On Target?

For example:

Group-worthy problems (Lotan, 2003) support rich connections and rich discourse.

Problems that offer multiple points of access open up the mathematics and the possibilities for engagement.

Problems whose solutions can be achieved using multiple representations similarly open up the mathematics and the possibilities for engagement.

Making things personal – connecting the mathematics with students’ personal interests and history – can be both motivating and mathematically enriching. (See, e.g., Gutstein & Peterson, 2005).

For example:

One can offer an expanded set of linguistic supports for ELLs, which have the property of making the mathematics accessible without over-simplifying the language or content. Techniques include partnering, having students communicate among themselves using their native language, and providing sentence stems that structure classroom discourse in supportive ways. (See Zwiers, Dieckmann, Rutherford-Quach, Daro, Skarin, Weiss, & Malamut,2017, for a very useful list.)

We can work to avoid or minimize activities or participation structures that repeatedly privilege the same subset of students of students (e.g., activities that reward speed over depth, such as timed tests)

As with Dimension 2, we can work to create and maintain a climate of intellectual safety, so students can take risks, see mistakes as learning opportunities, etc.

We can always be alert to participation patterns. Who tends to get engaged, in which circumstances? Who has useful things to say, but seems reluctant to jump in? Noticing specific inequitable participation patterns, e.g. at the beginning of the year a few white male students dominate the conversation, and problem solving about how to counteract these patterns in the short, medium and long term

For example:

We can make more use of participation structures that engage larger numbers of students, such as think/pair/share activities and poster representations with gallery walks. (Particular students can be designated as their group’s “explainers,” staying by their group’s poster to answer questions from the students who are rotating.)

There are arrange of tools we can use to provide the full range of students with opportunities for participation. There are, for example, equity sticks, a cup of popsicle sticks with students’ names on them, from which the teacher picks randomly. There are “whip-arounds,” where students in a small group or whole class have opportunities to speak in turn. There are group structures like “participation chips,” in which students start small group work with a small number of chips to “spend” on discussion turns. When they’re out of turns, they have to wait until everyone has spent their chips before the chips are re-distributed.

Of course, the ways such activities are implemented makes a big difference – we don’t want students to feel that they are put on the spot, but rather, given opportunities to share their understandings in an environment they feel safe in. We and our observation partners can be on the lookout for ways to implement them in ways that support an increasing number of students.

We can work to establish classroom discourse and participation norms, using sentence starters, group roles, etc. The sentence starters (e.g., saying “I disagree (or agree) with that because…” rather than “That’s wrong”) can make a difference, along with attention to tone and affect, noting student confidence, and more.