An evaluation of individualized instruction in mathematics in an apprenticeship program at the College of Trades and Technology

The purpose of the study was to evaluate individualized instruction in mathematics in the Beauty Culture apprenticeship program at the College of Trades and Technology. Stake’s model was used as the basis for evaluating the program. Seven variables were of particular inte3rest in this study: (1) the Beauty Culture students, (2) the nature of the mathematics curriculum, (3) the instructional materials and facilities, (4) the instructional activities, (5) time allocation, (6) achievement on the first writing of the final exam for each module, and (7) the number of students completing the entire program. -- Information and data about these seven variables were collected from a sample of 12 students employing the following techniques: observations by the investigator, formative and summative examination results, expectations of the trade theory instructor and a mathematics instructor, and the Beauty Culture course outline in use at the time. -- The students were 12 Beauty Culture apprenticeship students who had completed a 9 month pre-employment program and had returned for 8 weeks further schooling. They had all been working for a minimum of 50 weeks. In addition, the average age of the group was found to be 22.8 years. -- The curriculum was based on the Beauty Culture field with as much emphasis as possible on basic business practices. This was found to be consistent with what was expected (intents) and intended (standards). -- The instructional materials consisted of seven modules, 52 formative examinations, and 14 summative examinations, all of which were developed by the investigator specifically for this study. The facilities consisted of a typical classroom with individual student desks. -- The instructional methodology used in this study was individualized instruction, which was what was expected and intended. -- The time allotment of 16 hours working in class and 16 hours working out of class was considered to be sufficient. However, it was noted that students should not devote too much time to the easier modules at the beginning and neglect those that follow. -- It was found that at least 80% of the students succeeded on the first writing of the final examination for Modules 1 to 4 only, while at least 70% succeeded on the first writing of all seven modules. These results were consistent with what was intended for the first four modules, but were consistent with the defined standard of at least a 50% success rate for all seven modules. -- It was observed that, while 100% of the students completed the first four modules, only 67% completed all seven. These findings were inconsistent with what was intended (90%) and what was expected (80%). -- Six major recommendations were presented. The first suggested that 50%, and not 80%, of the students be intended to succeed on the first writing of each summative examination. The second recommendation stated that most students should do only half the exercises in the first two modules, thereby leaving more time to work on the remaining modules. It was next recommended that an assistant be provided to help with clerical duties. The fourth recommendation was that class size be limited to 15 students. The fifth recommendation was to study the feasibility of individualized instruction in other areas. The final recommendation called for a similar study with regard to the use of computers