The International Journal of Science and Mathematics Education published a research article by BYU Mathematics Education assistant professor Steven Jones, PhD, in August 2017.
The article “Teaching integration: How certain instructional moves may undermine the potential conceptual value of the Riemann sum and the Riemann integral” discussed the importance of teaching Riemann sum-based conceptions in introductory calculus classes, which are important for solving science and engineering problems.
It is common for calculus instructors to initially teach the Riemann sum and Riemann integral concepts when introducing integration in first-semester calculus. However, they also may send subtle messages to students that the concept is not important.
“What I am hoping to do is to remind instructors to really think about not just teaching shortcuts to calculate numerical answers, but what ideas can get students to set up the integration first,” said Jones.
Jones’s earlier research shows that students who use the Riemann sum concepts were more capable of setting up and understanding integrals for given physics contexts.
According to Jones’s research, most students think about integration as area under curve, instead of adding up lots of little pieces. There seems to be a disconnection between what the students learned about integration in math classes and how they need to apply it to science and engineering courses. Because the lack of emphasis on this conception in early calculus classes, students tended to abandon the Riemann sum idea.
“I think calculus is hard if it’s all computational based. If the instructors take more time to help students to unpack the ideas together, then the problems are not nearly as challenging,” Jones said.
(picture on the left: Dr. Jones was explaining how the topic of integral is like a big umbrella consists of many different problem-solving concepts.)
Read the full research article here: