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This publication contains sixteen abstracts of papers presented at the Research Reporting Sessions of the National Council of Teachers of Mathematics (NCTM) Annual Meeting. The investigations reported by Anthony, Creswell, Higgins, and Weise focus on curriculum and classroom innovations in the school mathematics program. Investigations by Gibbons, Pearce, Rector, and Wells relate to instruction and methods for teaching mathematical concepts. Research presented by Carry, Fey, Miller, and Vigilante is concerned with certain logical inference patterns and reasoning abilities in students. Bell and Gorth report the results of a survey of mathematics teachers with respect to current issues and a new design for evaluation in mathematics. Research on behavioral objectives for a seventh grade mathematics and for a freshman calculus course is reported by Bierden and Picard. (RP)

Included are papers presented at the 1969 University of Illinois Colloquium on the Preparation of Teacher Educators in Mathematics. The first paper, "On the Preparation of the Teacher of Teachers" by B. Othanel Smith, examines the prominence of research in the teacher training programs. The second, "Source and Supply of Leadership in Mathematics Education" by Howard F. Fehr, discusses the characteristics of leaders and the tasks of future leaders in mathematics education. The last, "Preparation for Effective Mathematics Teaching in the Inner City" by Irwin K. Feinstein, outlines what should be the mathematical and professional background of those teachers working with inner city children. Following each of these three papers are two response papers written by other mathematics educators. (RS)

This compilation of 64 papers on innovative programs in mathematics teacher education describes a great variety of current activity, including the use of individualized instruction, flexible grouping, tutorial programs, laboratory methods, new evaluation schemes, micro-teaching, computer assisted instruction, simulation, and field-oriented programs. Two-thirds of the programs concern elementary school teacher education, and are grouped according to emphasis as follows: content, content and methods integration, methodoloty, methodology and field experience integration, and field experiences. The papers on secondary teacher education are grouped under methodology and field experience emphases. (MM)

Paper presented at a regional convention of the National Council of Teachers of Mathematics, Atlanta, Georgia, November, 1971. Described is some of the recent literature in classroom communication analysis based on fundamental cognitive processes. A logical analysis of teaching and teacher verbal behavior is presented. Included is a description of the strategies of teaching involved in teaching concepts, generalizations, and skills in mathematics. The subsequent implications for training teachers of mathematics are discussed including applications to microteaching. (JG)

A keynote address for the Commission on Teacher Education of the National Council of Teachers of Mathematics Forum on Teacher Education, this paper briefly discusses what the author considers the major broad issues of both mathematics education and the education of mathematics teachers. Problems are outlined without a particular effort to propose solutions. Topics covered include the mathematical competence of teachers, the mathematics curriculum, methodology, the teacher as manager of the classroom mathematics instructional system, the teacher as manager of a student group, evaluation, the affective domain, integration of mathematics with other disciplines, research, mathematics teaching as a profession, and fiscal responsibility. (JM)

The first of the two major sections of this report deals with a review of the training of English and mathematics instructors. The results of a survey of English and mathematics department chairmen in 4-year institutions regarding their attitudes toward having or developing a specialized Master's degree program for the teaching of these subjects in the community college are presented. These results showed that for the two subject areas nearly 50% of the chairmen advocated the development of such programs in contrast to the considerably smaller percentage of schools actually having such programs. Section two of the report presented the results of an investigation of the occupational instructor preparation project at Southern Illinois University. Requirements for entering the program are discussed as well as program goals and objectives, practical and academic training received through the program, and financial aid to students enrolled in the program. (AL)

A self-assessment inventory of teaching competencies was devised for use by student teachers. The instrument was administered to 15 seniors prior to a methods course and student teaching and again after student teaching. Factor analysis of the pre- and posttest scores revealed five dimensions accounting for 77 and 68 percent of the variance, respectively. Differences in mean scores were found (p<.01) in favor of increased self-assessment. The instrument was then administered to 34 experienced high school mathematics teachers. It was found that the post-student teacher scores differed from the experienced teacher scores in only one perceived self-assessment. It is suggested that the change in scores from pre- to post-student teaching could be due to training, or more insightful assessment of abilities, or a combination of these and other factors. (JG)

