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Question for Math People re: college math: What is introductory algebra? Intermediate algebra?


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They usually come before College Algebra. Introductory is first, then Intermediate, then College. Introductory is sometimes also called Beginning. After College Algebra, the course names are not uniform. Sometimes Trigonometry and sometimes Precalculus, but both of these are fairly common.

 

Content-wise, a student who has passed AND UNDERSTOOD (this is important) high school Algebra I ought to place into Intermediate. A student who has passed and understood high school Algebra II ought to place into College Algebra or Precalculus, depending on the strength of their high school curriculum. Even if the placement test score indicates a higher placement, I would not recommend placing higher than that. However, if the placement test score indicates a lower placement, I would go with the college's recommendation and assume that the basics had not been thoroughly mastered.

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I did undergrad out in the UC system. There, there was only one quarter-long course before calculus. So in 9 weeks (10 counting finals), we covered all of precalc - college algebra & trig. If a student needed any earlier math, they could take it at a cc. I think that's appropriate.

 

It will vary from school to school whether precalc is considered "college" level or not. I vote not, however many schools will give college credit for it.

 

Look at course descriptions to see what content is in each class.

 

Where I'm teaching now, Introductory Algebra is basically high school Algebra 1. We review basic arithmetic (sigh), cover solving linear equations & inequalities, graphing linear equations and inequalities in 2 variables (along with slope & equations of lines), exponential arithmetic, polynomial arithmetic, scientific notation, factoring & solving quadratic equations by factoring.

 

Intermediate Algebra is basically Algebra 2. We cover arithmetic with rational expressions, solving rational equations, arithmetic with radicals, solving radical equations, solving systems of equations (2 variables, sometimes 3 depending on what text we use), review of graphing, generally including graphing absolute value functions, generally some talk about functions, occasionally discussing function arithmetic and inverses (again, dependent on text and timing), and graphing parabolas and solving quadratics by using the quadratic formula.

 

College Algebra includes rational roots theorem, graphing by translations, exponential and logarithmic functions, and depending on timing, conic sections.

Trigonometry includes trig.

 

And then you finally get to first year college level work.

 

I'm teaching developmental math... prealgebra.

I would be amazed if my 10 yo weren't able to pass my course.

But some students really need to start at a lower level. I'm just dreadfully frustrated by the students who are straight out of high school - who have a hs diploma - and then test into a course that is lower than they can get high school credit for.

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It will vary from school to school whether precalc is considered "college" level or not. I vote not, however many schools will give college credit for it.

 

 

Fortunately most non-stem colleges disagree with that. There are exceptions, but most of the majors my kids have looked at don't even require calculus for graduation. Some require only college algebra and some pre-calc. This is very much one of those university dependent question.

 

To the OP, many people on these boards use Introductory/Beginning Algebra texts for high school algebra 1, and Intermediate Algebra books for high school Algebra 2. I agree with Sue's equivalencies.

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  • 2 weeks later...

Thanks, everyone. Is Beginning Algebra the same thing as Introductory Algebra?

 

And to further muddy the water:

What is College Mathematics? I know that there is a CLEP test for College Mathematics. Would that be the same material as what is covered in Lial's Basic College Mathematics? Or maybe Introductory Algebra?

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Beginning and Introductory Algebra are two names for Algebra I

 

The CLEP college mathematics is essentially a math for liberal arts course and should follow high school algebra and geometry. I wouldn't recommend it unless the student's already picked a college and knows they'll get college credit for it. Many won't give credit for this because they want you to take THEIR version of the math for liberal arts course. It is not the same as BCM, which is before algebra 1.

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Beginning and Introductory Algebra are two names for Algebra I

 

The CLEP college mathematics is essentially a math for liberal arts course and should follow high school algebra and geometry. I wouldn't recommend it unless the student's already picked a college and knows they'll get college credit for it. Many won't give credit for this because they want you to take THEIR version of the math for liberal arts course. It is not the same as BCM, which is before algebra 1.

 

Thanks, Kiana. I know that CLEP offers a College Mathematics test that offers up to 6 hours of credit at some colleges, but that some colleges do not give credit for it. My son was a music major at a small private college; music majors were required to take only 2 math courses: College Mathematics and College Algebra. He took the CLEP tests for both and earned credit for each at his college.

