Diagnostic assignments will help mathematics students demonstrate their understanding and capabilities, allowing their teachers to work with them to resolve difficulties and misconceptions
Students studying the advanced 5-unit mathematics track in high school face a tremendous challenge. The learning process is highly demanding, it requires continuous effort, and grasping the material entails acquisition of deep knowledge. As the pace of teaching is fast due to the high standards of the curriculum, many students find the mathematics hard to understand, which can lead them to fall behind; and in many cases eventually to drop out.In order to provide students with the support they need on an ongoing basis, their knowledge and reasoning must become visible to their teacher. However this is not a simple task to fulfill, since most teachers hold only anecdotal evidence about students’ learning progress. The final test at the end of the term provides important summative assessment, but for many students, by then it is too late.
Cutting edge programs like the Mathematics Assessment Project (MAP) of Berkeley and Nottingham Universities, funded by the Gates Foundation, or the Silicone Valley Math Initiative (SVMI) of the Noyce Foundation, aim to help solve this issue. These programs have developed diagnostic assignments, which allow students to demonstrate their understanding and abilities in employing mathematical practices, and help their teachers to involve them in resolving their own difficulties and misconceptions.
The teaching style in classrooms in which this methodology is currently used is shifting from a traditional ‘chalk and talk’ instruction to the whole class, towards a more personalized effort that is adapted to the knowledge, pace and learning habits of each individual student. In such classes the students tend to take more responsibility for their own work, to engage in “productive struggle” with challenging tasks, and to learn through interaction.
In order to implement a similar methodology in Israel, the foundation turned to the Weizmann Institute to learn these programs and to plan an Israeli version. In response, Prof. Ruhama Even and Dr. Michal Ayalon have proposed a three-year program which includes the development of 45 diagnostic assignments covering the Israeli tenth grade curriculum of the advanced 5-unit track. The focus on tenth grade is due to the particularly high drop-out rates during or after this school year. The assignments will be developed by a team comprised of mathematics teachers, mathematics education researchers, and experts in evaluation from the National Authority for Measurement and Evaluation in Education. They will collect and analyze the characteristics of student learning and their specific difficulties via comprehensive interviews with a variety teachers, who will also pilot test the assignments in their classrooms.
The pilot test will lead to the development of teaching aids, including a guide of video-taped lessons showcasing the use of diagnostics, examples of student work, and suggestions for how to adapt teaching in accordance with difficulties which were diagnosed. The feedback from the teachers during the pilot phase will also be used in order to fine tune the assignments so that they are better implemented in classrooms.
Following the pilot, the project will embark on an implementation stage, in which the diagnostics assignments will be widely performed in Israeli tenth grade classrooms of the advanced mathematics track. A special website will be available to the professional community, master teachers will be trained to serve as teacher-tutors and professional development conferences and workshops will be offered to teacher-trainers, researchers and teachers.
It is expected that this program, in tandem with several similar programs funded by the foundation, will ultimately encourage a more student-focused teaching which will help teachers understand their students’ thinking and support them towards success in their advanced mathematics class in high school.