For those of you familiar w/ college level math...

[distancia]

Those of you who have taught or have experienced college level math--Calculus, etc. maybe you can answer a question for me. D and I are butting heads on this. :boxing_smiley:

 

In earlier years there is always emphasis on concepts such as "associative property" and "multiplicative inverse" and things like that.

 

Questions: Is it important that the student actually know what these properties are called? How important is it that the student understands what these phrases mean? Ditto for such terms as "whole numbers" "real numbers" "irrational numbers" kind of thing.

My D (17.5) is doing a whirlwind remedial math now and she is on fractions. She is balking at learning the terminology, she says as long as she can do the problem, there is no reason to know anything more. She says these terms will serve no purpose later when she gets into Pre-Calc and Calc (God bless her if she ever gets that far). :Angel_anim:

 

Next week she moves into a Pre-Algebra refresher. Again, I am anticipating tremendous resistance.:banghead: She says she "already knows this stuff" but when I gave her the placement test just last week she could do only 20% of the problems, the rest were "I forgot how to do it."

 

D is asking me to just give her a workbook so she can quickly (like, 1 day?) whip through the problems and then consider herself "all done". I, on the other hand, am insisting she at least sit through the Math-U-See video and work a few problems after each short episode. It should take her no more than a week, if she spends an hour a day on it. But I can't even get her to do that, she says it is "so beneath her" and she wants to immediately lunge into Pre-Calc...never mind that she needs a complete review of Geometry, which she never understood from Day 1.

 

Question: Is there any way I can make it clearer to her that these foundation skills are absolutely, positively essential to higher math? I need an expert to tell her...coming from me (Mom) just doesn't cut it. :willy_nilly:

Edited September 16, 2010 by distancia
I am going insane and I need emoticons that express this

[Twigs]

I'm not a teacher, but my degree is in Physics, so I did have lots of math!

 

Those terms are very important. As you get into Trig, Calculus, etc. there will be proofs of new concepts and the terms will be used in the proofs. A phrase such as "by the _____ property …" will be used and the teacher will expect the student to know that property. I also had definitions on exams, not just problems.

 

It is just as important to know the terms in math as it is in literature (narrative, character, plot), grammar (noun, vert, indirect object), music (largo, alto, percussion). If you are unfamiliar with the terms, you cannot even discuss the subject. This is just as true in math. A working vocabulary of a subject is one of the marks of an educated person.

 

Best wishes.

[Barb_]

Math is a language. In order to talk to people more knowledgeable than you (IE professors), you must be able to use the same vocabulary. I always tell my youngers that some days we learn concepts and some days we are just learning new vocabulary and rules for concepts we already know. Once we all agree on the terminology and the basic premises for higher math we can spend all of our time tripping around on higher level concepts and exciting new puzzles instead of saying, "You know that thing where it doesn't matter which term you add stuff with? Well this is kind of like that but different..." You just use the agreed-upon vocabulary.

 

Barb

[G5052]

I'm an IT community college professor, but I like chatting with the math professors, and one of their major beefs is that students don't know the definitions and therefore can't do more complex problems. According to them, this is also the #1 reason that students end up in remedial math. You won't get far without definitions.

 

My poor children drill on definitions as well as doing problems for this reason.

 

Just a thought -- have you actually taken her for placement testing at a community college? I know people who have done this when their teens claimed greater math skills than they knew they actually had. For $25 it was worth showing them that they still didn't have their algebra and geometry skills down. In my state, dual enrollment students can't take those courses at the CC -- they have to test as being ready for at least pre-calculus. So homeschooled students who aren't ready for pre-calculus at the CC either have to make that up at home, take a paid homeschool class, or graduate early and start regular enrollment at the CC.

Edited September 16, 2010 by GVA

[Sunshine State Sue]

First, I'll tell you a bit of my qualifications. I have a bachelor's in math and computer science that is 25+ years old. I have a master's in Industrial Engineering that is 20+ years old. I tutored Prob & Stat while I was a graduate student. I work as a programmer. For "fun", I took a Statistics class last summer at the CC. Ds is in 9th grade and we are working on Geometry (the only math class I hated) this year. I also do not have the best memory. Neither does ds. I am very, very willing to use reference materials. He barely bothers.

