Module 1 is introductory to this set of the five modules. Its purpose is to help teachers familiarize themselves with the goal of engaging all students in mathematically challenging work—a goal that can be decomposed into two parts: working with challenging tasks and differentiating instruction. Toward this end, Module 1 consists of three cases of practice for each of the two educational levels, (Pre-)primary and Secondary. The Cases of Practice provide activities and examples of how it looks when teachers begin their professional journey toward trying to engage all their students in mathematically challenging tasks and also, offer opportunities for analyzing practices and principles that support such work. Specifically, the first Case of Practice, entitled “Focusing on Mathematicaly Challenging Tasks”, will help teachers to consider what it means and what it is entailed in working with challenging mathematical tasks. Next, in Case of Practice 2, “Differentiating Instruction to Meet Students of Different Levels”, teachers will consider how, they can differentiate their work to meet students of different readiness/ability levels. Finally, in Case of Practice 3, “Concurrently Attending to the Work around Mathematically Challenging Tasks and Issues of Differentiation”, the two aspects of the aforementioned goal will be brought together; the case has been designed to help teachers understand that these two goals can work synergistically and should not be thought in opposition to each other.

There are several ways in which mathematically challenging tasks and differentiation interact with each other that will be further analyzed in each of the four individual modules that follow. Module 1 is intended to help teachers get a glimpse of the importance of selecting challenging tasks in their lessons and also, maintaining the level of challenge throughout task enactment; the issue of selecting and analyzing mathematically challenging tasks is analyzed in more detail in Module 2. Furthermore, the current module clarifies what differentiation is and what is not by surfacing difficulties and misconceptions around differentiation and creating a platform for discussing key differentiation practices with teachers. Although differentiation feels risky for many teachers and involves developing and refining a complex set of skills over a long period of time, this module purports to help teachers understand that differentiation is attainable when time and support are provided and that it is an integral aspect of instruction. Module 1 also aims to initiate a discussion about the potential of the two goals—working on mathematically challenging tasks and differentiation—working synergistically to each other. Although there are several ways this could be achieved—which are discussed in more detail in the remaining four modules—we decided to focus on the example of questioning which represents a crucial aspect of teaching and which can help enhance the harmonious functioning of the aforementioned dual goal. However, more about the role of questioning in supporting students work and mathematical thinking is provided in Module 3.