I’m sorry, Nee1, I have the Spanish version “El hombre anumérico” and just translated into English without checking. The original title in English is “Innumeracy: Mathematical Illiteracy and its consequences”, by John Allen Paulos (http://www.amazon.com/Innumeracy-Mathematical-Illiteracy-Its-Consequences/dp/0809058405/ref=sr_1_1?ie=UTF8&qid=1363382272&sr=8-1&keywords=innumeracy+mathematical+illiteracy+and+its+consequences).
Sorry for that!! 
Thanks for the link, NPLight. I’ll get the book.
I’ve been pondering this problem of innumeracy among the general populace. My thoughts are that this problem occurs because people rarely get to use their math skills in their daily lives. Their skills therefore become rusty due to lack of use. It’s not everyday you get to calculate the area of a triangle or find the second derivative of a partial differential equation. And with the presence of calculators, people’s mental maths skills decline even further.
Reading, on the other hand, is everywhere. You need to read grocery labels, to read aloud books to your kids, to read traffic signs, to read complex materials in books etc. So people tend to get better at reading and understanding complex material than they are at math. To therefore become as good at math as they are at reading, they need to put in special efforts to keep their math skills and knowledge fresh.
Thoughts?
I think you’re right about that Nee. I’ve forgotten more math than I currently know, how sad is that?
In browsing through the comments for Innumeracy: Mathematical Illiteracy and Its Consequences it seems that one of the themes addressed is the overall lack of understanding in probability. A few months ago, I read Think Fast and Slow, and while reading it my jaw dropped several times in astonishment at how stupid the typical person is and even experts that ought to know better.
Most people who are competent in math can still make significant mistakes in estimating probability. The “Let’s Make a Deal” situation incited a lot of anger from professors and mathematicians when they disagreed with the fact that if Monty Hall opens one of the three doors after you’ve chosen among three, that you will double your probability of winning by taking the deal and altering your choice. For reference: http://en.wikipedia.org/wiki/Monty_Hall_problem
A similar problem relevant to parents: suppose you find out that you’re pregnant, but with fraternal twins! You go in to get your ultra-sound and the radiologist is about to tell you the sexes. The woman spots the gender of both and is now about to reveal them to you. She says, “Okay, at least one of them is a girl, and…”…
assuming 50/50 birth rates for gender, what is the probability that the other child will be a girl, too?
Needless to say, the vast majority of people get this wrong.
The answer that most people give would be correct if the first born was a girl.
It is important to be aware of how badly equipped we are to get our heads around issues of probability and likelihood. We can all fall prey to similar traps when we are attempting to be rational.
Imagine a terrible disease that is absolutely fatal and affects only one in ten thousand people. You are concerned and decide to undergo a medical test to see if you have the disease. Your doctor explains that the test is 99% accurate-it will produce a correct positive or negative result 99% of the time. The envelope arrives a week later from the testing centre. You open the envelope, and read the contents. Staring you in the face is the answer that you dreaded: the results are positive. The test has indicated that you have this lethal disease. You are devastated.
How likely are you to have the disease?
Chris.
Chris… you Bayesian, you!
lol
My response is below in white. Highlight to view
These Bayesian problems seem to give me fits, but this one only took a few seconds so hopefully I didn’t miss something. My answer is 1%
The way I see it, there’s a false positive every 100 test; In a sample of 10,000 people we expect one infected and 100 false positives. Therefore your chances of being infected after getting a 99% accurate result of positive is 1/100.
Did I get it right?
Sonya, you’re right about my sentiments. 
As this thread has touched on dumbing students down, I’m hoping that sharing Glenn Beck’s recent post is relevant. I don’t normally follow Beck, but I like the panel he put together for this presentation.
I’ve been following Crystal Swasey on my own homefront:
http://www.utahnsagainstcommoncore.com/
This is scary stuff.
Now back to Saxon lol
I just wanted to put out a warning to all your mummies advancing your children’s math. PLease be careful to ensure your children do the Saxon books and CHAPTERS in order. Twice ( maybe 3 times) we have mixed up where we are up to in the books and my girl has done one a few chapters ahead of where she is at. It’s not good :nowink: she spends ages doing a chapter that she isn’t ready for, doesn’t know how to complete all the problems and makes Lots of mistakes.
