Filmed Lessons Demonstrating Effective Teaching

Teaching students how to solve complex applied mathematical problems by using modelling and reasoning skills requires distinct classroom pedagogy. Over the past three years, the foundation has been collaborating with the top educational developers in Israel to prepare new learning assignments that apply these skills and align with the PISA 5-6 proficiency levels. As a result, middle school teachers of excellence classes were preparing to use the new material in their classrooms. Approximately 800 teachers were exposed to the new materials during the past few months by participating in special in-service training programs and professional learning communities.

When trying to bring applied mathematics into their classes, however, many teachers reported genuine difficulties. They discovered that the teaching approach they routinely use is not as effective since it favors more structured learning and guided progress. In contrast, learning how to solve complex problems involves self-learning, independent progress, teamwork and open discourse. The teachers stressed that they need a stronger basis of knowledge in the context area of the assignment and to become more fluent in using statistics, simulations, algorithms and databases. They pointed to the fact that they never witnessed a fellow teacher teaching such tasks and were never exposed to best instructional practices.

To address this gap, we turned to Michal Ayalon of the University of Haifa. Ayalon was previously involved in developing a database of video clips of teaching five-unit mathematics in classes, supported by a grant from the foundation. Teachers subsequently used these clips within their professional development courses in order to improve their instructional practice. Ayalon is now proposing to develop a series of video clips with best teaching practices for applied mathematics in middle school excellence classes. It will include 25 lessons by teachers who implement applied mathematical tasks in line with the 5-6 proficiency levels of PISA.

The lessons will be collected from teachers who take part in programs operated by the foundation’s partners. Their lessons will be carefully analyzed to identify 15 effective teaching practices that promote the learning of applied mathematics. These 15 best practices will include asking questions that promote hypotheses, modelling the hypotheses mathematically and reasoning them out in the real world context; leading a mathematical discussion based on proposals for different solutions and evaluating them.

In addition, a special kit will be prepared with video clips, presenting the context areas in which the applied mathematics is used. The clips and the 15 core practices will then be deployed in various professional development frameworks. One hundred and twenty teachers of high ability groups and excellence classes in middle school will participate in the training that will prepare them to teach applied mathematics by using the designated pedagogy they acquired. All video material and pedagogical tools will be translated into Arabic as well and uploaded to a dedicated website.