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# Mathematics people--post here

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As the self-proclaimed Dolciani proselytizer of the Boards, it is perhaps appropriate for me to begin a Mathematics thread.

I have an MS in Math and am happy to discuss the subject online or in PMs; however, my expertise is not in Mathematics Education, so questions in that category may be better handled by someone else. Nor can I claim to have seen and compared all curricula.

But I am happy to share my experience as a parent of a homeschooled senior in high school as well as my previous post-secondary classroom experience.

Jane (who is looking for something to do with her life after her son leaves for college--maybe this thread can inspire me!)

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As the self-proclaimed Dolciani proselytizer of the Boards, it is perhaps appropriate for me to begin a Mathematics thread.

I have an MS in Math and am happy to discuss the subject online or in PMs; however, my expertise is not in Mathematics Education, so questions in that category may be better handled by someone else. Nor can I claim to have seen and compared all curricula.

But I am happy to share my experience as a parent of a homeschooled senior in high school as well as my previous post-secondary classroom experience.

Jane (who is looking for something to do with her life after her son leaves for college--maybe this thread can inspire me!)

Jane,

You would be an invaluable source for homeschoolers!! You should offer math and science classes.......you would be a blessing to any student that was lucky enough to enroll!!

I wish we were closer and then I could promise you 2 students immediately!!! :D

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Hi Jane,

Would you please let me know what is the good book to study operations of irrational numbers like squareroot(a*b) = squareroot(a) * squareroot(b). I think it belongs to pre-algebra, but I can't find the topic in 5th grade Math or Singapore.

Thanks,

Liem

As the self-proclaimed Dolciani proselytizer of the Boards, it is perhaps appropriate for me to begin a Mathematics thread.

I have an MS in Math and am happy to discuss the subject online or in PMs; however, my expertise is not in Mathematics Education, so questions in that category may be better handled by someone else. Nor can I claim to have seen and compared all curricula.

But I am happy to share my experience as a parent of a homeschooled senior in high school as well as my previous post-secondary classroom experience.

Jane (who is looking for something to do with her life after her son leaves for college--maybe this thread can inspire me!)

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Hi Liem,

Do you own the Dolciani Modern Algebra Structure and Method Book I? Irrationals are covered in chapter 11 and are done quite nicely. All of the operational rules are covered in the chapter after a section on the geometric interpretation of the square root. I mention this because of a nice irrational number activity that I saw the other day: Irrational Numbers Can "In-Spiral" You.

You are right though that the topic is usually introduced in pre-algebra. I no longer own any of those books so I can't point out a specific text. A good reference for basic math is the Lial Basic Math text. It is a workbook designed for remedial adult studies. I find it to be less than inspirational, but it provides loads of practice problems for students who need them.

Maybe you could send Blue Hen a PM with this question. She uses Singapore (and is an AP Stats teacher). Perhaps she can give you a page number.

Best regards,

Jane

Hi Jane,

Would you please let me know what is the good book to study operations of irrational numbers like squareroot(a*b) = squareroot(a) * squareroot(b). I think it belongs to pre-algebra, but I can't find the topic in 5th grade Math or Singapore.

Thanks,

Liem

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Hi Jane,

Thank you very much for the info. I have Dolciani Modern Algebra (I don't have the 60s edition, but the 1975). I will check it out. Really appreciate your help.

Liem

Hi Liem,

Do you own the Dolciani Modern Algebra Structure and Method Book I? Irrationals are covered in chapter 11 and are done quite nicely. All of the operational rules are covered in the chapter after a section on the geometric interpretation of the square root. I mention this because of a nice irrational number activity that I saw the other day: Irrational Numbers Can "In-Spiral" You.

You are right though that the topic is usually introduced in pre-algebra. I no longer own any of those books so I can't point out a specific text. A good reference for basic math is the Lial Basic Math text. It is a workbook designed for remedial adult studies. I find it to be less than inspirational, but it provides loads of practice problems for students who need them.

