3. The Need for Reform Reform! Don't we wish that our students could again attain the higher performance levels they reached in the 40s, 50s and early 60s? Instead of talking about "reform" we should be talking about regaining lost ground.
Keep in mind that when the Standards writers talk about reform they are talking about curriculum and teaching reform not about social reform that would send kids to school ready to learn (Goal 1). Has the council considered the implications of this situation? (See Enclosure 3 Crisis in school mathematics due to social conditions for which standards provide no remedy)
Enclosure 3 Crisis in school mathematics due to social conditions for which Standards provide no remedy.
The standards writers have failed to provide an analysis of existing conditions in order to show a need for these changes. While they refer briefly to "A Nation at Risk" they do not seem to realize that conditions deleterious to learning have intensified by at least one order of magnitude in the last 30 years. Consider that not all pupils are clear-eyed seekers of truth from Central Casting with unlimited time for data gathering and individual conferences. A very substantial number of our "students" come to school in no condition to learn. It is difficult to teach students who, due to social conditions outside of school, are bone-tired, terrified, drug sodden or absent. As Clarence Page says, "The public schools have become a dumping ground for the problems of the larger society." Maybe--just maybe--this has something to do with lower test scores. Plans to reform our schools overlook that about half of our youngsters grow up in families that are not adequately instilling traits that are pedagogically essential. Frequent divorces, a bewildering rotation of significant others, and parents who come home from work exhausted both physically and mentally have left many homes with a tremendous parenting deficit. Instead of providing a stable home environment and the kind of close, loving supervision that character formation requires, many child-care arrangements simply ensure that children will stay out of harm's way. As a result, personality traits essential for the acquisition of math, English and various vocational skills are often lacking. Children come to school without self-discipline, and they cannot defer gratification. Nor can they concentrate on, or mobilize themselves for, the tasks at hand.*
But an influential group of our math educators, who are insulated from these unpleasant classroom realities, seem to be completely unaware of the appalling school conditions that are prevalent in many depressed areas of our country including our inner cities. They have seized upon the present emergency, that was largely caused by these conditions, to proclaim a need for far-reaching changes in teaching and curriculum that have little substantive support in either research or experience and are not relevant to the problems that beset us. (The Titanic has hit an iceberg and is sinking. Let's rearrange the deck chairs.) The suburban schools in affluent areas don't need these changes. Their math departments are staffed by an elite group of highly trained, highly skilled professionals. While some suburban schools are beginning to have their problems (the rise of gangs and the sentiment that only "geeks" do homework) they are already incredibly good insofar as curriculum and instruction is concerned. The problems confronting schools in our depressed areas are, for the most part, not amenable to the changes proposed in the Standards. Since the Standard's writers have misapprehended the cause of the present crisis in school mathematics, how can we trust their solution?
Frank B. Allen
*From an article entitled, "First, educate the reformers" by the nationally syndicated writer Amitai Etzioni. (Chicago Tribune 7/9/91)
Comments on the NCTM's Standards on Assessment
The ten assessment procedures recommended by the NCTM "Standards" (pp 193-237) are so subjective and make such heavy demands on the teachers' time that they are not practical for a teacher working under normal teaching conditions. "Normal teaching conditions" implies five math classes averaging about thirty, plus at least one extra-curricular assignment. Therefore, let every speaker at the forthcoming ICTM "Leadership Conference" place the left hand on a copy of Stone-Millis "Plane Geometry", (Benj. H. Sanborn and Company, 1915) or some other strong geometry text from the period before they were emasculated , and take the following oath: "I solemnly swear that I have used the procedures I am about to advocate under normal teaching conditions for a period of at least two years. Moreover, I used these procedures in all five of my mathematics classes." If this decimates your speaking corps, as it will unless they resort to wholesale perjury, you can spend your time more profitably constructing examinations and tests which are valid measures of the students understanding of school mathematics. A teacher who can neither devise or select such tests should not be teaching mathematics.
Brief Comments about Certain Criteria
Alignment. We have sense enough to know that our tests should "measure the content of the curriculum" (p 193). Standards 4,5,6,7,8,9. We have always tried to ensure that our evaluation procedures (exams, tests, bids, etc.) measured mathematical power, ability to communicate (write clear explanations), reasoning, mastery of mathematical concepts, and proficiency with mathematical procedures. Standard 10. Mathematical Disposition. We have always sought to inculcate a positive attitude toward mathematics. However, it never occurred to us to use our perception of how well we had succeeded in this regard as a component of the students course grade. We thought that if the student had a favorable disposition toward mathematics this would cause him (generic) to study harder and would be reflected indirectly, but effectively, in his test grades. It is irresponsible for the NCTM to advocate assessment procedures which are devoid of any validation under normal teaching conditions in either research or experience. Moreover, if it were widely adapted it would so drastically change our procedures and criteria for measuring student progress that all comparisons with past records would be invalid. It is something like what would happen to baseball records if each batter were given four strikes instead of three. Lord Stockton once said, "The Liberals have once again come forward with many new and good ideas. Unfortunately, none of the good ideas is new and none of the new ideas is good". This analysis applies pretty well to the 9-12 Standards. The NCTM assessment plan is a new idea that is not good. Drop it.