Math Education Rant - Part 1

I just finished reading an article about classes created to help parents help their children with Common Core math homework. I also read the comments following the article. My reaction to the comments are the reason for this post.

Every few years the U.S. decides we need to change the way math is taught. This is said to be a response to students doing poorly of some national or international test. (It is seldom mentioned that changing a curriculum is a huge financial gain to those who sell curriculum, but that is fodder for another post.) 

Anyway, with the change new books and materials are purchased, websites are formed and subscribed to, schools pay consultants to train the teachers, and finally the new program is presented to the students. Ten years later it is discovered that some students are doing poorly in math and the process starts again. As the quality of children's understanding of math is bemoaned in the media, comments come in from math authorities (often engineers or other professionals who use math in their jobs) who insist that: 1. Math is easy, 2. Elementary teachers don't know how to teach it, and 3. It is a shame that young people can't make change anymore. As a teacher I have observed the following:

• There are some children who find working with math to be a wonderfully ordered process. They see the patterns, think math is an easy subject, and will learn and understand math regardless of how it is taught and who teaches it. These students easily learn whatever method is taught to do basic addition, subtraction, multiplication and division, grasp the concepts, and utilize their own shortcuts.
• The next group of students are the majority, who get through math class in the elementary grades with a bit of work. Some things come easily, some take a bit more work. Some of these children love math class and some hate it. But they get through it and have the ability to work with basic arithmetic before tackling algebra. 
• Finally we have a group of children who find math extremely difficult, if not impossible. Some of these students have dyscalculia, some have other learning differences (LDs), some have cognitive disabilities, but math to them has no logic. Every math class is a new day with no connection to material presented the previous day.

Let's look at how arithmetic may be presented to this student.
Example: 221-35 = 

1. Old math: We borrow one from the two next to it then subtract the 5 from 11, change the 2 to one, borrow from
   the next 2, subtract 3 from 11,  etc. See example 1. below
2. Newer old math. Regrouping - Same as borrowing only we show the place value concept so we don't borrow one, we borrow ten, (and 100) but the problem looks the similar to the first example with more changing
   
   numbers on the top See  2.
3. New math: See example 3. Understanding numbers - It is easier to subtract a zero so we round up the 35 to 40 and because it is easier to subtract 20 we first subtract 20  and then second twenty from 201 and add five to  181 giving us the 186 answer or one can subtract 30 from 20 for 191 and subtract five to get 186

So what does the really poor math student do? (The first time I saw a 4th grade student do this I was amazed. The second time I almost cried.)  221 - 35  =    Hmmm . . .  Can't take five from one but I can take 1 from 5,  and can't take three from two, so 3 minus 2 is 1 and two minus nothing is two, ergo the answer is 214! (This student is so happy to get through an easy problem without having to round, think about place values, write funny numbers on top, or subtract more than once that the thought of just looking at the answer and logically thinking it has to be less than 200 doesn't even make a blip on his radar.)

Of course the adult who found math easy rolls his eyes and blames the teacher. (This adult usually has a child who also finds math easy and has never enjoyed the experience of working with a child who sees math as the seventh circle of Hades.) The teacher sighs and works with the child using demonstration, questions, and maybe even concrete materials. The child nods and suddenly seems to remember that yes, we did do something like that last year. He dutifully corrects his work (with no real understanding of it) but if he doesn't have to subtract for the next few days he reverts back to old habits. So what can be done?

Next Post: What Can be Done