Eliane Stampfer just finished giving a talk called A Difficulty Factors Assessment of Fraction Representations. One small vignette: you can’t always assume your students have enough background knowledge to handle an assignment, even if that background knowledge is mind-numbingly basic.
For example, in a study on students’ ability to solve fraction equivalences and additions with and without illustrative pictures, it turned out that many students- about 20%- interpreted the equals sign ‘=’ as “write your answer here”, not as “the left side is the same amount as the right side.” So even on the most dead-simple equivalences, those students provided incorrect answers. And these were fifth and sixth graders, not kindergarteners! How many literate adults do you think there are who don’t understand what an equals sign means? Could it be as high as 20%? The thought is stunning.
I don’t think Eliane mentioned this term, but the phenomenon of teachers missing these super-basic stumbling blocks is known as the “expert blind spot”. It’s something you need to be wary of any time there’s a computerized tutor or intervention of some kind. Any system which is going to be deployed to more than a handful of students really needs to be piloted to find out where these super-basic misunderstandings and mistakes creep in. If you don’t catch them before deployment, you risk a massive flop as students struggle in ways the system isn’t designed to cope with.
Here’s an example from my own experience: I made a vocabulary tutor program for ESL students, and the design of the tutor assumed that students would be able to correctly spell the words they learned. Arabic speakers have severe and persistent difficulties spelling English words, however, so my Arabic-speaking students quickly became frustrated that their correct words were being rejected due to incorrect spelling. The point of the tutor was not to train spelling abilities, so this was a very unfortunate problem! I felt very bad for my students, but it was a valuable learning experience for me. I’ll be careful not to make the same mistake again!