Dolciani Math

[butterfly113]

I understand there are older versions and newer versions. It seems that it is more difficult to find the older versions, from what I have read. DS9 will be in 4th next year, working a grade level ahead in Math. We are currently using Horizons Math. He is expressing strong interests in engineering and design. He is obsessed with the mechanics of things, knowing how things work and why. he is a lego-aholic, and will build with anything he can get his hands on. He can also take things and find out of the ordinary uses for them. He thinks outside of the box. I am beginning my research for upper level Math, as it seems this will be his forte and field of interest. I want to be able to provide him with rigorous math programs which allow him to work at the best of his abilities.

All this to say, where can you purchase the Dolciani Math books and solution manuals? Is there somewhere to see samples? Any other curriculum you would recommend for future engineers? :lol:

[Jane in NC]

Beth in Central TX did her homework on older Dolcianis. Here is the thread which should provide you with guidance.

[Dee in MI]

It is easy to get student copies. You can get teacher's manuals for the algebra books, but it's harder (and more expensive). You probably won't get the solution manuals.

 

I have '94 foerster and '63 dolciani. I like my dolciani's, and plan to use them. But, honestly? the foerster's are solid. The problem sets are nice. My impression is that dolciani tends towards being mathematician's math, and that foerster's tends towards being engineer's math. But they're both solid, and both will work for either purpose.

 

I've also seen, but not thoroughly reviewed, Jacob's. To me, it seemed solid and very approachable. If I was working with a younger child, I'd consider Jacob's. It's seems a bit "warmer" than the other two.

 

Dee

[Colleen in NS]

My impression is that dolciani tends towards being mathematician's math, and that foerster's tends towards being engineer's math.

 

What does this mean? I'm not a math person, but I want to understand what I'm supposed to be searching for, for high school. My ds LOVES math concepts (he reads encyclopedia articles on trig and calculus for fun, and HE explained to ME what calculus was!!!) and can't wait for high school, but I'm in the dark....although Dolciani has been on my radar because of things I've read in the past about it.

[Dee in MI]

I'm going to make very broad characterizations here, and we've got some real smart mathematicians on this board that I'm embarrassed will be reading this. But here goes :) (For what it's worth, I was an engineer in my former life.)

 

Mathematicians love the structure of math. They are intrigued by the language of math. They're more likely to be intrigued by proofs and logic.

 

Engineers need to solve real-world problems, so their emphasis will be on "story problems", on translating the problems of physics, for example, into mathematical equations so that they can be solved.

 

Now, Dolciani has fantastic story problems. But the mathematical language of Dolciani is very formal. Foerster, I believe, is less formalistic. (Dolciani was a leader of the formalistic "new math" time.) The difference, however, is in degree, not kind. They're much more alike than different.

[Jane in NC]

I'm going to make very broad characterizations here, and we've got some real smart mathematicians on this board that I'm embarrassed will be reading this. But here goes :) (For what it's worth, I was an engineer in my former life.)

 

Mathematicians love the structure of math. They are intrigued by the language of math. They're more likely to be intrigued by proofs and logic.

 

Engineers need to solve real-world problems, so their emphasis will be on "story problems", on translating the problems of physics, for example, into mathematical equations so that they can be solved.

 

Now, Dolciani has fantastic story problems. But the mathematical language of Dolciani is very formal. Foerster, I believe, is less formalistic. (Dolciani was a leader of the formalistic "new math" time.) The difference, however, is in degree, not kind. They're much more alike than different.

 

Good job, Dee.

 

Yes, Dolciani is more formal in the mathematical sense. Students see proofs and do proofs starting in Algebra I.

 

Most math textbooks of recent years are written by math educators--not mathematicians. Dolciani was a mathematician. This sometimes mean that one is doing math for math's sake--not because it is required in a physics application. Mathematicians always begin their story with definitions, then build a system with proofs. Granted, this methodology does not appeal to all students--or to some math educators--who prefer a more "user friendly" approach.

 

Foerster is a fine book, but I'm sticking with my Dolcianis.

