HOW DO WORKING ON MATHEMATICALLY CHALLENGING TASKS AND DIFFERENTIATION PLAY OUT IN MODULE 2

Lesson planning is at the heart of successful teaching. Several scholars highlight the role of good planning, by arguing that it determines the resources a teacher can draw upon while trying to be attentive to the subject matter and the students; several scholars also emphasize its contribution to quality teaching (e.g., Lampert, 2001; Nilsson, 2009; Reynolds, 1992). In this respect, selecting, analyzing and modifying challenging tasks during lesson planning sets the ground for engaging all students in mathematically challenging work during teaching. In this context, the purpose of the current module is to help teachers improve their knowledge and skills in selecting and analyzing/modifying challenging mathematics tasks for all their students.

The module consists of three Cases of Practice. Analytically, in Case of Practice 1, entitled “Planning a Lesson: Selecting and Analyzing Mathematically Challenging Tasks”, teachers are first encouraged to consider what makes a task challenging by analyzing it and identifying its level of mathematical challenge as it originally appears in the curriculum materials and as it is enacted during teaching. Next, in Case of Practice 2 (that is, Planning for Differentiation: Considering the Task for Different Students) attention is centered on tasks per se, and teachers are expected to go deeper into identifying what makes a task mathematically challenging for different groups of students; they are also provided with opportunities to discuss how the mathematical challenge of a task can be adjusted to ensure that students are mathematically challenged at an appropriate level. After that, in Case of Practice 3 (i.e, “Planning for Differentiation: Bringing Considerations of my Students Into the Picture”) factors related to students which have been put at the background in Case of Practice 2 are brought to the forefront and teachers are encouraged and supported to consider some tools which will help them in thinking and analyzing student prior knowledge. They are also scaffolded to anticipate possible student alternative conceptions and solutions during the lesson planning phase; doing so is expected to help teachers become more prepared to capitalize on such conceptions and solutions should they arise during the lesson.

Participants of Module 2 are expected to be familiar with the dual goal of engaging all students in mathematically challenging work through the work they will have already done in Module 1. In Module 1, the work around this dual goal was organized around three categories, which correspond to lesson planning, student autonomous work, and whole-class discussion; these three phases are considered as three key parts, where the enactment of mathematically challenging tasks and differentiation can take place. Building on the work that will have been done in the introductory Module 1, participants of Module 2 will delve deeper into issues related to mathematically challenging tasks and differentiation during lesson planning. The remaining modules pertain to the other two phases of the lesson implementation (students’ autonomous work – Module 3; and whole-class discussion – Module 4), and to establishing a culture that fosters mathematical challenge and differentiation (Module 5).