On the upside once she goes back to do the ones she skipped she finds them dead easy! lol
She hasn’t gone much ahead but it seems to make a rather large difference when she is working above grade level and so each single skill is new to her. I assume if it was revision or she was working at grade level it wouldn’t matter as much.
Also children who know their plus and minus math facts ( reasonably well) but are still learning their times tables by rote can get started on 5/4. My 7 year old is finding it pretty simple. Although we are moving her at a slower pace to give her time to learn her math facts at the same time. She just needed a new challenge so we got started. She is doing a handful of problems each day to keep the info fresh in her head but still slow the pace slightly until those facts are internalised.
Thanks for the info. I’m working through the Saxon 65 book, and I’m finding that book will also be easy for a child who has multiplication, division, addition, and subtraction mastered. It teaches how to tell time, metric and US measurements (and their conversion), how to read calendars, fractions, decimals, probability, arithmetic and geometric sequences, even patterns. Simply put, it covers everything Saxon may cover in their k-3 book, plus lots more. It seems that my search for the perfect math curriculum is over. And the lessons are short and their explanations very clear and understandable. I can now see why Robinson said Saxon (from 54) could be used for self-teaching by a child who can read and comprehend well.
And I would recommend people skip the Saxon K-3 books, and just start at 54 and build up from there.
Yes, as you mentioned, a child that has math facts (multiplication, division, addition, subtraction) mastered is set for Saxon 54. The other things like patterns, calendar, time, measurements, etc., are covered in 54 and 65. My emphasis now with my boy is teaching him math facts. Just that and only that; nothing else. Once he’s gotten all those mastered, I’ll start him on 54. He’ll learn patterns, calendars, time-telling, and everything else in the 54 and 65 books. Thoughts?
PokerDad
Sorry for the belated response- yes your answer is correct. 
You are less than 1 per cent likely to have the disease and this fact is very counter-intuitive for most people.
Generally people will fail to factor in the fact that the disease only hits one in ten thousand people.
A positive result could mean that you are one of the 99% of people who have been correctly diagnosed.
Alternatively you could be part of the 1% of people who don’t have the disease but have been wrongly diagnosed that they do.
If 1,000,000 people are tested we would expect one hundred people to have the disease. Remember that the disease only strikes one in ten thousand people.
Ninety-nine out of this hundred will be correctly diagnosed as having the disease because the test is 99% accurate.
We know that 999,900 people out of the 1,000,000 tested won’t have the disease, but 1 per cent (or 9,999 of them) will be wrongly diagnosed as having it.
So you are either one of those ninety-nine who have it, or one of those 9,999 who don’t. You’re over one hundred times more likely to be in the second, safe, category.
The answer that most people give to the Monty Hall problem is correct if Monty doesn’t know which door the prize is behind.
Chris.
We had a fun time with the Monte Hall problem yesterday. Here’s my summary:
(quick background: 3 doors, one has a car, 2 have goats)
- Everyone involved knows that Monte will open a door that is not the one selected, but is a goat. That is part of the rules of the game.
- The contestant will pick a door (one of three)
- Monte will open a second door, which is a goat
- The contestant will be given a chance to change to the remaining door (the one not mentioned above), if he wants to.
Here’s our quick answer:
a) From (2, above), the odds that the contestant picked the right door is one in three
b) Opening the second door cannot change the odds of the first door, since that step was going to happen regardless of which door was chosen (i.e., no useful information was given to the contestant)
c) Therefore the odds of the that contestant picked the right door remains one in three
d) One third door remains not open and one of the two remaining unopened doors still has the car
e) Therefore the odds for that other door must then be two of three
As far as keeping track of the Saxon work, I had David do the work on loose leaf paper and then put it into a binder when he finished a section. That seemed to work well. With more than one kid, then obviously more than one binder.