 

Jane

[Sandra in FL]

Singapore Math)? It's a nice mix of challenging problems. When you're closer to middle school, then you could start searching for Dolciani books using

 

http://used.addall.com/

 

Type in "Dolciani" under author and "Solution" under keyword for Solution Manuals. These are the hardest to find. Once you've gotten one, then try for "Teacher" under keyword to get the corresponding teacher's manual. Then, lastly, try for the student text (which is usually easiest to find).

 

I found complete (Solution, TM & Student) texts for Structure and Method: Algebra 1, Alg 2 & Trig, Geometry and Math Analysis using this site.

 

HTH,

Sandra

[elegantlion]

If you keep your eyes open, or get a little help from friends, you can find some great Dolciani finds. I have found some on paperbackswap in the past, a 1972 pre-algebra, a 1975 algebra. I recently acquired a 1960s version of the algebra 1 and algebra II. I also just found a 1960s solution manual on amazon for 3.98. I was in heaven, thanks a friend who gave me a heads up.

 

Perhaps we should start a Dolciani hotline? Here's a link to the book I just received. It's a solutions manual not a teachers book. But it would give you someplace to watch.

[Dee in MI]

Jane, I just finished working through the '62 Algebra I and didn't see much emphasis on proofs. There is discussion of proofs in the teacher's edition, but the students don't have much assigned in the way of proofs. I did all of the A and B odds. I just started Geometry, and I know I'll see proofs there. Because I DID Dolciani Geometry in High School, back in the day :)

Edited March 6, 2009 by Dee in MI

[Jane in NC]

Jane, I just finished working through the '62 Algebra I and didn't see much emphasis on proofs. There is discussion of proofs in the teacher's edition, but the students don't have much assigned in the way of proofs. I did all of the A and B odds. I just started Geometry, and I know I'll see proofs there. Because I DID Dolciani Geometry in High School, back in the day :)

 

Agreeing that there is not much emphasis, but there was the occasion proof and what I would call more abstract demonstrations which require students to think beyond a basic algorithm or work comfortably with variables and generalized constrants.

 

In chapter 3 of my '65 edition, students are introduced to proofs along with the axioms of arithmetic. When students are asked in chapter seven to "show" that a quadratic is prime over the set of polynomials, they are performing what I refered to as a "more abstract demonstration".

 

Does your book have the "Extra for Experts" sections at the chapters' ends? There are some nice problems in these extra pages.

 

Happy Solving,

Jane

[Dee in MI]

I'd agree with this. There aren't formal proofs, but it has laid the groundwork. I'll probably see this more clearly as I work through the other books. I plan to work through all four Dolciani's (or at least the first three.)

[Colleen in NS]

I'm going to make very broad characterizations here, and we've got some real smart mathematicians on this board that I'm embarrassed will be reading this. But here goes :) (For what it's worth, I was an engineer in my former life.)

 

Mathematicians love the structure of math. They are intrigued by the language of math. They're more likely to be intrigued by proofs and logic.

 

Engineers need to solve real-world problems, so their emphasis will be on "story problems", on translating the problems of physics, for example, into mathematical equations so that they can be solved.

 

Now, Dolciani has fantastic story problems. But the mathematical language of Dolciani is very formal. Foerster, I believe, is less formalistic. (Dolciani was a leader of the formalistic "new math" time.) The difference, however, is in degree, not kind. They're much more alike than different.

 

This is great! Nice and simple so that *I* can understand. :D

 

So....when you look for a high school math series, do you have to consider whether your child leans more towards a mathematician's way of thinking or towards a real-world problem way of thinking??? Or do you decide what YOU want them to have? How do you decide?

 

And when you say Dolciani is formal, what exactly does that mean? Does it explain concepts in the same way as, say, Rod and Staff explains grammar concepts? (that seems formal to me, and I love it - it gets to the nitty gritty and makes it clear to me - it's clearing my grammar fog nicely)

 

Good job, Dee.

 

Yes, Dolciani is more formal in the mathematical sense. Students see proofs and do proofs starting in Algebra I.

