According to a new study by Vanderbilt University researchers, teaching basic concepts behind maths problems is more beneficial for students than the exact procedures to solve the problems.
The results may offer teachers new insights on how best to shape maths instruction to have the greatest impact on student learning.
"Teaching children the basic concept behind math problems was more useful than teaching children a procedure for solving the problems, these children gave better explanations and learned more," said Bethany Rittle-Johnson, assistant professor of psychology and human development at Vanderbilt University's Peabody College.
She added: "This adds to a growing body of research illustrating the importance of teaching children concepts as well as having them practice solving problems."
Usually maths teachers demonstrate a procedure for solving a problem and then have children practice solving related problems, often with minimal explanation for why things work.
"With conceptual instruction, teachers explain a problem's underlying structure. That type of instruction enables kids to solve the problems without having been taught specific procedures and also to understand more about how problems work. When you just show them how to do the problem they can solve it, but not necessarily understand what it is about. With conceptual instruction, they are able to come up with the procedure on their own," said another author of the study.
The researchers also studied if whether having the students explaining their solution to problems helped improve their learning.
Although self-explanation has been found to be beneficial in previous studies, the researchers found that when the students were given a limited time to solve the problem, the benefit disappeared.
Thus, they indicated that the benefit of self-explanation might partly come from the extra time a student spends thinking about that particular problem.
"Self explanation took more time, which left less time for practice solving the problems. When time is unlimited, self-explanation gives students more time to repair faulty mental models. We found conceptual explanation may do the same thing and make self-explanation less useful," said the study's co-author.