We Can Do by Moshe Kai with guest Robert Levy discussing Saxon Math.

Early Learning Early Learning General Discussions
281

Robert,

I agree with you. I’ve gone through Saxon 65, and it resonated with me. I kept thinking ``that was exactly how I was taught math’'. I saw those standard algorithms for division and multiplication alongside very clear explanations of the steps, just the way I was taught. There was no fuzzy new math stuff or the teaching of 50 different ways to do addition.

And there is another thing I’ve always pondered. Despite the promises of new math proponents (deeper math understanding, conceptual knowledge, blah, blah, blah), where are the Newtons, the Einsteins, the Eulers, that new math was supposed to produce? I haven’t heard of any yet, years after the implementation of new math. Rather, we are having poorer and poorer results in math. Food for thought.

Each time I think of the ``discovery’’ method for math, your amazon review here comes to mind. lol

[size=11pt] I'm an engineer with 2 college degrees and a professional engineering license, so I knew what my kid needed to learn. When I went through my education, we learned the great names in math, like Pythagoras, Newton, and Euler, who had made great discoveries contributing to the field. I noted that my kid's name was not among them, so I decided that it was probably best to leave the discoveries to those people, while my kid simply took advantage of the discoveries and had the material taught to him. I knew that it wouldn't be a lot of "fun", but I wasn't particularly interested in trying to make math fun - I have enough common sense to know that kids are learning little, if anything, if they are having a lot of fun. Other than Singapore Math, Saxon is the only method left in the United States that still uses the "Direct Instruction" method (memorizing times tables, etc.), as opposed to the "Discovery" method (where kids can spend 2 weeks coming up with different ways to solve 8 times 7). Direct Instruction is the traditional way to learn math, and I still haven't seen any data show why we, as a country, abandoned it (other than having our math scores drop to the bottom of the world). While our child is not a genius, he was able to complete this book, plus the next 3 books prior to Algebra 1/2 in just over a year (and well before the material covered in school). That pretty much assured him never having to worry about his math education. I will always be indebted to John Saxon for his genius in writing these books.
Link to the review - http://www.amazon.com/review/REDQUKUP25PSG/ref=cm_cr_pr_cmt?ie=UTF8&ASIN=1565775031&nodeID=&tag=&linkCode#wasThisHelpful.

lol lol lol lol lol lol

282

Nee don’t get me wrong I am not suggesting ANY of those things are missing from. Saxon 5/4 but just that kids will need some basic understanding of them before hitting Saxon 5/4 in order to be able to do the questions. I know Saxon has all the answers for the calender stuff. But uTube problem is there is only one line telling the kids which months have 30 days and which ones have 31. Now yes they can read this chapter and answer all the questions, even flipping back through the book when they forget it in 3 days time BUT realistically it takes more than just reading one sentance a couple of times to remember which months have how many days.
As to the teaching thinking…lets see if I can explain this one… Children need to have some idea of how to manipulate numbers and number patterns to do Saxon 5/4. Even if they know their math facts by heart they need some critical thinking ability to complete even the patterns in the 3 rd chapter. Complete this pattern 3,6,9,------,15 or 24,20,------,14. Kids who can’t think mathematically will come unstuck fast. They might also read the word problems and not have a clue where to start to solve the problem. I do believe that if you are willing to sit and work with your children thought he first 10 chapters then the children WILL learn the skills needed just by doing the questions. ( yes particularly the word problems) they just might need some initial support to learn HOW to think them through. I hope that makes sense?
Thanks for the word problem link. I will definitely check that one out!

283

I get it.

But I don’t think it takes critical thinking to understand the sequence you posted. A child that has all multiplication tables pat down will immediately recognise that sequence (3,6,9,------,15) to be the 3’s counting up and the next one (24, 20, …) to be the 4’s counting down

284

Ray’s New Primary Arithmetic looks FANTASTIC! 18 weeks to Saxon 5/4! Thank you so much! I’ve been ho-humming with math with no solid plan aside from “work on basic facts so we can get to 5/4”. This is the step-by-step practice we need.
I’ve been eying TMT’s approach as well though. I think my son would really enjoy doing the word problems in that book using the soroban to help. http://teachingmytoddlers.blogspot.com/2013/03/learning-soroban-japanese-abacus.html

285

Hi people,

When I hear the term “Higher Order Thinking Skills” it makes me cringe. The term, I believe, was popularized in the 1960s and just about everything from that time frame has been a disaster for the country, with the exception of the space program, and that was due to people educated well before the 1960s.