 

I don't think having the terminology on the tip of your tongue is absolutely necessary.

 

If she "already knows this stuff", but can only demonstrate 20%, she needs a refresher. She should be able to demonstrate her knowledge.

 

We used MUS from K through Algebra 1. One thing I really like about MUS is that I could give ds the test first. If he scored well, we'd skip the lesson. If not, we'd go over the lesson.

 

In the big scheme of things, I don't think Geometry is that necessary.

 

My 2c. There are others on this board (Jann in TX, for one) who probably know better than me. I'd take her advice over mine any day.

 

Good luck! And I hope your dd will thank you one day for caring enough to go through the pain of forcing her through remedial math. :grouphug:

[Sunshine State Sue]

Those terms are very important. As you get into Trig, Calculus, etc. there will be proofs of new concepts and the terms will be used in the proofs. A phrase such as "by the _____ property …" will be used and the teacher will expect the student to know that property. I also had definitions on exams, not just problems.

 

 

Math is a language. In order to talk to people more knowledgeable than you (IE professors), you must be able to use the same vocabulary.

 

I'm an IT community college professor, but I like chatting with the math professors, and one of their major beefs is that students don't know the definitions and therefore can't do more complex problems. According to them, this is also the #1 reason that students end up in remedial math. You won't get far without definitions.

 

 

Okay, I'm outnumbered. You can disregard what I said about this. ;)

[Julie of KY]

I'll agree with you Sue.

 

I'm a chemical engineer and I teach and tutor math and chemistry. I think it is absolutely necessary to know how to use all the properties of math, but knowing the language is not important to understanding the problems.

 

The language does become important to understand what a text is asking (name an integer that ...), understanding a professor, and math competitions.

 

To this day, I can't tell you which property is which. I know ab=ba, a+b=b+a; a(b+c)=ab+ac, etc, but I can't LABEL the properties. I know the general definitions of integer, whole number, etc., but I can't tell you the nitty-gritty of what includes zero etc.

 

I was competitive nationally in math exams in high school and top of my class in college, but I see numbers and ideas and not definitions. It also drove my calculus professors nutty that I couldn't memorize formulas, but I could derive them on the fly in the margins of my paper. Eventually I use the formulas enough to memorized them but if you UNDERSTAND them then you don't have to memorize any.

[Teachin'Mine]

Question: Is there any way I can make it clearer to her that these foundation skills are absolutely, positively essential to higher math? I need an expert to tell her...coming from me (Mom) just doesn't cut it.

 

If she insists that she doesn't need any review and is good to go for pre-calc, the easiest way to settle the issue is to let her do pre-calc. She may make it through a few lessons okay, but it won't take long before she'll be struggling if she hasn't fully mastered algebra and geometry. Sometimes it's easier to let them try what they think they can do, than to get them to agree with you. Have all the refresher materials ready for when she needs them. :)

 

I agree that the terminology is important.

[distancia]

Just a thought -- have you actually taken her for placement testing at a community college? I know people who have done this when their teens claimed greater math skills than they knew they actually had. For $25 it was worth showing them that they still didn't have their algebra and geometry skills down.

 

Yes, she tested at the CC a little over a year ago and her tests showed she needed to be in remedial math. Then she took 1/2 semester of Alg 2 and scored a 500 on her Math SAT--still not high enough to allow her into College Math, but putting her into Intermediate Math. Since she has now been 9 months without math I thought it best to bring her all the way back to fractions, since that is where last week's placement test showed her weaknesses starting at. D continues to insist she knows the math, and the problem is that "something is wrong with the tests."

[Dana]

In earlier years there is always emphasis on concepts such as "associative property" and "multiplicative inverse" and things like that.

 

Questions: Is it important that the student actually know what these properties are called? How important is it that the student understands what these phrases mean? Ditto for such terms as "whole numbers" "real numbers" "irrational numbers" kind of thing.

