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Training elementary mathematics teachers in a one-semester courseAuthor(s): WILLIAM B. CRITTENDENSource: The Arithmetic Teacher, Vol. 21, No. 5 (MAY 1974), pp. 428-432Published by: National Council of Teachers of MathematicsStable URL: http://www.jstor.org/stable/41190931 .Accessed: 10/06/2014 16:02

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Training elementary mathematics teachers in a one-semester course

WILLIAM B. CRITTENDEN

An associate professor in education at Houston Baptist University, William Crittenden is the only member of the faculty teaching mathematics education. He has sought a model that would yield the best possible results in training elementary teachers in one semester. He has also been a leader in the Houston area in the evolution of performance-based training.

W hen the writer joined the faculty of Houston Baptist University in 1968, he was given the assignment of prescribing the mathematics education training experiences for prospective elementary teachers. Since the college is primarily for the liberal arts and the curriculum includes a large number of required cources, there was only one three-semester-hour course available in which elementary teachers could be pre- pared in mathematics. A "prepared" teacher was defined as one who had -

achieved a prescribed level of mastery of mathematics content;

accumulated a theoretical and empirical repertoire of teaching strategies, tech- niques, aids, and activities; and

exhibited a positive attitude toward mathe- matics as a field of study.

The challenge was obvious and almost overwhelming. How could all three vital objectives be achieved in 45 hours of class- work during a single semester while the students were involved in from four to six other courses?

No other mathematics courses were required for elementary education majors at Houston Baptist University. The variability in requirements from college to college in

America in this field was highlighted by Fisher (1967) who found that 40% of 78 teacher-training institutions graduated ele- mentary teachers with three semester hours' credit (in mathematics or mathematics education) or less, and 90% required six hours or less.

The problem at Houston Baptist Univer- sity became acutely clear as early attempts to solve it resulted in failures. If content were emphasized and methods ignored, students later complained (justifiably) that they had received little or no preparation in how to teach mathematics. On the other hand, when methods were emphasized and con- tent ignored, supervisors of student teaching complained that the students so prepared made embarrassing content errors in their teaching efforts. When scales were used on a pretest-posttest basis to measure positive gains in attitude toward mathematics, it was found that few students showed changes of attitude and, when they did change, the change was just as apt to be negative as positive.

It was decided that more time for the training was absolutely essential. Even though it was "not possible to award more than three hours' credit, a laboratory was scheduled for a second hour three times per

428 The Arithmetic Teacher

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week. Thus, the class time was increased from 45 clock hours per semester to 90. Simultaneously, arrangements were made with a nearby public elementary school to permit classroom teaching experiences col- laterally with campus seminars.

Since this methods course occupied a position in the training sequence between the classroom observations of the sopho- more education major and the student teaching of the senior education major, a descriptive name for this intermediate activity was needed. The program was referred to as "student preteaching in elementary mathematics," and the par- ticipants became known as "student pre- teachers."

Students in the program were given pretests in mathematics content, attitudes toward mathematics, and knowledge of mathematics teaching methods. Those who failed to achieve 90% level of mastery of content were given individually prescribed programs in the areas of greatest weakness. No formal lectures in mathematics content were delivered during the semester, but free time was allowed during seminars to provide opportunity for learners to ask for needed explanations. All inquiries were satisfied. Checks of students' work on the programs were made as a control measure.

Pretest results revealed that 95% of the students were deficient in their knowledge of elementary school mathematics; more than 50% of them disliked or feared mathematics and lacked confidence in their ability to teach it; and all of them had a limited knowledge of mathematics teaching methods. Most of them reported that their referent source for teaching techniques was to be found in the way their elementary school teachers had taught them.

With excellent cooperation from the laboratory school staff, the student pre- teachers were assigned to classes that had been divided into small groups on the basis of mathematics ability. The host school had reorganized schedules to permit the intra- classroom group teaching experiences to occur simultaneously, thus permitting the

preteachers to form carpools. The labo- ratory teaching proceeded two days per week with a two-hour seminar on the college campus one day each week.

The on-campus seminar was devoted to building and demonstrating teaching aids. The elementary school mathematics cur- riculum was summarized in ten broad concept areas, and a team report was prepared for each concept area. Games, activities, developmental techniques, mani- pulative and demonstrative aids, and evalua- tive methods were surveyed. Each team produced a 30-page handout booklet con- taining drawings and descriptions of the teaching aids associated with each concept area. At the end of the course, each student had a collection of ideas for aids and techniques in teaching elementary mathe- matics that could be useful as a reference source.

The student preteachers were given teaching responsibilities immediately, each one teaching a group of pupils from the beginning day of his field experience. This precipitant beginning was ill-advised. The cooperating teachers complained that the preteachers made arithmetic errors in their teaching, and they resented being made responsible for teaching mathematics con- tent to the preteachers. In addition, the cooperating teachers expected that the preteachers would use huge quantities of teaching aids, which they didn't; pre- teachers tended to rely predominantly on workbooks and duplicated worksheets, especially in the beginning of the course.

The student preteachers were panic- stricken at being given such heavy re- sponsibilities so quickly when they were well aware of their state of unpreparedness. Since most of them feared or disliked mathematics anyway, the required teaching of it in the presence of experienced teachers, principals, or college observers, with no preliminary preparation acted as a crystalliz- ing agent on their attitudes, rather than as a stimulus to positive change.

Through trial and error, the student preteachers did learn to adjust their teaching

May 1974 429

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methods to the levels of their pupils. They did learn to manufacture and use teaching aids. And they did learn more mathematics content as a result of the seminar and laboratory experiences. Posttests showed significant gains in knowledge of mathe- matics content and teaching methods. However, the attitudes of the preteachers toward mathematics regressed, being more negative at the completion of the course than at the beginning.

The effect of the program upon the pupils in the host school was indeterminate. Subjectively, everyone involved in the program agreed that pupils responded positively to the use of aids and games, but no evidence concerning their achieve- ment gains or losses was available. The cooperating teachers complained that there was a lack of continuity in the program, caused by the presence of preteachers only two days per week. They were not eager to continue the program in other semesters, even with revisions calculated to eliminate mistakes.

Even though the student preteaching program as described achieved two of the three essential objectives, it was declared a failure. To be considered "prepared," an elementary teacher must have knowledge of mathematics content, mathematics teach- ing methods,