My first thought with the term “Higher Order Thinking Skills” (abbreviated as HOTS for now on) is that it is a term used by the education establishment to make parents feel inferior or incompetent when discussing the education of their kids. As far as I can tell, what the establishment says is that you can either have “Rote Memorization” (RM) or HOTS, but not both. RM includes things like learning addition/multiplication tables, doing math by hand, and, I guess, phonics. To them, calculators take care of all RM math tasks, so why bother teaching kids that material. For reading, they look at phonics as stupid, because they all read by sight, like us too (hence the push for “Sight Words”; how we got here doesn’t seem to matter to them).

In the case of math, I didn’t stumble on to Saxon until David was 6.5 years old (with Saxon 54), and he still managed to get 8 years ahead of his age level in short order. That gave him several years prior to Saxon to get through the RM part. My point is that there is room for both and I think one can safely say that RM skills are very, very good to have, since you won’t have a calculator with you every moment of your life and you don’t want your kid to look illiterate when he needs a calculator to add 12 and 17. On top of that, there’s no assurance that a calculator will always be permitted in every scenario of your kid’s life. For example, the college where my mother taught, New Jersey Institute of Technology, terminated the use of calculators on math tests while she was there. The kids there simply did not know arithmetic and the college did not want to be handing engineering degrees to them, setting them into a profession where mistakes cost lives. As to those kids, well, New Jersey introduces calculators in math classes in Kindergarten (or at least did, at the time), so I just feel sorry for the kids.

As to HOTS overall, I kind of look at it as a side effect from using a good curriculum…not a primary purpose. I think that I mentioned this earlier, but in David’s case, I had to make a call as to whether to stall his RM development in favor of HOTS, or to ignore RM. Specifically, he had no clue what 3 plus 4 meant, and as hard as I tried to teach him (i.e., apples, oranges, things like that) it was was hopeless. I finally concluded that he would be better off if he could manipulate numbers first, and then figure out what it all meant later. Likewise with reading - I didn’t care if he understood the words, because I knew that he had plenty of time for learning that. All I wanted when he was little was to simply be able to read the words. I feel that I was right on both counts.

(usual disclaimer: These are my opinions, based on my experience, feel free to ignore them if you don’t like them)

286

So I like the general idea. An di am all for NOT slowing kids down just because they don’t know how to explain their knowledge but my problem with it all is this
If your child has their math facts memorised but they can’t think then they actually can’t solve the word problems independantly. So what do you do? Do you work through the first 10-20 problems with them talking it through until they develop the thinking brain? Or try to send them to Saxon 5/4 with these skills already?
I ask because my two girls clearly have a good thinking brain. for the record my 7 year old did not recognise the second problem counting backwards by 4…she just didn’t understand what the book wanted from her…Odd. She had no problems with the word problems at all.
But my son who will have his math facts cored soon enough is no where near ready for Saxon 5/4 intellectually. Maybe I am selling him short. ( wouldn’t be the first time) and I am not concerned he is only 5 we have plenty of time. But I wonder how much manipulating of numbers children can actually do if they don’t understand their math facts.
I do believe a good math program should include memorisation and critical thinking or problem solving. Same as a good reading program needs whole words and phonics.

287
But I wonder how much manipulating of numbers children can actually do if they don't understand their math facts

My unprofessional SWAG opinion on this: it can be math or any other intellectual content, but no one can manipulate information that they do not possess. IMO, that’s the big danger of anti-intellectualism.

288

I don’t know if this is a good analogy, but this discussion somewhat reminds me of Laplace Transforms. For those who aren’t engineers or equivalent, Laplace Transforms is about the highest level of math reached when working towards an engineering degree, a couple of years beyond Calculus. They are used to transform what would be a very complex problem (differential equation) into a problem one can manipulate with Algebra 1, by going into some weird world of math (then once you do the manipulation, you back out and go back into the real world again). I kept struggling with them because I tried to understand the physical meaning of what they represented (after transforming). Finally, I gave up and just decided to do the math in the blind and see if I could solve the problems…and that actually did work, so I was finally able to do those problems. In other words, it wasn’t until I jettisoned my attempt at applying “higher order thinking skills” that I was able to do the problems.

