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The identification of teaching resources for low achievers depends upon analysis of student characteristics, teaching strategies, and mathematics curriculum content. Social and emotional problems of low achievers are often reflected in low motivation, short interest spans, antisocial behavior, high absence rates, and goals based only on the immediate future. These characteristics suggest that appropriate resource materials should be constructed in small units with provisions for individualized work, and should emphasize success and self-worth--possibly by including an incentive or reward system. An activity learning approach provides an excellent vehicle for promoting the following teaching procedures that are particularly effective with low achievers: (1) Employ repetition through spiraling; (2) Introduce small segments of material at a time; and (3) Use language which the class is likely to understand. Resource materials should have clear objectives which have some relationship to the immediate needs of the learner. Content material should develop desirable habits, attitudes, and appreciations as well. To do this, materials must combine low difficulty levels with high mathematical standards. (Author/CK)

This paper reviews teaching approaches and general resource materials for low achievers in both elementary and secondary mathematics classes. A survey of reported characteristics of low achievers is divided into two classes: (1) social and emotional problems, and (2) learning difficulties. Characteristics related to class 1 problems include: high rate of absence, goals for the immediate future only, low motivation, antisocial behavior, short interest span, and inability to see the practical use of mathematics. Characteristics related to class 2 problems include: a record of failure in mathematics, a fear of the subject, achievement scores at least two years below grade level, reading difficulties, inability to follow directions, tendency to leap to conclusions, and inability to generalize. Teaching approaches which have been reported as being successful include the use of computational aids, manipulative devices, and laboratory techniques. Also reported was the development of individualized short-term curriculum units, emphasizing success and immediate reward. The two bibliographies included are: (1) a bibliography of general resource material, and (2) an annotated bibliography of articles which have appeared in "The Arithmetic Teacher" and "The Mathematics Teacher" which suggest lessons for low achievers. (RS)

A clinical approach to teacher education used at the University of Illinois is described. It is characterized by the following: (1) a broad basis for providing input (using ideas of inservice teachers, professors, and undergraduate students); (2) continuity of professional education (involving inservice teachers in seminars); (3) team approach to professional education (seminars involving those referred to in (1) above, and the student teacher is not an apprentice but an active member of the team); (4) variety of experiences (elementary through senior high school and low-achieving to advanced classes); (5) individualized training (flexible assignments and responsibilities for students); and (6) "mini-teaching" (two or three teachers to a group of five or six students). One semester is devoted to the program having the above qualities. Appendices include discussion of mini-teaching, objectives, and conditions. (JG)

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)

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)

Plans for an international survey examining the areas of mathematics curricula, classroom processes, and changes in mathematics education since 1964 are discussed. Several reasons for U.S. participation in this survey are suggested. (DT)

Provides a computer program in BASIC language by which a least squares approximation of a straight line may be determined. (CP)

Basic statistical concepts are discussed, steps for generating data having any desired correlation are outlined, and a flowchart, a BASIC computer program, and sample results are provided. (DT)

This is one of a series of reports on the National Longitudinal Study of Mathematical Abilities (NLSMA). This report presents a sequence of analyses that explore the relationships between mathematics achievement and three sets of variables: pupil, teacher, and school for students in grades four and six, (NLSMA Reports Nos. 1, 4, 7, and 9 provide related background material.) Achievement criteria used were computation, structure, and a standardized test. While no extensive attempt was made to interpret the data, several results are clear. Under- and over-achievement varies a great deal according to the criterion used. In general, students using modern texts had better achievement on structure while students using conventional texts had better achievement on computation. Scales measuring pupil attitudes toeard mathematics and (to a lesser extent) self-concept and anxiety scales also tended to relate to under- and over-achievement. Teachers classes varied greatly on the mean residual achievement variable. There was a tendency for background variables to affect results before the attitude scales. For related documents, see ED 044 277 - ED 044 283, ED 044 310, ED 045 447, and SE 016 669 - SE 016 691. (LS)

Presents techniques for involving low achievers with essential mathematics requiring more than computational facility. Demonstrated is the need for students to be able to relate to the subject matter of mathematics - its structure and pattern, and its power - and only then be concerned with the precision, the computational skills, and the rules which are required. (RP)

Reviews the implications which the advent of the computer has for mathematics education in instruction, learning, and curriculum. The activities described are either representative of those occurring at present or very shortly to be realized. (PR)

In 1964, the International Association for the Evaluation of Educational Achievement (IEA) surveyed mathematics achievement in the schools of 12 countries, including the United States (Husén, 1967). Subsequently, surveys were conducted in six other school subjects involving some 23 nations(e.g., Comber & Keeves, 1973; Walker, 1976). In the United States, a special issue of J RM £ was devoted to the IEA mathematics survey (Volume 2, November 1971), and articles on the survey were written for NCTM publications (Willoughby, 1968) as well as for the press. Some countries, Australia for example, prepared national reports on the findings of the survey (Keeves & Radford, 1969). Recently, critiques of the IEA studies (Coleman, 1975) and (Freudenthal, 1975) have generated considerable discussion in some quarters.