Math education targets real-life problem solving
Editor's note: This is a second in a series of articles examining how education in the public schools has changed over the last 20 years.
Remember elementary school math?
It was a trial of learning about addition, subtraction, multiplication and division. It was a procession of fractions, decimal points and story problems.
Oh, remember those? Story problems that is. While all the work sheets with dozens of problems seemed overwhelming at times, it was the story problems that most people hated. At times it was hard to figure out what operation to use. It was hard to know what kind of answer you should come up with.
But the fact was, and is, that story problems, the ones most students hated the most, were the ones that most of us would use in later life. They weren't just numbers on a paper, they were what we would use to figure out costs of a fence surrounding our property or how much we would have to pay for five pounds of bananas.
Usually things in the abstract (like the dozens of problems on a page) are harder for people to decipher. But in the case of math they seemed easier than trying to figure out how quickly Mrs. Smith would reach Podunkville (58 miles away) if she rode a train that was traveling 37 miles per hour. It was because good memorizers could whip through rote math problems; but people who deduced things had a harder time.
"In the past students were good at math if they were also good at memorization," said Mika Salas, the Math Specialist for Carbon School District. "Just because a student can spit out the facts doesn't mean they are good at math."
Two years ago schools in Utah were told to go to a new program, called the Utah Common Core. The program is exactly like one being used in 40 other states, and Salas said that the impact of the program will be tremendous as students move up the ladder of grade level to grade level.
The new program was not the first one introduced in the state. People who were parents in the 1970s remember the "new math" of that time period. Then came a number of other programs all lasting only a few years before the state decided that teachers should use another method. But that was when few states cooperated with each other and all had their own programs. The problem was that students in various states were getting various kinds of math education. And many, when they graduated, found that they weren't prepared for college work, especially when they went out of state.
"When the states developed their own standards and methods, students weren't ready to compete nationally," said Salas. "Before Utah was an island unto itself. We had a hard time finding resources and text books to support our programs. Text book publishers write to comply with the large states."
The new math system, which was implemented two years ago, is taking hold. The program is set up to be sure that students can do math problems and understand math concepts in a number of ways.
Salas says that the new program is being instituted from kindergarten to 11th grade.
"The program is set up to put meaning behind it, to make it relevant," she says. "It levels the playing field for students."
That doesn't mean it is easier. That means it is more relevant. Instead of just coming up with the answer to a problem, the system takes into account how a student arrived at the answer, and how that answer could be used in the real world. The older systems trained kids not to think but to put out facts. The new one teaches them to think, deduce and come up with creative ways to get answers.
"For instance there was a fourth grade student that I saw that said he did not know his 20 times tables in the problem 20 x 5 = X," she said. "But he did know that 10 x 5 equaled 50 so he came up with 100 as the answer."
While this may simple to an adult who has been using math for many years, that is not that simple for students only schooled in using set facts. Salas says there are a number ways that the program can achieve breadth and depth.
â¢ Students can see it in a visual representation. A teacher may talk about one fourth of a rectangle in the abstract, but all representations under the program are demonstrated in a visual way as well. In other words, a rectangle is portrayed with a fourth of its area colored to show the student what it means.
â¢ That same rectangle can also be represented by a number or area. The student would learn an equation that would demonstrate how to figure the area that the number represents.
â¢ Use of the math to find the area applied to real life. For instance, the students would be sent out to find the area of a rectangular playing field at their school. They would be supplied no numbers but be expected to figure it out by doing what one does in real life to find the area; measure and calculate. This type of exercise is a reality check.
"We have done this with students and find that those that can do it in the abstract, can't figure it out when they are confronted with the problem of figuring the area in real life," said Salas. "They didn't even know how to start to measure the field."
The introduction of the program has not been without its snags. First of all younger children are much more likely to embrace what is being done, while those older ones that have been through the previous system have struggled some. And difficulty with a new program isn't just about the kids.
"In the 15 years I have taught there have been four different math cores," said Salas. "We have teachers that are still struggling a little with the program."
She said that it takes about three to four years of teaching something to be completely comfortable with a math program. While she didn't say anything about it, changes from one core to another after a few years can result in stunted education growth. But she sees some very positive things in the students.
There are also new words that students are using when they go home; things that parents are wondering about and what those terms mean. Salas is developing a glossary for people to use to understand what is being said and how it relates to the world of math as they know it.
"I see kids starting to put it all together, doing it more quickly and having fun with math," she said.
"I believe this is the biggest change the system has ever made in math but it is in the best interests of the kids. We will get there but it will still take some patience on the part of everyone."
She also hopes that parents will understand that the change, as difficult as it can be, will add up to a better math education for their children.