STEM, Precalculus or College Algebra Dual Enrollment considerations

[MarkT]

Instead of watching the first NFL TV game yesterday (my team is already eliminated) I read some pertinent chapters from this study as was pointed out by Arcadia:

http://forums.welltrainedmind.com/topic/574926-fyi-insights-and-recommendations-from-the-maa-national-study-of-college-calculus-2015/

 

If your future STEM student is using College Dual Enrollment to fulfill high school level material such as Precalculus you should read:

 

Chapter 5 Placement and Student Performance in Calculus I

page 60
"
Precalculus as currently taught in most post-secondary institutions in the United States does very little to improve student chances of success in Calculus I and can actually be detrimental."

 

I think the takeaway is make sure your student fully understands the Precalculus material covered by giving them a Calculus placement test or ALEKS and fill in any gaps before moving on to Calculus I.

---------------------------------------------

 

on page 65
It also has a nice discussion of the ACT Compass and College Board Accuplacer tests along with ALEKS.

 

I also learned about the topics that should be covered in a College Calculus I course.

 

 

 

Edited December 28, 2015 by MarkT

[regentrude]

I do not fully understand their conclusions. I am not sure they separate causalities and correlations.

Here are a few thoughts and observations about the STEM school at which I teach:

 

1. Being placed into precalculus, which is considered a remedial course and does not count towards almost all our majors, happens in two distinct scenarios:

Group 1 are students who excelled at math in high school, took AP calculus, failed to put in time for a thorough trigonometry review, and did not pass the placement test because they forgot all their trig while taking calc. For these students, an accelerated trig course can remedy the problem and they proceed without trouble. If their other math subscores are high, we place them in a trig crash course during O-week to have them ready for calc 1 right away.

Group 2 are students whose failing the placement test for calc indicates a lack of general math mastery and preparation. For some of those, this is caused by substandard high school education which could be remedied; I suspect, however, that taking precalc may not be sufficient to overcome years of deficient teaching for all of them. For others, failing the placement test indicates a lack of aptitude for which taking trig/precalc does not help at all. Even if they pass a remedial precalc, they will subsequently struggle in calculus.

Physics majors who place into college algebra/trig will typically not do well in the program.

 

2. For actual success in calculus 1 it is not, actually, necessary to know a lot about trigonometry or polynomials. Most of the material that is taught in "precalculus" has very little to do with success in calc. Far more important are thorough mastery of algebra 1 and the necessary work ethic. Many students who fail calc 1 are lacking basic algebra skills and also do not apply themselves in the class. STEM majors encounter calc 1 very early in their college career, when they may not have established good study skills and have no realistic expectation of the work load required for a college course. Most failing students simply do not put in enough time on task: 2 hours outside of class for every hour in class, or more.

I observe similar effects in introductory physics, but the earlier a required large course is taken, the worse the effects are. Calc 1 and chem 1 instructors struggle with this to a larger extent than I do, because their courses come before mine. I never see those students who cannot get their act together and put in sufficient time on task to make it through calc 1.

 

3. If I have to draw consequences for homeschoolers and DE, those would be:

Avoid DE precalculus courses at schools where those are considered remedial, since the student will end up in a class with students who have performance issues in math. If DE, take it at a school where the strong students take precalc as well.

When trying to get into calculus, make sure the student reviews trigonometry before taking the math placement test.

Success in calculus depends on algebra skills and work ethic. Make sure those are in place.

 

Edited December 28, 2015 by regentrude

[Guest]

Regentrude, that has been our experience in this house and with engineers and a math and science teacher FIL who is an engineer as well - students atrong in Algebra don't need precalc. Knowing algebra through and through to trigonometry is crucial and deficient teaching in those areas is what causes these kids to struggle throughout their degrees. Worse yet, the remediation often focuses on skills that are not back to basics concepts and therefore some of the fundamental holes in understanding and thinking remain. They may finally pass the course and move on but the working conceptual knowledge just isn't there.

[EKS]

For actual success in calculus 1 it is not, actually, necessary to know a lot about trigonometry or polynomials. Most of the material that is taught in "precalculus" has very little to do with success in calc. 

 

Finally, my suspicions confirmed!

 

I took Calculus I and II in college and passed with a solid understanding of (very) elementary algebra and little else and always wondered how that could be.  My performance in calculus wasn't strong by any stretch of the imagination, but it was good enough for me to be able to apply what I learned in a calculus based physics course (again, not a strong performance there either, but passing).