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Jane in NC

A discussion of high school mathematics classes

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Admittedly I am in an Algebra/Geometry/Algebra II-Trig/Precalc/Calculus box. I understand those who might want to include Statistics. I understand those whose children start Algebra early including a Number Theory class. For those who are advanced in Math, I see potential rabbit holes in Graph Theory or Combinatorics in high school.

 

But lately there has been discussion of business math, consumer math and accounting for high school math credits. Could we talk about the content of the first two? What makes them solid math classes for high school? Accounting, to me, is not math. Yes, it involves numbers. But just because something has numbers, does not make it math.

 

Granted, I am asking for a discussion where I need convincing. In other posts, people have said that consumer math uses real world examples for things like loans or budgeting. Why is this Math? Yes, it involves numbers--but the arithmetic involved is pretty basic stuff. Compound interest is usually studied in algebra as an application of exponents. If consumer math introduces material on the kinds of loans that are in the market place, is this really math?

 

I think a case might be made for a business math class that includes a number of application (word) problems and statistics.

 

Regarding investment: teaching students about financial instruments is not math in my eyes.

 

I have taught a technical math at the CC which I think could be adapted for high school. There were practical geometry/trig problems, situations with rates of change (flow of fluids), proportions (application of pesticides). I taught this to a group of middle aged men whose company required that they receive some sort of certification. These guys loved the course! This was the math they used in their jobs or in their weekend hobbies, so it was very real to them.

 

As more universities require applicants to have four years of math on their transcripts, I think that parents are seeking alternatives outside the standard path. I do not have a problem with that. I think I am having a problem with labeling something that is not math "Math".

 

Ducking tomatoes (and hoping for a fruitful yet not messy conversation),

Jane

 

P.S. Maybe someone could link me to some table of contents for consumer math curricula. I looked around the Internet and could not find anything specific.

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Hi Jane. Here is a sample that you can look at. BJU Consumer Math I will be interested in seeing where this discussion goes as I am still undecided about dd's math sequence.

 

Thanks for the link. It enabled me to see the table of contents and the first chapter. I am attending a big library book sale in the weeks ahead. I'll try to pick up some business/consumer math books for a deeper look.

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Well maybe it is because you are math person.

 

I was informed last week by a very science oriented person they weren't including biology in their high school plans bc they don't view it as a real science. Said all you do is memorize elementary stuff and no scientific skills are required. :001_huh:

 

I simply disagree.

 

I think there are many valid categories of math, same as there are of science.

 

Not sure if I can convince anyone otherwise though.

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I think there are many valid categories of math, same as there are of science.

 

 

Precisely! I do think that we (Americans--or maybe that is I, Jane-the-math-person) are stuck in a box with a certain mathematical sequence. It is not written in stone. In fact, there have been changes in the canon in my lifetime. While I saw probability in elementary and high school, I did not study statistics until I took a stats class for math majors in college. I spent more time studying analytic geometry than today's students who spend more time on modeling.

 

What I hope to do is open the conversation to possibilities. To be forthright, I felt that I should state my biases.

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I guess I will chime in here, since my son just finished his senior year of high school - woo hoo! (He worked ahead during Thanksgiving, Christmas, and on weekends)

 

He has been accepted, and will be attending, a university in SC for nursing, and has met all their prerequisites. For high school he had:

 

Alg I (BJU)

Geometry (BJU)

Alg II (BJU)

Consumer Math (half BJU math, half Dave Ramsey's Personal Finance)

 

My son LOVED Dave Ramsey's course! It is meant to take 1 semester, so after we were finished with Dave Ramsey, I filled in the rest of his consumer math course with chapters from the BJU Consumer Math book, with topics not covered by Dave Ramsey.

 

For science he had: (Apologia)

Biology

Physical Science

Chemistry

Advanced Biology (human anatomy and physiology)

 

He scored a 28 on the ACT test, earning him a $5,000 per year Life Scholarship.

 

His lowest score on the ACT was in math, which was a 25. If he had had Trig as a separate class, he would have scored higher. (From what I remember on the ACT, the last 7 problems in the math portion are trigonometry)

 

I gave him the option of Consumer Math for his senior year, or a trig/pre calculus type class, and he chose consumer math. He had a lot of other time-consuming classes this year, so I'm glad he chose consumer math. It was a very practical choice.

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I guess I will chime in here, since my son just finished his senior year of high school - woo hoo! (He worked ahead during Thanksgiving, Christmas, and on weekends)

 

He has been accepted, and will be attending, a university in SC for nursing, and has met all their prerequisites. For high school he had:

 

Alg I (BJU)

Geometry (BJU)

Alg II (BJU)

Consumer Math (half BJU math, half Dave Ramsey's Personal Finance)

 

My son LOVED Dave Ramsey's course! It is meant to take 1 semester, so after we were finished with Dave Ramsey, I filled in the rest of his consumer math course with chapters from the BJU Consumer Math book, with topics not covered by Dave Ramsey.

 

 

 

Congratulations to you and your son!

 

Does USC require three or four years of Math for applicants? This seems to be the sticky wicket for some parents on these boards. Colleges that formerly required three years of math now require four.

