How to lower one's expectation in teaching college algebra

[cbarker1]

Dear Everybody,

I am about to teach my first course, College Algebra at my university as an instructor of record. Most of the students take this course is just for liberal arts requirement for critical thinking. I feel like I have too high expectation of my students when I should not have too high expectation for them. While I was doing my notes for the first chapter in my text, I have some easy examples as well as harder examples. I don't want to include any more detail because I do not want my students to see one question in a quiz that I am planning to give soon. How do I lower my expectation from high to reasonable level?

Thanks,
Cbarker1

 

[Office_Shredder]

It's really hard to know without knowing what your expectations are.

I think the hardest thing to adjust to as a mathematician is that your students are not going to understand the concept of a proof. Even things like explaining FOIL as a repeated application of distribution is probably a struggle, because they aren't used to trying to think about things that way.

 

[cbarker1]

My expectation is that they know how to do the standard arithmetic operations on fractions, what are exponents and their rules, factoring polynomials...etc.

 

[kuruman]

Dear Everybody,

I am about to teach my first course, College Algebra at my university as an instructor of record. Most of the students take this course is just for liberal arts requirement for critical thinking. I feel like I have too high expectation of my students when I should not have too high expectation for them. While I was doing my notes for the first chapter in my text, I have some easy examples as well as harder examples. I don't want to include any more detail because I do not want my students to see one question in a quiz that I am planning to give soon. How do I lower my expectation from high to reasonable level?

Thanks,
Cbarker1

It is difficult to know what to expect when you do this for the first time so make a measurement. First day of classes give them a "placement test" with questions ranging in progressive difficulty from what you consider easy to medium hard. Tell them that it is for informational purposes only and that their grades will not be affected. The placement, of course, is for you not them but they don't need to know that.

 

[vela]

While I was doing my notes for the first chapter in my text, I have some easy examples as well as harder examples. I don't want to include any more detail because I do not want my students to see one question in a quiz that I am planning to give soon.

Chances are you could do the exact quiz problem as an example, and it wouldn't affect the quiz scores. Students generally don't learn by watching you do a problem. They have to work through the problem themselves.

One thing I found helpful was seeing exams from others who taught the same class. That gave me a good feel for what I could expect from the students on exams.

The main thing I'd suggest is to avoid the traditional class where you lecture and students just take notes. Instead, do a brief lecture and then give the class a quick problem to work on to practice what you just explained. That will get the students to engage with the material, and give you a better feel for what they're capable of.

 

[mathwonk]

"My expectation is that they know how to do the standard arithmetic operations on fractions, what are exponents and their rules, factoring polynomials...etc."

at my state university in the south, even these expectations were certainly not met by even the students in my basic calculus courses.

 

[mathwonk]

...
to follow up more precisely, my working assumption eventually became that entering students do not, on average, know anything. thus everything used must be recalled in some form. one must recall e.g. the basic tool for factoring polynomials, namely the rational root theorem, and the root/factor theorem (the one that changes roots of form r into factors of form (x-r)). and this was for students taking the standard math courses, not the liberal arts version. when simplifying fractions, one must work out all the steps,...

students actually argued that it was unreasonable of me to expect them to remember material from a course taken in the previous spring, and have it ready for use in the fall, since it was only natural to forget things over the summer. Lists of prerequisites for the present course, even if handed out on day one, and posted publicly in advance, were simply ignored. ... I need to stop now, but I hope you get the point.

As a practical matter, spend some time at the beginning getting to know your students, and their background, as well as their aspirations. Try to learn their names, so you can call on them. Try to be sympathetic with, rather than critical of, their knowledge gaps. Maybe try some version of the phrase we all hear from experts on news shows: "that's a very good question..."

and by the way, i hope you do keep high your expectations of how well your students will perform in your course. I.e. having low expectations of prerequisites, or rather accurate ones, actually enhance the likelihood of maximizing how much they will take away. so don't expect too much on day one, but expect a lot on the last day.

good luck!

 

[kuruman]

Most of the students take this course is just for liberal arts requirement for critical thinking.

