MHB Why is Precalculus such a challenging course for students?

[mathdad]

Algebra 2, Trigonometry, Intermediate Algebra and College Algebra cover most topics presented in a Precalculus course. My first question is simple: What is the purpose for a Precalculus course?

 

[Greg]

What is the purpose for a Precalculus course?

The purpose of precalculus is to ensure that the student has the necessary mathematical foundation to study calculus. One might argue that these topics could be learned as they come up but that would be a distraction that is best avoided, in my opinion. Also, one needs a good understanding of these topics in order to understand the development of the various concepts used in calculus.

 

[mathdad]

The purpose of precalculus is to ensure that the student has the necessary mathematical foundation to study calculus. One might argue that these topics could be learned as they come up but that would be a distraction that is best avoided, in my opinion. Also, one needs a good understanding of these topics in order to understand the development of the various concepts used in calculus.

I believe that students who have taken algebra 1 and 2, geometry and trigonometry, can jump right into a calculus 1 course.

 

[topsquark]

I believe that students who have taken algebra 1 and 2, geometry and trigonometry, can jump right into a calculus 1 course.

That depends on the student, of course. If the student is good at the basic topics then (s)he can move ahead. But my experience with teaching College Algebra shows that most students do not have that capacity so a review is necessary. (And there are a few topics in CA that you don't get in the basics such as the rational root theorem, etc.)

-Dan

 

[mathdad]

That depends on the student, of course. If the student is good at the basic topics then (s)he can move ahead. But my experience with teaching College Algebra shows that most students do not have that capacity so a review is necessary. (And there are a few topics in CA that you don't get in the basics such as the rational root theorem, etc.)

-Dan

You are right. I forgot that there are students and then there are honor students.

 

[Joppy]

You are right. I forgot that there are students and then there are honor students.

That depends on the student, of course. If the student is good at the basic topics then (s)he can move ahead. But my experience with teaching College Algebra shows that most students do not have that capacity so a review is necessary. (And there are a few topics in CA that you don't get in the basics such as the rational root theorem, etc.)

-Dan

Even then... Aptitude and title have no commonality. But i think we all get the point :p.

Maybe we can say; "Students who completed pre-calc to a more than satisfactory level (have a coherent understanding of material) are ready to tackle Calc head on!" xD.

 

[mathdad]

Even then... Aptitude and title have no commonality. But i think we all get the point :p.

Maybe we can say; "Students who completed pre-calc to a more than satisfactory level (have a coherent understanding of material) are ready to tackle Calc head on!" xD.

We must also remember that there isn't enough time in one semester to cover all precalculus chapters. Many important ideas are skipped and/or ignored leaving the students unprepared for calculus 1. Keep in mind that many precalculus professors skip the topic of limits. I think precalculus should start with a thorough review of logs, exponentials and trigonometry. The rest of the semester should be dedicated to teaching matrix algebra, polar coordinates, polar equations and limits.

 

[MarkFL]

When I was a student, one important topic covered in the Precalculus course that wasn't covered in College Algebra/Analytic Trigonometry was mathematical induction. We also covered series/sequences which had been glossed over in College Algebra.

 

[Theia]

Another point of view about this topic:

I had never heard about 'pre-calculus' before I joined some math forums like this one. Here, where I live, we simply studied algebra, geometry, trigonometry, vectors and then several courses calculus. There was nothing to prepare us to pure calculus. So yes, I can't see a point of 'pre-calculus' because I haven't studied it ever. :D But I guess, the reason why there is such topic, is somehow related to teaching habits of the country in question. (Wondering)

 

[mathdad]

When I was a student, one important topic covered in the Precalculus course that wasn't covered in College Algebra/Analytic Trigonometry was mathematical induction. We also covered series/sequences which had been glossed over in College Algebra.

I forgot to list mathematical induction. Of course, series and sequences which I hardly recall but very important in every sense.

 

[mathdad]

Another point of view about this topic:

I had never heard about 'pre-calculus' before I joined some math forums like this one. Here, where I live, we simply studied algebra, geometry, trigonometry, vectors and then several courses calculus. There was nothing to prepare us to pure calculus. So yes, I can't see a point of 'pre-calculus' because I haven't studied it ever. :D But I guess, the reason why there is such topic, is somehow related to teaching habits of the country in question. (Wondering)

The main problem with math courses (and most courses unrelated to math) is the JAMMING PART. Calculus 1 should two semesters long. The same with Calculus 2 and 3, but especially Precalculus.

Colleges love to SQUEEZE material that should be taught in one year into 4 months. This makes room for little learning of important topics per course. For example, in my Precalculus class taken long ago, our professor assigned 5 homework questions per topic and expected the students to be masters of advanced algebra. This makes zero sense.