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I have seen many of our homeschool families opt out of higher "pure" math choosing, instead, to have their student use consumer math or accounting to fulfill math requirements. However, it is interesting to look at our state standards for public/private school diplomas. As homeschoolers we do not have to meet those standards, but just about every college we've looked at requires more than our state standards. Many of our homeschool families choose to use the local community college and have the student take remedial mathematics courses after graduation. Here's the blurb for Oklahoma high school diplomas (regarding maths):

 

3 Units Mathematics

limited to Algebra I, Algebra II, Geometry, Trigonometry, Math Analysis, Calculus, Advanced Placement Statistics, or any mathematics course with content and/or rigor above Algebra I and approved for college admission requirements;

 

3 Units or Sets of Competencies Mathematics

1 Algebra I or Algebra I taught in a contextual methodology, and

2 which may include, but are not limited to the following courses: Algebra II, Geometry or Geometry taught in a contextual methodology, Trigonometry, Math Analysis or Precalculus, Calculus, Statistics and/or Probability, Computer Science I, Computer Science II, Mathematics of Finance*, Intermediate Algebra*; contextual mathematics courses which enhance technology preparation whether taught at a (1) comprehensive high school, or (2) technology center school when taken in the eleventh or twelfth grade, taught by a certified teacher, and approved by the State Board of Education and the independent district board of education; mathematics courses taught at a technology center school by a teacher certified in the secondary subject area when taken in the eleventh or twelfth grade upon approval of the State Board of Education and the independent district board of education; or other mathematics courses with content and/or rigor equal to or above Algebra I.

 

The * courses must follow an approved course outline.

 

I don't know of any consumer math courses or accounting courses that have a level of rigor above Algebra 1, but I also haven't looked at all those available.

 

Oklahoma has recently added a "competency" required for graduation entitled Personal Financial Literacy. My son is doing this course right now and I would call it "consumer math on steroids". It has some basic math but it certainly doesn't meet the rigor of algebra 1. I will be listing it as an elective.

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At my son's high school, students must complete three full years of mathematics, Algebra 1 or higher, in order to fulfill the mathematics requirement. At a minimum this sequence would be Algebra 1, Geometry, and Algebra 2.

 

Accounting and Consumer Math would fulfill the two semester requirement of Fine/Practical Arts and fall under a group of classes called Consumer Education which also includes:

 

Economics

Business Management

Financial Management

Intro to Business

Professional Development and Internship

 

This is just how our high school does things. I imagine others might differ.

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But lately there has been discussion of business math, consumer math and accounting for high school math credits. Could we talk about the content of the first two? What makes them solid math classes for high school? Accounting, to me, is not math. Yes, it involves numbers. But just because something has numbers, does not make it math.

Financial/ consumer math, to me, is applied algebra. If you've already learned about exponents and logs, you pretty much have it covered. I do think it's useful to learn, but I don't think it's new content, mathwise.

 

The way we've handled it is maybe kind of odd (we usually are... LOL). Officially, DS has had Algebra 1 (and geometry, statistics, and discrete math since then). We used Singapore NEM for algebra and geometry, and it does tend to be pretty strong on the financial applications end. He picked up exponents and logarithms from NEM and from various other bits and pieces along the way (needed logs for statistics, needed a lot of other things for science) and then this year we've done economics and finance/ investing as a social science, with plenty of math in there.

 

From all those bits and pieces and all the bits and pieces we've come to from the science end, I think we've just about covered Algebra 2. We never sat down with a book and practice problems, but with a couple small exceptions, easily remedied, we've hit most of the content... and I kind of like it that way! Instead of chugging through it on the math end, we dabbled in all the applications, coming around to formulae and procedures as needed. (I don't think it will make it to the transcript that way, but we'll probably end up with an Algebra 3 so it will be clear where he ended with that.)

 

So I guess... it's not that financial math isn't math, but that it isn't more math after Algebra 2. It's more like Applied Algebra 2. So if I were designing an ideal course of study, I think I'd combine it with the Algebra 2 credit and just arrange the other classes to correspond - so the year you do Algebra 2 you also do Economics and a science that requires trig (maybe physics?) We've not been that orderly about it, but that's sort of how it worked out anyway.

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Well maybe it is because you are math person.

 

I was informed last week by a very science oriented person they weren't including biology in their high school plans bc they don't view it as a real science. Said all you do is memorize elementary stuff and no scientific skills are required. :001_huh:

 

I simply disagree.

 

 

 

This person can't be terribly science literate if that's all they think biology is.

 

I've worked in both biology and physics research. Overall, it has seemed to me that the biologists are actually better versed in the scientific method and using statistics to disprove hypotheses.

 

Of course, if all this person teaches is a dorky low level, memorize until you can't think biology course, then I would tend to agree that THAT biology course isn't as "sciency" as a physics course that incorporates math.

 

But I would never teach that type of biology. Even to an elementary student.

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Financial/ consumer math, to me, is applied algebra. If you've already learned about exponents and logs, you pretty much have it covered. I do think it's useful to learn, but I don't think it's new content, mathwise.

For a student who would otherwise do only three years of math, I wouldn't object to a fourth year being financial/ consumer math. Not because I think it's really a whole year's worth of content, but because it's a good review for a non-mathy kid who doesn't plan to do anything beyond Algebra 2 in college. I certainly wouldn't recommend it for a future math or science major, who really needs to be finishing at least precalculus before college, but for a liberal arts or fine arts major I think it would be appropriate. I think for a business major I'd rather see something more (I would think they'd need precalculus too), but if it were a really substantial financial math, it might be appropriate.