At my institution (Northeast), about 30 years ago , the math department sat down and rethought what kind of one-semester course would be an appropriate math requirement for students in liberal arts who are not planning to pursue math beyond that point. Up to that point, the math distribution requirement was satisfied with one semester of remedial algebra. They were looking for something that would stick with the students and would be functionally useful. Here is the official catalogue description. It was, and in all likelihood still is, a fun course.

Applications of Finite Math
Introduction to mathematics of finite systems with applications, such as probability, statistics, graph theory, fair division and apportionment problems, voting systems. Prerequisites: Two years of secondary school algebra.

I was chairing the college committee that studied the course and eventually approved it. The supporting argument of the proposers was simple and rang true to me. Something like "If they haven't learned exponents, factoring polynomials, etc. after two years of high school algebra, let's not try to teach them again something that they have already rejected as useless. Let's teach them how to critically view and appraise everyday math seen in statistics, probabilities, bar graphs with suppressed zeroes, etc. It's the kind of math that students see applied and functioning in their everyday lives. Something they might take home with them and perhaps even explain to others."

Of course, @cbarker1, you have no choice but to teach the course and content as assigned to you. However, if you are not content just following orders, you might consider convincing the powers that be at your institution that a separate but fun terminal math course may be needed as a liberal arts requirement. The downside of that is that you might get the response "We agree, why don't you design such a course and make a proposal to us?" so be prepared.

 

[cbarker1]

At my institution (Northeast), about 30 years ago , the math department sat down and rethought what kind of one-semester course would be an appropriate math requirement for students in liberal arts who are not planning to pursue math beyond that point. Up to that point, the math distribution requirement was satisfied with one semester of remedial algebra. They were looking for something that would stick with the students and would be functionally useful. Here is the official catalogue description. It was, and in all likelihood still is, a fun course.

Applications of Finite Math
Introduction to mathematics of finite systems with applications, such as probability, statistics, graph theory, fair division and apportionment problems, voting systems. Prerequisites: Two years of secondary school algebra.

I was chairing the college committee that studied the course and eventually approved it. The supporting argument of the proposers was simple and rang true to me. Something like "If they haven't learned exponents, factoring polynomials, etc. after two years of high school algebra, let's not try to teach them again something that they have already rejected as useless. Let's teach them how to critically view and appraise everyday math seen in statistics, probabilities, bar graphs with suppressed zeroes, etc. It's the kind of math that students see applied and functioning in their everyday lives. Something they might take home with them and perhaps even explain to others."

Of course, @cbarker1, you have no choice but to teach the course and content as assigned to you. However, if you are not content just following orders, you might consider convincing the powers that be at your institution that a separate but fun terminal math course may be needed as a liberal arts requirement. The downside of that is that you might get the response "We agree, why don't you design such a course and make a proposal to us?" so be prepared.

Unlikely that I have powers to persuade the powers to be, for I am just an graduate student. College algebra is requirement for education majors and stepping stone for other math courses (like trigonometry and Calculus I).

 

[cbarker1]

we do have that option in another course, it is call Mathematic (other word for "point of view").

 

[kuruman]

Unlikely that I have powers to persuade the powers to be, for I am just an graduate student. College algebra is requirement for education majors and stepping stone for other math courses (like trigonometry and Calculus I).

Ah, yes. If it's a prerequisite for other courses, then there is nothing more to say or do. I thought it was a distribution requirement for liberal arts students. Good luck.

 

[Hornbein]

The supporting argument of the proposers was simple and rang true to me. Something like "If they haven't learned exponents, factoring polynomials, etc. after two years of high school algebra, let's not try to teach them again something that they have already rejected as useless. Let's teach them how to critically view and appraise everyday math seen in statistics, probabilities, bar graphs with suppressed zeroes, etc. It's the kind of math that students see applied and functioning in their everyday lives. Something they might take home with them and perhaps even explain to others."

I taught a college statistics course which the students hated. They were required to memorize and apply calculation procedures. That would have been useful seventy years ago but now such things are programmed into calculators. The students resented having to learn this useless skill. I thought it would have been better to teach them how to interpret and criticize the results of a statistical report. This would have been better in a world filled with badly applied statistics.

 

[symbolipoint]

It's really hard to know without knowing what your expectations are.

