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Calculus curriculum content to be revamped

<alculus sequence—calculus 1, 2 and 3—will change next year to reflect current trends in math education. The study of “Sequences and Series” will be moved to calculus 3, while components of multivariable calculus will be moved to calculus 2, according to Math Professor Laura Chihara.
Position papers from the Mathematical Association of America (AMA) and other organizations have criticized the current calculus sequence. The AMA says an overemphasis on complex algebraic manipulations and “breadth over depth” has plagued calculus pedagogy.

 “A lot of the students who take calculus are taking it because they need it for another major,” said Chihara. “So, there’s been a national conversation about trying to reorder the topics for that reason.”

 Vectors, double integrals and partial derivatives are more important than sequences and series to students majoring in other disciplines, according to Chihara. Faculty in other disciplines such as economics, physics, chemistry and geology expressed a desire for students to be introduced to multivariable topics earlier.

A few schools, including Williams College, have already made this change in the sequence. Most schools, however, still follow the sequence Carleton currently uses.

Math Professor Rob Thompson began discussions about changing the sequence after a positive experience teaching at Macalester College, where more radical changes in the calculus sequence had been implemented. Decisions about how to change the calculus sequence at Carleton were initially controversial among faculty.

“Everybody has an opinion about where certain things should be,” Thompson said.

“It’s hard to have a big picture conversation about calculus,” said Thompson. “I think people were concerned about a few things, rightfully. One was overloading one of the courses, like sticking too much stuff in calc 3. Another concern was textbook sources, because there are technically textbooks that do early multivariable but they’re not in the same state as regular textbooks.”

Thompson said other faculty were concerned about a “jumbled order” for visiting professors, who are often teaching calculus for the first time. The current separation of single and multivariable calculus has been in place for many years, according to Thompson.

“STEM education has evolved a lot since traditional ordering in calculus was established. And, calculus hasn’t changed that much,” said Thompson. “We’re doing away with some topics, for example special types of integration, like partial fractions.”

Other disciplines routinely use computational programs like Mathematica to solve complex integrals. Chemistry and Physics faculty are not concerned with students learning difficult integrations.

“There was a big shrug about integration techniques, nobody cares. Literally. And even the people who are doing hard integrals like in chemistry and physics, the answer is, ‘we’ll use Mathematica,’” said Thompson. “In doing mathematics, I use these techniques. But outside, it’s not that important. It’s just that the process of evaluating an integral is antiquated—nobody needs to do it anymore.”

The new Calculus II course will emphasize topics important to other majors such as differential equations and two dimensional topics. The new Calculus II will incorporate most of the material from the first half of the current Calculus III, according to Thompson.

Faculty in STEM disciplines were enthusiastic about the changes.

Beginning next year, the chemistry major will require students to take Calculus II instead of Calculus III, according to Chemistry Professor Joe Chihade. Chemistry has changed other requirements for the major as a result of the calculus change.

“The motivation from the Math Department’s point of view is, they don’t want students who are bored or not doing well in a topic that isn’t really the reason they’re taking the course,” said Chihade. “They recognize that nobody cares about sequence and series but mathematicians.”

Economics Professor Nathan Grawe similarly feels that the new sequence will benefit Economics majors.

“It won’t change any ECON requirements or pre-reqs.  But it will be helpful to some Econ students by moving Econ-relevant content earlier in the math sequence,” said Grawe.

The current Calculus II, or Math 121, will be phased out and replaced by the new Calculus II, or Math 120, next fall. There will be two versions of Calculus III offered next year. One will retain the current material for students who were taught sequences and series in high school or at Carleton. The other will be for students who took the new Calculus II.

There are still unanswered questions about what will happen as a result of the calculus change.

“Initially there was a lot of discussion about, ‘well yeah, but what if this happens, what if this happens,’ so of course we had to modify and address some concerns,” said Chihara. “So we don’t know what’s going to happen.”

According to Chihade, the chemistry department has made changes that would be difficult to reverse if the calculus sequence were reverted. Hence, the changes are expected to be permanent. Professor Thompson said that more controversial changes to the math curriculum, such as making Calculus II the prerequisite for differential equations, could become a possibility with the new calculus sequence. Further changes will be discussed at the end of the 2018 school year. 

 

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