It is not easy to try out new approaches to teaching math.  Principals are not prone to allowing teachers the time to experiment, and teachers do not welcome others into their classroom, especially since they do not truly have sufficient time to teach what is required.  Fortunately, I found an outstanding principal and group of teachers who allowed me this opportunity.  It took much time to prove myself and develop the confidence and acceptance of the teachers.  Initially, success was based upon intangibles such as increased interest in math.  However, in teaching addition I developed a testing and measuring process that can quantify the results.  At the end of the year, all the second and third graders took a "minute math test," and the results were plotted in a histogram showing the number of students in each of several ranges of completion times.  The second and third grade students had about the same performance, with the third grade students doing slightly better.  When the second graders were advanced to the third grade, after two weeks of school all the teachers were reporting that these students were at the same level as last year's third graders had been at the end of the semester.  The retention of the addition facts was at nearly 100 per cent.  Even children who were slower than average at learning seemed to have shown major improvement.

I conducted an experiment with students of nine teachers--three each from grades one, two, and three. It involved my spending only a half hour (fifteen minutes of effective teaching time) per week in each of their classes.  (I had taught all of the second graders when they were in the first grade.)  Each class had about twenty students, giving a total of sixty students altogether in the second grades under observation.  Because the teachers spent significantly more time with the children than I did, my presence was more of a catalyst than as the major reason for any improvement.  Each teacher had a different style, but I observed that in one form or another there was an exchange of teaching techniques.  As the teachers picked up on my approach, I learned much about teaching children from them and applied that learning as the semester progressed.  What impressed me was the ease with which the teachers learned and tried a new approach without detracting from the rest of their lessons.

But there was still more to the experiment.  At the end of the term, these second graders had also been taught how to multiply, normally taught in the third grade.  In a few weeks, the teachers and I will be able to determine how successful the techniques are for teaching the children multiplication.  The techniques for teaching both addition and multiplication are based upon the structure of our number system and using patterns to take advantage of this structure.  All factors will be reinforcing one another--teachers who understand math better than their colleagues, children who are excited about math because the techniques allow them to build their confidence, and study techniques that were taught to reduce the effort for the children to learn.  My one sadness in the success of the project is that the teachers will not need me in the classroom and I will miss out on the excitement of watching children enjoying learning.

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