Do you find yourself staring at your third graders math homework wondering what it is all about, even though you have an advanced degree in mathematics? Does your child jump from topic to topic in math without ever being able to master anything? Do the words spiraling, lattice multiplication, everyday math or conceptual math seem familiar? If you answered ‘yes’ to any of those questions your child may be part of one of the most lamentable education experiments ever conducted in the past 25 years. An experiment, that has parents, students and teachers up in arms in multiple states across the nation.
Yet, for many years, no one thought to conduct a randomized controlled study to understand whether this new ‘fuzzy’ math actually helps children learn mathematics. That is, no one until Dr. Kaminski and her colleagues at Ohio State University decided to challenge the common practice in many classrooms across the country of teaching mathematical concepts and facts by using “real-world” concrete examples.
Kaminski and her colleagues found that students who learn mathematics using abstract rules and facts are able to easily transfer their knowledge to a variety of situations in comparison to students learning math using ‘real world’ examples. In their view ‘real world’ examples tend to distract the learner from learning the underlying mathematical principle.
For example, there is the classic problem of two trains that leave different cities heading toward each other at different speeds.
Students are asked to figure out when the two trains will meet.“The danger with teaching using this example is that many students only learn how to solve the problem with the trains,” Kaminski said.
“If students are later given a problem using the same mathematical principles, but about rising water levels instead of trains, that knowledge just doesn’t seem to transfer,” she said.
“It is very difficult to extract mathematical principles from story problems,” Sloutsky added. “Story problems could be an incredible instrument for testing what was learned. But they are bad instruments for teaching.”
The researchers found that their results held for undergraduate students as well as 11 year old children. Their findings are at odds with the popular and enduring assumption held by many math educators that only concrete examples help children understand math. Kaminski et al., are repeating this experiment with elementary school children. They believe that the results are not likely to be all that different.
What does this all mean? Twenty five years ago, the University of Chicago Math Project with support from the National Council of Teachers of Mathematics (NCTM) and the National Science Foundation NSF, came up with the new ‘constructivist’ or ‘integrated’ math curriculum that emphasized understanding math concepts, constructing math rules from ‘real world’ examples, dismissing rote memorization of math facts like multiplication tables, throwing out ‘carry-over addition’ and other traditional ways of doing math and approving the use of calculators even in first grade classrooms.
The Everyday Math curriculum proposed by the University of Chicago is used in 175,000 classrooms and by 2.8 million elementary school students. Its counterparts are the Connected Math in middle school and Core-Plus Math in high school (names may differ from state to state). This math system rejects traditional math methods (the way we learned math in school) and seeks to integrate conceptual methodologies and connections to the ‘real world’ with math facts.
Today, more freshmen coming into college are taking remedial math than ever before in the history of US education. US students rank considerably lower than many other nations in math as assessed by the Trends in International Mathematics and Science Study. Across the country, there are angry parents and students who have been forced to turn to tutoring, after school math remedial programs, drilling at home or changing schools to avoid the integrated math curriculum and provide students with the math education they should be getting at school.
Almost twenty five years after the advent of reform math, the math wars continue to rock the nation. Some of us have heard it before and some like me are discovering it for the first time and are nonplussed. Aren’t twenty five years long enough to understand the effectiveness or ineffectiveness of a system? It is downright scary when scientists, mathematicians, and university professors all seem to agree that the new reform “integrated math” does not do justice. You can read some comments from university professors here.
My post is probably just touching the tip of the iceberg. I fervently hope Kaminski’s work is a start in the right direction.In my next post I hope to provide a little more detail on the differences between the integrated math and other math curriculums used around the country. In the meanwhile I would love to hear your comments on this integrated math system as well as any coping strategies that you may have to share with other readers.
Enakshi Choudhuri did her Masters in Counseling from Heidelberg College in Ohio and PhD in Counselor Education from the University of Iowa. She has taught and supervised undergraduate and master's level students and has worked with children, adults and college students at various agencies. She is also an author and book publisher. More posts on parenting and education can be found on her blog.