Best/most rigorous upper level math

[Grantmom]

I am seeing a lot of posts saying that MUS is not rigorous enough for upper level math, for those who are math-inclined and wanting to head toward math/science/engineering degrees. Is this really true? I was excited thinking this would be a good fit and we could just use it all the way through. My son is definitely very math and science oriented. I know he will want to be prepared to test well in math when that time comes, and I want him to feel well prepared. What is the best then? What about VideoText Interactive?

I would like to start with something now that we can follow all the way through for higher level math.

 

Thanks for sharing any opinions!

[lewelma]

AoPS is one of the most rigorous. Best, of course, depends on your child. AoPS uses a discovery style that does not fit all students.

Edited September 7, 2012 by lewelma

[WishboneDawn]

I'm not sure what rigor means in this context.

 

More and more for me it means the work my kids and I put into a program and it's a bit less about the program itself. I started my daughter on Singapore DM which is more "rigorous" in terms of the way it pushes conceptual leaps but it wasn't getting done because my daughter didn't like it at all. We switched to Foerster's Algebra where it's much more traditional and straightforward and now the math is not only getting done but much more work and a better quality of work that displays a deeper understanding.

 

Does MUS cover what needs to be covered for a math and science geared kid? That's the big question. If it does then I think the rigor part is up to you and your son. You can always supplement a bit but if MUS works, why change now?

[regentrude]

AoPS is one of the most rigorous. Best, of course, depends on your child. AoPS uses a discovery style that does not fit all students.

 

:iagree:

Probably the widest scope, most complex problem solving, and a mathematically rigorous presentation of the material that is lacking in many other programs. BUT definitely not a good fit for every student.

[Jane Elliot]

I am seeing a lot of posts saying that MUS is not rigorous enough for upper level math, for those who are math-inclined and wanting to head toward math/science/engineering degrees. Is this really true? I was excited thinking this would be a good fit and we could just use it all the way through. My son is definitely very math and science oriented. I know he will want to be prepared to test well in math when that time comes, and I want him to feel well prepared. What is the best then? What about VideoText Interactive?

I would like to start with something now that we can follow all the way through for higher level math.

 

Thanks for sharing any opinions!

 

I have 3 sons who are currently all math/science majors at university (2 seniors and a junior, all earning 3.9 or better.) When we were homeschooling them, it was apparent they would end up in math or science majors. We looked at MUS and quickly ruled it out.

 

We ended up using and liking Chalkdust for almost everything from PreAlgebra up. (We didn't try Chaldust geometry; we used Jacob's geometry instead. And one of our sons wanted to do the AP Calculus BC exam, so he used Thinkwell Calculus since Chalkdust Calculus only covers Calculus I.) We're still using Chalkdust for the kids still at home.

 

I really like Chalkdust. Dana Mosley is a very gifted teacher, explaining concepts in a way that makes math even more exciting for a math lover and makes it clear for a student who is not as math oriented.

[Serenade]

Where does Saxon fit on the rigor scale? I'm thinking it's a good solid, middle-of-the road program but am wondering if I am off base? I know a lot of private schools use Saxon, and they usually have good testing scores, but then it might be a factor of how much effort is put in, as someone mentioned upthread.

[Sunshine State Sue]

We used MUS from K through Algebra. I have a degree in math, fwiw. I thought MUS was strong and solid in the elementary years (with the exception of word problems which we supplemented using Singapore's Challenging Word Problems). I wanted to use it for high school, but decided after Algebra that it was not up to par. That was in 2008, and it has been improved on since then, though I'm still not convinced. Algebra 1 did not teach quadratic equations, which is standard in Algebra 1. I don't think the newest edition has it either, but I could be wrong. It was my understanding that they incorporated the Honors portions into the standard text. We used MUS Algebra along with LoF Algebra. MUS was easy-peasy. LoF was challenging, but did not fit ds's learning style.

 

Here are a 2 prior threads:

MUS through highschool?

MUS in High School

 

We used Foerster's Algebra (after MUS) and Discovering Geometry/Serra. Ds is now dual enrolled at CC.

Edited September 7, 2012 by Sue in St Pete

[Sunshine State Sue]

Where does Saxon fit on the rigor scale? I'm thinking it's a good solid, middle-of-the road program but am wondering if I am off base? I know a lot of private schools use Saxon, and they usually have good testing scores, but then it might be a factor of how much effort is put in, as someone mentioned upthread.

IMO, your assessment is correct - it's a solid program. I would have enjoyed it as a student. I was the type to buy math workbooks and take them on vacation with me. Detail-oriented, slightly OCD, perfectionist-ish, etc. I've seen complaints that it does not truly teach true mathematical thinking like AoPS would, but definitely solid.

 

Note: I have no personal experience with Saxon. I base my opinion on our hs evaluator who has a degree in math and 5 graduated STEM majors and my brother-in-law's experience of using it with my niece.