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I saw several consumer math syllabi and to me it just looked like applied algebra mixed with some common financial sense and then blown up into a high school course. It is maybe useful to cover as many people might lack that common financial sense and the ability to apply math in real world without an organized course that will teach them that, but it does not include new math, which is why I would have a problem with it as a math credit. To me, it's the kind of material that you "sneak into" algebra to demonstrate real life situations when to apply math, but do not make a whole new course out of it.

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This person can't be terribly science literate if that's all they think biology is.

 

:lol: actually the opinion was prejudiced by a doctorate in chemical engineering.:tongue_smilie:

 

I just looked stunned and said, "er.. Um... Why don't you tell your pediatrician that next time you take your kid in? Not to mention the explosion in the field of BIOchemistry in modern science in the last decade."

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At my son's high school, students must complete three full years of mathematics, Algebra 1 or higher, in order to fulfill the mathematics requirement. At a minimum this sequence would be Algebra 1, Geometry, and Algebra 2.

 

Accounting and Consumer Math would fulfill the two semester requirement of Fine/Practical Arts and fall under a group of classes called Consumer Education which also includes:

 

Economics

Business Management

Financial Management

Intro to Business

Professional Development and Internship

 

This is just how our high school does things. I imagine others might differ.

 

This is how I would categorize business or consumer math, too. They don't fit under the mathematics heading because they involve applications of arithmetic and algebra (even calculus in the case of economics), but they don't offer any new mathematics in and of themselves.

 

The larger problem here is the current system. Requiring four math credits of all students, combined with more & more kids starting algebra in middle school, is going to leave a lot of kids stranded by the end of high school. My county here in VA now requires all eighth-graders to take algebra. Crazy.:tongue_smilie: My LD niece had to settle for a 'certificate of completion' rather than a high school diploma because of the math requirement. No way, no how, could she pass four years of upper level maths. My friend who taught a self-contained special ed 8th grade class was required to introduce algebra to kids who could not yet handle basic arithmetic. I have a lot of sympathy for kids stuck in such a position.

 

The other problem as I see it is the current math progression. There are so many beautiful areas of math, but everyone's stuck in the same alg1 - geom- alg2 - precalc/trig - calc box. And don't get me started about the rush through algebra at the expense of a solid foundation! I've taught and tutored too many kids not to realize that a huge percentage of them are not internalizing what they learn in algebra. Sure, they reach calculus in high school, but they still are shaky on algebraic fractions, the distributive law, and other basic stuff.

 

Mathematicians certainly aren't all about algebra and analysis. What about number theory, combinatorics, topology, the more interesting parts of geometry (school geom is taught in a very boring way imho). AoPS, for instance, is beginning to address this lack. The current track is more suited to aspiring engineers.

 

Mathematics is so much more than numbers. My daughter just completed the second quarter of honors mathematics for freshmen at her university. A friend asked her how many actual numbers she'd seen in that course so far. Her quick reply was none.:)

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. And don't get me started about the rush through algebra at the expense of a solid foundation! I've taught and tutored too many kids not to realize that a huge percentage of them are not internalizing what they learn in algebra. Sure, they reach calculus in high school, but they still are shaky on algebraic fractions, the distributive law, and other basic stuff.

 

 

That has been my observation in my students as well.

I think part of the problem is the way math teaching is compartmentalized into "algebra", "geometry" etc. Everything neatly wrapped up into a box and a year of its own with no cross-contamination.

 

I believe it would be much more beneficial if algebra and geometry concepts were introduced throughout the years, alongside with teaching and reviewing arithmetic. (For example, in my school, 6th grade math covered, among other things, geometry of the triangle and congruency theorems; 7th grade linear equations with one unknown, 9th grade quadratic equations - but in between, there is still arithmetic, use of basic pre-algebra topics, various geometry topics. plenty of opportunity to use things like the distributive property, exponents, etc.)

I think separating everything into one year courses is detrimental (some of my students who have passed university calculus have horrible algebra skills because the last time they did certain things was in 9th grade.)

 

Mathematicians certainly aren't all about algebra and analysis. What about number theory, combinatorics, topology, the more interesting parts of geometry (school geom is taught in a very boring way imho). AoPS, for instance, is beginning to address this lack. The current track is more suited to aspiring engineers.

Mathematics is so much more than numbers.

Completely agree. Unfortunately, with the huge emphasis on arithmetic, most people DO believe math is just computation. Which is probably the least exciting and enjoyable part of mathematics.

(Fractals, anybody???)

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Well maybe it is because you are math person.

 

Exactly.

 

I'm struggling with the whole "math question" these days, as I've mentioned in other math-related threads.

 

My situation is that I have two kids who are talented in math but don't like it. Neither of them is likely to go into any career field that requires any advanced math. Both of them did algebra "early" and have run into problems stretching out the required years of high school math without getting into things they truly hate (calculus).

 

My daughter got through algebra II and then hit a wall. She did a semester of extra geometry using a text from Key Curriculum Press just so we could point to some kind of math on her transcript one year. She ended up taking a non-traditional path into early college, so it wasn't a problem.

