טכניון מכון טכנולוגי לישראל
הטכניון מכון טכנולוגי לישראל - בית הספר ללימודי מוסמכים  
Ph.D Thesis
Ph.D StudentTanhum-Zodik Iris
SubjectInstructional Examples in Mathematics: Teachers' Modes of
Use and Learning Opportunities
DepartmentDepartment of Education in Science and Technology
Supervisor Professor Orit Zaslavsky
Full Thesis text - in Hebrew Full thesis text - Hebrew Version


Abstract

The main goal of the study is to characterize teachers' choice and use of examples in and for the mathematics classroom. In addition, its goal is to trace teachers’ learning opportunities while using examples, and the contribution of these opportunities to their knowledge and experience. 

The study can be seen as a collection of 5 interrelated case studies of teachers. The participants of the study were five experienced secondary teachers (with at least 10 years of mathematics teaching), who taught classes of different grade level and achievement level. The data collected included 54 observed and documented lessons.

In all the observations, altogether 604 teacher-generated examples were identified opposed to only 35 student-generated examples. This suggests that the lessons observed were rather teacher-centred. The findings refer only to the teacher-generated examples. They point to six types of considerations that teachers employed in selecting or generating instructional examples. It should be noted that despite the variety of considerations, the use of examples appeared to be rather conventional. Only few cases can be seen as unique or creative in generating and using examples.

Throughout the classroom observations it became clear that some of the examples teachers use are planned in advance (i.e., pre-planned (317)) while others are chosen or constructed on their feet either in response to classroom interactions or as part of the way they plan to conduct the lesson (i.e. spontaneous examples (287)).

Some of the observations captured moments of teacher-learning. These moments form a collection of learning opportunities for teachers, in the course of dealing with examples. The analysis of the nature and conditions of these learning opportunities sheds light on ways in which teachers' craft knowledge develops.

A conceptual model was built as a result of reflection on the findings. The model describes the interconnections between teachers' knowledge, their personal example spaces, their lesson plan with a focus on their choice of examples, their interactions with students leading to possible learning events for teachers.  

The significance and contribution of this study is in expanding the theoretical knowledge on examples by characterizing the ways of choosing and using examples in teaching mathematics. It provides a model that sheds light on the dynamics of the process. The rich collection of observations that includes numerous example-related classroom events could be turned into simulations of practice-based cases and serve for teacher education and professional development activities.