289

So continue with faith?
Robert do you remember if your son could figure out the first word problems independently or not when you first started?
I think I will test my son on a couple just out of curiosity :slight_smile:

290

I kept David’s work, but can’t find it right now. The only things that I remember giving him trouble were the time problems and the cube problems (where there’s an arrangement of cubes next to each other, and then the outside of the arrangement gets painted, and you have to figure out how many cubes get painted on 1 side, 2 sides, or 3 sides - it’s an ingenious problem, by the way - requires higher order thinking skills - LOL). The clock problems were more my fault, because it took a bit to develop a method for them - and then he was fine.

I’m not sure what you mean by faith, but if you mean teaching math without any attempt at physical representation, then yes, it worked great for David. I was surprised myself, or I wouldn’t have wasted my time trying to teach him the concepts first. But he did have something to fall back on, which was that he could count. Once he could count, then he could do the arithmetic (addition and subtraction problems) on a number line, which he did at the beginning. Then the number line (which was on a marker board) slowly got less detailed, as numbers were erased, so he had to interpolate between what was left, then there were no numbers, just tick lines, and then no number line at all. So, he had to use the number line in his head, which worked (He struggled a bit, so I asked him what was wrong. He told me the number line in his head didn’t have any numbers, so I gave him permission to repopulate the numbers…then he was fine). For whatever reason, times tables went much faster, and he picked them up right away.

I realize that it defies logic, but it did work for us.

291

Manda,

How Saxon teaches word problems in the beginning is simple. Addition problems are called: some/some more. So you have 5 apples and Billy gave you 2. Now how many do you have?

Subtraction problems are: some/some went away.

In the above example, you ask the child if it is a some/some more or a some/some went away. You ask the question before the child tries to solve the problem. Then let them figure it out. It worked very well. The kids are asked the question in Saxon 1 over and over so it gets ingrained.

You can demonstrate with manipulates a couple times. This should solve your problem.

292

Manda, I would just start the Saxon 54. We had tried doing the word problem book that comes with Jones genius Math 3 kit and my son totally struggled with it, we started the saxon and everything is so gradual that somehow he learned it. I haven’t tried going back to that word problem book, but I know that the problems he is doing now (at the end of Saxon 54) are a lot more complex, so I would just have him start on faith.

293

There might end up being a Saxon war in my house. lol if I star my son on it I will then have 3 kids doing 5/4. The younger 2 will be racing each other tot he finish and my oldest will be starting the next one very soon…possibly just to be sure she stays ahead of her siblings! Lol
No I don’t think I will start him just yet. Sooner than I thought though perhaps. Math facts for a bit longer first.
Thanks Robert. A number line makes sense. In a way that is a manipulative. It gives a physical representation of the sequence. It would have helped get the answer right even if the understanding wasn’t yet there.
I really want to start them when they DO have some understanding. Just to make life easier for me. :yes: I am figuring I have some time to spare as I teach math facts so I may as well do something. I also don’t really want all three kids on the same book! That will be a nightmare later on!
My daughter had some problems with the time questions also. She seems to have it all sorted now though. Practice and redoing all the ones she got wrong was the key. Telling the time was no problem but telling the time past in reverse had her stumped.

294

Sonya and Linzy,

Thanks for the help in answering the question and I agree with what you wrote. You guys are much closer to Saxon than I am now. And I agree, their word problems do build up in difficulty, but in a controlled manner so as not to leave the kid lost.

Manda,

We had our own “Saxon Wars” in our house, but of the opposite type, where it was one kid doing all he could to get away from doing math problems (LOL). Unfortunately for him, his parents weren’t particularly interested in him being happy while learning nothing (as opposed to being unhappy and learning math), so he lost those battles. Yes, the number line approach worked very good, as he was otherwise lost. It seems easy for us parents to think that kids should just be able to memorize 100 combinations of numbers (i.e., the addition table), but at that age and with no experience with numbers it’s a total blur to them, or at least David, where he would simply guess at the answer, even if he saw the flash card 10 seconds ago…that’s why many kids start out counting on their fingers. The number line was similar, but, being on a marker board, I could wean him off it, which is what I did. I have no clue how things would have went without it.

