We chatted on twitter about this question for a bit. What predictions can you make about the predictions that were made? Click through to check your answers!

It's #mathmistake time! What percent of kids got this right? What was the most common wrong answer? Percent on that? pic.twitter.com/lNbaDxUeXx

— Michael Pershan (@mpershan) August 18, 2014

Here are the results from the 59 students who answered this question on an exam:

How would you give feedback to the students who wrote “infinity”?

Imagine that you were to give feedback to the students who wrote “-3/7.” What feedback would you give?

## 2 replies on “Sum of an Infinite Series”

I’m a bit out of my waters here because it’s been ages since I’ve engaged with this domain with live students, but seeing no other comments to this very interesting prompt, I’ll share some initial ideas.

A crucial rule of feedback is that should be more work for the receiver than the donor (@dylanwiliam). So this is making me think that I want students to make sense of the other answers, or at least one other answer: “A student selected ‘infinity’ for the value of this sum. What were they thinking? What would you say to them?” Another idea is to ask them to work out some partial sums – practice (doing operations with signed rational numbers) with purpose. Or some what-if questions: What if the common ratio were positive? What if the common ratio were -5/4? -4/4? Then this could be used to get them to think about some bounding. (The positive case also can lead to a visual representation. I guess the negative case could also, if you separate odd/negative and even/positive terms — which is actually how I worked it out in the first place.)

I think the common threads through these thoughts of mine is that this is not designed as a diagnostic question: the student answering (A) does not give me a lot of confidence about the degree or kind of their understanding. And so putting effort into feedback seems premature. I like the “icon” approach (described at http://improvingteaching.co.uk/2014/02/09/what-if-you-marked-every-book-every-lesson-reinventing-the-feedback-wheel/ by London history teacher @HFletcherWood): minimize your effort, maximize the prompts for productive student thinking using a previously-seen problem and the concrete supports of other answers and solution paths.

I confess I was tired when solving this and just realized the absolute value of the answer had to be less than 3/4, so the answer had to be A.