 

My son is just-turned 13 and has already done algebra and geometry. He was not ready to move on this year and so is taking a "liberal arts math" class to review and stall. Even so, I don't think he'd be interested in jumping back onto the straight path to calculus. He'd hate it and not absorb anything. So, we're going to take an Art of Problem Solving detour. He may not have anything past algebra II on his high school transcript.

 

I'm sure math-y people find our lack of interest as appaling as I find it when I see people posting about English and arts classes I think are substandard.

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(Fractals, anybody???)

They're scary. :001_huh:

I don't know how people can look at that for longer than a second without going insane. They freak the heck out of me. :D

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They're scary. :001_huh:

I don't know how people can look at that for longer than a second without going insane. They freak the heck out of me. :D

 

May I suggest that you take a look at Gleick's book Chaos? Although published few decades ago, it provides a good introduction for the non-mathematician.

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I believe it would be much more beneficial if algebra and geometry concepts were introduced throughout the years, alongside with teaching and reviewing arithmetic. (For example, in my school, 6th grade math covered, among other things, geometry of the triangle and congruency theorems; 7th grade linear equations with one unknown, 9th grade quadratic equations - but in between, there is still arithmetic, use of basic pre-algebra topics, various geometry topics. plenty of opportunity to use things like the distributive property, exponents, etc.)

I think separating everything into one year courses is detrimental (some of my students who have passed university calculus have horrible algebra skills because the last time they did certain things was in 9th grade.)

 

I would love to revamp the US math system along these lines. We desperately need more continuity and review and less compartmentalization in our math instruction. For example, shoving geometry into a nine-month slot is just so silly. Geometrical ideas tie in to all other parts of math: coordinate geometry involves algebra, trigonometry of course involves geometry (and I can't begin to tell you how many kids have to be retaught the basics of geom when they reach trig), and there's even geometric probability.:)

 

The bonus I think is that more kids might actually like math if it were taught as an integrated whole. The current textbooks out there (and I see them when my tutoring students come) are poorly-written, boring, and would surely turn me off to math if I were a teenager today.

 

Completely agree. Unfortunately, with the huge emphasis on arithmetic, most people DO believe math is just computation. Which is probably the least exciting and enjoyable part of mathematics.

(Fractals, anybody???)

 

Sure, come on over. I have a few cool fractal books on my shelf that I've been meaning to get to someday.:D

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May I suggest that you take a look at Gleick's book Chaos? Although published few decades ago, it provides a good introduction for the non-mathematician.

Thank you for the recommendation, I'll look into it (and ask kids to cover the pictures of fractals before I get to reading the book LOL). :)

 

I meant what I wrote quite literally though: looking at fractals disturbs me. They're so creepy visually. Once I thought I would go insane and the picture was completely "capturing" me in itself. It felt so surreal and so scary. Maybe I just looked at it too attentively, but I really feel uncomfortable with those pictures.

How does one get rid of that feeling?

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I may regret posting now, and reading the three pages later.... but here goes!

 

I homeschooled ds thinking I had to have him ready to calculus by college, no wiggle room, have to. Then he goes to college, tests (wrongly) into calculus, and he will never touch math again because he failed it (and he was on scholarship and a very good student). Then he tells me about his friends in his new major, English, that just can't do math. Then I find out about art students (my dh) who can't do math. And the college lets you use computer class for math credit and they have a 101 for those who can't even do college algebra. Then a light came on for me. Some kids are not going to take higher maths just like some won't take higher level sciences.

 

I am the daughter of an engineer. I was going to provide the world with two math/science students. My dc love the subjects. But, and a big but, I always had to slow the pace down for both dc in math and science because they are creative temperaments. The college moves too fast for them in those subjects. Now, in art, poetry, literature, writing, my dc excel in those.

 

So, with dd, I am pretty sure she is not ready for college algebra or precalculus next year. I actually want to do another year of algebra and she does too. I am torn between keeping her home, or sending her to cc for her senior year. CC doesn't have below college algebra (ds college is too expensive to go to part time). So, if she does math there, I may have to pick the accounting. I think I would have a better chance of her taking the higher maths if she continues to feel that she can do it and it isn't too difficult.

 

I do agree that accounting is somewhat different, but having taken it myself, and having worked in accounting and banking, it does take more of a math type of mind to do it. You are constantly balancing, adding, putting in opposite accounts, and having to find where you are off. So, I do feel it is a valid class, and for one who can't do the higher math, a good option.

 

All in all, students should do math at a level that they don't feel overwhelmed. And some will get further in it than others.

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I would gladly turn over development of the entire U.S. math curriculum to Kathy In Richmond, Jane in NC and Regentrude. When can you start? (I am not in favor of national required curricula, but you get my drift here I hope.)

 

Your observations make much sense.

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Thank you for the recommendation, I'll look into it (and ask kids to cover the pictures of fractals before I get to reading the book LOL). :)

 

I meant what I wrote quite literally though: looking at fractals disturbs me. They're so creepy visually. Once I thought I would go insane and the picture was completely "capturing" me in itself. It felt so surreal and so scary. Maybe I just looked at it too attentively, but I really feel uncomfortable with those pictures.

How does one get rid of that feeling?

 

You know it is funny but a woman in our choir gave a devotion using pictures of fractals. She had a slideshow going while she read discussed how although these patterns can look unorganized up close, they really are not when looked at from a distance. Then she compared that to our lives and how God has patterns even in the most disorganized events in our lives. It was really cool. I didn't find them disturbing, though.

