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A description and evaluation are given of the Individualized Mathematics (IM) program. IM is an outgrowth of the work of the Learning Research and Development Center (LRDC) at the University of Pittsburgh. The program has developed and implemented manipulative lessons for primary grade (K-3) students. Like other LRDC programs, this one includes such components as specific instructional objectives, lesson materials to teach each objective, a testing program for monitoring pupil progress, and specific procedures for using these components in the individualized instruction. The emphasis in this program is on the use of manipulative materials for lessons in which the students have a high degree of self-management. The results of two years of development and investigation showed that the program (1) was manageable, (2) permitted independent study, (3) facilitated pupil progress, (4) produced desired achievement test results, and (5) needed modification to make costs and storage requirements more feasible. (JP)

The purpose of this paper is to report on a pilot investigation of the operation of the Bloom and Carroll hypothesis which states that aptitudes are predictive of rate of learning given a situation in which the time allowed for learning is unlimited, and pupil perserverance, ability to understand instruction, and quality of instruction are optimized for each student. Data for this study were obtained for six separate samples of elementary school students in the individually prescribed instruction project from grades 2 through 6 studying in six different units in arithmetic; sample size varied from 42 to 182. The analyses were carried out in three steps: 1) the correlation between aptitude and rate of learning using two measures previous year rate of learning, and non-verbal I.Q. using Lorge-Thorndike: four rate measures were included as described by Wang (1968); 2) examination of the effectiveness of each aptitude measure as predictors of a composite rate measure; and, 3) examination of the other variables using the two measures in step one plus aptitude measures of mathematics achievement using the Stanford Achievement Tests and Lorge-Thorndike. Multiple regression analysis was used to investigate the composite contribution of these measures of Carroll's variables to each of the four learning rate measures. The three analyses substantiated the hypothesis that there is no simple relationship between pupil aptitude and rate of learning. (Author/SBE)

Many programs for individualization of instruction are based on a curriculum structure involving a careful sequencing of instructional objectives and larger units of learning content. A methodology that may be useful in the formative evaluation of the sequential and structural properties among predefined curriculum units and specific instructional objectives was investigated. The three distinct research populations consisted of the student enrollment in three schools employing the Individually Prescribed Instruction (IPI) system for elementary school mathematics. To examine these structural relationships, as they are found in different content areas and levels, student performance on unit placement tests and pretests in thirty IPI mathematics units consisting of 173 specific objectives was investigated through scalogram and simplex analyses. The usefulness of these procedures in providing suggestions for the revision and refinement of curriculum structures was demonstrated. Alternative structures and sequences suggested by this evaluation program may be helpful in providing guidance for curriculum and testing specialists in the design of future curriculums in IPI mathematics. (Author/PR)

Most of the evaluation activity associated with the Individually Prescribed Instruction (IPI) Project is formative evaluation, that is, evaluation that provides feedback for indicating areas or operations where improvements are needed. This paper describes the program for formative evaluation and presents some data obtained in some representative formative evaluation studies. Most of the data concerns the variety of levels and speeds at which children in the same grade work. (JY)

Individually Prescribed Instruction (IPI) depends upon a structured curriculum made up of sequences of behavioral objectives which the student must master in moving from one level of ability to some subsequent higher level. The curriculum designer has the responsibility of specifying, with varying degrees of exactness, how the typical pupil would move from a beginning level of ability to some final level of ability. An overall sequence spanning several school years may be thought of as progression of units with specific objectives. The term "unit" has a relatively specific meaning when used in the context of the IPI curricula. It involves some unitary ability composed of a limited number of objectives. The overall goal for a unit should be well enough defined so that it describes how a pupil would be evaluated to determine whether or not he had the abilities indicated by the goal of the unit. (JY)

The evaluation of an educational innovation can serve as an aid in the development of the innovation, and it can provide a basis for making judgments with respect to it. This report discusses the Individually Prescribed Instruction (IPI) program and its approach to evaluation. IPI evaluation activities are carried out in six areas: the program plan, the operating program, the school context, pupil behavior, teacher behavior, and unplanned influences and other variables. (JY)

Criteria to be used in evaluating the quality of the form in which Individually Prescribed Instruction (IPI) objectives are stated include writing the objective in terms of observable pupil behavior, stating the performance in terms of an "action verb", specifying the object of the action verb, stating the context or conditions for displaying the desired pupil behavior, and accompanying the objective with an example of achievement evaluation. (SP)

Two ways of interpreting raw test data are norm-referencing and criterion-referencing; the former yields information based on some type of ordering of the person on the person's dimension, while the latter tells whether or not students can exhibit a given performance. Criterion-referenced information can be ordered into a criterion-referenced score, depending upon the extent to which it is possible to order the items on the criterion dimension. This method of handling information is particularly useful in the unit-objective testing method of individualizing instruction employed in Individually Prescribed Instruction (IPI) projects. (SP)