 

Most math textbooks of recent years are written by math educators--not mathematicians. Dolciani was a mathematician. This sometimes mean that one is doing math for math's sake--not because it is required in a physics application. Mathematicians always begin their story with definitions, then build a system with proofs. Granted, this methodology does not appeal to all students--or to some math educators--who prefer a more "user friendly" approach.

 

Foerster is a fine book, but I'm sticking with my Dolcianis.

 

Jane

 

Would you be able to answer my questions to Dee, too?

 

And now for a really stupid question - what exactly are proofs? I remember the word from my h.s. geometry class and I vaguely remember a chart where we had to list why something was true. Does the word axiom have something to do with it? (I'm so embarrassed to be asking!!!!)

 

And lastly, what do you mean in the sentence I bolded above?

[Jane in NC]

 

So....when you look for a high school math series, do you have to consider whether your child leans more towards a mathematician's way of thinking or towards a real-world problem way of thinking??? Or do you decide what YOU want them to have? How do you decide?

 

Given that I studied mathematics in undergrad and graduate school, I gravitate to mathematics "done right". Many homeschool parents search for a self taught or video curriculum that does not rely on a great deal of parental input. (This in itself can be a challenge because a lot of kids are going to need some "face time" with someone explaining a mathematical concept. Books, videos and dilligence do not always cut through the fog!)

 

There have been discussions and debates on this board for years on what makes a good mathematics program (for some parents this means One My Child Understands, for others it means One that Prepares My Child for a Rigorous College Math Program).

 

There is a group of us not only on this board but in other cyber communities who advocate for a return to the math texts that came on the scene in the '60's, the so called "New Math". Others snort with derision when they read this. A quick look at history may explain the issue. After the Russians launched Sputnik, Americans raised the bar on education. Here is a passage from a New York Times article from 1982 that explains what happened:

 

In January 1958, President Eisenhower twice appealed to Congress, stressing the importance of education to national security, and that July Congress passed the National Defense Education Act, identifying math, science and foreign languages as areas in which the nation had a special stake. Financing of educational programs by the National Science Foundation also began to soar.

 

The net result was a truly remarkable crash program to upgrade the nation's educational resources. By 1973 half a million secondary schoolteachers in math, science, languages and, eventually, other areas, had gone through summer workshops and other federally supported programs to raise their skills. Thousands more had received graduate fellowships.

 

The next priority was curriculum reform. In the years after Sputnik, the N.S.F. poured more than $100 million into new curriculums that revolutionized the teaching of the sciences. The ''new math'' and the so-called ''alphabet soup'' curriculums, such as P.S.S.C., the Physical Science Study Committee, were designed to incorporate the latest findings into high school textbooks and to break the traditional cycles of reading-lecture-recitation. ''High school science curriculums went from Newton to Einstein in little over a decade,'' recalled Harold Howe 2d, a former United States Commissioner of Education.

 

Granted, the New Math was not successful for every child, nor did every teacher know how to teach it. It intrigues me that President Eisenhower saw in 1958 what a disadvantage and security threat we had facing us because of the lack of foreign language instruction in our classrooms! Yet foreign language instruction was the first piece of the post-Sputnik educational reforms to go. Oops--going off topic!

 

And when you say Dolciani is formal, what exactly does that mean? Does it explain concepts in the same way as, say, Rod and Staff explains grammar concepts? (that seems formal to me, and I love it - it gets to the nitty gritty and makes it clear to me - it's clearing my grammar fog nicely)

 

"Rigor" suggests a certain austerity, but precision is more applicable here. A Dolciani math text will begin with the definition of a set. Why? Because numbers are classified into sets and one needs to know the difference between the various sets (integers, reals, complex). To do something with numbers, one needs an operation, say addition. Assumptions that are made are called axioms. For example, you know that if you when you add two integers together (say 4 and 7) that order doesn't matter (4 + 7 = 7 + 4). We say that the integers are commutative over addition--but don't assume that this is true for every set over every operation. It is not. A rigorous math book is clear in specifying definitions, axioms, theorems.

