Productive Struggling in Math

How do we challenge students in our classroom?

Is it through extension problems?  Is is through performance tasks?  Is it through projects?  Is it a discovery problem before the lesson actually begins?

We each challenge our students in various ways - it is good for students to struggle and to challenge themselves.

In the past month, my 7th grade students have been struggling with creating a container using our only 3D printer.  The container had to hold the crayons they created from scratch in their science class.  The math component was being to design a box within a box that fits nicely together.  The creating of the box was not the struggle but it was the 'attending to precision' that was the productive struggling piece.  Students printed their initial boxes and then started to realize that the two boxes did not go nicely together - to much space or they did not fit together.  As students realized their mistakes you could see them be more careful in how they designed the second box and this was seen as they successfully printed their final boxes.

With my 8th graders, the productive struggle has been with volume.  Students were given five different tasks around the concept of volume using cylinders, cones, and spheres.  The task was for students to create two different cylinders with the same volume, two different cones with the same volume and two different spheres with the same volume.  Also they had to create a cylinder and a cone with the same volume; and a cone and sphere with the same volume.  They really struggled with these tasks.  I would ask guiding questions to encourage them to try different methods.  I would encourage them to put numbers into the formulas and determine what happens.  And then it happened.  One group got an answer, then another group got the answer, and then the guiding from these successful groups allowed other groups to also find success.

Productive struggling in a classroom is good for students.  I would suggest generating some possible questions ahead of time to assist students in not giving up.  I would limit the amount of time you allow students to struggle before putting in some scaffolds to assist the students.  A lot of times students will struggle, find success, and then revisit what they have done and realize that there is another better way to solve the problem.  These type of discoveries can rarely be taught but rather discovered by the students.

I encourage you to have your students 'struggle' through meaningful and relevant work so that they can feel success and discover something new about the content and themselves.

Still teaching and loving it,

      Kevin Stott                         

De Anza Middle School