From What iS? to What iF?

To open opportunities for students’ math reasoning, change the questions.

Instead of What iS? Ask What iF?

The questions look similar. Yet they imply very different responses.

  • What iS? “Give an answer”
  • What iF? “Consider the possibilities”

Too often, students experience math as a pursuit of “What iS?” rather than an exploration of “What iF?

Take graphs and functions for example,

  • What iS a graph of a function?
  • What iF a graph represents a function?

The first question implies that students should give an answer – a graph of a function. The second question implies that students consider possibilities for graphs that represent functions.

Questions communicate what gets privileged.

Rather than just telling students that their math reasoning is important, ask questions that privilege reasoning rather than answer finding.

The Same Situation. Two Different Graphs.

Students have many opportunities to use different types of representations to show the same relationship between variables (e.g., graphs, tables, equations).

Students also benefit from opportunities to use different forms of the same type of representation (two different looking graphs) to show the same relationship between variables.

Wonder how that can be?

Check out this Desmos Toy Car Activity.

The Toy Car

Students explore how each variable changes, then they sketch different graphs to represent the same relationship between variables.

Students might be surprised that the sliders stay on the vertical and horizontal axes. When only one variable is changing, a line is sufficient to represent that change.

Graphs can be more meaningful for students when they understand what the variables are measuring. To begin, ask students how they might measure the toy car’s total distance traveled and the toy car’s total distance from the shrub.

Students’ reasoning is more important than the accuracy of their graphs. Encourage students to question, explore, and discover!