I think the hardest thing to adjust to as a mathematician is that your students are not going to understand the concept of a proof. Even things like explaining FOIL as a repeated application of distribution is probably a struggle, because they aren't used to trying to think about things that way.

A mathematician can teach College Algebra, and just as well, an engineer, computer scientist, physicist, and a few other STEM types could also teach College Algebra.

A couple of courses which lead up to College Algebra as prerequisites are Geometry, and Intermediate Algebra. GEOMETRY course does include PROOFS.

You can bet your ... whatever... that students who qualify to reach enrollment to College Algebra already learned to understand and use this F.O.I.L. method and the Distributive Property. This they learned by the time they had finished Introductory/Elementary Algebra.

 

[symbolipoint]

my working assumption eventually became that entering students do not, on average, know anything. thus everything used must be recalled in some form. one must recall e.g. the basic tool for factoring polynomials, namely the rational root theorem, and the root/factor theorem (the one that changes roots of form r into factors of form (x-r)). and this was for students taking the standard math courses, not the liberal arts version. when simplifying fractions, one must work out all the steps,...

students actually argued that it was unreasonable of me to expect them to remember material from a course taken in the previous spring, and have it ready for use in the fall, since it was only natural to forget things over the summer. Lists of prerequisites for the present course, even if handed out on day one, and posted publicly in advance, were simply ignored. ... I need to stop now, but I hope you get the point.

WOW! I could tell you about what I witnessed among the other students and the instructor during my first day or two attending my first time as a college student in "Introductory Algebra", ... but I should rather not say. Let me just say, it was disappointing and frustrating and surprising.

 

[symbolipoint]

Back to the post #1, what is the justification for "Liberal Arts" students to earn credit for "College Algebra"? We can understand damn-well why science & engineering students need College Algebra, but not too clear is why the Liberal Arts people need this course.

 

[Office_Shredder]

A mathematician can teach College Algebra, and just as well, an engineer, computer scientist, physicist, and a few other STEM types could also teach College Algebra.

I would expect most of those people to be familiar with the idea of a proof as well by the time they finish their degree, and would think explaining foil as an example of distribution to be conceptually trivial.

A couple of courses which lead up to College Algebra as prerequisites are Geometry, and Intermediate Algebra. GEOMETRY course does include PROOFS.

You need to adjust your expectations down more if you are relying on your students who decided they didn't like doing math and are studying something unrelated to it to have mastered the concepts of all the prerequisites.

The people who actually know all that are probably taking calculus.

I would also be surprised if geometry is actually a prerequisite. I think in most schools it is not, and you never have to take geometry.

You can bet your ... whatever... that students who qualify to reach enrollment to College Algebra already learned to understand and use this F.O.I.L. method and the Distributive Property. This they learned by the time they had finished Introductory/Elementary Algebra.

They probably know what foil is, that's not the same as being able to explain it.

I might be a little pessimistic, but if you are relying on their extensive previous coursework to carry them through your course I think you will find them struggling. I guess mathwonk agrees with me

Back to the post #1, what is the justification for "Liberal Arts" students to earn credit for "College Algebra"? We can understand damn-well why science & engineering students need College Algebra, but not too clear is why the Liberal Arts people need this course.

This is a totally reasonable question. I don't actually know. I think it's probably because everyone knows people who are in a STEM field are smart, so figure if they teach people math, those people will be smart and useful too (I don't mean to imply that only people who do stem are smart and useful, or that everyone who does stem is smart and useful)

Ironically, if you wanted people to learn to be rigorous in their logical thinking, which is often one of the professed reasons for teaching math, then you would want to do a proof based course.

 

[symbolipoint]

They probably know what foil is, that's not the same as being able to explain it.

I might be a little pessimistic, but if you are relying on their extensive previous coursework to carry them through your course I think you will find them struggling.

Some several years ago was a short period of understanding that FOIL, Distributive Property, long-hand Multiplication according to Place Value, and Multiplication using Lattice Method, all came together as being all the same thing.

 

[cbarker1]

Back to the post #1, what is the justification for "Liberal Arts" students to earn credit for "College Algebra"? We can understand damn-well why science & engineering students need College Algebra, but not too clear is why the Liberal Arts people need this course.