Edited September 7, 2012 by Sue in St Pete

[Candid]

I think Singapore's upper level programs like DM and NEM are also rigorous. My ds went from finshing them to AoPs Pre-Calculus book (not online course) without a flicker of hesitation.

[Candid]

More and more for me it means the work my kids and I put into a program and it's a bit less about the program itself. I started my daughter on Singapore DM which is more "rigorous" in terms of the way it pushes conceptual leaps but it wasn't getting done because my daughter didn't like it at all. We switched to Foerster's Algebra where it's much more traditional and straightforward and now the math is not only getting done but much more work and a better quality of work that displays a deeper understanding.

 

I absolutely believe that you have part of the equation here. The work must get done, it must get done at a high level for any program to be rigorous, but if we use a math program that doesn't cover all the topics then the student can't make it to the rigorous level because their materials don't support them in that. (Note: I'm not saying that about any specific program you mention but as a general truth.)

 

Does MUS cover what needs to be covered for a math and science geared kid? That's the big question. If it does then I think the rigor part is up to you and your son. You can always supplement a bit but if MUS works, why change now?

 

I think the questions you begin with are the correct ones, but the answers must be evaluated by someone who understands what math is needed for an engineer or other math oriented student.

 

This is can be difficult for some home school moms to evaluate. I read a lot of reviews and I make decisions by comparing reviews, evaluating reviewers, and comparing the actual scope and sequence of programs when I can.

 

I think that is what the OP is doing. She's read enough reviews to make her begin to question whether MUS will adequately cover the material a math oriented student will need to have covered by graduation. So now she is looking for more advice as to other programs to look at.

[Mom22ns]

Algebra 1 did not teach quadratic equations, which is standard in Algebra 1. I don't think the newest edition has it either, but I could be wrong. It was my understanding that they incorporated the Honors portions into the standard text. We used MUS Algebra along with LoF Algebra. MUS was easy-peasy. LoF was challenging, but did not fit ds's learning style.

 

Sue is right on this.

 

We are still using MUS. My kids didn't find Algebra easy at all. Ds followed it up with LoF and thought the challenge level stayed about the same even though he had already completed MUS Algebra though. For us the combination has been a good fit. My kids aren't in college, so I can't say how it will come out for us in the end, but their math standardized test scores were very good at the end of last year.

[WishboneDawn]

 

I think that is what the OP is doing. She's read enough reviews to make her begin to question whether MUS will adequately cover the material a math oriented student will need to have covered by graduation. So now she is looking for more advice as to other programs to look at.

 

Good point.:001_smile:

[Sebastian (a lady)]

Where does Saxon fit on the rigor scale? I'm thinking it's a good solid, middle-of-the road program but am wondering if I am off base? I know a lot of private schools use Saxon, and they usually have good testing scores, but then it might be a factor of how much effort is put in, as someone mentioned upthread.

 

I think it is difficult to assess how effective Saxon is as a program.

 

For one thing, it IS widely used in private schools. But that means the students using it in that setting are getting a period a day of instruction from a specialist math teacher, in addition to their homework time.

 

I also think that Saxon is THE math program most likely to be used in ways other than how the program is laid out. There are many families that skip the fact sheets and mental math or only do half of the mixed practice sets. That might or might not be a problem for their kids' retention and understanding. But if problems develop, it seems a little unfair to castigate a program that was used in an al a carte manner rather than as designed.

 

I think Saxon can give a solid math footing, at least up through pre-Algebra. My older kids used it almost exclusively and were consistently in the high 90s on standardized exams. (But they also did well on testing in the very early years, so it's difficult to tease out what is the math program and what was just them.)

 

I don't think there is any math program that will teach a student math, especially upper level stuff, without work on the part of the student, and often the parent. I don't think there is one that you just buy and voila, the student learns. (I'm not personally a fan of video based or computer based instruction. It's been too easy for my kids to zone out or become passive receptors rather than active learners. I'll use something like Khan Academy on occasion, but a full screen based course is not in our future for math. I have enough issues with staying on top of the language courses we're using.)

 

For algebra we did make the switch to AoPS (with Dolciani as an occasional supplement), and I'm pleased that we did. The spiral that served us so well in the younger years might not have been so beneficial in the teen years. I like that AoPS makes them take a concept to extremes, not just through common usage. Just as an example, a Saxon pre-algebra lesson on exponents would include raising a number to the second, third and fourth power. The chapter on exponents in AoPS included negative and fractional exponents and fraction problems where there were positive, negative and fractional exponents in both numerator and denominator that had to be simplified. The principles were the same in both books, but the required application went farther in AoPS (imho).

[Serenade]

IMO, your assessment is correct - it's a solid program. I would have enjoyed it as a student. I was the type to buy math workbooks and take them on vacation with me. Detail-oriented, slightly OCD, perfectionist-ish, etc. I've seen complaints that it does not truly teach true mathematical thinking like AoPS would, but definitely solid.