 

Christine

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I believe it would be much more beneficial if algebra and geometry concepts were introduced throughout the years, alongside with teaching and reviewing arithmetic. (For example, in my school, 6th grade math covered, among other things, geometry of the triangle and congruency theorems; 7th grade linear equations with one unknown, 9th grade quadratic equations - but in between, there is still arithmetic, use of basic pre-algebra topics, various geometry topics. plenty of opportunity to use things like the distributive property, exponents, etc.)

I think separating everything into one year courses is detrimental (some of my students who have passed university calculus have horrible algebra skills because the last time they did certain things was in 9th grade.)

I agree with this.

I had that type of non-compartmentalized math (and simultaneous sciences) at school and I'm doing the same with my kids. I notice MUCH better math competencies that way and it makes more sense to teach it that way.

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As more universities require applicants to have four years of math on their transcripts, I think that parents are seeking alternatives outside the standard path. I do not have a problem with that. I think I am having a problem with labeling something that is not math "Math".

 

QUOTE]

 

 

I've been wondering the same thing. My middle one hates math. He will not major in math or go into a field that requires math. That said, he isn't that bad, but does everyone really NEED calculus. The summer before my senior year, I suddenly thought... I'm going to be a music major. Why in the world do I want to do Calculus? Do I want to work that hard.. no. So I dropped it and didn't have math my senior year. The only thing I had to have at college was College Algebra..what a joke. It was the easiest class. I know people failed it, but math was easy for me. My son is doing Algebra right now as an 8th grader. I've wondered what we will do hi senior year... I was thinking taking math at a CC that would be a repeat of what he already had like College Algebra or Trig, but how would colleges look at that??

 

Christine

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I would gladly turn over development of the entire U.S. math curriculum to Kathy In Richmond, Jane in NC and Regentrude. When can you start? (I am not in favor of national required curricula, but you get my drift here I hope.)

 

Your observations make much sense.

 

:D The Benevolent Mathematical Triumvirate! :D

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I agree with this.

I had that type of non-compartmentalized math (and simultaneous sciences) at school and I'm doing the same with my kids. I notice MUCH better math competencies that way and it makes more sense to teach it that way.

 

and HOW precisely are you doing that and with what materials?

 

*begs the non mathy mother on pins and needles*:lurk5:

 

I completely agree with integrating subjects AND with teaching to conprehension, rather than checking off as done simply bc they put in the time.

 

I find integrating language arts easy for me to comprehend and manage, but I have zero idea of how to do so for science and math.

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Financial/ consumer math, to me, is applied algebra. If you've already learned about exponents and logs, you pretty much have it covered. I do think it's useful to learn, but I don't think it's new content, mathwise.

 

The way we've handled it is maybe kind of odd (we usually are... LOL). Officially, DS has had Algebra 1 (and geometry, statistics, and discrete math since then). We used Singapore NEM for algebra and geometry, and it does tend to be pretty strong on the financial applications end. He picked up exponents and logarithms from NEM and from various other bits and pieces along the way (needed logs for statistics, needed a lot of other things for science) and then this year we've done economics and finance/ investing as a social science, with plenty of math in there.

 

From all those bits and pieces and all the bits and pieces we've come to from the science end, I think we've just about covered Algebra 2. We never sat down with a book and practice problems, but with a couple small exceptions, easily remedied, we've hit most of the content... and I kind of like it that way! Instead of chugging through it on the math end, we dabbled in all the applications, coming around to formulae and procedures as needed. (I don't think it will make it to the transcript that way, but we'll probably end up with an Algebra 3 so it will be clear where he ended with that.)

 

So I guess... it's not that financial math isn't math, but that it isn't more math after Algebra 2. It's more like Applied Algebra 2. So if I were designing an ideal course of study, I think I'd combine it with the Algebra 2 credit and just arrange the other classes to correspond - so the year you do Algebra 2 you also do Economics and a science that requires trig (maybe physics?) We've not been that orderly about it, but that's sort of how it worked out anyway.

 

It sounds like you can do what you are doing because you are comfortable with Mathematics. And that is obviously not true for all homeschool parents.

 

My hat is off to a couple of homeschool Moms on the WTM board who are less than comfortable with the subject but who have been brushing up on their high school math skills before their students reach high school. This demystifies the subject for them. I believe that they have discovered Math is not what they thought it was and (gulp) the subject can be even fun and beautiful.

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and HOW precisely are you doing that and with what materials?

For sciences, you have this thread where we discussed a bit the approach of teaching sciences simultaneously, and you have a basic division of topics I use (adopted from various school systems, NOT representative of how Italian schools do it). Math is similar, though I'm more in line with the division found in regular Italian school curriculum, only a bit accelerated.

 

Custom-designed: normal Italian texts, supplemented by other mostly Italian materials + I started adding in AoPS for the math-loving kid.

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I would love to revamp the US math system along these lines. We desperately need more continuity and review and less compartmentalization in our math instruction. For example, shoving geometry into a nine-month slot is just so silly. Geometrical ideas tie in to all other parts of math: coordinate geometry involves algebra, trigonometry of course involves geometry (and I can't begin to tell you how many kids have to be retaught the basics of geom when they reach trig), and there's even geometric probability.:)

 

The bonus I think is that more kids might actually like math if it were taught as an integrated whole. The current textbooks out there (and I see them when my tutoring students come) are poorly-written, boring, and would surely turn me off to math if I were a teenager today.

