A beginning for student teachersAuthor(s): FRANCES L. JENKINSSource: The Arithmetic Teacher, Vol. 14, No. 3 (MARCH 1967), pp. 209-211Published by: National Council of Teachers of MathematicsStable URL: http://www.jstor.org/stable/41187268 .

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A beginning for student teachers

FRANCES L. JENKINS, Colorado Springs, Colorado

Mrs. Jenkins reports experiences she had while teaching mathematics at Wasson High School in Colorado Springs, Colorado. She is now a secondary supervisor of mathematics for her school district.

With the increased popularity of, and emphasis on, science and mathematics fairs, I found myself faced three years ago with a unique situation. I had been teaching honors mathematics classes at all levels, and it seemed appropriate to enrich this curriculum with projects for the regional science fair. After our school produced two regional winners - students under other teachers - I found that great interest had developed in having all honors students participate. Not wishing to promote proj- ects just for the sake of entering a science fair, with the only goal being that of win- ning, I looked for additional ways to in- terest my students and to enrich their mathematics background. Three kinds of projects looked promising as paths the students might take for their independent study. It was decided that a student might -

1. Engage in a project as original as possible for entry in a science fair

2. Undertake a research project on some phase of mathematics of spe- cial interest to him as an individual

3. Act as a member of a teaching team of two students

Each type of project required a full written report, with bibliography when ap- propriate, plus visual aids to be used in giving a ten-to-fifteen-minute report on the project to the class. Incidentally, I quizzed the students on the reports that were made, which practice helped to keep the quality of the reporting high.

Our experience with the third type of project is the subject of this article.

At the time of the experience here re- ported, many of our elementary schools and some of our junior high schools had not introduced any modern concepts in their teaching of mathematics. Some of my students had become so impressed by the powerful impact of these concepts, and by their tying together of ideas that had seemed unrelated, that they wanted younger students to know about them too. Out of their enthusiasm was born the idea that juniors and seniors of high mathematics ability might teach some elementary and junior high school classes. Each student interested in teaching and becoming a member of a teaching team found another student who was also interested. Their project followed the design of writing three complete lesson plans for an agreed- upon grade level. These plans were very detailed and complete with objectives, out- lines of subject matter to be taught, and methods (including key questions) of pre- senting the subject matter. Some form of visual aid besides the blackboard was re- quired. Dittoed practice sheets were made. Finally, some type of follow-up lesson, such as supplementary questions or games, was prepared, to be used by the regular teacher at her discretion. The set of three lessons was so planned that each lesson could be presented individually or in a sequential group of three. Each student teacher knew what had been taught to the class pre- viously, so he could either build on the last lesson or give needed background ma- terial for the current lesson. In most cases, the complete set of three lessons was re- quested by the elementary schools and

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was so taught. The formation of these lesson plans required some conferences with me to set up the format. But such complete lesson plans I have not seen for many, many years. Their excellence was one of the selling points for our proj- ect, persuading the regular teachers to give up precious classroom time. More- over, thorough planning added much to the confidence of the student teachers when they actually taught a lesson. The first year, 1963/64, our plans were made to teach the fourth and seventh grades. We chose these grades simply because we had the SMSG texts for them. These texts were the keys to our lesson-planning - for subject matter content methods, and the ability level of our students.

Subjects of the lessons ranged from sets to intuitive geometry. On the seventh- grade level, one exceptionally well-prepared lesson was done on the development of the number system from the naturals to the reals (including the complexes, also, if the students were ready to handle them), based on the postulate of closure.

We had five teaching teams of two stu- dents each the first year. After they started teaching, several other students volunteered as substitutes. However, the best teaching by far was done by thé stu- dents who had developed the lessons. We had all combinations on the teams - both boys, both girls, and a boy and a girl.

The hardest part of the entire project was setting up times when the high school students could leave school. We kept transportation problems to a minimum by teaching only at junior high schools and elementary schools in the vicinity of the high school. Two students per team lent flexibility to the scheduling and also gave us a teacher if the assigned one was ill.

