טכניון מכון טכנולוגי לישראל
הטכניון מכון טכנולוגי לישראל - בית הספר ללימודי מוסמכים  
M.Sc Thesis
M.Sc StudentWeingarden Merav
SubjectProfessional Development for Explorative Mathematics
Instruction
DepartmentDepartment of Education in Science and Technology
Supervisor Dr. Einat Heyd-Metzuyanim
Full Thesis text - in Hebrew Full thesis text - Hebrew Version


Abstract

As part of the reform in education that has been taking place in Israel recently, there has also been a change in the rational of the mathematics curriculum. As part of this reform and the transition to 'meaningful learning', which goal is to develop students' ability to think, create and study by themselves, the new mathematics curriculum instructs teachers to teach in a way that the student will understand and think and not just memorize.

This transition to 'meaningful learning' and to instruction that will advance this type of learning is not simple. The teachers need to adapt to different instructional approaches and different teaching methods with which they are not familiar. The main way teachers can familiarize themselves with those instructional approaches and methods is within professional development (PD) efforts. Such PD, in which teachers learn new instructional approaches and practices for teaching exploratively together with attempting to implement these practices in class, has hardly been tried in Israel.   

The kind of instruction that underlies the PD that promotes 'meaningful learning'  has been defined, through the commognitive framework, as explorative mathematics instruction. The main three characteristics of explorative mathematics instruction are: (1) a cognitively demanding task and maintaining its demand throughout the lesson; (2) creation and design of participant frameworks that encourage accountability throughout the classroom discourse, both accountability for mathematical knowledge and its justification and accountability to the learners' community; (3) exposure to different realizations of the mathematical objects to encourage the objectification process.

In this study, I examined the implementation of this kind of PD in Israel and the change (if any) in instruction following the PD. 

The study followed four mathematics teachers of 7th and 8th grades who participated in PD training sessions. As part of the PD, the teachers were asked to implement a lesson according to what was learned in the PD. The four teachers taught, altogether, six lessons. We observed, video recorded and transcribed all lessons. In addition, the teachers were interviewed before and after the lessons, and the lesson planning sessions were recorded. The six lessons were analyzed using three tools. Each tool assessed a specific characteristic of explorative mathematics instruction. (1) Instructional Quality Assessment (IQA) (2) Accountable Talk Coding (AT) (3) Realization Tree Assessment (RTA).

The results of the study showed that, in general, compared with the implementation of a similar PD in the USA, the implementation of the Israeli's PD for explorative mathematics instruction was a success. Most of the teachers succeeded in maintaining the high cognitive demands of the task, encouraged the accountability for reasoning and to the community and exposed their students to different realizations of the mathematical object.

In addition, we observed some change in the instruction of one teacher following the PD. The change in some characteristics of explorative instruction was more prominent (the level of accountability during the discourse). The change in the other characteristics of explorative instruction was subtler (maintaining the cognitive demands of the task and exposing students to various realizations of mathematical objects).