The letter to parents

Jan 23, 2002 ' Elementary School, ..CA

Dear Parents and Students of GATE Class: An Intro to Calculus

The students are doing great. I am amazed at their ability to grasp concepts and to think for themselves.

As an enrichment to the in-class time I am providing some at-home study materials. Please note these materials are not to be viewed as problems to be solved but as projects to be explored.  We are looking for self directed investigations. By this I mean that students should look for patterns in existing problems and create their own as they wish. Parental assistance is welcome; just remember this is suppose to be fun!

What is important in this course is the process of thinking and exploring concepts. Whatever the students try and come up with on their own I would like to see and would like to share with the rest of the class.

You may be wondering what part of calculus we are trying to teach at this grade level? The handouts will give you a taste. My objective for this class is to get across the mathematical notion of infinity as found in infinite series and sequences. Once this concept is rooted then the concepts of a derivative and an integral become easier to grasp. In working with infinite series and sequences a number of other topics are brought forth because they are needed as support. For example, the topics of notation, exponents, decimals, and decimal to fraction and fraction to decimal conversions are some of the supplementary notions covered.

For those of you who are interested there is an excellent web site you may wish to visit and explore with you child: http://www.mathman.biz.

This course is based directly on the materials available at this site.

If you have any questions you may contact me at  ..

Sincerely,

Update

On Feb. 14, 2002 Don received this email from Andy

Don,

I've got 2 more classes with the intro to calculus for 4th graders at .. Elementary school in CA. It has been a kick! Challenging at times. The kids are on their lunch time and so maybe a bit more squirrely than in regular class hours.

Here is a teaching technique for chapter 1 that I stumbled on that you may already be aware of but it was so amazing yesterday that I have to tell you.

As usual a group of the students have a real hard time settling down. They wander all over the class room and lately have been shooting rubber bands at each other. At this age their attention span is short. It works both ways they can wander off and then wander back. When their attention wanders back to the material it is as intense as when it is on something else. Not being an "official" teacher I have not tried to herd them in any conventional way. What helped me discover this natural focus is some of the kids had gotten out peg boards with pins in them spaced about the same distance apart as that on "spotty" paper and were busy making figures with rubber bands on the boards. It is a way to make art instantly without any consumption of resources other than some broken rubber bands.

A light went off in my head as I was thinking of how to get their attention back onto the "lesson" of how did one of the students work out the 1/x series for x = 2, 3, 4, 5. I put 4 of the boards together and one student, Eric, who has mastered the calculation of 1/x on a sheet of spotty paper started to use different colored rubber bands to denote the terms of the partial sum. And that is when the Wow happened. They all got into the act and started doing their own calculations with the rubber bands. It is seems that the tactile nature of working with the peg boards and rubber bands was more engaging that drawing on a large sheet of spotty paper on an easel.

  You probably have used these materials. It is so obvious in hindsight but the serendipity of it in action really made an impression on me and made my day.

The kids are really getting it.

Thanks to your materials. They have been the basis of teaching the ideas. I've worried that I may be driving Chapter 1 into the ground with 2 months of classes once a week for about 40 to 30 minutes each devoted to it. But I've come at it from different angles each week, and returning to the same theme over and over. Yesterday when I said time is up a couple of them said: "already?"

  Sincerely,

Andy