 

 

And now for a really stupid question - what exactly are proofs? I remember the word from my h.s. geometry class and I vaguely remember a chart where we had to list why something was true. Does the word axiom have something to do with it? (I'm so embarrassed to be asking!!!!)

 

And lastly, what do you mean in the sentence I bolded above?

 

A mathematical theorem is a proposition; if we make certain assumptions, a specific conclusion will follow. If you have a right triangle with side lengths a and b, hypoteneuse c, then a^2 + b^2 = c^2. If you can prove this is true for all right triangles in general (not just your favorite triangle with sides measure 3, 4 and 5 inches respectively), then you have a general theorem--a general truth for your system. So a proof is a series of logical steps leading from your assumptions to the conclusion.

 

Long winded as usual, but always wishing you the best, Colleen.

 

Jane

Edited March 6, 2009 by Jane in NC
clarity

[butterfly113]

Praise the Lord i have some time before DS9 gets to all this! In high school I took through trigonometry... yet it's fuzzy! It will come back!

Anyway, am I correct then in understanding the teaching the Dolciani Maths will give DS what he needs if he desires to get into a top engineering program? What if he chooses something more science related...? Should I take another route? At what point do you really know which direction to go in? I want to be sure he has the Math covered, but depth is KEY! I'm starting to get a little nervous over here!

Also, he is in 3rd completing Horizons 4th. Doing well, loves it, grasps it, and can explain it thus far. Should I keep him in Horizons through 6th? Should I switch to Singapore or BJU? After 6th grade math, can he then go into Pre Algebra? That would be his 6th grade year... as he is a year ahead. Should I spend an extra year (his 6th) on decimals, percents and fractions, say with Life of Fred or the Key to series?

You ladies are awesome! I appreciate all your input! :bigear:

[Dee in MI]

Colleen,

 

I have a kid with an engineering mind, and we're using Dolciani. But I've reviewed Foersters and Jacobs. If Dolciani wasn't available, I'd not lose sleep about using them :) And Larson is probably in the same category. (I've seen it but not studied it, but it is used by my good friend whose husband is a physics teacher and has some pretty smart kiddos.)

 

I've seen many people who wanted to be engineers but couldn't handle the math. I'm trying to give my son the groundwork to get through higher level engineering math. Not everyone has this goal.

 

Dee

Edited March 6, 2009 by Dee in MI

[Dee in MI]

Butterfly, I didn't use Horizons, but the general rule is, Don't Change Math Programs Without a Good Reason!

 

Unless you're having a problem with Horizons, stick with it. Supplement if you like. You should be ready for pre-algebra by seventh.

 

If you'd like to get a taste of Dolciani and a supplement for higher elementary grades, look at Modern School Mathematics: Structure and Use (7 and 8, or Course 1 and 2) or the Dolciani Pre-Algebra course. They give a taste of sets and properties other mathematical terms, and the early chapters can certainly be done by a bright fifth grader.

 

(Don't get the sixth grade Dolciani book! It's not got the same flavor at all. It's muddled and confusing. It isn't written to the student like the books for older grades.)

 

Dee

[Colleen in NS]

OK, I've read, now I'll be absorbing, then I'll come back to make a reply. Dee and Jane, these are great explanations for me.

 

Butterfly, I'm glad you commented positively...I was sorta cringing because I sorta hijacked your thread with questions!!:D This is stuff I've been wondering about for awhile, but didn't really know where to begin asking high school math questions - now I'm getting some clues!

[butterfly113]

Colleen,

 

The way I see it... We are all parents trying to give our children the best education we can. We are in this together. Some are more geared mathematically, some towards language arts, and others sciences... yet the final goal is for our children to achieve to the best of their abilities. Right? ! ;) These children are our future leaders of this nation. They are the ones that will be leading when we are rocking our grandkids in the rocking chairs on our front porches! :lol:

[Storm Bay]

Dd really likes the 1965 Dolciani. Mine came with no answers or solutions. A mathy mom on this board scanned and sent me the odd numbered answers last year which helped for months and months. I put the solution guide on my Amazon wish list and just recently got one. It cost about twice as much as the text and is in worse shape, but I'm happy! I haven't found a TM, but don't need it for this dd. Not sure about the next 2 dc, but we have a collection of Algebra texts now (okay, 4 Algebra 1 books) so I'm hoping we're all set.

