Creating Open Ended Math Questions

Can an open-ended question have only one correct answer? Traditionally, math classes have made extensive use of closed, algorithmic questions. For instance, students might be required to calculate 212 x 5. Not only is there one correct answer (1060), but the faint potential of an open-ended opportunity was generally snuffed out as students completed the algorithm in a predetermined (or closed) fashion. 

Fast forward to present day, and here is an example of a question that some educators are terming open-ended:

How many triangles can you find in the figures below?

This question has one correct answer. This does not mean that the question is unworthy of student effort to solve, but it does not meet the definition of an “open” question.

Closed skills have their place. When practicing my slap shot for hockey, I find it useful to line up pucks in my backyard and practice my shooting accuracy and release. This practice builds my confidence and helps me to shoot the puck autonomously – allowing my brain to be freed up to process other aspects of the game. However, I recognize that this practice in isolationwill not translate to authentic situations in my games. In games, I will be facing open situations. For instance, I will be moving at speed, there will be a defensive player in front of me, probably a back checker as well, and a goalie staring me down – a far cry from shooting at an empty net in my backyard. 

In contrast, if I go to the local rink and watch the junior team practicing, their coach is constantly creating scenarios for the players to work through that emulate on ice situations. Players are evaluated on how they respond and react to 2 v 1 and 3 v 2 rushes – first in practice and finally in games. These drills are open ended – the players have infinite options as to what they will do; they choose when to pass, shoot, fake, drive the net – and they are making these decisions based on what the other players are doing. There is more than one “right way” to be successful. Most importantly, success cannot always be measured in scoring a goal. Sometimes great plays are stymied by great saves and sometimes goals are scored that are not deserved. It is the process that matters more.

How does this relate to math? 

  • Our assessments need to look more like the 3 v 2 on ice rushes (game simulations) than me shooting pucks in my backyard.
  • The performance must be evaluated in context 
  • We need to lean into (celebrate) the subjective nature of assessing process and performance as opposed to outcome
  • Open tasks cannot be assessed by a computer (note contextual and subjective points above); a trained coach or teacher is required

Questions I ask myself as I design open ended math questions:

  • Is this question really open ended?
  • Are there multiple correct answers? 
  • Will I notice and celebrate a variety of approaches to solve the math?
  • Have I created an authentic scenario (or a reasonable facsimile) for my student? 

To read more about my thoughts about open ended math question development and assessment, check out The ANIE (Assessment of Numeracy in Education).

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