 

Note: I have no personal experience with Saxon. I base my opinion on our hs evaluator who has a degree in math and 5 graduated STEM majors and my brother-in-law's experience of using it with my niece.

 

Thanks for your input on this. I appreciate it!

 

We've just started with Saxon this year, using Saxon Algebra 1/2, and so far I've been very pleased. It has worked well for my son. Shockingly, he is actually reading the lessons himself and "getting" it. He previously used Horizons and was able to switch from Horizons 5 directly into Algebra 1/2 with no problem, which is why I was wondering about it a little bit.

[Serenade]

I think it is difficult to assess how effective Saxon is as a program.

 

For one thing, it IS widely used in private schools. But that means the students using it in that setting are getting a period a day of instruction from a specialist math teacher, in addition to their homework time.

 

I also think that Saxon is THE math program most likely to be used in ways other than how the program is laid out. There are many families that skip the fact sheets and mental math or only do half of the mixed practice sets. That might or might not be a problem for their kids' retention and understanding. But if problems develop, it seems a little unfair to castigate a program that was used in an al a carte manner rather than as designed.

 

We are using the book exactly as indicated, not skipping any problems. But Algebra 1/2 is the first Saxon program we have used. We used Horizons previously, and I know we did not do everything that the program said to do.

 

I think Saxon can give a solid math footing, at least up through pre-Algebra.

Do you think Saxon is not as good once Algebra starts?

 

 

For algebra we did make the switch to AoPS (with Dolciani as an occasional supplement), and I'm pleased that we did. The spiral that served us so well in the younger years might not have been so beneficial in the teen years. I like that AoPS makes them take a concept to extremes, not just through common usage. Just as an example, a Saxon pre-algebra lesson on exponents would include raising a number to the second, third and fourth power. The chapter on exponents in AoPS included negative and fractional exponents and fraction problems where there were positive, negative and fractional exponents in both numerator and denominator that had to be simplified. The principles were the same in both books, but the required application went farther in AoPS (imho).

 

Wow, that does sound quite a bit more advanced. My son has done well with math, but I think the above would probably freak him out at the moment. LOL, it would freak me out! As I mentioned above, we went directly from Horizons 5 to Saxon Algebra 1/2, and while he has so far made 95s and above on the tests, he's already being stretched. Sounds like he is probably good where he's at, but I might do well to consider AoPS for my youngest son, who in all likelihood will end up in an engineering school.

 

Thanks for your input!

[Miss Marple]

I think Singapore's upper level programs like DM and NEM are also rigorous. My ds went from finshing them to AoPs Pre-Calculus book (not online course) without a flicker of hesitation.

 

Agree. Mine went from DM 4A directly into college algebra at our local university. This is the highest level they will allow any concurrent student to take. My boys have commented that much of what they are doing in their concurrent courses (college algebra and trig) is repetition of their Singapore DM courses.

 

From what we've used, I would say AoPS and Singapore are the most rigorous. I like both but the best program is the one that fits your teaching style and your student's learning style best and is the one that will get done. It's no good having a rigorous program on hand if it doesn't get done because it is a poor fit.

Edited September 7, 2012 by CynthiaOK

[Kimm in WA]

We used MUS for our 3 boys through Algebra II and they moved to Chalkdust Pre-Calculus without any problem in 10th grade. I made the switch because each of them were planning on doing dual-enrollment in 11th and 12th and I wanted them to be able to get used to a "regular textbook".

 

They all scored verye well on the ACT and transitioned to community college classes in high school with NO problem. Oldest son did Calc I, II, and III at the community college while still in high school. Next two boys, who are still very math-inclined (although not AS much as the oldest), took Calc I in 11th grade at the CC without any problem.

 

Oldest DS was accepted to our state's most rigorous university and was one of only 30 students to be directly-admitted to their electrical engineering department. He went on to take higher math at the university without any problems.

 

SO, all that to say that if you have math-included students MUS can be a good fit. If your student needs more problem sets to "get" a concept they may need something else.

 

HTH,

Kimm

[Gwen in VA]

Mary Dolciani is an author of many math textbooks ranging from pre-algebra, algebra I & II to precalculus (or "advanced mathematics"). Her books are outstanding and often used in public school honors classes.

 

I have graduated three using her texts (with the geometry book by Jurgenson, Brown, and Jurgenson thrown in the middle somewhere). My kids were beyond well-prepared for the SAT's, SAT-2's, and calculus. (Two are in engineering and one was a math major...)

 

I have been interested in AoPS but the time commitment involved scared me. The Dolciani books required more or less an hour a day for 180 days and that was it.

 

The only problem with the Dolciani books is finding the answer key / teacher's manual, but they are out there.

[Joan in GE]

I liked Saxon best through 3rd grade due to all the manipulative use built into most lessons as well as parental involvement.