Discussed is a research project designed to measure the relative effects of audiotape versus videotape feedback in a microteaching situation. Teachers were randomly assigned to one of three groups; audiotape feedback, videotape feedback, control. The teachers in the two feedback groups participated in an instructional sequence on microteaching procedures which involved about 13 hours of instruction in a four-week period. Teachers were asked to conduct tutoring sessions before and after the training sequence. Videotapes of these sessions were rated for the teacher's use of diagnostic questions, demonstration techniques, evaluation examples, practice phases, and verbal praise. The results indicate that videotape and audiotape feedback are generally equally effective in producing gains in these tutoring skills. (CT)

In a synthesis of literature on reading in mathematics, it was noted that there is a broad basis of research in this area on which to base instruction of definite reading skills important in arithmetic achievement. It was stressed that the vocabulary of arithmetic texts runs at readability levels higher than the performance levels of students in the grades in which the books are used and that the vocabulary of arithmetic texts does not greatly parallel or overlap that of reading texts; thus children must be taught special word attack skills and vocabulary for arithmetic comprehension. They must recognize that verbal arithmetical material is conceptually packed with a high density factor which requires at least three kinds of reading adjustment: adjustment to a slower rate than that used for narrative materials, varied eye movement including types of regressive eye movements, and intentional rereading. Two or three sets of symbolic meaning may be involved within one context; thus a student's vocabulary must include technical words, signs, and symbols. All of this requires an attitude of aggressiveness and thoroughness; the student must read to grasp the total idea and the sequence and relationship of ideas. Specific attack steps, tables, and a bibliography are included. (BT)

The desk calculator has been promoted as invaluable to the teaching of mathematics, though this claim has not been supported by controlled experimental studies. Using empirical methods, this study was designed to test calculators with two groups of ninth grade students and one group of fifth grade students in three differing instructional settings. Experimental and control classes were designated for each group, and, in addition, one ninth grade group contained a class to control for the "Hawthorne effect." An attempt was also made to control for differences in teacher performance. The findings were equivocal concerning the effect of calculators on the students' performance and on their self-confidence and attitude toward mathematics. Teacher enthusiasm for use of the calculators bore no relation to the machines' effect on student performance. Rather, this enthusiasm appeared to be a function of the calculators' effect on student-teacher interaction and their potential as toys to provide classroom diversion. The lower the average IQ level of the group, the higher was teacher enthusiasm. At worst, the machines took up space and cramped daily operations. At best, they gave a feeling of increased productivity to students not previously capable of it, thereby easing classroom behavior problems. (GO/MT)

Reported are 49 citations of documents related to teacher and student characteristics in science and mathematics education. The documents included represent research reviews, conference reports, research reports, position papers, textbooks, manuals, speeches, and other types. Citations are categorized in alphabetical order by author, and indicate source, availability, and major ideas of the document. The bibliography updates, but does not replace, bibliography 20 (ED 026 286) and bibliography 10 (ED 021 773). (RH)

The study was designed to develop, test, and refine a model of teaching behavior for teachers of a first course in algebra. The model described five categories of teaching behavior which should be exhibited by algebra teachers. To aid in observation of these behavior categories, a modified Flanders interaction Analysis instrument was developed and is included in the report. The instrument was used to categorize verbal behavior of three ninth grade algebra classes each of ten teachers. A pretest of math ability and posttests of algebraic achievement and attitude toward the teacher were administered to the students in each of the ten classes. No significant differences were found between student achievement and attitude in relation to ratings of teachers on (1) years of teaching experience or (2) number of semester hours of credit in mathematics. However, teachers who had high correspondence to the model had higher student achievement and significantly (.05) higher student attitude toward the teacher than teachers having low correspondence to the model. (JG)