Developing High Order Mathematical Thinking Assignments

A recently commissioned study found out that there are almost no learning materials available to middle school teachers that support high order and applied thinking skills in line with the PISA excellence levels. The mathematics curriculum in middle school is focused on procedural fluency and has almost no room for these advanced skills. Teachers therefore devote most of their efforts to building a strong base of knowledge and technique, and dedicate less time to using mathematics to solve problems in different contexts that are outside the realm of the pure mathematics.

In the PISA exam of 2018, there was a slight drop in Israel’s mathematics excellence rate from 8.9% in 2015 to 8.8% in 2018. Other countries, such as Estonia, Norway, Poland, the UK and the Netherlands have improved significantly in these measures. In these countries, the middle school mathematics curriculum has shifted towards ‘real mathematics’ and ‘mathematical reasoning’, that are at the core of the PISA mathematics framework. In Israel, when the Ministry of Education would want to move in this direction, it would find that the the pool of learning material that supports applied mathematics, is scarce.

To address this need, we approached the University of Haifa, a center for expertise in mathematics teaching and the home of the National Centre for Mathematics Teachers. In recent years, the foundation has assisted projects, which were championed by Roza Leikin, including the professional learning communities for five-unit mathematics teachers (“Five Club”), a community for middle school teachers, and the development of incremental tasks for the five-unit track and for the 7^th-9^th grade classes. Roza Leikin is now working with Marc Applebaum, who has experience in developing PISA items.

They are proposing a program to develop 50 mathematics assignments based on the 5-6 levels of PISA, alongside 75 assignments based on 3-4 levels of PISA. Students will learn through a teaching approach that is practiced in Shanghai, starting with the excellence levels (5-6), in order to develop students’ self-regulated learning, and if needed to use the medium (3-4) level assignments as scaffolding. This approach has proved to be very effective in the development of higher thinking skills. The assignments will build on mathematical content that is part of the 8^th and 9^th grade curriculum and will be implemented in excellence classes across the country.

The assignments will be developed both in Hebrew and Arabic, together with a group of five teachers. Each assignment will include a teachers’ guide with instructions on mathematical knowledge and teaching strategies. Following the first six months of development, 15 teachers will start piloting the assignments in their classrooms. In addition, these teachers will join a teacher leader community with academic guidance to support them with implementation.

In the second and third years, these teachers will lead at least 75 additional teachers in city-based PLCs, where they will focus on teachers’ abilities to teach contextual problems. The progress of students will be measured by a diagnostic test that will be developed specifically for this project.

* The text presented above shows the grant as approved by the Foundation Board / Grant 358