Teacher training for work in Individually Prescribed Instruction (IPI) depends heavily upon an intensive orientation to this specific system and to the theory and rationale underlying it. It can be fully successful only if it involves very extensive experience in actually working under this system in the classroom. Also, effective operation of an IPI school seems to demand weekly or bi-weekly teacher planning sessions that have as their major functions the further training of teachers and the planning of necessary adaptations in materials, plans, and procedures. It is assumed that just as the IPI program is subject to continuing study and improvement, so will the procedures for teacher preparation be the target of continuous upgrading. (Author)

C. M. Lindvall's introduction to the IPI project is based--as is the project itself--on Robert Glaser's National Society for the Study of Education (NSSE) Yearbook chapter entitled 'The Design of Instruction'. The project concerns itself with identifying the proposed student terminal behaviors and structuring them into some meaningful total curriculum; diagnosing the student's preinstructional behavior; developing and evaluating sequential objectives in the carrying out of the instructional process, and measuring learning outcomes. This last step is not dealt with in the IPI papers. (GO)

A group of students normally distributed in aptitude and given the same instruction will produce a normal distribution of student achievement. It has been contended that if each of five primary variables in learning are optimized for each student, all students should be expected to achieve mastery of the material. These variables are (1) aptitude of student, (2) quality of instruction, (3) ability to understand instruction, (4) perserverance, and (5) time allowed for learning. This study investigated this hypothesis with an individualized learning program (ILP), in which all students were supposed to attain mastery on each lesson before going on in the program. Students in grades two through six were given aptitude tests, and their performance in the ILP was compared with the test results. Little relationship between rate of learning and aptitude was found when variables number two, three, and four were ignored or were assumed to be operating at an optimum level for all. Thus, either the variables should not have been ignored or the experimental design in this study was faulty. Aptitude may still be found to be the most important factor in rate of learning. (WD)

Lindvall's observation system has been designed to assess elementary school students' behaviors in an Individually Prescribed Instruction (IPI) project. It measures the self-directiveness of the student by determining how pupils use their classroom time when they are not actively being guided by a teacher. The system focuses on student behaviors, and student interactions with peers and instructional materials, as opposed to student-teacher interaction. The coder surveys the entire classroom every two minutes for each listed activity; thus, after two minutes, each pupil will have been coded as performing one of these activities. Ten two-minute coding periods are obtained for each lesson. Five activity categories are included: (1) independent work--14 categories; (2) teacher-pupil work--three categories; (3) non-instructional use of pupil time--eight categories; (4) pupil-pupil activity--two categories; and (5) group activity--nine categories. This document also contains a description of IPI program components and instruction for coding and summarizing results. (GDC)

Three roles of evaluation used in Individually Prescribed Instruction (IPI) projects are defined in this monograph: the regular and systematic evaluation of pupil achievement for the purpose of adapting instructional experiences to individual needs, the continuing evaluation of all elements of a developing educational program as an aid to this development process (formative evaluation), and the evaluation of the results produced by an educational program for purposes of making judgments concerning its value (Summative evaluation). Each role, based on a systematic perception of educational program goals, planning, operation, and assessment, is then described in terms of the operations that the Learning Research and Development Center of the University of Pittsburgh is carrying out in the context of the IPI projects. (Author/SP)

The term evaluation is used here to mean either the procedure of gathering pupil data to use in planning and monitoring individual programs or the procedure of gathering and analyzing data in such a way that it leads to improvements in materials and in the instructional system. The author reviews the Winnetka Plan and the Eight-Year-Study. He then proposes a model which makes use of criterion-based measures of pupil achievement and demonstrates how this evaluation program is carried out using the program for Individually Prescribed Instruction as an example. He describes the computer-based instruction program, the Bucknell Continuous Progress plan, and Project PLAN, together with their measures for evaluation. Some future directions are suggested for evaluation procedures in programs for individualized instruction. (JY)

Following a general discussion of the goals of individualized instruction, the role of the teacher in an instructional system developed at the Learning Research and Development Center of the University of Pittsburgh is described. (LS)

Activation of telomerase is a crucial step during cellular immortalization and malignant transformation of human cells and requires the induction of the catalytic component, human telomerase reverse transcriptase (hTERT), encoded by the hTERT gene. It is poorly understood how the hTERT gene is activated in human cancer cells. In the present study, we examined the hTERT gene copy number in human cancer cell lines and in primary tumor tissues. Amplification of the hTERT gene was observed in 8 of 26 (31%) tumor cell lines and 17 of 58 (30%) primary tumors examined (8 of 21 lung tumors, 3 of 10 cervical tumors, 5 of 19 breast carcinomas, and 1 of 8 neuroblastomas). In addition, 13 of 26 (50%) cell lines and 13 of 58 (22%) primary tumors displayed gain of hTERT gene copies with 3-4 copies/cell. The present findings imply that the hTERT locus may be a frequent target for amplification during tumorigenesis and that this genetic event probably contributes to the dysregulation of telomerase activity occurring in human tumors.