 

Currently, I am teaching a small group of girls (children of friends) in my home each day. Two of my students (9th & 11th grades next year) just. do. not. get. math. Both plan to go on to college, and our state university system admission requirements include 4 years of high school math, beginning with Algebra 1 (or Math 1 if the high school uses integrated math). That means Algebra 1, Geometry, Algebra 2, and an additional math beyond Algebra 2. Students can no longer get a math credit for Consumer Math, but I think it can be counted for elective credit. So... for now I am planning to have my students take College Mathematics their senior year. I don't think they would ever be able to handle Algebra 3/Precalculus or Calculus. I don't care if they don't get college credit for it--I'm not even sure they would bother to take the CLEP test.--I just need a 4th math (that they can pass) to put on the transcripts!

 

P.S. I'm hoping someone can recommend a good College Mathematics textbook.

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I'm planning on using Thinking Mathematically by Blitzer. There is also a youtube channel with review videos for all chapters of the book, www.youtube.com/user/blitzerthinkingmath .

 

Thanks for the recommendation. Is this book used in college mathematics courses--"math for non-math majors" or "liberal arts math"--but not remedial?

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Thanks for the recommendation. Is this book used in college mathematics courses--"math for non-math majors" or "liberal arts math"--but not remedial?

 

I haven't taught from it, but I'd say it's likely pretty remedial and for non majors.

At our cc, this text is used for a terminal course that wouldn't get transfer credit at the university. The course at our school is less than algebra 1 but a bit more than prealgebra... kind a survey course. Some business math, some set notation, but nothing that leads anywhere.

 

You can look at Interact software and see types of problems in multiple different texts (most things that Pearson publishes).

 

You can see on your cc or university website if they have any type of flow-chart for math courses within the math department.

 

If someone told me they were taking "college mathematics" I wouldn't know what they were taking... and I've been teaching at the cc for about 15 years now.... It's just not a standard phrase.

 

You may want to look at course descriptions in a college course catalog. That'll tell the topics they cover in a course. You can also look at what texts they use. Many schools have their syllabus online. THat may give some useful information for you too.

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. I don't think they would ever be able to handle Algebra 3/Precalculus or Calculus. I don't care if they don't get college credit for it--I'm not even sure they would bother to take the CLEP test.--I just need a 4th math (that they can pass) to put on the transcripts!

 

 

I think it can just take starting at the right level...as basic as it needs to be...and then progress.

I met a good friend when I TAed for a calc 1 class he was taking. He'd come from a poor high school, took math starting at the lowest possible level at a cc in the country. He was one of 4 A grades out of a calc class of 70!

 

He started at the right level and was motivated.

 

I see students every semester who have 3 or 4 years of math at the high school level...including precalc...who test into developmental math because they just didn't learn the material.

 

So some ideas for your class... You can see where they are and try to fill in blanks (I can almost guarantee fractions and word problems are a gap). I'm not sur what our call the class though.... That's where you might be doing the "basic college math". You could do statistics. A course on set theory or logic. Logic was something I recall students taking to get a quant requirement in college that wasn't math or science :). ALthough logic is math, it was taught by, I think, the philosophy department.

 

You could also check out high school course descriptions. I've looked at local schools some and they have a lot of different names for courses....see if any of the names give you ideas!

 

Good luck!

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Thanks for the recommendation. Is this book used in college mathematics courses--"math for non-math majors" or "liberal arts math"--but not remedial?

 

 

It's usually used in Liberal Arts Mathematics courses (i.e. math for non-math majors- sometimes called A Survey of Mathematics). Here is a breakdown of CLEP College Mathematics topics, all of which are covered in Thinking Mathematically:

 

10%

Sets

  • Union and intersection

  • Subsets, disjoint sets, equivalent sets

  • Venn diagrams

  • Cartesian product

 

10%

Logic

 

  • Truth tables

  • Conjunctions, disjunctions, implications, and negations

  • Conditional statements

  • Necessary and sufficient conditions

  • Converse, inverse, and contrapositive

  • Hypotheses, conclusions, and counterexamples

 

20%

Real Number System

 

  • Prime and composite numbers

  • Odd and even numbers

  • Factors and divisibility

  • Rational and irrational numbers

  • Absolute value and order

  • Open and closed intervals

 

20%

Functions and Their Graphs

 

  • Properties and graphs of functions

  • Domain and range

  • Composition of functions and inverse functions

  • Simple transformations of functions: translations, reflections, symmetry

 

25%

Probability and Statistics

 

  • Counting problems, including permutations and combinations

  • Computation of probabilities of simple and compound events

  • Simple conditional probability

  • Mean, median, mode, and range

  • Concept of standard deviation

  • Data interpretation and representation: tables, bar graphs, line graphs, circle graphs, pie charts, scatterplots, histograms

 

15%

Additional Topics from Algebra and Geometry

 

  • Complex numbers

  • Logarithms and exponents

  • Applications from algebra and geometry

  • Perimeter and area of plane figures

  • Properties of triangles, circles, and rectangles

  • The Pythagorean theorem

  • Parallel and perpendicular lines

  • Algebraic equations, systems of linear equations, and inequalities

  • Fundamental Theorem of Algebra, Remainder Theorem, Factor Theorem

 

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Thanks for the recommendation. Is this book used in college mathematics courses--"math for non-math majors" or "liberal arts math"--but not remedial?

