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.
Example: 221-35 =
- Old math: We borrow one from the two next to it then subtract the 5 from 11, change the 2 to one, borrow from
- 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 See 2.
- 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
Next Post: What Can be Done