In my school, in our liberal arts requirement for critical thinking, you can do philosophy or mathematics-college algebra, pre-cal, calculus 1, trigonometry, or math perspective courses. Some people have to take it for there education degree as requirement to get license in my state.

 

[symbolipoint]

In my school, in our liberal arts requirement for critical thinking, you can do philosophy or mathematics-college algebra, pre-cal, calculus 1, trigonometry, or math perspective courses. Some people have to take it for there education degree as requirement to get license in my state.

Thanks for the try, but I cannot yet recognize the justification about which I asked. Philosophy, Pre-Calc/College Algebra, "Math Perspectives" are each far too different from each other; and "license" requirement is not the same as "justification".

 

[cbarker1]

Thanks for the try, but I cannot yet recognize the justification about which I asked. Philosophy, Pre-Calc/College Algebra, "Math Perspectives" are each far too different from each other; and "license" requirement is not the same as "justification".

Here is the list of course that satisfy this requirement.

 

[cbarker1]

No malicious issues from this pdf, it is just a list of course.

 

[berkeman]

Some people have to take it for there education degree as requirement to get license in my state.

What kind of license? I can see the Business Statistics pre-req for an MBA, maybe. But what other professional licenses in Liberal Arts would require math classes?

 

[cbarker1]

Mostly Teaching licenses in my state. They might have to pass college algebra to go to the next course (business math course), or the nursing students might have to pass college algebra to go into elementary stats.

 

[symbolipoint]

The best answer to my question about "justification" goes to the "modern" meaning of Liberal Arts, as explained in https://en.wikipedia.org/wiki/Liberal_arts_education , the Modern Usage section of that article.

 

[berkeman]

Mostly Teaching licenses in my state. They might have to pass college algebra to go to the next course (business math course)

That makes sense, thanks.

or the nursing students might have to pass college algebra

OMG, I hope so for nursing students! There is a fair amount of mental math that we use in EMS and I know that is used in nursing.

Practice Problem: Safe Dosage Range

Billy is an 8-month-old infant who weighs 7 kg. He has been prescribed acetaminophen 100 mg every 4-6 hours PO for a fever. The recommended dosage range for infants is 10-15 mg/kg/dose. Calculate the acceptable dosage range for Billy and determine if the prescribed dose is safe.

1. Calculate the low end of the safe dosage. Start by identifying the goal unit. For this problem we want to know the dose in milligrams:

https://wtcs.pressbooks.pub/nursingskills/chapter/5-12-safe-dosage-range/

 

[vanhees71]

Well, I can't find anything wrong with demanding some exposure of philosophers with mathematics although mathematics nowadays is not understood as part of philosophy anymore but building, together with informatics, an own group of sciences called "structural sciences".

 

[Drakkith]

As a former student and tutor myself (within the past 5 years) I can confidently say that we students do our utmost best to completely and utterly disappoint you when it comes to expectations about most things. Especially when it comes to subjects we aren't interested in.

Learning is difficult. It requires an enormous amount of effort and time, and the majority of people will have to be forced, kicking and screaming almost, to simply do their homework, let alone put in any extra time and effort at something they don't really understand even if they pass the course. This is doubly true for those people who never developed a good learning and work ethic in high school. College is so much more challenging that not only do they have to learn the material, they also have to learn how to learn at the same time.

 

[vanhees71]

As a former student and now tutor I don't blame the students but rather their high school teachers. It's amazing, at least in Germany, how much effort is put into the system by politicians and so-called pedagogics experts with the only result making it weaker and weaker with the years. Just these days they repeated another study on the outcome of teaching at the high schools, and everything went down compared to the results of the same study about 10 years ago.

I think the biggest mistake is to think that by lowering the standards in content you could make school education more just towards students with a less "academic background" of their parents. Although it's the declared goal in Germany to make the educational system better to gain a better education for this group, the OECD always tells us that this system is among the ones failing this goal most in the developed countries. In my opinion to lower the standards is the opposite that helps particularly these pupils. You'd rather need a better standard the expose them to the more advanced topics of higher education.