My D (17.5) is doing a whirlwind remedial math now and she is on fractions. She is balking at learning the terminology, she says as long as she can do the problem, there is no reason to know anything more. She says these terms will serve no purpose later when she gets into Pre-Calc and Calc (God bless her if she ever gets that far). :Angel_anim:

 

 

Question: Is there any way I can make it clearer to her that these foundation skills are absolutely, positively essential to higher math? I need an expert to tell her...coming from me (Mom) just doesn't cut it. :willy_nilly:

 

I have a MAT in mathematics education and have been teaching at the cc for (urgh) over 14 years now. (Hitting MAJOR burnout with this first set of tests I'm grading this weekend.) I have taught developmental math (in some cases to students who didn't even know their multiplication tables) up through calculus 1.

 

Depending on how far your daughter will go in math, it may be possible that she doesn't need to know the terminology for commutative, associative, identity, and inverse properties. (I think it's still good and important to know them... for instance it's neat to know that not all multiplication systems have the commutative property (a*b=b*a). Matrices don't.) The distributive property is one that she will have to know by name.

 

Understanding what they mean is important though.

The identity property for multiplication means that we can multiply by 1 and we have the same number. This is crucial because it is how we write equivalent fractions. If you don't understand that that is because multiplication by 1 doesn't change the number (the identity property of multiplication), then you're not doing math, you're doing some type of magical alchemy.

 

(Sorry if I'm punchy and this isn't making enough sense... I'm just back from a really frustrating class trying to teach students how to solve linear equations and getting "But I do it..." "Why do I have to..." etc. I was telling my husband on the drive home that I can teach my 8-yr-old how to solve a linear equation by "do this, then this" and he would be able to solve them but he wouldn't be understanding it. I swear that's what so many of my students are doing. And then the nitwits are resistant to making any changes... but what they're doing ISN'T WORKING!!!! (And I really don't want to grade their tests! Yes, they're that bad. I have students who still haven't bought the dratted textbook. They are going to flunk.) Sigh.)

 

I do teach types of numbers. The history of math is pretty cool and there are some neat stories with irrational numbers & the Pythagoreans.

 

Terminology does matter - and having really good skills with fractions is important. Pick up any algebra textbook. Rational numbers is your basic arithmetic with fractions. Rational expressions expands that to where your numerator and denominator are polynomials instead of integers. The patterns and procedures are still the same. So for adding two fractions, you need a common denominator (multiply by 1... there's that identity property of multiplication again!). Same thing happens when adding two rational expressions... but now finding the common denominator gets much nastier... especially if you don't understand what you were doing initially.

 

I see so very many students who think they already know the material because they've seen it before and have the "I don't need to know that" attitude. They're wrong.

 

Taking the placement test would be a very good idea. I see students who have taken calculus in high school place into what's the equivalent of algebra I or lower... because they don't understand the basics. It is the very basic algebra skills that really hurt students later on, so it's crucial to have them SOLID.

 

(Questioning whether to post this after blathering on and venting so much... happy to expand on anything if there are more questions but only after I've slept... and son's sniffling, so it may be a long night... (sigh). Hope something may be some help.... and I'm coming from two rough classes with some students with poor attitude and a dreadful set of tests. So if I caused any offense, I apologize. But basically, tell your daughter a math instructor tells her to buckle down and learn the stuff. Doing the problems means very little. It's only if you can take a cumulative test and do well on it that you've actually learned the material.

[Barb_]

But basically, tell your daughter a math instructor tells her to buckle down and learn the stuff. Doing the problems means very little. It's only if you can take a cumulative test and do well on it that you've actually learned the material.

 

Great post, Dana. I agree. The answer isn't the point. The process is the point.

[Julie of KY]

I agree. Your daughter has to understand the math before she can do anything with it.

[creekland]

I have a MAT in mathematics education and have been teaching at the cc for (urgh) over 14 years now. (Hitting MAJOR burnout with this first set of tests I'm grading this weekend.) I have taught developmental math (in some cases to students who didn't even know their multiplication tables) up through calculus 1.

