| The way the child is being taught is because the teacher or course administrator has misunderstood the purpose of teaching arithmetic via repeated addition. Repeated addition is relying on the fact that children see the world in a very concrete way and have not started to understand concepts in a more abstract fashion. Thus you use objects to explain concepts, like: every cat has one tail, I have 3 cats so how many tails are there in total? You introduce notation in the class, but I can't see how it is valuable to use an abstract expression like 1x3 without a concrete description of the example of cats and tails. After all, you aren't really teaching repeated addition, you are just using it as scaffolding to provide an insight into multiplication! The fact that the answer given can be shown as wrong has already demonstrated that the child (and parent!) was annoyed because it made little sense to mark it as wrong. It probably caused more harm than good, because now the child questions their understanding of the subject matter, yet ironically they do appear to have grasped the concept! So at this point, the poor pedagogy of the teacher in misusing the counting technique means that the child starts to doubt themselves unnecessarily, they become locked in to a scaffolding technique that will later need to be discarded anyway. When they hit non-integer rational numbers - numbers with decimal points - they aren't going to be able to add these together, instead they will need to grasp that you can scale down numbers if you multiply any rational number between 0 and 1. |
You may be right. This is the interesting part of the discussion, and you've framed it well. I think it can be scaffolding technique also for the application of definitions, the expansion of symbols to their definition. Perhaps there is a better way to say that (or other examples), but the point is that I don't think that the exclusive value in teaching the technique is soon-to-be discarded scaffolding for multiplying numbers.
> the child (and parent!) was annoyed because it made little sense to mark it as wrong
The impact that the -1 has on the child is also interesting. I think it scored 1 out of 2, so it wasn't marked "wrong" so mach as "partially correct". It should be clear to the student that they basically got it right but slightly misapplied the technique, due to the comment, shouldn't it? If it isn't, it's the result of too much focus on the grade and too little focus on the comment.
It seems to me more likely that it's parents and other adults who see this -1 so negatively, and impose that on the kids. I would have been upset as a kid, too, but the sooner someone could have gotten me to be okay with quantitative imperfection, the better.