Pencil and Paper; the Benefits

One of the usual identifiers of a "new math" program/teacher is that there is very little pencil work. Fuzzy math people have been all over the map on this idea, straddling the line, trying to appear neutral, denying that they are against pencil and paper work, denying that they are opposed to learning and drilling on math facts. Now, some are making a turn around and publicly say they do not oppose use of pen and paper practice, but look closely and they provide little to none.

Now, I must explain that "new math" proponents are not opposed to pencil and paper work. They assign students work involving lists after lists after lists and all sorts of writing assignments. It's pervasive in every chapter throughout the books they love. But that use of pencil and paper is OK, because the "new math" teachers are doing it. Not only is it OK, it's desired! It's just not OK if I do it in my traditional classroom, using traditional books and traditional methods.

It's been several years now, but I took a little class called "Teaching in Texas Today" offered by a local school district. It was designed for people who were teachers but who had been out of the classroom 10 years or more or for people who were interested in becoming certified. It sort of brought you up on things that were new in education and each week we had a different instructor. One instructor showed us new ways to be sure that students were learning new concepts. (She used math as her example) Students were all given cards to raise in the air to give their answers. Teachers could easily identify the students who had the correct answer by looking at the card the child held up. No pen or pencil work was required. Students were encouraged to do the work mentally. And I'll never forget her saying, "Once you see that the student has done several correctly, you don't need to burden them by requiring that they do any more." (I'm not opposed to mental math -- I love it, my children love it and some even thrive on it. I use it every day, but not at the expense of proper pencil and paper practice.)

Soon afterward, I returned to teaching, and I've thought of the instructor's words many times, primarily, when I see how quickly some students forget newly taught material. Even with practice and practice, there are those students who will still struggle. All it takes is a 2-3 day sick spell, and they're lost. (I'm not talking about that student who can think it through, figure it out mentally in 10 seconds. If that is your student, you are not reading this blog. I'm talking about the students who can't figure it out instantly, but who need to be given a method to use to get the answer until they can figure it out by themselves.)

There is something about the "doing of the problem", about the "using of the pen or pencil" that helps children learn. I don't meant that "helps them 'remember'". We've all known that for a long time. But now we know that "the doing" actually helps children "learn". We now know that there are some children who learn by doing, by moving, by writing, by some sort of physical motion. And for them, it is in the actual doing of the work that they "get it". Using and moving concrete items (blocks, counting sticks, pennies) to solve problem is a must for these kids. Walking, physically moving, through the steps in the problem is also important for these children. But along with these actions, we know that there are those children, for whom it it a terrible mistake to restrict the pencil and paper. We rob them of their way of learning. For these students, there is a need for clear step by step procedures to follow and practice, practice, until they figure it out because this is the way they figure it out.

Oh, I forgot! I'm not supposed to be teaching them procedures or methods. We should be allowing them a chance to figure it out and discover their own methods of getting the right answer. You, the parent, may have been given such an answer when you've explained that your student doesn't understand what's being taught. You may have even been told NOT to teach them your old methods because children need to figure it out. Never mind that it might take them months, and that the rest of the class has long gone on to something else. So you're told not to help yor student and your student may even be publicly embarrassed in class if you do. So you are told NOT to intervene. Teachers are told not to intervene.

But I can't do that to your student. And as a parent, in your heart of hearts, you don't want to do that either because you see what it does to their confidence. You see the frustration and the discouragement and you want to help, NOW, not next semester, or next year.

And I do not agree that only if a person is mentally thinking on his own, deciding on his own methods to try to use solve a problem, that only then will he be engaged. Students who are going carefully through a step-by-step method can be very "engaged" because that is the method that gets their brain going. You will see them whispering, talking through the steps, and that is good. Yes, they can be very engaged. And they are learning.

(I'm going to cut my original post here and post the remainder on a new page, "Intervention".)