“… San Diego State has joined a couple of dozen math departments across the country that are rethinking the way they teach math.” …
http://hechingerreport.org/high-failure-rates-spur-universities-overhaul-math-class/
I don’t think the issue is with how universities teach math - I think the issue relates more to how high schools prepare students for college-level work, especially college-level mathematics.
Anecdote:
I was required to take Calculus I as part of the requirements of my University’s Honors College - I am a Political Science major at a school where the major is entirely qualitative, not quantitative. (i.e. all theory, no number crunching.)
My Calculus I section was reserved for Engineering and Physics majors but I managed to snag a seat at the last minute because they hadn’t filled to capacity during registration (the professor was highly praised by everyone and the time was perfect for my schedule.)
I had taken AP Calculus in high school but only received a 3 on the exam (no credit) – I found the college class equivalent very easy. I finished with something like a 98% average by the end of the semester.
However, I noticed a trend in the class - every student who hadn’t received any exposure to Calculus prior to the course seriously struggled - even students who were enrolled in extremely quantitative-based fields like Mechanical Engineering and Physics. I sat in front of two Physics majors who would lament low exam scores in the course every week, despite putting forth genuine effort in studying/tutoring/visiting office hours/etc.
The issue is that a student reaches their senior year of high school enrolled in “Honors Pre-Calculus and Trigonometry” and the college assumes (correctly or incorrectly) that the student has the prerequisite knowledge required to pass/excel in Calculus I. But that’s not the case most of the time - a standard high school pre-calculus course pales in comparison to its college level counterpart; it shouldn’t be treated as an equivalent and utilized as a legitimate prerequisite. Students should not enroll in the “next course up” from their last high school class, regardless of what a 90 minute placement exam tells them – the college course/professor is going to anticipate that your prerequisite knowledge is far more comprehensive than what was actually taught to you in high school.
I noticed the same pattern with my friends; students who “repeated” the last math class they took in high school did very well and were able to move up to higher division math courses with ease; students who jumped to the next level straight away ultimately struggled and either had to repeat the class or had to designate it as “pass/fail.”
I’m probably misquoting history, but The University of Texas at Austin created the ALEKS exams for Chemistry and Calculus, because they noticed the discrepancy of entering freshmen abilities.
I think you needed 80 score to enter Introductory Chemistry, 70 for differential Calculus, and 80 for integral Calculus.
Even though I took Calculus in HS, I took Differential in fall and Integral in spring freshmen. I knew I had gaps in my knowledge, so I wanted to take the 2 semester route to finish my math requirement.
High school precalculus/trigonometry is supposed to be a solid prerequisite for calculus, whether calculus is taken in high school or college. Of course, at some inferior high schools, this may not be the case, so colleges use placement tests to determine whether the student has the prerequisite knowledge to go on to the next level. It does look like your college’s math placement tests are inadequate to give proper placement, so it needs to revise its placement tests.
Lots of students successfully go on to the next level of math in college, in all of the following situations:
- high school precalculus/trigonometry → college calculus 1
- high school calculus AB → college calculus 2
- high school calculus BC → college calculus 3, linear algebra, and/or differential equations
Students who are still unsure of whether to move on to the next course in the sequence can try the college’s old final exam for the course whose material they are supposed to know, so that they can check their knowledge against the college’s expectations.
I think you are correct, In my high school we didnt even need pre calc
So I know people trying to perform in Calculus without even basic pre knowledge.
This is why common core (I like the idea not the way it is currently implemented) is a good idea