 

Kathy,

 

I think you are on to something in a way in suggesting that integrated math is the way to do. But, I do think that there are current math texts labeled "Algebra I", "Geometry", and "Algebra II" that provide for more of that integration and ongoing review than typical texts. I'm thinking of the Dolciani/Brown books for example.

 

I see as a bigger problem in math education two things. The first of which is that in many places, teachers that are teaching higher maths don't have degrees in math. I think most will agree that a teacher with a real love and enthusiasm for a subject will be more likely to generate excitement in his/her students.

 

Second, in my experience, the school schedules don't allow enough time for students to really learn higher maths well. Class periods aren't long enough, and there are too many interruptions in a typical school calendar for assemblies, fire drills, standardized testing days, etc.

 

My own local school district has changed its calendar to a trimester system so that students have time to take more elective courses. This scheduling change means that students have one fewer course (5) per trimester and each one meets for 10 more minutes/day. But, the change also means that core courses like English and Algebra II only need to be taken for 2 trimesters (or 2/3 of the school year) to earn a full credit in the subject. I've seen this schedule result in a course where the pace is too fast to thoroughly cover everything, so the content taught is only "an inch deep".

 

So, if the WTM math triumvirate is able to redesign the curriculum and also deal with the other problems I mentioned, I think you all should be up for a Nobel prize!

 

Brenda

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So, if the WTM math triumvirate is able to redesign the curriculum and also deal with the other problems I mentioned, I think you all should be up for a Nobel prize!

 

Brenda

 

And when you need beta testers I volunteer ds and myself. :D

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Kathy,

 

I think you are on to something in a way in suggesting that integrated math is the way to do. But, I do think that there are current math texts labeled "Algebra I", "Geometry", and "Algebra II" that provide for more of that integration and ongoing review than typical texts. I'm thinking of the Dolciani/Brown books for example.

 

I see as a bigger problem in math education two things. The first of which is that in many places, teachers that are teaching higher maths don't have degrees in math. I think most will agree that a teacher with a real love and enthusiasm for a subject will be more likely to generate excitement in his/her students.

 

Second, in my experience, the school schedules don't allow enough time for students to really learn higher maths well. Class periods aren't long enough, and there are too many interruptions in a typical school calendar for assemblies, fire drills, standardized testing days, etc.

My own local school district has changed its calendar to a trimester system so that students have time to take more elective courses. This scheduling change means that students have one fewer course (5) per trimester and each one meets for 10 more minutes/day. But, the change also means that core courses like English and Algebra II only need to be taken for 2 trimesters (or 2/3 of the school year) to earn a full credit in the subject. I've seen this schedule result in a course where the pace is too fast to thoroughly cover everything, so the content taught is only "an inch deep".

 

Oh yes, I agree wrt Dolciani texts, Brenda. After all, I was brought up on Dolciani myself in the dark ages.:tongue_smilie: I was talking about the new kind of textbooks used in the schools around here these days. They have lots of photos, extraneous information (let's sell 'em on math by inserting a bio of a football player....) I've never had a tutoring student show up with Dolciani.:)

 

And I detest the block schedule for math, also. A few years ago I did a long-term substitute teacher job for a calculus class here in the public schools. They were on a semester block schedule, & I was expected to teach AP calculus from Sept to Jan. Can I just say frustration? You're right; math ideas need lots of time to percolate. Add in required assemblies, fire drills, snow days,...

 

So, if the WTM math triumvirate is able to redesign the curriculum and also deal with the other problems I mentioned, I think you all should be up for a Nobel prize!

 

Brenda

 

Sounds like fun! Sign me up any time. :)

 

...Off to check on an apple pie in the oven for a belated Pi Day celebration with my math club this afternoon. Math & dessert...how's that for a first step toward integrated learning?

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Do the fractals in nature bother you?

Fractals being the organization behind apparent chaos I would have guessed they would appeal to you. Guess not, hunh?

Is it the limited infinity in the pictures that you find daunting? (Limited as in limited vocabulary going on forever and not including anything new?) That is a bit scary. I prefer my infinities to have more variation in them than the ones in the most common pictures of fractals.

-Nan

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It is pretty daunting and absorbing to consider infinity. I guess I'm more like the arrow in the the paradox most of the time and only get sucked in when I want to.

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Kathy,

 

I think you are on to something in a way in suggesting that integrated math is the way to do. But, I do think that there are current math texts labeled "Algebra I", "Geometry", and "Algebra II" that provide for more of that integration and ongoing review than typical texts. I'm thinking of the Dolciani/Brown books for example.

 

I see as a bigger problem in math education two things. The first of which is that in many places, teachers that are teaching higher maths don't have degrees in math. I think most will agree that a teacher with a real love and enthusiasm for a subject will be more likely to generate excitement in his/her students.

 

Second, in my experience, the school schedules don't allow enough time for students to really learn higher maths well. Class periods aren't long enough, and there are too many interruptions in a typical school calendar for assemblies, fire drills, standardized testing days, etc.