Another wrong idea is what's called "competence orientation". Particularly in STEM this is a counterproductive idea. It means you just train on "solving" a lot of standard problems without really understanding, why these standard solution techniques solve the problem. I'm always amazed how little students understand about the intuitive meaning of basic calculus and vector algebra although these are among the prime subjects in the two final years of high-school education in math. E.g., they know very well, how to find the local extrema of a real function, but when you ask them, why the first derivative should vanish and why the 2nd derivative shouldn't or what happens if it does, they all too often don't know. That means that the fundamental ideas behind calculus have not been taught adequately. To be able to mechanically take derivatives of all kinds of functions without knowing that it is the slope of tangents of the graph of this functions is pretty useless for what you need as a STEM student at university.

 

[symbolipoint]

Another wrong idea is what's called "competence orientation". Particularly in STEM this is a counterproductive idea. It means you just train on "solving" a lot of standard problems without really understanding, why these standard solution techniques solve the problem.

"Competence" is not used exactly the same way in every region, in every system of education. Some institutions categorize parts of their system as Competence Based, and include very precise and thorough course objectives.

 

[vela]

My expectation is that they know how to do the standard arithmetic operations on fractions, what are exponents and their rules, factoring polynomials...etc.

Don't be surprised if some students still have trouble with these basics. I've had physics and engineering students who make some pretty basic mistakes. I feel often it's that students don't realize that expectations have changed. A student might feel he or she has an adequate handle on a technique if they can eventually get to the right answer after a mistake is pointed out to them, but I tell my students that they shouldn't be making these kinds of mistakes anymore, the math is only going to get harder in subsequent years, and they need to figure it out now. Of course, the advice might fall on deaf ears, but when they start losing points on exams for dumb mistakes, it usually provides the needed motivation.

That said, I don't find the horror stories one often hears to be terribly representative, either. I find most of my students have a decent handle on previous material, but they're just, to my mind, terribly slow at doing calculations. That was the main adjustment to my expectations (regarding math) I had to make.

 

[Mark44]

A couple of courses which lead up to College Algebra as prerequisites are Geometry, and Intermediate Algebra. GEOMETRY course does include PROOFS.

You and I had a conversation several years ago about geometry. Very few colleges or community colleges offer courses in geometry, despite the fact that you found one in So. Calif. that does offer such a class.

I would also be surprised if geometry is actually a prerequisite. I think in most schools it is not, and you never have to take geometry.

Probably true.

Back to the post #1, what is the justification for "Liberal Arts" students to earn credit for "College Algebra"?

This is a totally reasonable question. I don't actually know. I think it's probably because everyone knows people who are in a STEM field are smart, so figure if they teach people math, those people will be smart and useful too

Or maybe it's the desire of college math departments to insist that a "college-educated" person should be well-rounded enough to actually know a little bit of mathematics, at least up to the level attained in the 14th century. Certainly, students in medical-related fields such as nursing should have enough algebra skills to be able to calculate drug doses based on patient weight.

When I was in grad school a young woman lived in another apartment in the house where I was living. She was an art major, and confessed to me that she had never learned how to do long division. I didn't say anything, but I was shocked to learn that someone who had made it all the way to a university didn't know something as simple as ordinary arithmetic.

 

[symbolipoint]

A couple of courses which lead up to College Algebra as prerequisites are Geometry, and Intermediate Algebra. GEOMETRY course does include PROOFS.

From Mark44:

You and I had a conversation several years ago about geometry. Very few colleges or community colleges offer courses in geometry, despite the fact that you found one in So. Calif. that does offer such a class.

They were common enough offerings at the CC's at the time. I had still seen many of the CC's still listing them a few years ago. I'll have another look online sometime tonight to see what is where these days.

 

[symbolipoint]

When I was in grad school a young woman lived in another apartment in the house where I was living. She was an art major, and confessed to me that she had never learned how to do long division. I didn't say anything, but I was shocked to learn that someone who had made it all the way to a university didn't know something as simple as ordinary arithmetic.

An easy tutoring opportunity, but maybe without your being paid.

 

[symbolipoint]

The question about presence of Geometry courses, from post #31 & #32:
I just checked online information for four community colleges within a local 12 mile radius.
2 had it and 2 did not.

 

[Mark44]

The question about presence of Geometry courses, from post #31 & #32:
I just checked online information for four community colleges within a local 12 mile radius.
2 had it and 2 did not.

That's a very small sample.