 

If you go for the Dolciani, check to see if the odd numbered answers are in the back--if you shop on Amazon, you can contact the seller. Some have them, some don't.

 

Dd likes the language in the book and plans to major in biochem, not math (but I keep hoping I'll get one who does, despite the current economy). But she also likes the language of Gelfand's, which is very much big on the theory.

 

We have a Foerster's, but she hasn't read it. She also liked Lial's, but Lial's begs a teacher, at least it did for her, and she likes to learn by reading the text. Dolciani fits the bill, and she rarely needs help understanding it.

[Storm Bay]

Colleen,

 

The way I see it... We are all parents trying to give our children the best education we can. We are in this together. Some are more geared mathematically, some towards language arts, and others sciences... yet the final goal is for our children to achieve to the best of their abilities. Right? ! ;) These children are our future leaders of this nation. They are the ones that will be leading when we are rocking our grandkids in the rocking chairs on our front porches! :lol:

 

:iagree:

[Colleen in NS]

Given that I studied mathematics in undergrad and graduate school, I gravitate to mathematics "done right". Many homeschool parents search for a self taught or video curriculum that does not rely on a great deal of parental input. (This in itself can be a challenge because a lot of kids are going to need some "face time" with someone explaining a mathematical concept. Books, videos and dilligence do not always cut through the fog!)

 

OK, yes, I have noticed this and wondered about the pros and cons of letting kids go on their own vs. still needing a math teacher for high school. I guess it depends on the student. I know a 17 year old girl who took herself all the way through Saxon Calculus by herself by the time she was 16 and I'm sure she understands it - she's brilliant. But I think she's exceptional. And I guess because math wasn't my strong thing in high school (I dropped out of pre-cal - I just didn't get it), I want to make sure I can (or someone can - good point about it being a real person) take them as far as they can/want to go. It would be nice if I could actually understand all that math finally, too. Like I said, R&S is taking away the grammar and writing fog - SWB is taking away some more writing fog, and maybe Dolciani would take away my math fog. I wish I could get my hands on some to have a look.

 

There have been discussions and debates on this board for years on what makes a good mathematics program (for some parents this means One My Child Understands, for others it means One that Prepares My Child for a Rigorous College Math Program).

 

Thanks for explaining this!

 

There is a group of us not only on this board but in other cyber communities who advocate for a return to the math texts that came on the scene in the '60's, the so called "New Math". Others snort with derision when they read this. A quick look at history may explain the issue. After the Russians launched Sputnik, Americans raised the bar on education. Here is a passage from a New York Times article from 1982 that explains what happened:

 

In January 1958, President Eisenhower twice appealed to Congress, stressing the importance of education to national security, and that July Congress passed the National Defense Education Act, identifying math, science and foreign languages as areas in which the nation had a special stake. Financing of educational programs by the National Science Foundation also began to soar.

 

The net result was a truly remarkable crash program to upgrade the nation's educational resources. By 1973 half a million secondary schoolteachers in math, science, languages and, eventually, other areas, had gone through summer workshops and other federally supported programs to raise their skills. Thousands more had received graduate fellowships.

 

The next priority was curriculum reform. In the years after Sputnik, the N.S.F. poured more than $100 million into new curriculums that revolutionized the teaching of the sciences. The ''new math'' and the so-called ''alphabet soup'' curriculums, such as P.S.S.C., the Physical Science Study Committee, were designed to incorporate the latest findings into high school textbooks and to break the traditional cycles of reading-lecture-recitation. ''High school science curriculums went from Newton to Einstein in little over a decade,'' recalled Harold Howe 2d, a former United States Commissioner of Education.

 

Granted, the New Math was not successful for every child, nor did every teacher know how to teach it. It intrigues me that President Eisenhower saw in 1958 what a disadvantage and security threat we had facing us because of the lack of foreign language instruction in our classrooms! Yet foreign language instruction was the first piece of the post-Sputnik educational reforms to go. Oops--going off topic!