 

Depending on how far your daughter will go in math, it may be possible that she doesn't need to know the terminology for commutative, associative, identity, and inverse properties. (I think it's still good and important to know them... for instance it's neat to know that not all multiplication systems have the commutative property (a*b=b*a). Matrices don't.) The distributive property is one that she will have to know by name.

 

Understanding what they mean is important though.

The identity property for multiplication means that we can multiply by 1 and we have the same number. This is crucial because it is how we write equivalent fractions. If you don't understand that that is because multiplication by 1 doesn't change the number (the identity property of multiplication), then you're not doing math, you're doing some type of magical alchemy.

 

(Sorry if I'm punchy and this isn't making enough sense... I'm just back from a really frustrating class trying to teach students how to solve linear equations and getting "But I do it..." "Why do I have to..." etc. I was telling my husband on the drive home that I can teach my 8-yr-old how to solve a linear equation by "do this, then this" and he would be able to solve them but he wouldn't be understanding it. I swear that's what so many of my students are doing. And then the nitwits are resistant to making any changes... but what they're doing ISN'T WORKING!!!! (And I really don't want to grade their tests! Yes, they're that bad. I have students who still haven't bought the dratted textbook. They are going to flunk.) Sigh.)

 

I do teach types of numbers. The history of math is pretty cool and there are some neat stories with irrational numbers & the Pythagoreans.

 

Terminology does matter - and having really good skills with fractions is important. Pick up any algebra textbook. Rational numbers is your basic arithmetic with fractions. Rational expressions expands that to where your numerator and denominator are polynomials instead of integers. The patterns and procedures are still the same. So for adding two fractions, you need a common denominator (multiply by 1... there's that identity property of multiplication again!). Same thing happens when adding two rational expressions... but now finding the common denominator gets much nastier... especially if you don't understand what you were doing initially.

 

I see so very many students who think they already know the material because they've seen it before and have the "I don't need to know that" attitude. They're wrong.

 

Taking the placement test would be a very good idea. I see students who have taken calculus in high school place into what's the equivalent of algebra I or lower... because they don't understand the basics. It is the very basic algebra skills that really hurt students later on, so it's crucial to have them SOLID.

 

(Questioning whether to post this after blathering on and venting so much... happy to expand on anything if there are more questions but only after I've slept... and son's sniffling, so it may be a long night... (sigh). Hope something may be some help.... and I'm coming from two rough classes with some students with poor attitude and a dreadful set of tests. So if I caused any offense, I apologize. But basically, tell your daughter a math instructor tells her to buckle down and learn the stuff. Doing the problems means very little. It's only if you can take a cumulative test and do well on it that you've actually learned the material.

 

:iagree: And it sounds like you work in our CC (though not likely if you are in the south). Just yesterday hubby overheard a prof telling a student that around 75% of the students coming into the college need remedial math. It's not the dual enrolled students as they have to test into Pre-Calc or Calc, but otherwise it's a mix of just graduated high schoolers to older folks returning to school.

 

We've had kids from our high school finish Calculus, then test into remedial math too. Way too many kids memorize steps instead of learning the math.

[Sunshine State Sue]

D continues to insist she knows the math, and the problem is that "something is wrong with the tests."

This sounds *exactly* like my ds. :banghead:

[kiana]

. D continues to insist she knows the math, and the problem is that "something is wrong with the tests."

 

Many students where I am insist this. We used to let them take the next course up (just one course up) if they begged really hard and had good grades in high school in a comparable course. Fewer than 10% of these students were successful. We no longer allow this.

 

Fractions are a critical skill. I am not convinced that knowing all of the properties by name is critical if pre-calc or introductory calc is the highest she's going, although knowing the properties themselves is absolutely essential. If she's going further, yes, she will need those. For example, in calc 3 we're doing vectors at the moment. It is very simple to say 'the dot product is commutative, the cross product is not', but it is much more difficult if one has to say 'you remember that thingie that lets us switch the order of multiplication? in this one, that thingie works, but in the other one, it's backwards!'

