From the news wire, this story about educational research:
Hold the marbles: Abstract approach best for math | Science | Reuters
CHICAGO (Reuters) - Frustrated math students may have a good excuse — some of the teaching methods meant to make math more relevant may in fact be making it harder to understand, U.S. researchers said on Thursday.
I wish they’d included a link to the original study.

April 25th, 2008 at 10:23 pm
Did I mention I am doing Math Intervention this year? They used college students in the study. I hope that I wouldn’t need marbles at that age to solve probability, but if I did I probably wouldn’t tell anyone. Research shows that most younger students need the concrete or the manipulative before learning how to do formula, or write number sentences.
April 26th, 2008 at 4:54 pm
I read this article and really just can’t disagree more. After teaching math for nine years and loving math myself, I can’t see how abstract symbols could be more meaningful to a child than using concrete, real-world examples.
April 26th, 2008 at 8:29 pm
I think that what they are trying to say here is that concrete basics are nessasary to understanding more abstract problems. For example: If you don’t know 2 +3 = 3 + 2 it makes it hard to go to a word problem that talks about walking 2 miles north and than 3 miles west, is that the same as walking 3 miles east and 2 miles south. Very simple examples, but hopefully you see what I mean. Some of the students get caught up in the symbols or operations of a problem when they don’t know them well.
April 29th, 2008 at 10:35 am
[…] From Phaedrus and his refrence to this blog, where the following was stated: For example, they studied different approaches at teaching the basic mathematical property of commutativity — that you can switch up the order of elements and still get the same answer, as in 3 + 2 or 2 + 3 equals 5. […]