Maybe you could send Blue Hen a PM with this question. She uses Singapore (and is an AP Stats teacher). Perhaps she can give you a page number.

Best regards,

Jane

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Hi Jane

I consider myself a math person too, although I don't have as good a claim as you.

I did one year in university in Physics, and had to take many math classes, including Advanced Calculus II. More than half the credits I earned that year were in math for scientists. Then I switched to engineering, where I was known as the math person in the classroom.

I did some math at the masters level too, but only statistical. And funnily enough my masters was half in psychology. Very little math in that half.

DH placed first in the country in math competitions when he was in high school. He also earned a full bursary to MIT, which he didn't take.

There's math in our blood in this family. And then there's DD, the artist. The completely non-mathy person. Where does she come from?

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There's math in our blood in this family. And then there's DD, the artist. The completely non-mathy person. Where does she come from?

Hi Cleo,

You might want to check out the math/art activity that I mentioned earlier in this thread. Your DD may enjoy it!

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... a nice irrational number activity that I saw the other day: Irrational Numbers Can "In-Spiral" You.

Thanks for this link, Jane. My husband now plans to use this activity in a "Math in the Real World" class that he is teaching at our local homeschooling center.

Regards,

Kareni

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Thanks for this link, Jane. My husband now plans to use this activity in a "Math in the Real World" class that he is teaching at our local homeschooling center.

Regards,

Kareni

May I suggest another activity that his students might enjoy? Years ago we visited the Alexander Graham Bell house in Nova Scotia where I learned that Bell was obsessed with all things aeronautical of the time period including tetrahedral kites. Here is an activity that I did with some of the children at the Montessori school my son attended. We made gorgeous tetrahedral kits in vibrant tissue which we suspended from the ceiling. They were lovely! I would suggest using glue (either a glue stick or preferably white glue dabbed on carefully with a toothpick) as opposed to tape.

Enjoy!

Jane

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Jane,

The tetrahedral kite activity looks wonderful. I'll pass it along to my husband as well. Thanks!

Regards,

Kareni

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Dd is looking for an Algebra 2 program. She successfully used Lials for Algebra 1, and is currently using Jacobs and Discovering Geometry for Geometry.

Not sure if Lials covers Algebra 2 or not.

What would you recommend for a very strong math student (although young at age 12).

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I think it was Jann in TX with whom I took the math advice!

Jann or Jane, both perfectly suitable to answer my question!:)

Thanks again

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jane-i have to go back and see if you were one of the responders to my thread about my 7 yo wanting to learn algebra....if not, can you advise me as to what curriculum/book might be good for him? He's a math-y kid, loves math problems, but he's still 7.

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I think it was Jann in TX with whom I took the math advice!

Jann or Jane, both perfectly suitable to answer my question!:)

Thanks again

Not sure if Jann in TX is checking out this board. Maybe you should PM her?

I suspect that she might recommend Lial's for Algebra II but I would not. While Lial's Alg II is thorough, I find it to be less than inspirational for someone interested in the theory behind the math. While I adore the Dolciani texts, they do not have the support materials that some of the other books have. If you need solution manuals, these can be tough to find for the old Dolcianis.

Perhaps Larson with Chalkdust for videos if you need them? Foerster's Algebra II/Trig is a solid text.

Considering your child's age and ability, I would also consider the Art of Problem Solving. These are books for the math minded.

Best regards,

Jane

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jane-i have to go back and see if you were one of the responders to my thread about my 7 yo wanting to learn algebra....if not, can you advise me as to what curriculum/book might be good for him? He's a math-y kid, loves math problems, but he's still 7.

Wow--this is beyond my knowledge base. You are using Singapore, I see. You might want to stick with that and move into the Art of Problem Solving.

Another thing that I might consider is buying or borrowing some Ivan Moscovich books. He has collections of mathematics and logic puzzles that are quite interesting. Certainly much food for thought for a seven year old!