The one variable which could not be predicted was the actual teaching done by the students in the classroom. They were interested; they were well-prepared. But how would they react to seventh graders or fourth graders, and how would the younger students react to them? So

we planned a trial run. Each member of a team taught our high school mathe- matics class, using one of his lesson plans and all his visual aids. It was amazing how a group of sixteen- and seventeen-year- olds became, on request, nine-year-olds, and asked questions on that level. After the lesson was completed, a critique was held:

"This is the first time these kids have seen the symbol </>. You must write more legibly."

"I can't see what you are writing on the blackboard."

"If you don't explain more thoroughly and simply, they will not understand."

"I thought your presentation of the concept of the intersection of sets very good and clear - and at their level."

These were typical comments given to the student teachers during the critique.

The elementary schools, in particular, were enthusiastic and interested. The junior highs were also interested, but two factors created difficulty: (1) the rigid scheduling of junior high schools (as well as senior high schools) made it hard to schedule the student-taught classes, and (2) junior high school teachers disliked giving up time badly needed for the regular cur- riculum. However, we received full coop- eration from three junior high schools and three elementary schools.

The second year of the undertaking, we decided to limit ourselves to the three elementary schools primarily because of the ease of scheduling. All three prin- cipals and their fourth-grade teachers will- ingly had "arithmetic" when the student teachers were available. This decision helped with the transportation problem since many of the high school students lived in the areas of the elementary schools and could easily walk to their classes to teach.

One big problem was the tendency for a student teacher to forget to let me know if he had to be absent from school. He was not yet used to the idea that a sub- stitute would be needed for him or, at

210 The Arithmetic Teacher

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least, that the cooperating teacher had to be notified of the cancellation.

The same procedures, otherwise, were followed during the second year, 1964/65. This time we had four teams, two com- posed of boys and two composed of girls. I was pleasantly amazed at the interest the boys had in teaching.

The results of the students' teaching were extremely gratifying. They were en- thusiastically welcomed by the fourth graders. In most cases, their presentation was above average. Only when the prin- cipal of the school came in to observe did one student teacher lose her poise. One boy, a star basketball player, made quite an impact on his students. He was so aware of what he had not understood at their age that he did an excellent job of getting ideas across. One class of fourth graders gave him a standing ovation on his last day; at another school, the prin- cipal's secretary made a special call to

tell me how well the student had taught. The original purpose of this type of

project was twofold: to help high-ability high school mathematics students learn how to plan and prepare a lesson teaching some mathematical concept, and to share some of the new ideas in mathematics with elementary school students. But by far the greatest result was not the realization of either of these purposes. It was, rather, that these students really enjoyed teaching and built terrific rapport with their fourth graders. So often a prospective teacher sees classroom teaching as the last part of teacher training, and he may have lost interest in teaching (if he ever had it) before he reaches this stage. My young athlete had never considered teaching be- fore this experience. Now it is definitely in his fields of interest - and on the ele- mentary school level.

This is a powerful way to really interest high-ability students in considering mathe- matics teaching as a career.

The mathematics of supermarket shopping We are aware that in recent years the mathe- matics offered to the "general" student has been the subject of growing interest and concern. The interest of leaders in mathematics education is evidenced by the increased incidence of this topic at mathematics conferences throughout the country. Hardly any such gathering of note takes place without at least one section devoted to solving the problem of mathematics for the slow learner. Concomitant with this interest is the ever-present concern that present mathe- matics offerings are not well received by certain students. Much discussion has taken place; but, frankly, very little seems to have been accom- plished. Again and again we are told how to recognize these students; endless conjectures are made concerning the origin of their non- receptive attitudes; and we are belabored with a recitation of the problems with which teachers of these groups must cope. However, very few

practical and successful suggestions are made. I am going to be so bold as to offer one.

Most teachers of general mathematics know that the most successful lessons are those that are "different," those that somehow or other tap an elusive chord of response in these hard- to-interest students. Lessons that are different require a persistently creative teacher, one who constantly brings in new devices and then, regardless of how successful these were at the time of introduction, is ready to drop them in favor of something else when interest wanes. This flexibility requires constant, nerve-racking planning - in fact, more creative planning than is required for teaching the top academic sec- tions. It requires also a thick-skinned individual who is not discouraged when some carefully thought out lesson plan fizzles. If one can pa- tiently work out even a few successful activities per year, just imagine the repertoire of lessons

(Continued on page 215)

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