Talking about teaching math opens one up to choruses of “You’re doing it all wrong” among those who have been indoctrinated into the various catechisms of math education. One of those is “Never tell a student they made a mistake”. I guess this is because it affects their confidence and self-esteem and therefore is anti-growth-mindset. (On the other hand, we have Jo Boaler telling us that students should be encouraged to make mistakes because it makes their brains grow.)
I have no problem telling a student they made a mistake, though I do it by saying “That’s not what I got. Anyone else get an answer?” When many students make a mistake I capitalize on this and say “OK, so far we have …. ” (I rattle off the various answers), and then many hands go up among those who want to be part of what is now perceived as a fun game. But if only one person makes the mistake, I’ll try to see if they know what they did wrong. Sometimes the student knows; other times, I might know and I’ll give my opinion. And still other times we don’t know, but I’ll give another similar problem and the student who made the mistake usually will try again. At least that’s been my experience. But to make the math ed progressives reading this entry feel better, I’m no doubt doing something wrong.
For eighth graders, it’s a little trickier, because they are very self-aware at this stage of their lives and can be very guarded. Some teachers use mini-whiteboards on which students write the answer and hold up the boards for the teacher to then say “Right, right, nope–try again, …” etc. I do a variation of this. I don’t use mini-whiteboards. Instead, I’ll tell them to do the problem in their notebooks, and then I go around. If someone has the wrong answer and they write out their steps, I can point out the mistake, and they can then re-do it. For those who get it right, I’ll tell them so. If the person who got it wrong initially then gets the right answer, I call on that person to tell the answer to the class. In this way, the person is not singled out for making a mistake, and they feel confident in giving the answer to the class, knowing it’s correct and not fearing the teacher saying that it’s wrong in front of their peers.
But when time pressure is an issue, you sometimes have no choice but to tell someone they are wrong. I make note of those who are not getting it, and during the time that I allot for students to start on their homework (a term which has now morphed into “practice problems”–I guess “homework” is too risky a word in view of self-esteem and growth mindset fantasies) I spend the most time working with them.
For those students in eighth grade who really should not be in such class but who are placed there because of parents’ insistence, there are a number of options I exercise. I may recommend to the parents that they hire a tutor. Another alternative (which may occur even if the student has a tutor) is to recommend that the student repeat algebra in 9th grade. Some go along with this, but others do not.
If these ideas are offensive to some of you, please realize that I wear my shirts tucked in, avoid Apple products, and use a point-and-shoot digital camera rather than take pictures with my cell phone. I am semi-anachronistic and am determined to stay that way. It’s only a matter of time before my out-of-date habits become the latest fad. By that time, I’ll likely be dead, in which case they’ll probably name a brick-and-mortar bookstore after me.