Jane

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From what I learn from this site (from Jane NC, Kathy Richmon, Blue Hen ...), if you kids love math and you and your kids have time, here is what I would like to do:

-Dolciani for Math concepts. The great thing of Dolciani is that it comes to the point.

It is very concise and it has problems that build a great Math foundation/proof skill (esp problems belong to category C).

-AofPS is for more challenging and difficult problems. If you want easier or application problems, Foerster is good.

-Gelfand's books are good supplements too.

Liem

Wow--this is beyond my knowledge base. You are using Singapore, I see. You might want to stick with that and move into the Art of Problem Solving.

Another thing that I might consider is buying or borrowing some Ivan Moscovich books. He has collections of mathematics and logic puzzles that are quite interesting. Certainly much food for thought for a seven year old!

Jane

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thank you (both) who responded.

We have looked into the AOPs, and it looks interesting (to say the least).

Not sure which direction to take, and we do have some time (about 8 weeks and she will finish Geometry).

I think I can find Dolciani on Ebay. It sure gets the kuddo's:001_smile:

Thanks, Moki4

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...

Dd is looking for an Algebra 2 program. She successfully used Lials for Algebra 1, and is currently using Jacobs and Discovering Geometry for Geometry.

Not sure if Lials covers Algebra 2 or not.

My daughter was not as advanced as yours, Moki, in that she did Algebra I in 8th grade (Lial's) and Geometry (Jacobs') in 9th grade. She did go on to use Lial's Intermediate Algebra for Algebra II. It was a good choice for her.

Regards,

Kareni

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Kareni, well thank you for the lials support. Jann did PM me with other advice, but she still recommends Lials intermediate Algebra next.

I really appreciate the new "experts exchange".

Thanks to ALL!!:)

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Jane -- I love your activities suggestions. My daughter and I had a largely activities-based math program for years because problems with writing made it impossible for her to line up numbers in columns or even write them the right way around (reversing 51 to 15, for instance) until late elementary age. We then used a lot of Marilyn Burns math, which uses activities to kick-start or inspire math work.

Now that my daughter is taking algebra, I find these types of things either lacking or lame, at least those that I find in the textbooks; and I'm having a hard time finding outside materials. We both miss them. I would be so very, very appreciative of any or all activities you could suggest for algebra and geometry.

I would also be interested in any reading you could suggest about irrational numbers. I think I read somewhere that the ancient Greeks and Romans feared them because they made the order and stability of the rational number system seem suddenly shaky or imperfect? Could you point me towards a book or article?

Thank you so much!

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Hi KarenAnne,

Your daughter may be a bit too old for Hans Magnus Enzensberger's book, The Number Devil, but it may still be fun to borrow from the library. Google books provides a preview here.

Tarquin is a British publisher that has created a number of great hands on activity books that work well for middle school or high school aged students. A university bookstore may carry them or they can be ordered online. The website is over here.

Let me think about some irrational number activities. I just saw your message and must run out the door.

Best,

Jane

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I was just told that our Dd (12), who just finished Geometry, and who will be ready for calculus as a 9th grader, will not receive math credits for Alg 1, alg 2 and geometry because she took them as a 7th grader.

Is this correct? I just assumed that she would keep advancing, and take classes at the CC as needed. But if so, she won't get HS credit?

Is this correct???

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You might want to ask this question on the high school board, or maybe the accelerated learner board. There are several possibilities, including graduating her early and early college, which might make sense for a child who's doing calculus at 14.

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But I am happy to share my experience as a parent of a homeschooled senior in high school as well as my previous post-secondary classroom experience.

Jane (who is looking for something to do with her life after her son leaves for college--maybe this thread can inspire me!)

Jane,

I just saw this post.

We math folks need to stick together. I hope you stay around the boards and help us out. :)

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Jane,

I just saw this post.

We math folks need to stick together. I hope you stay around the boards and help us out. :)

Thank you! I think I should be of more help once this crazy senior year is over!

