Refactoring Calculus: How One Math Educator Wants to Streamline First-Year Courses
Simplifying and Refactoring Introductory Calculus
Jonathan Bartlett argues that introductory calculus is overloaded with redundant techniques that burden students. He proposes a simplified framework that reduces memorization while increasing flexibility, potentially reshaping how calculus is taught to beginners.
Students have to memorize a diversity of processes for essentially performing the same task.
- jgord
I have strong opinions on how Calc should be introduced - visually.
I think we don't cover basics like the distributive rule in school very well, and that it should be a much more nuts n bolts visual / measuring / counting experience.
Ive attempted to outline how I think this stuff should be taught, by making a video tour of the concepts - from Counting, to Distributive rule / algebra, to Quadratics then the Derivative, here :
https://www.youtube.com/playlist?list=PLEInJ-Z4qBKYxbK1Mm13g...
All of these things are covered in some great books :
W W Sawyer Vision in Elementary Mathematics
Algebra by Gelfand
Calculus by Thomas
We have superb resources now like 3Blue1Brown, KhanAcademy and ArtOfProblemsolving.com / BeastAcademy .. so you _can_ get your kids a superb math education, even as many schools seemingly give up on teaching Algebra and Calculus.
- cool_dude85
Got to the place where he says "As you can see, this is identical to the d/dx() operation except that the result is not divided by dx."
What does it mean with his d() operator to "divide by dx"? All of a sudden it seems like he has changed dy/dx from unfortunate notation that sort of looks like a division into something that actually is dividing two meaningful things, dy and dx? And so what the hell are dy and dx?
- richard_chase
I think Stewart's Calculus is excellent and it is rightfully the standard textbook. No modifications needed in my opinion.
- xiphias2
,, additionally, moving limits to the end of a first-year course allows students to develop intuitions around the derivative first before seeing the formal proof of their validity’’
Waiting a year to get from intuition to theorems is a perfect way to ruin math.
Math is not supposed to be easy/simple, but it supposed to be a great way to understand systems based thinking.
At the same time there could be more examples taught on why these building blocks were historically needed and what they are used for solving nowadays.
- bee_rider
Looks like this came out nearly 8 years ago, so… how’d it work out? Given the way job titles work these days I guess we could have some Senior Engineers here who learned calculus from this paper…