The TRF Model for Math Instruction

Author's note: the following is a thinkpiece-in-progress about the Task-Resource-Forum model that I've been using to drive my online instruction. I will be attempting to flesh it out more fully in the coming months. If you have any questions about TRF and how it can best be used, please feel free to reach out to me.

Step 1: Task

Good tasks in mathematics are often problem-focused. Rather than focusing on procedural repetition, these tasks ideally allow multiple entry points for students at different levels and with different backgrounds to approach the problem in the way they are most comfortable. Examples of these tasks are present in the curricula of Interactive Mathematics Program (IMP) and College Prepatory Mathematics (CPM), both of which "organize learning around a series of complex problems," (McCaffrey et al., 2001). These curricula have outperformed traditional lecture-based courses (Bump, 2004) and, in this author's opinion, are more fun than learning from lecture [CITATION NEEDED].

A good task in the math classroom should have the following features:

• Multiple entry points (it should be possible to craft an answer using different sets of tools, skills, or strategies)
• Low Floor, High Ceiling (one can understand the problem and work at solving it even with limited knowledge of the mathematics involved, but many more paths to a solution or more solutions may present themselves as a student gains more knowledge of mathematics; Boaler, 2014; Meyer, 2012)
• Perplexity (the task makes the student curious about a question that math can help them answer; Meyer, 2012)

Step II: Resource

In the traditional, physically-together math classroom, the best step after a question is posed through a task may be to discuss the problem in small groups or as a class. When possible, this is a good idea and will be discussed in Step III below; however, some learning must be asynchronous and it may be best to let students get started on their investigation with a small, valuable, answer-free resource (probably a video, information sheet, or diagram).

Some features of a good resource:

• Small (shorter videos are more engaging, according to Guo et al., 2014; the same goes for a small info sheet instead of a textbook chapter)
• Valuable (the resource is rich with relevant information, containing a "key" that allows the learner to unlock some path towards a solution)
• Answer-free (the resource does NOT directly offer a solution to the task; instead, it may offer a step towards a solution, a mathematical relationship that can help, or an example of an attempted solution)

Step III: Forum

Students must have a space to express and discuss their ideas. This can be accomplished in the physical classroom simply through a class discussion; in the digital classroom, there are options for both synchronous and asynchronous environments.

For synchronous environments, the Forum can be, much like the class discussion, conducted all together over Zoom or a similar meeting platform. Students can discuss their ideas, learn how their peers used the Resource to respond to the Task, and evaluate each other's solutions.

In asynchronous environments, the Forum functions as a discussion board. Possible platforms could include a Google Doc, Google Classroom threads, a Slack channel or Discord server, Flipgrid, or another online discussion platform.

In either environment, the Forum is absolutely necessary as it serves not only as a space for students to refine their ideas, but also as a place for them to connect with each other as peers and with you as a mentor. It is critical for student mental health and to continue to set appropriate norms for the classroom.