Jane

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I was just told that our Dd (12), who just finished Geometry, and who will be ready for calculus as a 9th grader, will not receive math credits for Alg 1, alg 2 and geometry because she took them as a 7th grader.

Is this correct? I just assumed that she would keep advancing, and take classes at the CC as needed. But if so, she won't get HS credit?

Is this correct???

Hello Moki,

More selective colleges are generally interested in seeing that your child has continued to advance throughout the high school years; they often look for three or four years of math taken during high school. So, if your daughter continues to take math throughout high school, she will have no problems. If those courses are Precalculus, Statistics, Calculus, and Differential Equations, the admissions officer will understand that your child must have taken Algebra I and II as well as Geometry at some earlier date.

Does that make sense?

Regards,

Kareni

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Yes, your response is correct! That is what I thought, but wanted to make sure (charter school teacher was wrong)

I would never consider her repeating those courses just to get HS credit. I want her to continue on the rigorous math path (she likes it!)

Thanks a bunch:)

Moki4

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You're quite welcome, Moki4. And best wishes to you and your daughter; she sounds like an intelligent young woman.

Regards,

Kareni

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i don't know if my college level math experience will be that useful, but i am a retired math professor from university of georgia, with a phd in algebraic geometry from U. of Utah, and 35+ years experience teaching algebra, geometry, calculus, differential equations, logic and proof, topology, real and complex analysis, algebraic curves, surfaces, cohomology, and so on... from freshman year up through phd level courses.

i also home taught my older son on weekends from jacobs' algebra until the school he was also attending won out for his allegiance. so i am not as expert or experienced as a home schooler as others here. last summer i taught a 2 week course from euclid's elements at epsilon camp, for very precocious 8-10 year olds, with lots of help from the kids and the camp staff (including Kathy in Richmond). i am probably most qualified to explain and discuss actual math concepts, and suggest sources. i know very little about stat or computers, but i had one undergrad course in probability, and own a mac.

everything on my webpage is free, but most are at the college level or above.

http://www.math.uga.edu/~roy/

however the epsilon camp geometry notes are also there, #10. near the bottom. they are right above the notes of a "math camp for fields medalists", the famous woods hole meeting from 1964. I have many other notes that are not posted, on calculus, differential topology, algebraic geometry, rigorous real numbers for advanced high school students...

we started a thread on physics forums, called "who wants to be a mathematician?" where basic advice is offered to students from high school and up trying to get the training they need for that role. Lots and lots of advanced books are mentioned there.
many of your gifteds are mostly too young now but that is temporary!

if we math types are worried that interest in math is low, that thread has over 600,000 hits; not competing with susan boyle, but surprizing.  [edit: Oct. 2014, # hits now over 950,000.]

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Unfortunately I do not know well many of the math books and series being discussed here. My impression sometimes however from the comments is that there is sometimes little appreciation for the difference in levels of sophistication of different books.

I mean that a geometry course for instance would presumably start off just with familiarizing the student with shapes, as many diverse and beautiful shapes as possible. Constructions would play a key role here, including three dimensional figures, e.g. building and coloring regular polyhedra, which always appeal to children.

At some point however, questions should begin to be introduced about the material, and a discussion of how to answer them creatively. I.e. what things we can observe lead us to deduce other true phenomena that are less obvious? I consider this stage the beginnings of mathematics. (How long is that circle? Can we construct a square with the same area as the inside of that circle? What is the relation between the volume of a cylinder and a cone on the same base?)

I would suggest that a parent can best enjoy being the guide who determines what level the student can appreciate, if the parent pursues and learns as much as possible of the subject from a higher point of view than the student is on. Then they can experiment with introducing deeper perspectives as the student comprehends them.

I.e. no doubt certain well regarded series used widely can simply be followed to their end, but certain courageous individuals persuaded me last summer to teach Euclid itself to brilliant 8-10 year olds, many of whom who proved more ready to appreciate it than many college students in the past.

