When the practice is done

Have a look at this image. 

It’s a pretty standard worksheet, no bells or whistles, just practice of arithmetic*. What I would like you to think about is what you do with it. Of course, you mark it as it has been marked, or something similar, and probably record the results. Maybe you don’t mark them wrong the same way, make your ticks are different. The question is, then what? Does it go back to the learner to correct? Does it get filed into a binder or glued into a notebook? Do you take a digital image of it and store it on the cloud? Do you file it away in a folder for reports or consultation evenings / afternoons? Maybe you think this is a starting point and they will get better with more exposure to teaching or practice in your class.

But maybe, you could use it to inform the learner’s next steps and yours!

Come again? You may say, this is one sheet in a two week plan that I have. This is only one of many pieces of practice that I have planned for addition within 20. How on earth do you expect me to change my plan now? I have deadlines, and targets, and 29 other learners in the class.

Let’s look at the page again, with some annotations this time. 

The annotations, when brought together, might inform you of the following:

  • Addition up to 10 seems OK.
  • Doubles seem to be known but perhaps not understood.
  • ’10’ does not seem to be counted for sums more than 10.
  • I need to talk with the learner about 10 and beyond

Would this be cause to begin your plan again? Well, no, but I hope it would encourage you to look at your next steps to see how you can incorporate a way of showcasing misconceptions like the ones on the worksheet in future lessons. You might miss your deadline, you might, but think about the positive benefits for the learners in your care; think about the positive benefits for you, when you go on to explore subtraction, or other ideas, and you needn’t worry (as much) about similar misconceptions occurring again? Is that worth an extra day or two? I hope so. And, who knows, you might even be able to incorporate exploring the misconceptions within your initial plan without missing a beat.

By approaching practice as more than an exercise in displaying understanding but also a way to gather information for future learning, you can improve both your experience in the classroom, as a guide, and that of the learners with whom you work.

A wise lecturer in math once asked my first year class a great question: what is mathematics? After a number of attempts, the response that came closest, in her mind, was, the study of patterns. As an educator, I feel it is my job to find patterns in learning, which often come from patterns in mistakes. As an educator in math, I feel it is one of my main goals to encourage an awareness of patterns in a) the larger world and b) in the abstract world of forms and figures.

Take the time to do more than mark correct or incorrect! Look for the patterns! Be a mathematician!

*The worksheet was made and shared on OneNote so as to not waste paper and allow me to keep all learner efforts organised and shareable with the home. All feedback here is available to learners and their families wherever they have an internet connection.

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