 

ds3 gave up on Saxon Algebra II after doing Jacob's for geometry - he said he wasn't learning anything new and he was on lesson 30 or more. That was probably just review built into the system but it really frustrated him. We ended up using Dolciani Algebra II after a brief time with Foerster, though then did Foerster for Precalc and Larson for Calculus...

 

dd did Dolciani for Prealgebra and Algebra and is starting on Geometry while finishing Algebra (we did a detour for the Swiss math exam).

 

I like Dolciani a lot but for dd it would be better if there was a bit of review built into each lesson. I think that is Saxon's strength for children who need review to remember concepts. There is review at the end of the Dolciani chapter but it doesn't seem like enough for her though for ds3 it was plenty.

 

But I much prefer getting more of a topic developed over a bunch of lessons, than the 'bytes' you get with Saxon...I think some kids don't feel like they've really mastered any concept with the Saxon book because the lessons come in these pieces. They can do the problem when they see it but there could be a consciousness missing. You could ask them - did you cover Multiplication of Binomials Containing Radicals and they might not be able to tell you because it was just one of 130 lessons without any mental chapter heading to slot that lesson into...(talking mental organization here - folders in the brain or learning hooks). Maybe other kids couldn't either even when it was a part of a chapter - I was just trying to think of an example that might work...

 

Maybe I'm the only one that bothers...I'd like to hear from some math teachers about that actually - whether it matters or not..

 

Joan

[regentrude]

But I much prefer getting more of a topic developed over a bunch of lessons, than the 'bytes' you get with Saxon...I think some kids don't feel like they've really mastered any concept with the Saxon book because the lessons come in these pieces. They can do the problem when they see it but there could be a consciousness missing. You could ask them - did you cover Multiplication of Binomials Containing Radicals and they might not be able to tell you because it was just one of 130 lessons without any mental chapter heading to slot that lesson into...(talking mental organization here - folders in the brain or learning hooks). Maybe other kids couldn't either even when it was a part of a chapter - I was just trying to think of an example that might work...

 

Maybe I'm the only one that bothers...I'd like to hear from some math teachers about that actually - whether it matters or not..

 

 

It did bother us greatly when we used Saxon. My kids want to thoroughly explore and master a concept before moving on to the next topic, and it drove them nuts that Saxon delivered an incremental sound bite, then switched to something entirely unrelated, only to return to the next bite a few lessons later.

The method makes it hard to see the conceptual thread and underlying theory, because it suggests that math is composed of many seemingly unrelated different problem types. To illustrate what I mean: some students end up thinking there are many different types of linear equations: with integer coefficients, with fractional coefficient, with negative coefficients, with the variable on both sides of the equation, with the variable on one side of the equation... but really, it is all the same, there is only one kind of linear equation -and it is so much easier to recognize this than to learn algorithms for every conceivable sub-type of problem.

So, one concern I have with Saxon would be that students may end up being able to solve the problems (and many undoubtedly do), but won't develop a feeling for the underlying structure of the mathematics and for the broad concepts.

 

ETA: I am not a math teacher, but I teach physics and I see my students apply their high school math on a daily basis. What strikes me is that, while most of them are fairly decent at manipulating equations, the majority has no feeling for what they do, why they do it, how to detect that they made a mistake, what outcomes to expect. They are performing math by rote, like computers, but have not been trained in mathematical thinking. From my encounters with Saxon, I did not feel that the program teaches mathematical thinking; it looks as if it might produce exactly this kind of students.

 

(As an aside: In addition to this methodical issue, some of the explanations we came across in 8/7 were simply not mathematically sound. )

Edited September 8, 2012 by regentrude

[MAIMOM]

I have 3 sons who are currently all math/science majors at university (2 seniors and a junior, all earning 3.9 or better.) When we were homeschooling them, it was apparent they would end up in math or science majors. We looked at MUS and quickly ruled it out.

 

We ended up using and liking Chalkdust for almost everything from PreAlgebra up. (We didn't try Chaldust geometry; we used Jacob's geometry instead. And one of our sons wanted to do the AP Calculus BC exam, so he used Thinkwell Calculus since Chalkdust Calculus only covers Calculus I.) We're still using Chalkdust for the kids still at home.

 

I really like Chalkdust. Dana Mosley is a very gifted teacher, explaining concepts in a way that makes math even more exciting for a math lover and makes it clear for a student who is not as math oriented.

 

:iagree: We used Saxon for Algebra 1/2 and I liked it to a degree. The difficulty arose when we reached a topic I could not help the kids to understand. No matter what I did they just did not get it.

 

This year my DD is in PreCal and I knew we needed a teacher for her. I found Chalkdust for my 6ht grader actually and my 10th grader said "mom, that guy makes it easy. I could learn from him." It is expensive but well worth it. We are several weeks into Precal and she is enjoying math. I love that you also get email access to Dana Mosley if your student gets stuck. If you buy a used copy you can pay a little more to have the teacher support also which is what I did.