 

My own local school district has changed its calendar to a trimester system so that students have time to take more elective courses. This scheduling change means that students have one fewer course (5) per trimester and each one meets for 10 more minutes/day. But, the change also means that core courses like English and Algebra II only need to be taken for 2 trimesters (or 2/3 of the school year) to earn a full credit in the subject. I've seen this schedule result in a course where the pace is too fast to thoroughly cover everything, so the content taught is only "an inch deep".

 

So, if the WTM math triumvirate is able to redesign the curriculum and also deal with the other problems I mentioned, I think you all should be up for a Nobel prize!

 

Brenda

 

They have attempted to do this in Georgia with less than stellar results. They renamed the classes Math 1, 2, 3, 4 and all students had to take all 4 classes to graduate. The first students under this system are now juniors, and 20% do not have a single math credit because of the integrated math. The state has just ruled that they will allow the "Math Support" classes to count as math credit towards graduation, and further, each county will be allowed to go back to the traditional math if they desire. But it's really been a huge mess, I think, because the teachers are unprepared to teach the math this way.

 

As the parent of children with high functioning special needs, I still maintain that there needs to be a path for children who will not be pursuing higher education but that will still allow them a diploma so they can get some tech training or an entry level job and be able to work towards supporting themselves.

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They have attempted to do this in Georgia with less than stellar results. They renamed the classes Math 1, 2, 3, 4 and all students had to take all 4 classes to graduate. The first students under this system are now juniors, and 20% do not have a single math credit because of the integrated math. The state has just ruled that they will allow the "Math Support" classes to count as math credit towards graduation, and further, each county will be allowed to go back to the traditional math if they desire. But it's really been a huge mess, I think, because the teachers are unprepared to teach the math this way.

 

 

 

DH teaches math in GA. I've asked him repeatedly about the new curriculum, and he has mixed feelings about it. As far as I can tell, it's a really demanding, rigorous curriculum that's probably great for kids who easily grasp math concepts, and not so great for kids who struggle with math. I imagine this varies by county, but in our county they now have only two tracks (accelerated and regular), where they used to have three (honors, college-prep, non-college prep). So DH's classes now have a much wider variety of math abilities than they did last year (with bigger class sizes because of budget cuts. perfect combination!). On the other hand, he says that his juniors this year are way ahead of his juniors under the old curriculum as far as math ability goes. The whole department is currently panicking about the graduation test the juniors are about to take. I think the real test might be to see how kids who have done the new curriculum K-8 do when they get to high school....if the curriculum stays around that long. I haven't heard much about how things are going at the elementary level.

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A well done integrated curriculum would be beneficial even for students who are weak in math. Because right now, the splitting into "algebra1", "geometry" etc makes no sense as a *progression*: some algebra 1 topics are easy, and some are much more challenging; some geometry concepts can be understood in middle school, others only much later. So, by mixing the topics as it is done in my home country, they are also ordered by level of difficulty.

Introducing the easier concepts early, and waiting with the more complex ones, it gives students with weak math skills a better chance at success as well, because then it is not "all -or -nothing". As I said, plane geometry of triangles does not have to wait till 10th grade- kids can do that in middle school because it is not very abstract. Linear equations with one variable is something an average 7th grader can understand. OTOH, some of the more complex topics can be pushed back because the don't have to be fit into the year course.

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Accounting, to me, is not math. Yes, it involves numbers. But just because something has numbers, does not make it math.

Have you ever figured an amortization schedule? The present value of future money or the future value of present money? Just calculated taxes-all of them? (I need an evil grin simile.)

 

There is a lot of math there, but most of what I listed is not beginning Accounting. You deal with present and futures values in Junior level classes at college.

 

If a child is able I think they are better off doing more traditional maths, and not what I would consider these soft math topics. But my dh, while brilliant, didn't finish Algebra I till his senior year. In his case it was because he had to understand why, and by the time he figured it out the class was on the next topic. He ended up perpetually behind, yet each year he retook it he would keep up with more and more of the class because each time he figured more of it out. He probably would have finished much earlier if someone has only explained why and let him go at a slower pace.

 

For those kids who just aren't ready for it, I think these soft maths have a place and real world applications.

 

We are math heavy here, so my plan is to do Lial's on a traditional sequence, then follow it up with Singapore's Discovering Math at a slower pace (which is integrated). That way they get more review, and a different way to look at things.

 

Heather

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Have you ever figured an amortization schedule? The present value of future money or the future value of present money? Just calculated taxes-all of them? (I need an evil grin simile.)

 

 

Amortization schedules are determined by difference equations. Some high schoolers might see them in a discrete math class, but I don't think difference equations are part of the usual high school curriculum.

 

Many people use amortization schedules but do not know the mathematics of their construction. Do you know if difference equations are covered in consumer math books? I was envisioning this as part of a good business math course.

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And when you need beta testers I volunteer ds and myself. :D

 

me, too; me, too!!!!!

 

No - I love order ;) - but those images are sometimes daunting, they soak you into them.

 

You are cracking me up!!:lol: I just discovered fractals a year or two ago, and I thought they were so cool! I tried drawing some, and it got dizzying, so I do know what you mean, though. :D

 

:lurk5: so I can finish reading this thread thoroughly tomorrow. Jane scores again with a thought-provoking thread!

