Cognitive Tools for Learning High-Order Applied Mathematics Tasks

To learn real-world mathematical thinking problems in middle school, a unique skillset is required. These skills are new to both students and teachers in Israel, since in the regular, traditional curriculum the tasks are almost free of the need to make interferences, focusing the students on applying technique and abstract thinking. In contrast, applied tasks are typified by a high verbal load, rich data which at times is irrelevant, multiple representations (tables, graphs), and complex situations of vagueness and uncertainty. When solving such tasks, students need confidence to deal with unfamiliar tasks, to shift from spatial information to mathematical language and to move smoothly from the particular to the general.

In order to support students and teachers in this transition, the foundation turned to Orly Rubinsten, an expert in mathematical cognition from the University of Haifa. Rubinsten’s research indicates that the acquisition and performance of mathematical skills are also influenced by cognitive skills. These skills include the ability to focus on the task without losing confidence, to plan the process of finding the solution within a large verbal load, and to identify the right information required to solve the problem.

Rubinsten is proposing a pilot program that will develop tools tailored specifically for dealing with cognitive skills required when solving applied mathematics tasks. It will include building attentive control, which is the ability to pay attention to small details, and monitor and filter the information provided in the task. Another element is emotional regulation, the skill to deal with the effects of stress arising as a result of uncertainty. Teachers will have the students ask themselves questions related to emotional regulation, so that they understand what happens to them when working on problems and facing uncertainty.

The tools will be integrated with 12 real-life context tasks at PISA proficiency levels 5-6, which are complex, challenging and allow for errors. The tasks will be developed in collaboration with Gali Shimoni of the Israel Center for Excellence through Education, who is an experienced developer of mathematics tasks at the PISA proficiency levels 5-6 The tasks will be presented in an online training booklet for the students to work on in class, as well as a separate booklet for the teachers that will also include explanations on how to teach the tasks.

The pilot program will commence with five teachers who will also be part of the development team. The teachers will participate in a course of 30 hours during which they will be exposed to the tasks and practice using the tools. Each teacher will receive instructional coaching once every two weeks by the development team, which will observe the teachers and give them feedback. The success of the program will be measured by a diagnostic tool developed by the program development team as well as a diagnostic test developed by CET, which will assess the students’ mathematical performance in alignment with the 5-6 levels of PISA in mathematics. The goal is for 80% of the students to pass the test.

* The text above shows the grant as approved by the Foundation’s Board of Directors / Grant 489