I do agree the child must put forth the effort. Dana Mosleys instruction makes it easy to understand.

[Pegasus]

We've used MUS from the beginning and I've read countless threads related to MUS on various forums. Almost all of the replies/comments fall into two categories:

 

1. I didn't think MUS was enough for high school so I switched.

 

2. My students used MUS for high school and did well on college testing and in their college math courses.

 

There is a distinct lack of comments about how someone used MUS and it wasn't good enough to prepare their students for success at a higher level. There is only speculation that it wouldn't be enough, along with the success stories.

 

For what it is worth, DH and I hold 3 technical degrees (engineering and architecture). We think MUS provides very solid math prep.

[Sebastian (a lady)]

I liked Saxon best through 3rd grade due to all the manipulative use built into most lessons as well as parental involvement.

 

ds3 gave up on Saxon Algebra II after doing Jacob's for geometry - he said he wasn't learning anything new and he was on lesson 30 or more. That was probably just review built into the system but it really frustrated him. We ended up using Dolciani Algebra II after a brief time with Foerster, though then did Foerster for Precalc and Larson for Calculus...

 

dd did Dolciani for Prealgebra and Algebra and is starting on Geometry while finishing Algebra (we did a detour for the Swiss math exam).

 

I like Dolciani a lot but for dd it would be better if there was a bit of review built into each lesson. I think that is Saxon's strength for children who need review to remember concepts. There is review at the end of the Dolciani chapter but it doesn't seem like enough for her though for ds3 it was plenty.

 

But I much prefer getting more of a topic developed over a bunch of lessons, than the 'bytes' you get with Saxon...I think some kids don't feel like they've really mastered any concept with the Saxon book because the lessons come in these pieces. They can do the problem when they see it but there could be a consciousness missing. You could ask them - did you cover Multiplication of Binomials Containing Radicals and they might not be able to tell you because it was just one of 130 lessons without any mental chapter heading to slot that lesson into...(talking mental organization here - folders in the brain or learning hooks). Maybe other kids couldn't either even when it was a part of a chapter - I was just trying to think of an example that might work...

 

Maybe I'm the only one that bothers...I'd like to hear from some math teachers about that actually - whether it matters or not..

 

Joan

 

When I was doing observations for my MS Ed, one of the classes I sat in on had just finished up a unit on fractions (this was 6th grade). The teacher announced that they were done with fractions and that they could take their notes out of their binders, because they wouldn't need them again that year. I thought that was one of the worst things that you could tell a student. It makes it sound as if fractions and decimals and percentages aren't connected and related to each other. And I thought that it was probably going to serve as a prompt for the students to forget most of what they'd just been studying.

 

This is one of the reasons I liked Saxon in early grades. The constant review was good on my leaky kids. And I liked that they rarely felt like a topic was a big new scary leap.

 

I cannot comment on Saxon Algebra for the simple reason that we didn't try it.

 

Both Dolciani and AoPS make my kids apply what they learn in mentally stretchy ways. I feel like AoPS especially has de facto review built into the lessons because the problems require you to apply what you learned before. But I also like that Dolciani will have a dozen progressively harder problems on a topic.

 

Somehow it feels more fitting to dwell on a topic in algebra than it did at the younger grades.

[G5052]

Of course there are some that I wouldn't recommend, but the bottom line is that they're thoroughly learning the material and seeing it applied in different applications. That is less common than one would think :glare:.

 

I never expected to like Saxon, but it "clicks" with my oldest, and he's thriving in Algebra II. Because I have a math/science background, I do quiz him orally and scruntinize his exams more closely that most. I ask him "why" quite a bit. And although it would not be my first choice, I'm willing to admit that it works for him. I loved Jacobs Algebra, but he bottomed out with it and we went to Saxon Algebra 1/2 about half way through and didn't look back.

 

My next one is starting Algebra 1/2 because I have the book, but I'm watching to see if the same is true there.

[Melissa in NC]

I earned my degree in Chemical Engineering. We are currently using Singapore DM. I find it very rigorous and touches on some things I did not get exposed to until college. I work some of the tougher problems with her by asking leading quesitons so she does not get frustrated.

[Grantmom]

Thank you all so much for your thoughtful discussion. I think I'm more confused now though! Sounds like there are many wonderful programs that I hadn't even researched yet! I do get that what you put into it makes is what makes it rigorous, I just wanted to be sure that whatever we get will cover and prepare him for the kind of higher level math he will want to be able to do in college, and help him score well on tests to get into the kind of college he would like to go to.

 

So, as for determining what fits his style, how do I do that without trying them all out? Some of these are super expensive. The Chalkdust for example looks really steep. Before this thread I was thinking about the VideoText Interactive, but the Chalkdust website compares their program to the VT and says it is not as comprehensive. I thought I really liked the idea of the VT, when I watched the intro video it made so much sense and I was kind of excited about it. But now I feel like I need to look at these other suggestions closer first.