A parent can only prepare to probe the abilities of their child by experimenting in learning material at a higher level themselves I suspect.

The "experts" thread here started by proposing such instructional seminars for parents but I am not aware that any have surfaced. would it be a good idea to have a community reading course of some advanced material? or is this too time intensive for already busy parents (and experts)?

Perhaps less ambitious would be an experts review of various books that reveal the level of sophistication of those books. E.g. it became clear on a related thread that some parents were misled as to whether AoPS geometry contained "proofs", when what was meant was whether the proofs were written in a certain familiar style.

It might of interest and use to some to discuss which geometry books do contain "proofs", in the sense of logical discussions. Even an explanation of what the word "proof" refers to in different contexts could be useful.

Since I am new here I am unaware how familiar everyone may be with Terry Tao, a successful example of accelerated education in math.

here is an article about him written when he was about 13. He is now a Fields medalist and math professor at UCLA.

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I just got my catalog for "the great Courses", including one for 24 lectures on calculus, 30 minutes each, by Michael Starbird. I have listened to one free lecture on Shakespeare from this company in Chantilly, VA, and greatly enjoyed it, but the courses are ridiculously expensive. Today they are advertising the normally \$254.95 series of calculus lectures for \$39.95. Apparently math does not sell well. I do not know anything about these lectures nor about Professor Starbird, but they may interest someone at that price.

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I just got my catalog for "the great Courses", including one for 24 lectures on calculus, 30 minutes each, by Michael Starbird. I have listened to one free lecture on Shakespeare from this company in Chantilly, VA, and greatly enjoyed it, but the courses are ridiculously expensive. Today they are advertising the normally \$254.95 series of calculus lectures for \$39.95. Apparently math does not sell well. I do not know anything about these lectures nor about Professor Starbird, but they may interest someone at that price.

Mathwonk: it has nothing to do with math not selling well - ALL courses go on sale on a regular basis, often very deeply discounted. They constantly have something on sale for 70% off. Many of us on this board have large collections, and nobody ever pays the regular price. 70% discount is standard; 85% discount and more is worth shooting for. Best sales right after Christmas.

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Thank you regentrude! As a mathematician I felt so dissed! Now I know its not just us. That's great to know.

(Let's see, if I did the math right, this one is indeed almost 85% off.)

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Thank you regentrude! As a mathematician I felt so dissed! Now I know its not just us. That's great to know.

(Let's see, if I did the math right, this one is indeed almost 85% off.)

No, it is not just math, LOL.

I must say, though, that I do not consider the format to be lending itself very well to math and introductory science courses, because one can not learn those passively by watching lectures - one has to practice problem solving. I can, however, absorb large amounts of history and literature discussions from listening to lectures while driving ;-)

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My hubby borrowed some of the Great Courses DVDs from the library and he found them too dry in terms of presentation. My kids are too pampered by Rusczyk's animated voice on his AoPs videos to listen to the Great Courses DVDs.

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I just got my catalog for "the great Courses", including one for 24 lectures on calculus, 30 minutes each, by Michael Starbird. I have listened to one free lecture on Shakespeare from this company in Chantilly, VA, and greatly enjoyed it, but the courses are ridiculously expensive. Today they are advertising the normally \$254.95 series of calculus lectures for \$39.95. Apparently math does not sell well. I do not know anything about these lectures nor about Professor Starbird, but they may interest someone at that price.

I don't know anything about the course, but Great Girl just got an A in her course (Discrete Math) with Dr. Starbird. She loves him. They all do. He's apparently a fantastic teacher who makes the obscure clear.

It wasn't 70% off, though, I can tell you that. But it included office hours.

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Hi Jane,

Thank you very much for the info. I have Dolciani Modern Algebra (I don't have the 60s edition, but the 1975). I will check it out. Really appreciate your help.

Liem

Thanks a lot for the resource. I was also looking for it... :)