Steven Jones recently published a book chapter titled “What education research related to calculus derivatives and integrals implies for chemistry instruction and learning.” Steven has answered a few questions about this chapter below:
Who would you say is the target audience for this chapter?
The primary target audience is chemistry teachers and chemistry education researchers, though it also contains relevant information for science education teachers/researchers in general
What is the big problem you hoped to address with this chapter?
Undergraduate mathematics and science educators have clearly documented a gap between the mathematics students learn in their math classes versus how that same mathematics is used in science or engineering fields. There is a major push to understand the reasons for the divide and what can be done to help bridge the gap. This paper was meant to summarize a portion of calculus education research that would be useful for chemistry teachers and education researchers in understanding the reasoning required in using calculus in chemistry, some of the difficulties chemistry students encounter in using mathematics, and some of the disconnects in meanings for the same concept between pure math versus applied science.
What are some of the key ideas in the chapter?
The paper reviews different areas of calculus education research and reports on some of the implications for chemistry teaching and learning. The areas reviewed were: rate and covariation, layers within concepts and representations of those concepts, the usage of differentials, and integration. For rate and covariation, some implications were to attend more explicit to the two quantities involved in the rate, to guard against treating *all* rates as though with respect to time, and to develop continuous images of change (rather than in chunks). For layers and representations, some implications were to be aware of all the elements and ways of representing there are for a given concept, to help students attend explicitly to these different elements and representations, and to ensure connections between them. For differentials, some implications were that, culturally, mathematicians and scientists think about differentials *very* differently, and that students will likely have been given messages about differentials in their calculus classes that contradict how scientists regularly use differentials in their work. Finally, for integration, some implications were that the area and antiderivative meanings given to integrals in calculus classes tend to overshadow the key scientific meaning of the Riemann sum structure, and that science teachers may need to develop this meaning explicitly for their own students.
What are some of the main ideas you hope your audience will take from the chapter?
My larger hope is for mathematics instructors and science instructors to become much more aware of some of the disconnects and divides between pure mathematics and the use of mathematics in science. But, further, I hope this awareness can help math instructors and science instructors begin to dialogue and understand each other in ways that can make learning for students more connected and continuous between their mathematics classes and their science classes.