Making sense of math
The old days of math class went something like this: The teacher would scrawl out a problem on the chalkboard, show the class what she was doing, and then hand out worksheets for her students to replicate it.
There’s no question that approach worked for some. But for many, it didn’t, leading students to fall behind in math. That’s because there is always more than one way to answer a math problem. But rote memorization ignores this and discourages many students from pursuing math.
“Children are intuitive about math,” said Iowa Department of Education Consultant Judith Spitzli. “They have a basic understanding about how to go about solving a math problem. But it has to make sense to them for the full understanding.”
And it’s that very concept – helping children understand how math is applied in our world, in addition to understanding how to use the mathematical procedures – that is at the heart of a professional development program, Cognitively Guided Instruction, or CGI, for educators. The professional development has brought some 400 educators across the nation to Des Moines during the Seventh Biennial National Mathematics Conference July 10-12.
The conference is co-hosted by the Iowa Department of Education and Iowa State University’s Center for Excellence in Science, Mathematics, and Engineering Education.
The conference educates teachers to recognize the different forms of student learning and how to adapt their teaching styles to ensure all students are progressing. It also enables the teacher to get students to the next level of understanding and complexity of mathematics.
“Students go about figuring out math problems in different ways,” said Department Consultant Richard Bartosh. “For instance, if you have eight rocks and then pick up some more, some students will count them altogether and arrive at 14. Others will count out eight and separate them from the pile, and then continue counting until they get to 14. From there, they will go back and figure out how many they had to add to get to 14. Yet another group might count out 14, take eight they started with and move that out and count the remaining number. Still another group will say, ‘Well, I have eight, and I know that seven-plus-seven is 14, and so if I already have eight, I need six more to get to 14.’”
Bartosh said these different approaches recognize that kids of different ways of approaching math problems.
“If you’re taught just one way of thinking about math problems, it’s sort of like expanding a student’s ability to spell words without explaining the definition of them,” he said. “They may know how to spell them, but they will not have any way of applying the words to their world.”
Studies show that both Iowa and the nation are not effectively competing in mathematics achievement internationally. And the jobs that most nations seek – those in the science and engineering fields – require strong math and problem-solving capabilities.
“If you look at our graduate schools in engineering and science here in this country, you will find that most of the students are international,” Bartosh said. “That underscores the importance of American schools building a strong base in mathematics and being able to solve problems in a variety of ways.”