teaching k8 --- january 1992 -- p34
a college professor says, "your children are not thinking." Today, the teacher who heard it writes, "During math I now see excitement, enthusiasm and concentration."
leyden note:
constance kamii (kam-mee) who wrote the autonomy article your read is the "college professor" in Alabama. Everything in this course ties together -- autonomy - uniformity - constructivism - perceptual psychology - science education.
Probably all grownups have memories of those special elementary teachers in their lives who created so much excitement about math, and got everyone so involved that the entire class, having been caught up in the challenges, would frequently shout, "Give us something harder."Invariably, teachers who created such an exciting math environment, and in the elementary grades they usually taught in self-contained classrooms, made everything exciting. Was this excitement contagious ? Did other classroom teachers in the same building catch the mood, helping it spread throughout the school ? Did an entire building thus come together to create a learning environment second to none? The answer, probably , is "yes."The next question, of course, becomes obvious. "Can it happen today ? Is it happening today ?"
And why not?
Certainly today, in these times, when good education for our kids is on everyone's agenda, the change that many, many schools, fit the mold is not only a distinct possibility, but from what we've seen in the schools, we've visited, it's often a reality.Nowhere is that more apparent than at Hall-Kent Elementary School in Homewood, Alabama, a suburb of Birmingham. Walking through its doors -- are there any educators who cannot "smell" a good school simply by walking the halls ? -- an observer cannot fail to be aware there's something special in the air.
Jack Allison, a teacher for 15 years, and an administrator for five additional years, is now in his second year as principal of Hall-Kent School. He and his predecessor. Gene Burgess, have done what all good principals seem to do -- provide an atmosphere, through leadership, inspiration and commitment that stimulates teachers to do their thing. The result is excitement and achievement, as we witnessed in the classroom of Linda Joseph.
Linda Joseph is a 2nd grade whose counterparts in the classrooms throughout Hall-Kent School are what make the building possess that certain "feeling" we mentioned earlier, that "something special in the air."
We spent a good part of the school day with Linda and there was a bonus -- Dr. Constance Kamii - professor at UAB, was there, too. Dr. Kamii, the author of many articles on teaching mathematics and also the author of two books - who has been working with teachers in the building since September 1984.
Young Children Reinvent Arithmetic: Implications of Piaget Theory 1986
Young Children Continue to Reinvent Arithmetic's: 2nd grade 1989
The thrust of Dr. Kamii's efforts have been implementation of a "constructivist primary math program." Linda now in her 7th year working with the program,is an enthusiastic participant as Dr. Kamii conducts and publisher her research.Linda, supported by the teachers at the school echoes the statement in Kamii's most recent book.Piaget's research and theory, called constructivism, have shown that children acquire number concepts and operations, by construction from inside and not by internalization from the environment. No drill and practice, no memorization of the multiplication tables. Just thinking, lots of thinking.
We saw it working in Linda's class, as kids attacked a math problem logically and methodically worked their way through 3-digit addition orally, without paper and pencil. How many adults could do the same.
Dr. Kamii is a firm believer in encouraging children to reinvent arithmetic. When children reinvent arithmetic, she says, they develop both competence and confidence. This is because it is a result of children using their intuition and natural way of thinking.
"If we encourage them to develop their own ways of thinking rather than require them to memorize rules that do not make sense to them, children develop a better cognitive foundation as well as confidence," she says.
"Children who are confident will learn more in the long run than those who have been taught in ways that make them distrust their own thinking." Strong, unequivocal statements ? Yes, indeed, and Dr. Kamii can cite research to back up everything she says. She is a serious researcher; and her statistics, developed over many years classroom research and careful testing, corroborate her conclusion that constructivist math can make a significant difference in not only the enthusiasm with which children learn math, but in the final, measurable results.
In the second book by Dr. Kamii, in which Linda Joseph wrote some of the chapters, and in our conversations, Linda highlighted some of the significant mileposts she reached as she became more comfortable with Dr. Kamii's new approach to teaching math.
When Connie Kamii first came into my room I thought she would be impressed with my classÕs performance. Instead she said, 'Your children are not thinking.'
"I realized she was right, because I had often said to myself, 'Some of them are not using their heads.'"
Her idea was to use situations in daily living, and games, to encourage children to build their own knowledge of arithmetic.
In looking back at her first year in the program, Linda wrote, "Math was thus no longer something dished out on a piece of paper that was to be filled in with right or wrong answers. In fact, paper was rarely used at all. Math became something tht occurred whenever a question concerning numbers came up, and I stopped saying, 'We arenÕt doing that today,' or; 'Wait until math time.'"
The conversation turned to other curriculum areas and it soon became apparent we were talking with someone who uses a whole language approach, not only in reading, but math, science and social studies. And, as she pointed out, she never misses a chance to bring math into the picture, no matter what she may be teaching at the moment. "Math crops off everything," she added with her infectious smile.And it can be fun. In fact, Linda writes, "Nobody had ever told me to make math fun. Nobody said, 'Get excited.' I, too, invented my own procedures for encouraging children to construct." During her second year, Linda wrote, she began to test the children against the accepted norms. She also made her own personal observations, based on her own experience with the child. These personal observations seemed to give her the most accurate measure of each child's progress and competencies.
"The best way for me to tell a child's ability was actually to play with him or her. By playing with the children, I could assess firsthand how well they reasoned with numbers."
"When parents came for conferences, I could give specific facts, such as, 'Your child knows the sums up to 10 quickly and easily, as well as the doubles up to 7+7. He has difficulty with sums between 11 and 18; so we have been playing Quince together.'"
If parents offered to help by drilling the children with flashcards, she writes, "I quickly decline, referring them to research which indicates that memorization of 'facts' is not desirable. I ask them, instead, to help by playing games in which the child does most of the decision making."
Discussions in class, as we observed, play a major role in math. These cover, in the main, (1) situations in daily living, (2) games, and (3) teacher-initiated discussions of computational and story problems.
During our visit, in a group discussion and story problem revolving around a situation Linda had posed for them, the children were responding with "agree" and "disagree" to solutions their fellow students presented to certain mathematical problems -- for instance, adding in their heads 245 and 145.
And, as the discussion became more animated, children would explain how they had arrived at their answers. Their logic was easily understood, even though they often arrived at widely divergent solutions.
These children were, indeed, thinking. Which, after all, is what school is all about.
ALLEN RAYMOND is also the author of the letter to me - about knowing Richard Feynman. Allen was an ENGINEERING MAJOR at Cornell -- and his career is that of an editor for a children's magazine. Life is strange.Just goes to show -- you go to college for knowledge --- and what you do with it is up to you. You don't go to college "to be a teacher" --- because you'll only be in an elementary school 6.6% of the rest of your life !