Creating a New Vision for Public Education in Texas challenges us with a premise within The New Learning Standards in which all students have access in all content areas to rigorous curriculum:
II.k When competent, caring teachers provide properly designed learning experiences in inspiring social environments, all students will engage and can meet or exceed a reasonable variance to the standards.
With this, mathematics educators ask themselves: How does my lesson design foster a safe environment in which students are willing to take risks and engage in challenging curriculum? The challenge of all students engaging in mathematics greatly impacts lesson design. How can we design learning experiences in which all students can actively participate and be inspired to solve problems?
Kathy Struck, 5th grade mathematics educator at Denton Creek Elementary in Coppell ISD has this image displayed in her classroom for her students:
The image, from Yummy Math’s task, Canstruction, is presented in a 3-Act style:
- Act One: Take a look at the pic. What questions come to mind?
- Act Two: How many cans does it take to build this structure? What information do you need to determine this? How did you determine your solution? What else did you notice that is mathematical?
- Act Three: [this is when the solution is shared and compared to the students’ work.]
Three Act Mathematical Tasks, described by Dan Meyer include:
- Act One: Introduce the central conflict of your story/task clearly, visually, viscerally, using as few words as possible.
- Act Two: The protagonist/student overcomes obstacles, looks for resources, and develops new tools.
- Act Three: Resolve the conflict and set up a sequel/extension.
Three Act Mathematical Tasks such as Canstruction provide opportunities for all learners to engage in the problem. When there are multiple entry points to solve a problem, we refer to the problem as having a low floor-high ceiling. NRICH Maths refers to these as Low Threshold High Ceiling Tasks (LTHC):
A LTHC mathematical activity is one which pretty well everyone in the group can begin, and then work on at their own level of engagement, but which has lots of possibilities for the participants to do much more challenging mathematics.
More Three Act Mathematical Tasks from these authors:
- Dane Ehlert
- Graham Fletcher
- Nathan Kraft
- Mike Wiernicki
- Organized by National Council of Supervisors of Mathematics
For the latest in Mrs. Struck’s class, follow her on Twitter: @kstruck5c