This post shares instructional strategies for the design and implementation of group-worthy tasks and for balancing differentiation and rigor in heterogeneous mathematics classrooms.
How do you engage gifted learners with varying levels of mathematics preparation in group tasks? How can we use group tasks to counteract the labels students bring regarding their math ability or aptitude?
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Embracing the challenge of varying backgrounds in mathematics
Our classrooms today are heterogeneous in multiple ways, and the multifaceted diversity of each group of students I work with is something that I cherish. With that said, a challenge I consistently face—particularly in classrooms with students of varying mathematical preparation—is in promoting appropriate mathematical rigor for all students. This challenge sparks a differentiation question: How can one engage learners of varying mathematical backgrounds without resorting to grouping strategies that amplify and perpetuate existing inequities in students’ opportunities to learn?
One technique for engaging students of varying mathematical backgrounds is to design and facilitate “groupworthy” tasks. In building on her work with colleagues at Stanford University on Complex Instruction, Rachel Lotan coined the term groupworthy in the early 2000s to describe tasks that are
- centered around a meaningful disciplinary idea,
- complex and open-ended, with several starting points, and
- contingent upon the input of multiple students (i.e., require interdependence).
Such tasks should have built-in mechanisms for keeping individuals and groups accountable for the group’s final product.
As a part of the practice of Complex Instruction, groupworthy tasks aim to promote disciplinary rigor for students of varying mathematical backgrounds while simultaneously reducing, rather than reinforcing, gaps in students’ opportunities to learn meaningful mathematics. The latter point concerns equity, and matters for all students, including those who are gifted and talented!
From groupwork to groupworthy
Indeed, many of us have likely participated in—or facilitated—group assignments or projects where one student did most of the work, while others watched from the sidelines. This dynamic often leads one group member to be frustrated that their group members did not do more, and others resentful that they could not help more. Gifted and talented students can fall in either of those two categories, depending on the nature of the group and the task itself. Indeed, if we simply hand worksheets to students to complete in groups, it should come as little surprise if such dynamics emerge.
Groupworthy tasks center around meaningful content or problems so they engage more learners. By being complex and having several starting points, they allow for students’ diverse strengths to benefit the group, and by having built-in mechanisms for individual and group accountability, they keep students’ eyes on the group’s collective success.
So if this all sounds great, a natural question is, “Where do I get started?”
Creating groupworthy tasks can be difficult, and my primary suggestion is to take things slowly as you get started. I will be among the first to admit that not all of the collaborative assignments I facilitate for students are truly groupworthy. And that’s okay—change takes time. Furthermore, not all assignments can even be groupworthy, especially in a mathematics course. Part of the challenge, then, is in identifying tasks that have the potential to be groupworthy, and building or modifying from there. Below are questions to think about as you get started.
Reflection questions for getting started
1. Why am I placing students in groups for this assignment or project?
There are myriad reasons that we place students in groups in day-to-day mathematics teaching. We believe students can assist one another if they get stuck on a problem. We know that the workforce requires good collaborators. If the group turns in one assignment, there’s also less grading. All of these reasons, among others, are legitimate rationale for having students work with one another. But do we typically think about status and how that might influence the way we design group tasks?
The practice of Complex Instruction is predicated on the notion that students always have some status in the classroom; that is, they tend to be viewed as either “good” or “bad” at a subject, and such labeling influences how they are positioned within groups. By promoting multiple entry points, multiple representations of the material, and multiple strengths of students, groupworthy tasks aim to counteract the labels that students often come into the classroom with.
As you reflect on the activities or assignments that you already have, consider how they might serve to amplify or reduce status issues. If they are likely amplifying students’ existing status in the classroom as “good” or “bad” at the subject, then it might be time to modify the assignment! The reflection below includes one strategy for doing this.
2. What strengths does this assignment rely on for successful completion?
One of the things I love about working with gifted and talented students is the diverse strengths that they bring to the classroom. Groupworthy tasks are designed to leverage—indeed, require—these strengths. Though mathematics is often viewed in popular discourse as a subject concerned with getting correct answers, and standardized tests tend to not help in dispelling this myth, the collaborative assignments that we design can still encourage a plurality of competencies and strategies for success in engaging in mathematics.
By actively attending to multiple routes and strengths for success in an assignment, we can shift what it means for students to be “good” or “bad” at mathematics. To borrow language from Jo Boaler of Stanford University, we can shift students’ mathematical mindsets.
