Program for learning modeling and reasoning skills in real life contexts

High-order mathematical thinking requires deep mathematical knowledge and an arsenal of skills. Among these skills are the ability to devise mathematical models and to reason the choices and decisions the student made by applying mathematical arguments. These skills can be applied both in solving complex abstract problems, as required by the five-units track in high school, as well as in dealing with real-life contexts, as it is entailed by the 5-6 levels of the PISA mathematics framework.

Nevertheless, the middle school curriculum in Israel in mathematics sidelines these skills. Its focus is on building a solid foundation of knowledge and technique that is also needed for high school. As a result, many middle school students are not sufficiently prepared to tackle complex mathematical problems, both in pure and abstract mathematical context, and especially when applying mathematical knowledge in other fields, such as science and technology.

As part of the foundation’s effort to seed the development of instructional material that would concentrate on mathematical modeling and reasoning, we approached Ruhama Even of the Weizmann Institute of Science. Even is a veteran partner of the foundation in a program that created diagnostics tasks to prepare students for five-unit mathematics. During this program, Even identified that students lack the modeling and reasoning skills and recommended to the Ministry of Education to integrate them in the curriculum.

Now, Even is proposing a new program that will focus on the instruction of modeling and reasoning skills in real-life contexts. The program will include 15 study units of various aspects of mathematical modeling (e.g., constraints, equations, functions and defining variables) and argumentation (e.g., identifying data, deriving conclusions and mathematical reasoning) that are required in order to solve complex problems. The study units will be characterized by a rich theme, multiple variables and constraints, and integration of different strategies and skills.

The units will be developed in Hebrew and Arabic, aligned with both the 9^th grade curriculum and the 5-6 levels of the PISA framework. The success of the program will be measured by at least 80% of the participating students meeting the 5-6 levels of PISA in a diagnostic test, developed by CET.

* The text presented above shows the grant as approved by the Foundation Board / Grant 420