I agree that once a kid is proficient on math facts Saxon will pick up from there, with Saxon 54. As others said, Saxon covers a lot more than just number manipulation, it basically covers everything. I think that I said earlier on this thread that, after David had been through a few books, I went to a bookstore and looked at a study guide for one of our state tests (Texas). I was blown away by it, because it looked like John Saxon had simply copied his book - I couldn’t find one question in that guide that was missed by Saxon. And keep in mind that I had been desperately searching for something that could actually teach David math, and I looked at a lot of stuff before I stumbled into Saxon. Just about everything talked about how much fun their particular approach was. That sent my defenses because I know that learning math is not fun - or at least fun in the way they conveyed. It is tedious and tiring. About the only way it can be “fun” is the joy when the kid accomplishes something…but that still isn’t fun until it’s over - so still not fun while they’re learning.
The saddest thing for this country was how the Big Education tore down Saxon prevented it from taking over in math - they had to know what was possible, which is why that bunch had to do what they did.
As far as Glenn Beck - I don’t follow him, but on stuff I’ve heard him talk about, I have yet to see where he’s been wrong on just about anything. The reason that I don’t follow him is that it’s too depressing - depressing that he’s almost always right, and depressing that he’s been marginalized at the same time.
nee,
I think it is important for them to have a solid grasp of their math facts (i.e. they can calculate the right answer within a few seconds) even if they are not completely memorized. The program we use for the math facts is called sterling math facts. It costs like $10.
You can chose individual facts to work on, or ranges, or all of one type of equation or all equations or solve for an addend/multiplier (like an algebra problem). You can also chose the amount of time they have to answer each problem and the number of problems. It keeps track of missed problems so you can do a set of the most commonly missed, or make sure a certain percentage of each sets problems are the ones you child misses regularly. You can then look at their results in a pie graph or in a graph with time as the x axis to see how they are improving.
We do 250 problems a day for my 6 year old. He does all add/sub/mult/div 0-12. We use a time out of 8 seconds, but his average time per a problem is 4 seconds.
We start with the Sterling Math facts, then he does the warm up math facts page from Saxon, then he reads the chapter, he then does the mental math/problem solving, lesson review and finishes up with the 30 problems.
We use either the forms from the back of the tests/worksheets book or a form I found online for him to write his answers on or one I found online (I’ll attach to this post). My husband or I correct it and then he works through the corrections on his own looking up the ones he missed if he didn’t understand it, usually it is silly mistakes from having messy handwriting.
Any he misses after the second time through we watch him work to see where he is going wrong and redirect him. Usually however, when he does it with us watching he is more careful and will get it right.
Linzy - we’ve been using Sterling Math for my son, he was doing great on easy ones like +1 and +2 but now is struggling with +3. Did you work on memorizing the facts before having them use it, or do you just let them keep getting the wrong answer until they memorize the right one? do you let them count on fingers, use a number line, abacus, teach them the math dots, etc? just curious what your process is there. Thanks for any advice you can give!
Nee your focus on math facts and math facts only is a very sound plan. I am considering this for my boy but I think he likes math too much…he will need something else too. So I was thinking through what else is useful for Saxon success and I decided the only thing it doesn’t teach is " how to think" it doesn’t teach the problem solving skill of thinking through a possible route to an answer.
Basically I concluded that math facts plus a few random word problems throughout the day and a fairly solid idea of calendars is all that’s needed.
Math facts should include halves and quarters of 100 ( and 1000 while you are at it) to save you time later.
The calendar stuff needed is days of the week months of the years and that 30 days has September song.
Yes it truly is a self taught math course. I almost never help my kids out. They just learn it then do it. They fix their own mistakes easily enough and I rarely have to help them get to an answer. Even my 7 year old is mostly independant. She just likes company while she does it.
LDS Mom,
For my older son he had already been using flashcards before we switched over. Our problem was that he would dawdle with the flashcards forever, hence the timeout feature is very helpful.
For my 3 year old, I put the time out at 30-45 seconds. The first few times through the new problems I read it out and make it easier to understand. So I’ll say for 3+1 "If you have 3 and I give you one more, how many do you have?, or What’s one more then 3?, or What come one after 3?, one, two, three _____? Then I’ll help him type it in. After we’ve done it a few times, I just let him get it wrong and see the answer and type it in right himself. I think lots of repetition will help it really sink in.
With my older son we let him “figure out” the problems, and now he often will go to calculating first even if he knows the answer. With my younger I"d rather he just learn them by heart as an instant response.