As an example, consider a seventh-grade lesson where the objective is for students to develop a robust understanding of the relationships between side-length parameters and the surface area and volume for a rectangular prism. One route for having students learn the material would be to have them compute the surface area and volume for a variety of rectangular prisms. Would success in such an assignment, though, require more than computation?
An alternative route might be to have students (in groups) generate a theory about the relationships between the parameters, surface area, and volume, in as many ways that they can, the idea being that they are to present some sort of sales pitch to a company’s marketing team for a new box design. The theory they generate should be accessible to a lay audience (i.e., the marketing team). As a part of the assignment, one could create task cards that provide each group member with a core responsibility in relation to the assignment that they are responsible for. The responsibilities need not be just the typical ones like record keeper, facilitator, etc.; instead, they might include different box requirements or presentation aspects that each group member is responsible for. Of course, the route mentioned here (in contrast to the simpler one mentioned first) would involve more time and supports for students. Nonetheless, if designed appropriately, it could be more meaningful, mathematically rich, and conducive to a host of skills (e.g., technological, entrepreneurial, spatial, etc.) important to the core task.
Another example, slightly different with respect to the type of product students generate, comes from my teaching of Advanced Mathematical Problem Solving with TIP’s eStudies program. Each week in the seven-week course, students tackle a brain teaser in groups, and present their findings in the form of a paper, slideshow, or video, among other possibilities. A challenge I have had with designing brainteasers in the past (and that still comes up) is to ensure that all students in a group are both able and nudged to contribute in a meaningful way. In noticing that some students enjoyed the technical aspect of writing up the work, whereas others excelled in organizing the group or verbally sharing their results, I decided to formalize those strengths into formal roles for a brain teaser this past summer. For the last brainteaser of the course this past year, the task was for students to create a screencast explaining the group’s solution. There were several important elements students had to consider in creating a screencast (e.g., writing the equations in Google Documents or LaTeX, creating a script for the screencast), each of which required the student to understand the mathematics involved. Allowing students to choose their role appeared to make them more excited to complete the brainteaser. It also demonstrated that there are multiple means of being talented in mathematics.
3. How am I assessing students, both as individuals and as a collective?
As alluded to in the text and tasks above, interdependence is a key characteristic of groupworthy tasks. Students should ultimately rely upon one another to develop the group’s final product—whatever that product may be.
To keep students accountable as individuals, consider having them write brief reports about their experience in completing the assignment. Given the right prompt, the report need not merely be one about “who did what.” Instead, one can have students reflect on the assignment itself, and metacognitively about they might improve their work as collaborators in the future. The following prompt is one that I have used in the past to engage students in meaningful reflection that illuminates for me how they contributed to their group’s product:
- What did you learn about ____ as you worked with your group members on ____?
- Was the process of working in a group challenging for you? Why or why not?
- If you were to work with this team in the future, what might you do differently?
- If you were to help develop a “best practices” guide for someone working in a team on an assignment like this in the future, what are two tips you would you include in it, and why?
Elizabeth Cohen and Rachel Lotan (among others involved in conceptualizing Complex Instruction) also suggest that one use rubrics—or some form of clear expectations—for the group’s product, too.
Developing groupworthy tasks is an exciting challenge for educators. It requires us to think about the diverse strengths that our students bring to the table, and in relation, the diverse ways that one can be “good” at mathematics. Though designing new tasks or adapting existing ones is a work-intensive endeavor, it becomes easier over time. But the payoff is worth it.
Students of all prior preparation levels are more likely to be engaged with the material, and those in gifted and talented programs are likely to find both cognitive and social challenge in collaborating in a context where collaboration actually matters.
For readers: How do you engage gifted learners with varying levels of mathematics preparation in your discipline? How can we use group tasks to counteract the labels students bring regarding their math ability or aptitude?
Boaler, J. (2015). Mathematical mindsets: Unleashing students’ potential through creative math, inspiring messages and innovative teaching. John Wiley & Sons.
Cohen, E. G., & Lotan, R. A. (2014). Designing Groupwork: Strategies for the Heterogeneous Classroom Third Edition. Teachers College Press.
Featherstone, H., Crespo, S., Jilk, L. M., Oslund, J. A., Parks, A. N., & Wood, M. B. (2011). Smarter together! Collaboration and equity in the elementary math classroom. Reston, VA: National Council of Teachers of Mathematics.
Lotan, R. A. (2003). Group-worthy tasks. Educational Leadership, 60(6), 72-75.