not want to discuss the students who have avoided memorization entirely and view mathematical rules as matters of opinion, rather than fact.
As for that "landmark" book, I'll let someone with more knowledge on the topic have the final say:
On April 12, 2000, The National Council of Teachers of Mathematics (NCTM) released Principles and Standards for School Mathematics (PSSM), a 402 page revision of the NCTM Standards....
Not surprisingly, we will show here that the NCTM has not rediscovered arithmetic. Similar to the original NCTM Standards, PSSM is vague about the major components of arithmetic mastery:
Memorization of of basic number facts
Mastery of the standard algorithms of multidigit computation.
Mastery of fractions
The NCTM has toned down the constructivist language, but they still stress content-independent "process skills" and student-centered "discovery learning". Similar to the NCTM Standards, PSSM emphasizes manipulatives, calculator skills, student-invented methods, and simple-case methods...
The NCTM says they want to maximize "understanding", but they still fail to recognize that specific math content must first be stored in the brain as a necessary precondition for understanding to occur. Although rarely the preferred method, intentional memorization is sometimes the most efficient approach. The first objective is to get it into the brain! Then newly remembered math knowledge can be connected to previously remembered math knowledge and understanding becomes possible. You have to "know math" before you can "understand math", "do math", or "solve math problems."
We conclude this introductory section by noting that there is evidence of a battle within the NCTM, with some voices crying out for genuine arithmetic. These voices were heard in the Principles and Standards for School Mathematics: Discussion Draft (PSSM Draft), published in October, 1998. At later points in this document you will find quotes from both PSSM and PSSM Draft. The quotes from PSSM Draft do not appear in PSSM, the final version published in April, 2000. The voices of reason have been largely silenced!
More information here. Other voices of reason - Bill, Bas, Mike - feel free to fill up the comments with more information, in case I've missed something.
Posted by kswygert at March 15, 2004 12:30 PM