טכניון מכון טכנולוגי לישראל
הטכניון מכון טכנולוגי לישראל - בית הספר ללימודי מוסמכים  
Ph.D Thesis
Ph.D StudentDolev Lea
SubjectConsiderations in the Design of Learning Tasks for Teachers:
The Case of Classification of Mathematical Items
DepartmentDepartment of Education in Science and Technology
Supervisors Professor Boris Koichu
Professor Orit Zaslavsky
Full Thesis text - in Hebrew Full thesis text - Hebrew Version


Abstract

The present research had two interrelated goals: one was to characterize teachers' activities when performing classifications tasks involving mathematical items and the second was to identify design considerations of classification tasks as a learning tool. A classification task involves a set of cards containing examples of mathematical items which the learners are asked to divide into sub-sets according to various criteria. During the first stage of the present research, the teachers were given a classification task that included a set of examples of graphs and algebraic expressions. Later on, in three subsequent stages, teachers were given three versions of a classification task involving loci of points. In all, 140 classifications were collected that were offered by 128 mathematics teachers working in 37 teams. The research was conducted according to the design-based research approach.

The main findings indicate that teachers offered classifications according to varied mathematical criteria. The initial classifications were usually based on surface feature of the mathematical items, while subsequent classifications relied on implicit features of the items. When developing such classifications, learners located features that were common to different mathematical items, i.e. they connected different mathematical items. The small number of classifications of this kind indicates a difficulty in identifying more than one mathematical concept in the same example (in the same item). Furthermore, it was noted that during the classification activity, teachers did not always take advantage of the transitions between different mathematical representations (verbal, graphic, symbolic).

The research reveals that the variance in the teachers' level of mathematical knowledge was not mirrored in the activity: teachers who specialized in high-level high-school mathematics offered both valid and invalid classifications and focused on mathematical topics similar to those offered by junior high school teachers.

As for design considerations, it was found that removing the graphic and symbolic items from the collection led to more profound classifications involving the verbal representations. .

The research suggests that the connected view of mathematics should indeed be addressed in professional development programs among mathematics teachers with different levels of mathematical knowledge. The research also makes a theoretical contribution that is manifested in the conceptual organization structure developed for the design of the research tasks, which emphasizes the importance of learning tasks in refreshing new perspectives on the body of mathematical knowledge. Such a structure can serve in the design of varied learning tasks for teachers.