 

I really like the idea of the programs that have a video with them, because although I took up to AP Calculus in HS and took higher level math in college, it has been 20 years since I have used any of that stuff and I know I cannot explain things. I like the idea of having a "teacher" even if on a screen, actually explain the concept and work out problems along with you. But, maybe that is just *my* need. I don't know!

[Grantmom]

Also, are there certain programs that will or won't "count", as in, on my own homemade transcript, for these requirements for college? How do you even do this?

 

Also, with AoPS, they have different courses, like intro to algebra and intermediate algebra, so do you combine the 2 to count for Algebra? Or is the first like Algebra 1 and the second like Algebra 2? Sorry, feeling so lost.

[regentrude]

Also, with AoPS, they have different courses, like intro to algebra and intermediate algebra, so do you combine the 2 to count for Algebra? Or is the first like Algebra 1 and the second like Algebra 2?.

 

 

No! The book Introduction to Algebra covers a lot more than any other traditional algebra 1 text; the algebra 1 part is chapters 1 through 12 or 13. The Intermediate Algebra text covers not only algebra 2, but some material usually covered in precalculus.

 

So, if you just want algebra 1, either use chapters 1-13 of Intro to Algebra for a scope comparable to a standard course, or do all of Intro to Algebra for a course that contains a lot more. This is the thickest book and the one that takes the longest time to finish. Some students take more than one year.

[Grantmom]

No! The book Introduction to Algebra covers a lot more than any other traditional algebra 1 text; the algebra 1 part is chapters 1 through 12 or 13. The Intermediate Algebra text covers not only algebra 2, but some material usually covered in precalculus.

 

So, if you just want algebra 1, either use chapters 1-13 of Intro to Algebra for a scope comparable to a standard course, or do all of Intro to Algebra for a course that contains a lot more. This is the thickest book and the one that takes the longest time to finish. Some students take more than one year.

 

 

So, in terms of writing a transcript though, how would you apportion that? I may be thinking ahead too far here, but I really need to feel like I have a solid plan for high school math so that he can achieve his goals for college.

[Joan in GE]

ETA: I am not a math teacher, but I teach physics and I see my students apply their high school math on a daily basis. What strikes me is that, while most of them are fairly decent at manipulating equations, the majority has no feeling for what they do, why they do it, how to detect that they made a mistake, what outcomes to expect. They are performing math by rote, like computers, but have not been trained in mathematical thinking. From my encounters with Saxon, I did not feel that the program teaches mathematical thinking; it looks as if it might produce exactly this kind of students.

 

The teacher announced that they were done with fractions and that they could take their notes out of their binders, because they wouldn't need them again that year. I thought that was one of the worst things that you could tell a student.

 

....

Somehow it feels more fitting to dwell on a topic in algebra than it did at the younger grades.

 

Thanks regentrude and Sebastian!

 

And Sebastian, I can agree that the teacher was sending the wrong message...

 

Joan

[regentrude]

So, in terms of writing a transcript though, how would you apportion that? I may be thinking ahead too far here, but I really need to feel like I have a solid plan for high school math so that he can achieve his goals for college.

 

My DD covered the complete Intro to Algebra book in one school year (plus summer), and I listed it as algebra 1.

My DS has covered chapters 1-15 of Intro to Algebra in a bit more than one school year; this will be listed as algebra 1. He will cover the last six chapters of the book and a large part of Intermediate Algebra as part of his algebra 2 course.

 

ETA: Since both of my kids are going through all the books anyway, it really does not matter where I break it up, they'll learn all of it. In the end, they will have math through multivariable calculus, and nobody cares how I define "algebra 1" or "algebra 2". Even breaking it up after chapter 13 for "alg 1", you will still have a course much more rigorous than the typical high school algebra 1 courses.

Edited September 10, 2012 by regentrude

[Candid]

So, in terms of writing a transcript though, how would you apportion that? I may be thinking ahead too far here, but I really need to feel like I have a solid plan for high school math so that he can achieve his goals for college.

 

Personally, I don't feel you have to make your course work fit to a standard program. Since I used Singapore and then switched to AoPS, I plan to simply use the book titles as the course titles. With the Singapore materials I will add the word Singapore to the beginning of the book title.

 

Back up materials can include a scope and sequence.

[kiana]

ETA: I am not a math teacher, but I teach physics and I see my students apply their high school math on a daily basis. What strikes me is that, while most of them are fairly decent at manipulating equations, the majority has no feeling for what they do, why they do it, how to detect that they made a mistake, what outcomes to expect. They are performing math by rote, like computers, but have not been trained in mathematical thinking. From my encounters with Saxon, I did not feel that the program teaches mathematical thinking; it looks as if it might produce exactly this kind of students.