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:D The Benevolent Mathematical Triumvirate! :D

 

All hail the BMTs! :D

 

Speaking of integrated math, here is a discussion of integrated math at NCTM. Is this what you mean when you say integrated math?

 

http://www.nctm.org/resources/content.aspx?id=1662

 

LittleBug posted a question about SIMMS Integrated Math on the Afterschooling Board. I've never heard of it. Do any of you have an opinion about it?

 

http://www.kendallhunt.com/simms/

 

The idea of integrating math is intriguing, but I wonder if it would get convoluted along the way, especially since compartmentalizing has been done for so long here in the U.S. What think the BMTs and others?

 

******

 

Regarding kids who struggle with math, my son's high school offers three to four levels of difficulty for all core classes. Some students need a little help with fundamental concepts, while others need more challenge. The idea looks good on paper, but I'll have to see what actually happens next year when he's there full-time. I've learned through the years that what you see is not always what you get! That is what I find to be the most frustrating part of dealing with schools.

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New York uses integrated math...they've switched to calling it Integrated Algebra, Integrated Geometry etc. instead of Math A, Math B. Most parents hate the elementary strands because they require thinking...the most complaints I've ever heard came from parents of high acheivers who didn't acheive on the 3rd grade test one year...among other questions, they were asked to state 2 ways on shape was different from another...and many hadn't followed the teacher when she asked them to think through the differences by comparing and contrasting. They had memorized the shapes and names, but weren't able to compare and contrast on the fly. Middle school is the same way. The only big omission I see is the lack of depth...everything is simple - no complex fractions yada yada B or C Dolciani type problems. The minor problem is that they use the calculator too much for combinatorics. The Dolciani books are better as they include the graphical and symbolic explanations.

 

Consumer Math - when I was in high school, this was the class taken if you did not do well in prealgebra. It was a second run through, with more applications to real life. The students that struggled in middle school go here first, before Basic Algebra and Integrated Algebra I.

 

Accounting - uses business software here and most of the learning is about different forms of businesses. Plus in that it forces attention to detail. Most take this after I.A.I.

 

Business Math here is a dual enrollment course.

 

In NY high schools, there are two diplomas - basic and advanced. Advanced requires the Integrated Algebra I, Integrated Geometry and Integrated Alg.II/Trig sequence. Basic requires I.A.I. and two others. Those can be consumer math, accounting, business math, or any of the halfspeed or bridge math classes.

 

It is going to take changing the way business is done in the elementaries to successfully teach math to all. Here, they won't do small group instruction with grouping by instructional need, preferring whole class instruction with rTi, but they haven't trained sped teachers in how to teach math in a nonrote way so it is a dismal failure. The successes are coming with swapping classes - a teacher that knows math will teach math to another class while that class's teacher teaches social studies in his class. Many of the older teachers (which is what most districts here have due to the many boomers not retiring and the laying off of the newer hires) have degrees in their subject, with the teaching degree as the master's.

 

I think basic students are getting the short end by allowing consumer math, business math, and accounting to count, but on the other hand, many parents don't want to admit that the kid needs more work on the 5-8 topics or do anything constructive about it. I am of course, not speaking about special needs students, just gen ed. Succeeding in math takes sustained daily effort and a classroom that allows one to think uninterrupted for a few minute at a time. I don't know that any diverse school in this budgetary crisis can offer that.

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Mathematicians certainly aren't all about algebra and analysis. What about number theory, combinatorics, topology, the more interesting parts of geometry (school geom is taught in a very boring way imho). AoPS, for instance, is beginning to address this lack. The current track is more suited to aspiring engineers.

 

Mathematics is so much more than numbers. My daughter just completed the second quarter of honors mathematics for freshmen at her university. A friend asked her how many actual numbers she'd seen in that course so far. Her quick reply was none.:)

 

My husband is completing his masters in mathematics, wanting to go on for a doctorate (with a specialization in combinatorics) and he says, at this level, they do not work with actual numbers much at all! It's the theory and what "world" (I forget the word he uses--domain? maybe) of numbers that theory applies to that matters

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P.S. Maybe someone could link me to some table of contents for consumer math curricula. I looked around the Internet and could not find anything specific.

 

Alpha Omega Consumer Math - this is the math program that we're looking at having dd14 work through, possibly next year. (She isn't ready for it quite yet - she's currently working a few other programs.)

 

I don't really understand why you're saying that other math programs aren't "math"... they might not be the sort of math classes that YOU would choose, but that doesn't mean that they aren't math classes.

 

I don't pay much attention to what the local high schools do, but I know that even there they have different "levels" of math -- I don't know what they call them nowadays, but it used to be Practical, General, Academic, and Advanced (I think? Not positive what the last one was called.. the high level math for kids going off to math-oriented careers and such) ...

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I don't really understand why you're saying that other math programs aren't "math"... they might not be the sort of math classes that YOU would choose, but that doesn't mean that they aren't math classes.

 

 

Accounting is accounting--not math in my book. Just because numbers are involved does not make a discipline math.

 

Perhaps your question leads to a question much larger than this thread: What is Mathematics?

 

It seems that consumer math involves arithmetic and basic algebra. The new concepts involve things like the definitions of the kind of loans that are in the marketplace. Is that math or is that business or finance?

 

I am not saying that consumer math is invalid. I am questioning how it fits into the framework of mathematics.

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