The operational curricula of mathematics 8 teachers in British Columbia
Creators: name: Dirks, Michael Karel
Publisher: name: University of British Columbia
Year: 2010

description: The purpose of this study was to describe the mathematics curricula as actually implemented by a sample of Mathematics 8 teachers in British Columbia. A survey of previous research indicated that knowledge about the mathematics subject matter which teachers present to their students and the interpretations which teachers give to that subject matter is sparse in spite of the importance such knowledge might have for the curriculum revision process, textbook selection, the identification of inservice education needs, and the interpretation of student achievement results. The Mathematics 8 curriculum was divided into three content areas: arithmetic, algebra, and geometry. Within these content areas a total of 16 topics were identified as among the basic topics of the formal Mathematics 8. course. Four variables were identified as representing important aspects of a mathematics curriculum. The first of these, content emphasis, was defined as a function of the amount of time a teacher spent on each content area. The other three variables, mode of content representation, rule-orientedness of instruction, and diversity of instruction, were defined as functions of the content-specific methods teachers used to interpret the topics to their students. Class achievement level and the primary textbook were identified as having strong potential relationships with a teacher's operational curriculum. These were used as background variables in this study. The data for this study were collected as part of the Second International Mathematics Study during the 1980/1981 school year. The sample consisted of 93 teachers who submitted five Topic-Specific Questionnaires throughout the school year regarding what they taught to one of their Mathematics 8 classes. Each class took a 40 item pretest at the beginning of the school year. The 27 classes with the highest class means were designated as "high achievement classes" for this study while the 27 classes with the lowest class means were designated as "low achievement classes." Among the findings of this study were: (1) Wide variation existed in the emphasis given by teachers to the three content areas with 60% giving at least one area light or very light emphasis. (2) The median proportion of class time allocated for geometry was slightly higher than for algebra or arithmetic. However, teachers showed the most variation for this content area spending between 0% and 66% of their courses on geometry. (3) In low achievement classes somewhat more time was spent on arithmetic and somewhat less time on geometry than in high achievement classes. (4) Teachers using a text which placed more emphasis on a particular content area tended to spend more time on that content area in their classes. (5) The mode of representation of mathematical content was slightly more abstract than perceptual in general. (6) The median mode of content repesentation varied substantially among topics. (7) Teachers of low achievement classes tended to present mathematics in a slightly more abstract and rule-oriented way than teachers of high achievement classes. (8) A weak positive association was found between the level of diversity in the textbook used and the level of diversity in the operational curricula of teachers using that textbook.