 

[topsquark]

The main problem with math courses (and most courses unrelated to math) is the JAMMING PART. Calculus 1 should two semesters long. The same with Calculus 2 and 3, but especially Precalculus.

Colleges love to SQUEEZE material that should be taught in one year into 4 months. This makes room for little learning of important topics per course. For example, in my Precalculus class taken long ago, our professor assigned 5 homework questions per topic and expected the students to be masters of advanced algebra. This makes zero sense.

College learning is far faster in pace than any similar high school treatment would be: one semester of college corresponds roughly with one year of high school. This is, at least, one of the problems that an American student needs to deal with almost right away. Our high schools, in general, do not give as much prep as private schools and most international ones. American high schools really do not prepare the student for college paces, which is about the same in all countries. That's one of the major problems I had with teaching College Algebra and Intro Physics...I felt I had to bring the students along with the "pace shock." From conversations I've had foreign high schools do a much better prep job.

-Dan

 

[mathdad]

College learning is far faster in pace than any similar high school treatment would be: one semester of college corresponds roughly with one year of high school. This is, at least, one of the problems that an American student needs to deal with almost right away. Our high schools, in general, do not give as much prep as private schools and most international ones. American high schools really do not prepare the student for college paces, which is about the same in all countries. That's one of the major problems I had with teaching College Algebra and Intro Physics...I felt I had to bring the students along with the "pace shock." From conversations I've had foreign high schools do a much better prep job.

-Dan

I agree. Foreign students enter college in the USA and are totally in shock to know that American students who trained in public schools can barely read and write and solve basic math problems.

I was a substitute teacher for 8 years. As a sub, I was not allowed to teach. Some teachers left lesson plans to follow but most did not care if the students missed a day of learning or should I say a day of test prep.

 

[topsquark]

I agree. Foreign students enter college in the USA and are totally in shock to know that American students who trained in public schools can barely read and write and solve basic math problems.

I was a substitute teacher for 8 years. As a sub, I was not allowed to teach. Some teachers left lesson plans to follow but most did not care if the students missed a day of learning or should I say a day of test prep.

I had fun with my substitute teaching. I have a Master's in Physics so I could handle the Physics classes as well as almost all of the Math classes. I had no practical experience in teaching the classes to HS students but I got lots of calls. :)

-Dan

 

[mathdad]

I had fun with my substitute teaching. I have a Master's in Physics so I could handle the Physics classes as well as almost all of the Math classes. I had no practical experience in teaching the classes to HS students but I got lots of calls. :)

-Dan

Students in the inner city ghettos eat subs for lunch. It was so hard to complete a lesson plan. Regular teachers have no respect for subs.

They talk badly to their students about subs. I remember getting punished for teaching a fifth grade class how to add and subtract fractions. One little girl praised my teaching style. The regular teacher got jealous and told the main office staff not to let me cover her class again.

 

[Joppy]

Another point of view about this topic:

I had never heard about 'pre-calculus' before I joined some math forums like this one. Here, where I live, we simply studied algebra, geometry, trigonometry, vectors and then several courses calculus. There was nothing to prepare us to pure calculus. So yes, I can't see a point of 'pre-calculus' because I haven't studied it ever. :D But I guess, the reason why there is such topic, is somehow related to teaching habits of the country in question. (Wondering)

That's true too. Come to think of it, i didn't do 'pre-calculus' either. It was, in a way, presented at the start of a Calculus 1 sort of course as a couple of weeks of high school math revision.

In fact, I've only adopted the terms pre-calculus, calculus 1 etc. since it seems to be the universal term which encompasses the content that those subjects.. encompass. I believe the American education system is a large contributor of propagating these terms?

 

[Joppy]

Students in the inner city ghettos eat subs for lunch. It was so hard to complete a lesson plan. Regular teachers have no respect for subs.

They talk badly to their students about subs. I remember getting punished for teaching a fifth grade class how to add and subtract fractions. One little girl praised my teaching style. The regular teacher got jealous and told the main office staff not to let me cover her class again.

What's that movie called where the teacher working in a sort of ghetto area manages to 'connect' with the students? xD

 

[mathdad]

What's that movie called where the teacher working in a sort of ghetto area manages to 'connect' with the students? xD

I think you mean Stand and Deliver (1988). A teacher, Jaime Escalante, teaches AP Calculus to a bunch of ghetto students. This movie is based on a true story.

 

[Joppy]

I think you mean Stand and Deliver (1988). A teacher, Jaime Escalante, teaches AP Calculus to a bunch of ghetto students. This movie is based on a true story.

That's the one!

 

[mathdad]

That's the one!

The real Jaime Escalante died a few years ago from cancer. He was a truly gifted teacher. The actor who played Jaime Escalante is still alive.

 

[mathdad]

Students are not learning in the inner city public schools. Students pass algebra 1 and 2 by the skin of their teeth. No wonder precalculus is a nightmare to most of them.