295

Question for Robert:

in reading reviews, it seemed as though perhaps 8/7 & Algebra 1/2 are redundant. Your thoughts on that? If they are, would this be about the time when David was really upset about doing math or was that at a different time if you recall?

Is Algebra 1/2 or Saxon 8/7 necessary - or, in your opinion can either or both be skipped?

Regarding Algebra 1, 2, and Advanced Mathematics - do you think I could get by with a teacher’s edition & solutions manual, or would I need the entire kit? Teachers edition seems to have the answers at the back but not written in the lessons, so if you had an honest student, perhaps the teachers of these particular books would work?

I think that’s as high as they go. Any suggestions on texts for higher stuff like Calc (perhaps David would have some input there)?

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You could just tear out the answers in the teachers edition. You may need to remind it. Realistically I think we might cut all the spines off and turn them digital anyway. They are very bulky…more so in my case with three kids and thus 3 books to lug around.
Also just so every one knows only the higher levels have the answers at the back the lower levels of the teachers editions have the answers right next to the questions!
I am interested in something harder also. Our kids will get to the end well before they finish high school ( age wise) so something to keep them busy for a year of two would be nice. Though we could just switch to quantum physics :biggrin:

297

There is a Saxon Calculus as well as a Physics book. I thought there was a Trig book as well but google isn’t confirming this for me.

298

Hi PokerDad,

David was so far ahead by the time he was at Math 87, I said what the heck, just do it. As far as his anger towards the math world back then, it didn’t matter which book he was using it was PURE TORTURE (to him) - that’s how we both remember it. As you note, Math 87 is basically optional in their series - if the kid is good in math, it’s not really needed (per Saxon’s advice). I liked the idea of him having a chance to sharpen up his skills before advancing to Algebra, so I recommend it in all cases (unless there’s a real time crunch in some way).

As far as Algebra 1/2, I said on Amazon that it is simply the best math book ever written, and I stand by it. That book, more than any other, blew my mind away as to how it got kids ready for Algebra. Saxon doesn’t consider it option and neither do I, by a long shot. When you get there, you’ll see what I mean.

I only had the Homeschool Editions, so I’m not familiar with the Teacher’s Editions. Even the Homeschool books had at least some of the answers in the back, and being David is like me (in the bad ways), I too ripped out those pages, so he would have to do the real work. But I only used the text book and the solutions manual, so I think you’re good, based on the answers being removable.

As to Saxon Physics and Calculus, I did buy both, but didn’t use either. It was pointed out by someone that Saxon Physics is not calculus-based, which means it’s not college-level Physics. I checked my book and he’s correct…no integral signs. So the book is still probably good to learn on, but you’ll need a more advanced book to cover college level (such as below).

Regarding other books. One piece of advice I can think of is to use the ratings at Amazon starting at Calculus and College-level Physics. Unlike the earlier grades, I don’t think you’ll have to deal with the bile of the public school establishment when it comes to judging those books, as they usually don’t care about college-level kids on a science/engineering track (they have other ways to reach them).

For Calculus, he used: Larson, Hostetler, Edwards, 5th Edition (50%)
For Physics, it was Serway and Jewett, 4th Edition (50%)*
For Linear Algebra, it was David C. Lay, 3rd Edition (50%)
For Partial Differential Equations, it was Richard Haberman, 4th Edition (15 to 20%)

The percentages after the books represent the approximate percentage of answers at the end of the book. In the first 3 cases, they have answers to the odd-numbered problems. In the last one (which is quite a way up there in the math world), it’s only scattered answers…hopefully junior will be taking at least that class in college. The Physics books also has a partial solutions manual that will help you work through around 20% of the problems (in addition to the odd-numbered answers) - I actually worked through the first half of that text book (for the fun of it) a year ago… challenging!!