 

 

:iagree:

 

I can't tell you how many students I've seen during our quantitative literacy class, who plug the numbers into their calculator, make a trivial error, and end up with a ridiculous answer like $9.13 as a monthly payment for a $400,000 mortgage. They circle the answer and move on, because ... well, that's what the calculator said, even though anyone here who's ever made a mortgage payment (and many who haven't) would say 'huh? that's ridiculous!'

 

Somehow, the 'that's ridiculous' part of the brain seems to get disengaged during math class.

[regentrude]

I can't tell you how many students I've seen during our quantitative literacy class, who plug the numbers into their calculator, make a trivial error, and end up with a ridiculous answer like $9.13 as a monthly payment for a $400,000 mortgage. They circle the answer and move on, because ... well, that's what the calculator said, even though anyone here who's ever made a mortgage payment (and many who haven't) would say 'huh? that's ridiculous!'

Somehow, the 'that's ridiculous' part of the brain seems to get disengaged during math class.

 

Yep. I have students calculate the mass of planet Jupiter, and some got 1.9kg (the equivalent of four cans of soup) and circled that as their final answer, without blinking an eye.

[Sebastian (a lady)]

So, in terms of writing a transcript though, how would you apportion that? I may be thinking ahead too far here, but I really need to feel like I have a solid plan for high school math so that he can achieve his goals for college.

 

What I am doing is putting Algebra 1 on the year that we do the first part of the book and Algebra 2 on the year when we do the second part of the book. We will be doing them sequentially, with geometry following Algebra 2 (because that seems to be the sequence envisioned by AoPS for using their books).

 

For my kids, Algebra 1 will be "above the line" with an indication that it was completed before 9th grade. For one kid, Algebra 2 will also be completed before 9th grade.

 

 

I don't know if this helps, but here are the course descriptions I wrote up for Algebra 1 and 2 (I may tweak the Algebra 2 description after we complete the year). [We did a little less of the AoPS book than Regentrude recommended, because I added in a couple chapters on polynomials from Dolciani. I also added the chapter on trigonometry from Dolciani so we were ready to start physics this year. So some parts of my description go beyond just the AoPS book. NB: I based this on the description of the AoPS online class and tweaked to reflect what we'd completed and emphasize where we'd spend more time.]

 

=========

 

Algebra 1

Algebra 1 covers the fundamental concepts of algebra, including exponents and radicals, linear equations and inequalities, ratio and proportion, systems of linear equations, working with polynomials, and factoring quadratics. This course also included an introduction to geometry and trigonometry.

Textbooks:

Art of Problem Solving Introduction to Algebra, Richard Rusczyk, AoPS Incorporated (2010), ISBN: 978-1-934124-14-7 Chapters 1-11. (This text contains both Algebra 1 and Algebra 2 material.)

Modern Algebra: Structure and Method Book One, Mary Dolciani, Houghton Mifflin Company (1962)

Completed: Fall 2011 – Spring 2012

AMC 8 Math Exam:

 

Algebra 2

Fundamental concepts of algebra, including linear equations, systems of equations, quadratics, factorizations, complex numbers, graphing, functions, sequences and series, special functions, exponents and logarithms.

Textbooks:

Art of Problem Solving Introduction to Algebra, Richard Rusczyk, AoPS Incorporated (2010), ISBN: 978-1-934124-14-7 Chapters 12-25. (This text contains both Algebra 1 and Algebra 2 material.)

Completed: Fall 2012 – Spring 2013

[Joan in GE]

Yep. I have students calculate the mass of planet Jupiter, and some got 1.9kg (the equivalent of four cans of soup) and circled that as their final answer, without blinking an eye.

 

It may partly be a lack of real life experience....My father (architect) said that many young architects and engineers will get wrong answers for sizes of beams etc and not think anything due to lack of hands on experience...Maybe it is the plug-and-chug mentality too...

[regentrude]

It may partly be a lack of real life experience....My father (architect) said that many young architects and engineers will get wrong answers for sizes of beams etc and not think anything due to lack of hands on experience...Maybe it is the plug-and-chug mentality too...

 

But seriously, EVERY student has had life experience with a soup can or soda bottle in real life. The fact that Jupiter is a huge planet and must be larger than a two liter soda bottle should not require additional "life experience", just common sense and the habit of thinking about the possible validity of answers.

[Joan in GE]

just common sense and the habit of thinking about the possible validity of answers.

 

But that's it with plug n chug - they don't get the habit of thinking - isn't it? Ok, the math programs could contribute to this problem as well if they're also plug and chug...

 

What about "a little self-doubt" to help them think of checking as well?

[regentrude]

But that's it with plug n chug - they don't get the habit of thinking - isn't it? Ok, the math programs could contribute to this problem as well if they're also plug and chug...

 

yes, that is what I find. It starts with simple arithmetic. Examples like this:

if a student divides some number by a fraction that is less than one, the student should expect his answer to be bigger than the original number and should check if this is really the case.