 

Thank you, Jane! I get the part about making reforms after Sputnik and how teachers upgraded skills and why money was poured into new programs. What I don't get is the term, "new math." (remember, I'm mostly math ignorant) I always had the impression that "new math" was math that didn't make logical sense. Mind you, I've never read anything about it (oh, now I'm really cringing at confessing my ignorance out here in public!!), but I guess I've heard those snorts of derision with the term and never thought about it.:lol: So - what was the 1960's new math all about? Is it about teaching the definitions and axioms and theorems beforehand, then teaching how to solve problems? If so, why would that have been a problem? What was math teaching before that? (why do I have the uneasy feeling I'm unknowingly opening a can of worms??)

 

(hee hee, your comment about foreign language keeps me going on Latin - I narrowly focus on the fun and rigor of language learning - never thought about the lack of it being a potential security threat! :D)

 

"Rigor" suggests a certain austerity, but precision is more applicable here. A Dolciani math text will begin with the definition of a set. Why? Because numbers are classified into sets and one needs to know the difference between the various sets (integers, reals, complex). To do something with numbers, one needs an operation, say addition. Assumptions that are made are called axioms. For example, you know that if you when you add two integers together (say 4 and 7) that order doesn't matter (4 + 7 = 7 + 4). We say that the integers are commutative over addition--but don't assume that this is true for every set over every operation. It is not. A rigorous math book is clear in specifying definitions, axioms, theorems.

 

A mathematical theorem is a proposition; if we make certain assumptions, a specific conclusion will follow. If you have a right triangle with side lengths a and b, hypoteneuse c, then a^2 + b^2 = c^2. If you can prove this is true for all right triangles in general (not just your favorite triangle with sides measure 3, 4 and 5 inches respectively), then you have a general theorem--a general truth for your system. So a proof is a series of logical steps leading from your assumptions to the conclusion.

 

Long winded as usual, but always wishing you the best, Colleen.

 

Jane

 

Wow, this is great. It makes me think that Dolciani is to math as R&S is to grammar (in my mind, this is good).

 

Colleen,

 

I have a kid with an engineering mind, and we're using Dolciani.

 

I'm trying to give my son the groundwork to get through higher level engineering math.

 

So do you mean that you think Dolciani will give a good groundwork for another type of higher level engineering math?

 

And that brings another question to mind - in my high school we had Algebra 1, Geometry, Algebra 2, Pre-Cal, and Calculus. I took Algebra 1 in 8th grade and could have gone through calculus (if I understood it). How far into these do the Dolciani books go? Is trig part of these subjects I listed? And is engineering math different from the subjects I listed?

 

Colleen,

 

The way I see it... We are all parents trying to give our children the best education we can. We are in this together. Some are more geared mathematically, some towards language arts, and others sciences... yet the final goal is for our children to achieve to the best of their abilities. Right? ! ;) These children are our future leaders of this nation. They are the ones that will be leading when we are rocking our grandkids in the rocking chairs on our front porches! :lol:

 

Thanks, Butterfly! I just didn't want to rain on your parade! I hope these posts have been helping you the way they've been helping me!

[Jane in NC]

 

 

Thank you, Jane! I get the part about making reforms after Sputnik and how teachers upgraded skills and why money was poured into new programs. What I don't get is the term, "new math." (remember, I'm mostly math ignorant) I always had the impression that "new math" was math that didn't make logical sense. Mind you, I've never read anything about it (oh, now I'm really cringing at confessing my ignorance out here in public!!), but I guess I've heard those snorts of derision with the term and never thought about it.:lol: So - what was the 1960's new math all about? Is it about teaching the definitions and axioms and theorems beforehand, then teaching how to solve problems? If so, why would that have been a problem? What was math teaching before that? (why do I have the uneasy feeling I'm unknowingly opening a can of worms?

 

So do you mean that you think Dolciani will give a good groundwork for another type of higher level engineering math?