Those are the books he used, and he liked them all - but we don’t have any real basis for comparison, and we don’t know how they’ll be for a home school environment. Also, you can try, but don’t expect to have much luck getting your hands on solution books for college-level text books, as the publishers are pretty tight about distribution. Finally, in case it’s not obvious, there’s no need to get later editions of any book - as you’ll see the earlier editions can be picked up for next to nothing.

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To Tamsyn,

I think there is now an optional Saxon Geometry Book, but no Trig book that I know of.

As it was, the original series didn’t have either Geometry or Trig, but rather integrated them through their series of math books. Saxon didn’t like the idea of a kid completing Algebra 1 and then taking 15 months off before continuing on with Algebra (i.e., Algebra 2), so he built in the Geometry to the Algebra books. Trig, I think, he just squeezed into the Algebra 2 and Advanced Math books.

300

This is what I’ve found and referred to in the past. It is from Art Reed, who is kind of a Saxon math expert. As you can see in some cases you may skip Math 87, but never Algebra 1/2 (http://www.usingsaxon.com/newsletterpage-2012.php)

FAST MATH TRACK: Math 76 - Algebra 1/2 - Algebra 1 - Algebra 2 - Geometry with Advanced Algebra - Trigonometry and Pre-Calculus(combined make up the Advanced Mathematics book) - Calculus. NOTE: The Saxon Advanced Mathematics textbook was used over a two year period allowing the above underlined two full math credits after completing Saxon Algebra 2. (TOTAL High School Math Credits: 5)

AVERAGE MATH TRACK: Math 76 - Math 87 - Algebra 1/2 - Algebra 1 - Algebra 2 - Geometry with Advanced Algebra - Trigonometry and Pre-Calculus. (TOTAL High School Math Credits: 4)

SLOWER MATH TRACK: Math 76 - Math 87 - Algebra 1/2 - Algebra 1 - Introduction to Algebra 2 - Algebra 2 - Geometry with Advanced Algebra. (TOTAL High School Math Credits: 4)

NOTE 1: YOU SHOULD USE THE FOLLOWING EDITIONS AS THEY ARE ACADEMICALLY STRONGER THAN THE EARLIER EDITIONS ARE, AND MIXING THE OLDER EDITIONS WITH THE NEWER EDITIONS WILL RESULT IN FRUSTRATION OR FAILURE FOR THE STUDENT.

            Math 76: Either the hardback 3rd Ed or the new soft cover 4th Ed. (The Math content of both 
                          editions is the same)

            Math 87: Either the hardback 2nd Ed or the new soft cover 3rd Ed. (The Math content of both 
                          editions is the same)

            Algebra 1/2: Use only the 3rd Edition. (Book has the lesson reference numbers added)

            Algebra 1:  Use only the 3rd Edition. (Book has the lesson reference numbers added)

            Algebra 2:  Use either the 2nd or 3rd Editions. (Content is identical. Lesson reference numbers
                                 added to the 3rd Ed)

            Advanced Mathematics:   Use only the 2nd Edition: (Lesson reference numbers are found in
                                                             the solutions manual, not in the textbook)

            Calculus:  Either the 1st or 2nd Edition will work.

NOTE 2: WHEN RECORDING COURSE TITLES ON TRANSCRIPTS, USE THE FOLLOWING TITLES:

              Math 76:  Record "Sixth Grade Math."

              Math 87:  Record "Pre-Algebra."(If student must also take Algebra 1/2, then use "Seventh Grade 
                             Math")

              Algebra 1/2:  Record "Pre-Algebra."

              Algebra 1  &   Algebra 2:    Self explanatory.

              Advanced Mathematics:   Record "Geometry with Advanced Algebra" (1 credit) if they only 
                                                    complete the first 60 - 70 lessons of  that textbook.
                                                            
                                                    Record "Trigonometry and Pre-calculus" (1 credit) if they have
                                                    completed the entirety of the Advanced mathematics textbook.

                                                    Under no circumstances should you record the title "Advanced 
                                                    Mathematics" on the student's transcript as the colleges and 
                                                    universities will not know what math this course contains, 
                                                    and they will ask you for a syllabus of the course.

             Calculus:  Self explanatory.