Search

This paper explored (1) the developmental trend of student level of reasoning across grade level in pattern generalization; (2) the mediatory role of task variables in the developmental trend of student level of reasoning within and across tasks; and (3) developmental trend of student level of reasoning associated with strategy use across grade level. A test designed to measure student level of reasoning was given to a sample of 1232 students from grades 4 to 11 from 5 schools in Lebanon. The Structure of the Learned Outcomes or Responses (SOLO) was used as a theoretical model. Results show that student level of reasoning exhibited an increasing trend across clusters of grade levels and that there were several SOLO levels in each cluster of grade levels. Type of task (immediate, near, far) and function type (linear, non-linear) seem to mediate the development of level of reasoning across grade level but the complexity of the task (simple, more complex) did not. Students used several strategies in each cluster of grade levels and the developmental trends of student level of reasoning associated with strategy use were not uniform and varied across clusters of grade levels, thus supporting a neo-Piagetian interpretation of the results. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to explore middle school in-service mathematics teachers' ability (1) to identify and explain students' actions in pattern generalization and (2) to account for the variation in teachers' explanations of students' actions in terms of task and teachers' factors. Two questionnaires were developed: (1) a questionnaire to measure teachers' ability to identify students' actions while finding the nth term in the pattern generalization and (2) a questionnaire to measure teachers' ability to explain students' actions in different tasks. The two questionnaires were given to a sample of 83 middle school in-service mathematics teachers from 22 schools in Lebanon. Analysis of data shows that teachers seemed to have the ability to identify students' actions while finding the nth term in the pattern generalization and that teachers' explanations of students' actions in different tasks are lacking in terms of identifying variable-related counting elements. The results of stepwise multiple regression show that teachers' ability to explain students' actions to find the general term depends on their ability to explain students' step-by-step counting or drawing. [ABSTRACT FROM AUTHOR]