 

And that brings another question to mind - in my high school we had Algebra 1, Geometry, Algebra 2, Pre-Cal, and Calculus. I took Algebra 1 in 8th grade and could have gone through calculus (if I understood it). How far into these do the Dolciani books go? Is trig part of these subjects I listed? And is engineering math different from the subjects I listed?

 

 

 

Answers to some of your questions...

 

The "New Math" was a term coined in the '60's, I believe, to describe the pedagogy that evolved in the post-Sputnik era. The new math included more emphasis on the abstract but also topics required by new technology. For example analog devices used binary and hexadecimal arithmetic, so school children learned to change from base 10 to base 2 or base 16. We were not necessarily told that there were applications--we learned that base 10 is not the only system for arithmetic and saw a more general view of what arithmetic means.

 

There is a term "Fuzzy Math" that I don't quite understand (although I will note that there are some terribly interesting sets called "Fuzzy Sets" that mathematicians do study). I believe that the term was used to describe a pedagogy that involved process more than answers. Again, there may be something valid here. The answer doesn't really matter in math from my standpoint--a correct process matters. But if the process is one about self discovery and self esteem (that has nothing to do with proper mathematics at all), then the pedagogy is indeed "fuzzy". There are articles on the Math Wars that will provide additional information.

 

I used Dolciani for Algebra I, Geometry, Algebra II/Trig, and then a course called Analysis (sort of a precalculus although much of a modern precalc course is found in Dolciani's Algebra II/Trig text). If there is a Dolciani Calculus book, I don't know of it. (I graduated from high school after 11th grade so I did not study Calculus until college.)

 

Students in engineering disciplines take Calculus (Differential, Integral, Multivariable) and Differential Equations. Some will also take a linear algebra or numerical analysis course, depending on their specialty. Perhaps even more math if they are inclined. To succeed in these courses, one wants a firm foundation in those high school courses. Dolciani will do it, as will other curricular materials. (I do not believe in one size fits all.)

[Storm Bay]

OK, yes, I have noticed this and wondered about the pros and cons of letting kids go on their own vs. still needing a math teacher for high school. I guess it depends on the student. I know a 17 year old girl who took herself all the way through Saxon Calculus by herself by the time she was 16 and I'm sure she understands it - she's brilliant. But I think she's exceptional.

 

My dd learns well by reading, and this is how I learned most of my high school math. Not sure that it means we're exceptional or just plain geeky/different. Some of us are just hardwired differently, and I found Algebra rather easy. Other things that people thought were easy weren't so easy for me. Now, at what point dd will need to switch to a teacher, I'm not sure, but Nathaniel Bowditch was self-taught from books, so it can be done.We're not in his league of brilliance, so dd may need a teacher by the time she gets to Calculus. We do study a book that teaches theory, etc, behind things (Gelfand's Algebra, which actually has you multiplying and dividing in binary so that you get it, demonstrates why the rules of negative numbers are so, etc.) Apparently the honours math program at our local high school is good, but I'd like to wait until we finish our Geometry, and then Dolciani Algebra 2 before looking into that.

 

OTOH, there are some things dd needs a teacher almost holding her hand to learn. Essay writing is one of the main subjects where this is so.

 

Thank you, Jane! I get the part about making reforms after Sputnik and how teachers upgraded skills and why money was poured into new programs. What I don't get is the term, "new math." (remember, I'm mostly math ignorant) I always had the impression that "new math" was math that didn't make logical sense.

 

I'm a product of new math. Actually, of a combination. I started with straight Arithmetic until I was in Grade 5, and then did new math. It was cool, logical and, once I got used to set theory, fun. Not that I would have admitted that. But, like any great math programme, it got watered down and/or taught by people who didn't get it or weren't mathy or where afraid to teach math. I'm not sure if we did that all the way through or if they'd switched by the time I was in later high school. I went to 4 high schools in 5 years, which didn't help.

 

So do you mean that you think Dolciani will give a good groundwork for another type of higher level engineering math?

 

 

ETA this was sent early by mistake and I had a whole other paragraph which is now lost in cyberspace...Aaargh!

[Colleen in NS]

Thank you, ladies, for all this great information. I'm filing this thread away for future reference.