 

The attitude of 'I already know this, I just don't test well' is a very bad one to have. There is a large difference between 'I know this well enough to stumble along if I have the book open to an example next to me' and 'I know this well enough to rapidly answer questions with the book SHUT', which is the real prerequisite for moving on. Many students confuse the former with the latter, and it sounds like that's what she's done.

 

Why does she want to take precalc? Is it just because it's the next math class that she hasn't taken? What is she looking at studying?

[creekland]

 

Fractions are a critical skill.

 

 

At our school (ps) fractions have only been taught via calculator for years. Now that these youngsters have moved up into the high school, we're reaping the rewards of this. It's not pretty. They tell me they are starting to change things in grades below. It will be more years before we see the change higher up.

 

Two of my boys caught the change to calculators. My middle son is absolutely superb at math, but at his 8th grade assessment, he couldn't do fractions without a calculator. We pulled him out of ps after 6th grade and I never caught it until then. It literally took him just two weeks to get them, and now (11th grade - post pre-Calc), no fraction trips him up - even the more difficult ones with imaginary numbers or radicals. WHY couldn't they have taught the kids fractions without calculators in elementary? I simply don't understand (or agree with) their reasoning. In our higher level math classes high school kids will simply skip over problems that have fractions in them. They find them confusing and few will try to understand.

 

My youngest son took longer to catch up to grade level, but he's there now.

 

I am not convinced that knowing all of the properties by name is critical if pre-calc or introductory calc is the highest she's going, although knowing the properties themselves is absolutely essential. If she's going further, yes, she will need those. For example, in calc 3 we're doing vectors at the moment. It is very simple to say 'the dot product is commutative, the cross product is not', but it is much more difficult if one has to say 'you remember that thingie that lets us switch the order of multiplication? in this one, that thingie works, but in the other one, it's backwards!'

Cute! And VERY true.

[distancia]

Why does she want to take precalc? Is it just because it's the next math class that she hasn't taken? What is she looking at studying?

 

She wants to go into Biology and 1 year of Calc is required.

[Teachin'Mine]

Ask her what test would be accurate enough to determine whether she knows her math. Saxon has an online Algebra II exam - which she should be able to do well on if she's ready for pre-calc. Your assessment of her needing more work is accurate, the question is how to get her to see that.

Edited September 16, 2010 by Teachin'Mine

[flyingiguana]

Associative property and commutative property -- nope, she doesn't need to know the names (did I even get them right?), but she definitely needs to know how to work with those concepts.

 

Rational, integer, imaginary numbers etc -- definitely she needs to know these. These aren't just names.

 

But it sounds like she's got bigger issues than memorizing a few terms. She does need a good review. Doing algebra without understanding fractions would be, well, difficult. And doing calculus without the algebra is basically impossible.

 

My qualifications: degrees in physics, biology, and statistics -- and a daughter that I got through calculus (starting with the calculus BC AP test, and then tutoring her through a semester of calc 3 where her professor apparently hadn't a clue as to how to do the problems and could only copy formulas and proofs out of the book onto the board -- no, it wasn't a cc. No, the professor wasn't an untenured adjunct who'd never taught before. Apparently, one can run into bad teaching anywhere.)

[In The Great White North]

Question: Is there any way I can make it clearer to her that these foundation skills are absolutely, positively essential to higher math? I need an expert to tell her...coming from me (Mom) just doesn't cut it.

 

How much time to do you have to convince her? If she can't remember how to do pre-algebra, it should only take a week or so to convince her that she can't do pre-calculus without it. After she gets every problem wrong and fails the first test, will she be convinced? If she decides for herself that she has to really learn the pre-algebra and algebra, she work much harder at it than if any "expert" tells her to.

 

BTW, if she only got 20% of the problems correct, the definitions are the tip of the iceberg.

 

Are there any younger siblings or friends she could help with their homework? That would cement it for her. She probably learned it well enough to recognize it the first time around - learning it well enough to teach it is much harder.