I live in a city with 4 colleges. A community college, two state universities and a Keiser University. All four use Blitzers Thinking Mathematically as a 2 semester, college level text for math --- for non-majors.

 

The classes are mostly called "Liberal Arts Math 1" and "Liberal Arts Math 2". I know for a fact that 6 other universities in my state

use the same or similar books for classes of equal weight. the class is worth 3 College credits.

The classes are called Liberal Arts I and II or a Survey of Mathematics I and II.

 

You have to have passed Intermediate Algebra in order to take Liberal Arts at every school I checked into.

 

The CLEP College Mathematics Exam gives credit for the Liberal Arts Sequence, depending on how you place on it, though I don't know the exact details.

I think that there is also an exam for College Algebra, but I'm not 100% sure about that. I know some students took a Placement exam at our CC and got credit for PreCalc and Trig. I think it is possible to place into Calculus 1, if you just know who to ask and where to look.

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I live in a city with 4 colleges. A community college, two state universities and a Keiser University. All four use Blitzers Thinking Mathematically as a 2 semester, college level text for math --- for non-majors.

 

The classes are mostly called "Liberal Arts Math 1" and "Liberal Arts Math 2". I know for a fact that 6 other universities in my state

use the same or similar books for classes of equal weight. the class is worth 3 College credits.

The classes are called Liberal Arts I and II or a Survey of Mathematics I and II.

 

You have to have passed Intermediate Algebra in order to take Liberal Arts at every school I checked into.

 

The CLEP College Mathematics Exam gives credit for the Liberal Arts Sequence, depending on how you place on it, though I don't know the exact details.

I think that there is also an exam for College Algebra, but I'm not 100% sure about that. I know some students took a Placement exam at our CC and got credit for PreCalc and Trig. I think it is possible to place into Calculus 1, if you just know who to ask and where to look.

 

 

Thanks! Yes, there is a College Algebra CLEP exam. My son was a music major at a small private college; music majors were required to take only 2 math courses: College Mathematics and College Algebra. He took the CLEP tests for both and earned credit for each at his college. We didn't really look closely at the College Mathematics since he didn't have to take it, so I was wondering exactly what it is. How does it compare to PreCalculus? Does it contain Trigonometry?

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It's usually used in Liberal Arts Mathematics courses (i.e. math for non-math majors- sometimes called A Survey of Mathematics). Here is a breakdown of CLEP College Mathematics topics, all of which are covered in Thinking Mathematically:

 

10%

Sets

  • Union and intersection

  • Subsets, disjoint sets, equivalent sets

  • Venn diagrams

  • Cartesian product

 

10%

Logic

 

  • Truth tables

  • Conjunctions, disjunctions, implications, and negations

  • Conditional statements

  • Necessary and sufficient conditions

  • Converse, inverse, and contrapositive

  • Hypotheses, conclusions, and counterexamples

 

20%

Real Number System

 

  • Prime and composite numbers

  • Odd and even numbers

  • Factors and divisibility

  • Rational and irrational numbers

  • Absolute value and order

  • Open and closed intervals

 

20%

Functions and Their Graphs

 

  • Properties and graphs of functions

  • Domain and range

  • Composition of functions and inverse functions

  • Simple transformations of functions: translations, reflections, symmetry

 

25%

Probability and Statistics

 

  • Counting problems, including permutations and combinations

  • Computation of probabilities of simple and compound events

  • Simple conditional probability

  • Mean, median, mode, and range

  • Concept of standard deviation

  • Data interpretation and representation: tables, bar graphs, line graphs, circle graphs, pie charts, scatterplots, histograms

 

15%

Additional Topics from Algebra and Geometry

 

  • Complex numbers

  • Logarithms and exponents

  • Applications from algebra and geometry

  • Perimeter and area of plane figures

  • Properties of triangles, circles, and rectangles

  • The Pythagorean theorem

  • Parallel and perpendicular lines

  • Algebraic equations, systems of linear equations, and inequalities

  • Fundamental Theorem of Algebra, Remainder Theorem, Factor Theorem

 

 

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