Interesting tidbit today at work:
So far, at work, and beyond, there have been a grand total of two people that have asked how David managed to get so far ahead for his age, while hundreds of people (at least) know of him. The rest, I speculate, figure that Einstein or someone like him transplanted some brain matter into David, and therefore there is no way that their kids could ever hope to achieve the same. The two people are a Chinese immigrant in New Jersey and a Russian immigrant here in Houston that I work with (I’ve mentioned the Russian before, here).
Anyway, the Chinese immigrant got a bit weird and my wife is no longer in contact with her, but the Russian woman, that I work with, seems to understand the importance of parents providing primary instruction and has talked with me a bunch about David. So I ran into her today and she quickly mentioned that, now, 11 more people in her Russian group (I assume mothers of young children) are now using Saxon Math. She said that was because I told her about it, and then the other 11 parents saw it, and immediately concluded that was exactly what they were looking for (keep in mind, they all, likely, speak and understand English fluently). So they saw Saxon Math and, I suspect, the way they were taught came to mind, and they knew that Saxon was the way to go. In Russia, they didn’t waste time trying to convince kids of that Che and Mandela were great mathematical minds - instead they just taught math.
I plan to ask more questions the next time I see her. This country may yet be saved, but it will only be due to parents that take the primary education (reading and math) of their kids into their own hands.
Thanks so much for sharing this with us. It always makes my day better hearing about things like this. Especially since a friend of mine who teaches in the school system has told me its no longer about educating children it’s all about the numbers. She is getting tired of fighting the system and is being looked down upon by her colleagues all because she cares that each of her students are not only becoming familiar with but are learning and understanding what she is teaching.
Yes, I read obsessively about the state of education in our country and I don’t know why. It only depresses me. Here locally there are 35 kids per a class with one teacher, a teacher I know was saying that not even half the kids even turn in their homework, so the idea of teaching kids individually or at their level or spending time trying to challenge kids that are ahead is laughable. She just wants to get most of them close to grade level and is grateful for the ones who are above grade level, because she figures they will take care of themselves and even if they don’t make gains they will be where they need to be to advance. Luckily we are homeschooling, but it still is so incredibly sad to me, I just wish I could do something, I know it’s not abusive but it feels like it sometimes to me.
All the Russian parents I knew when I taught in Moscow were a little scary-obsessed with their kids getting perfect grades and working hard at school, so I’m not overly surprised that the Russian group would start doing Saxon. Especially considering that the schools generally stream with a maths or humanities focus. The maths stream in the school I worked at was teaching 15 year olds what I didn’t cover until 18 (and both schools were in the top handful for the respective countries).
Mandab, if you need a good source of story problems for your boy, you might want to look at Ray’s New Primary Arithmetic. Excellent vintage book that teaches mastery of math facts but with use of story problems. That might serve as a stop gap for your boy while he learns the math facts by rote. There is a FREE copy online here - http://archive.org/details/raysnewprimarya00raygoog. To download a pdf, click ``All Files: HTTPS’’ on the left hand side of the page. You’ll find several file formats. One of those is a pdf.
I’ve gone through all the lessons in Saxon 54 and 65, and there are loads of word problems there. So Saxon teaches thinking. Calendars are covered in 65, with explanations of leap year, decade, century, months, days, etc. Fractions are also explained in 65, etc, etc.
As for the idea of focussing on math facts and math facts alone, I learnt that from the Robinson yahoo group. Loads of those parents focus on that alone. (According to Robinson, it can take a while for a child to master multiplication tables, division and subtraction, and addition). So those parents focus on just that, using math flashcards and programs such as Sterling Math or the free flashcard program (www.xtramath.org). Once the child masters his facts, they move the child straight to 54. And Robinson says in that video on his website (at 29.27 minutes), that Saxon 54 was the first introductory book John Saxon wrote; and that Saxon K- 3 were simply busy work introduced by the publishers and padded out to fit the public school grade levels.
On this thread, Linzy explains more on math facts and how she used them to move to 54. Link - http://forum.brillkids.com/teaching-your-older-child/swann-family-10-children-with-ma-at-age-16!-book-review-and-discussion-thread/msg94278/#msg94278. Thank you so much, Linzy.