Consensus Report on High Order Mathematics

As problems in the 21st century become more complex, their solutions require the use of sophisticated, quantitative modeling and high-order thinking. As a result, the importance of studying mathematics in Israeli schools is as important as ever. Many surveys and focus groups reveal that students are convinced of the importance of studying mathematics to their future lives. However, at the same time, when asked about their curiosity and affinity for mathematics, many students claim that they lose interest at a relatively early stage.

A recently published State Comptroller’s Report explained this phenomenon as a mismatch between the mathematics taught in school and the mathematics experienced and needed in life. Specifically, students in excellence tracks study only formal and abstract mathematics and as a result, they are ill prepared to solve real-life complex problems by using data, algorithms and mathematical models. The PISA research demonstrates this failure for 15-year-old students, and the PIAAC research for adults reveals that they do not overcome this hurdle even later in life.

The Trump Foundation works to cross this bridge, advocating for high order mathematics that encompasses both abstract and applied mathematics. In high school, the focus at the five-unit level is on the abstract, whereas in middle school, the learning process concentrates on applied mathematics. However, taking a broader perspective for the long term, Israel’s mathematics education must find an adequate balance between these various approaches. In order for such a combination to occur, the local professional community should reach practical understandings.

The University of Haifa proposes to address this need by convening a series of discussions. The university’s Department of Education is suited to the task. It is the largest education department in Israel and home to the National Center for Mathematics Teachers, which operates most of the professional development for mathematics teachers in Israel. Its researchers, under Dean Roza Leikin, are involved in innovative development efforts, currently focusing on applied mathematics and creative thinking for middle schools. Recently, the department was ranked in the top 75 in world by the Shanghai index (higher than Oxford and Cambridge).

The university plans a collaborative study to produce a framework for mathematics teaching in Israel for the next decade. The process will include a literature review of key concepts and approaches, consultations with local and international experts and with teachers, local authorities and government officials. A steering committee led by Dean Leikin will lead the process, with the possible participation of distinguished scholars such as Zbigniew Marciniak from Poland, Merrilyn Goos from Ireland, Avi Berman from the Technion and Dina Tirosh from Tel Aviv University.

The proposed study will seek to address the following questions: What constitutes high order mathematical thinking, what are its basic building blocks (e.g., abstract, applied, creative, critical, analytic, etc.) and, how can they be learned, taught and measured?; What strategies could be implemented to advance high order mathematical thinking in Israeli secondary schools (e.g., writing standards, developing materials, training teachers, convening conferences, publications, advising on policy, etc.)?

Answers to these questions will drive the preparation of a consensus framework document that would articulate insights and agreements. It will also seek to recommend how to advocate for the implementation of the planned framework. The university is considering creating a knowledge center around these themes and therefore, the study will also address the following questions:

1. What could the University of Haifa take upon itself in order to further promote high order mathematical thinking in secondary schools?
2. In creating a knowledge center, which are relevant entities in Israel (particularly government and universities) and abroad with whom it would be necessary to develop professional and financial cooperation?
3. What are the next steps the university plans to take in defining a vision, objectives, targets, metrics, actions, collaborations, budget, funding sources, and timetable for setting up a knowledge center?

* The text above shows the grant as approved by the Foundation’s Board of Directors / Grant 442