If he squares something that is less than one, the answer should be smaller - expect and check.

If you take the square root of something that is of the order of 10^14, you should get something of the order of 10^7 - expect and check.

Most math programs do not emphasize this enough. And the earlier calculators are allowed, the worse the problem becomes.

Edited September 10, 2012 by regentrude

[Joan in GE]

expect and check.

 

This will be my new mantra.....

 

And I'll use your examples to show why..:001_smile:

 

Most math programs do not emphasize this enough. And the earlier calculators are allowed, the worse the problem becomes.

 

I'm happy to communicate this to my dd who has been chomping at the bit to be allowed to use a calculator for her math lessons...

 

Joan

[Sebastian (a lady)]

yes, that is what I find. It starts with simple arithmetic. Examples like this:

if a student divides some number by a fraction that is less than one, the student should expect his answer to be bigger than the original number and should check if this is really the case.

If he squares something that is less than one, the answer should be smaller - expect and check.

If you take the square root of something that is of the order of 10^14, you should get something of the order of 10^7 - expect and check.

Most math programs do not emphasize this enough. And the earlier calculators are allowed, the worse the problem becomes.

 

I wonder if one of the problems lies in the very phrasing used in math classes. I've not run into "expect and check" but I have seen "guess and check".

 

To my ears, "guess and check" seems to emphasize a randomness to the potential answer, rather than a reasonable estimate.

 

I think that many classrooms also do not make a student check his work (as in working the problem in reverse) or to redo problems that are wrong. So there is no penalty to the erroneous answer (except the grade on the homework, if there is any - and of course the penalty of failing to comprehend).

[kiana]

yes, that is what I find. It starts with simple arithmetic. Examples like this:

if a student divides some number by a fraction that is less than one, the student should expect his answer to be bigger than the original number and should check if this is really the case.

If he squares something that is less than one, the answer should be smaller - expect and check.

If you take the square root of something that is of the order of 10^14, you should get something of the order of 10^7 - expect and check.

Most math programs do not emphasize this enough. And the earlier calculators are allowed, the worse the problem becomes.

 

100%.

 

Things like -- you might not know exactly what the square root of 27 is, but you should be able to say 'five and a bit' with confidence.

[MomsintheGarden]

We've used Chalkdust with several of our children, two of whom graduated and are now math + other STEM majors. When our dd wanted to use CD for her AP Calculus BC exam study, we contacted CD. Dana Moseley told us about his new recordings of the second half of the calculus book. We bought those plus the Solutions Manual for the 2nd half of Calc, plus a prep book. She studied all and got a 5. She's doing just fine in her math classes at college.

 

Just wanted to put it out there that it's now possible to use CD through Calc II/the BC exam.

 

I'm enjoying this discussion!

 

GardenMom

 

We ended up using and liking Chalkdust for almost everything from PreAlgebra up. (We didn't try Chaldust geometry; we used Jacob's geometry instead. And one of our sons wanted to do the AP Calculus BC exam, so he used Thinkwell Calculus since Chalkdust Calculus only covers Calculus I.) We're still using Chalkdust for the kids still at home.

 

I really like Chalkdust. Dana Mosley is a very gifted teacher, explaining concepts in a way that makes math even more exciting for a math lover and makes it clear for a student who is not as math oriented.

[Jane Elliot]

We've used Chalkdust with several of our children, two of whom graduated and are now math + other STEM majors. When our dd wanted to use CD for her AP Calculus BC exam study, we contacted CD. Dana Moseley told us about his new recordings of the second half of the calculus book. We bought those plus the Solutions Manual for the 2nd half of Calc, plus a prep book. She studied all and got a 5. She's doing just fine in her math classes at college.

 

Just wanted to put it out there that it's now possible to use CD through Calc II/the BC exam.

 

I'm enjoying this discussion!

 

GardenMom

 

Thank you for posting this! When ds wanted to do the Calc BC exam, I called Dana Moseley and asked if he had DVD's available. He didn't then, but I was hoping he might consider making some. I'm so glad to hear that he did. They might come in handy for some of my other dc.

[Grantmom]

Thank you for all of these wonderful suggestions and info. Still pouring through everything and trying to figure it out. I had initially thought we would move from Right Start and go into VideoText Interactive. Right now I am leaning towards doing some kind of arithmetic review (like with Khan and LoF) and then moving into AoPS pre-algebra. If it's too much, we could back up and do something like Math U See pre-algebra as an intro, then move back to AoPS. What do you think?

[Grantmom]

Oh, another thing I liked about the Video Text was that the guy in the intro said he basically reviews and re-teaches fractions/decimals/percents at the beginning of VideoText, because he thinks the way we learn it, again, is not conceptual enough.

 

I think I am having a hard time letting go of the idea of doing VideoText Interactive, because it is what I thought we would use for a long time, before I knew of all these other options.

 

I also really like the way the Chalkdust looks, but not sure if we could afford it.