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Sequencing

Anticipating students’ solutions to a mathematics taskMonitoring students’ in-class work on the taskSelecting student strategies and students to share themSequencing students’ solutions purposefullyConnecting students’ approaches & the underlying math

"As educators plan student learning experiences, it is important to focus on student understanding and sense making, the interconnectedness of the categories, and the application of skills in problem-solving contexts both in and outside the classroom."

– Focusing on the Fundamentals of Math – A Teacher’s Guide, p.4

In what order is it best to sequence student solutions that are shared? Why?

The purpose of the discussion is to examine the mathematics in the goal of the lesson. Careful selection of work is important but also careful sequencing of that work. For example, presenting the strategy that most students did before those that few students did promotes more students taking part at the beginning of the discussion. Or the teacher may present more concrete strategies before abstract ones as this allows for connections between simple and sophisticated strategies. Or you, the educator, may choose to present misconceptions first, especially if common, so that the misconception is addressed then applied to a correct solution.

An educator’s flexibility in the sequencing approach can support the learning goal. This is NOT show and tell, rather, this is scaffolding.

The educator is leading this discussion, thinking back to the goal of the lesson and the anticipated responses, to bring out the big ideas in the math for this task. What do you want students to take away from this? Sequence the solutions to build on student thinking.

Here is a possible sequence for the caterpillars and leaves student solutions:

Martin (scaling up by collecting sets—picture),
Jamal (scaling up—table),
Janine (unit rate—picture/written explanation);
and Jason (scale factor—written explanation).

This ordering begins with the least sophisticated representation (a picture) of the least sophisticated strategy (scaling up by collecting sets) and ends with the most sophisticated strategy (scale factor), a sequencing that would help with the goal of accessibility.

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