Crap/Connected Mathematics 4/4 Saxon shows How to Divide Fractions!

[abcwritestartread]

I used Saxon in First Grade it was great, direc, systematic, explicit instruction no wasted time with junk. Now in nyc they mandated Everyday Math junk, what a waste of time junk, the kids cannot master simple math now. God help this country between whole language teachers college junk and the crazy math curriculum, the only safe kids are the homeschooled. Christine

[sleeper2345]

Where is the mathematical rigor in Saxon? The rules are provided without reasons. Does this have anything to do with mathematics? Is that what mathematicians do? Of course not. The lack of mathematical rigor in this textbook is embarrassing.

[janetvandermeulen]

THANK YOU. I didn't know there still was a true math book available. My daughter has Connected Math . I read an entire 80-page CM book and figured out the whole book was about a single linear equation WHICH THE BOOK NEVER GIVES YOU! Once I gave her the equation, she zipped through the book...turns out that parents are NOT SUPPOSED to give their children the equation, the students MUST figure it out by trial and error, even if it means they are all totally confused and HATE MATH.

[jelewis2]

I used to think the Saxon texts were slow and plodding and didn't cover enough, and I still do think the Calculus book didn't, because when I was in high school we used the Saxon texts and the Calculus book only went part-way through Calculus AB, but with the horrors I've seen recently from the reform movement (I entered kindergarten in 1990), I know I wasn't missing out on anything.

[sleeper2345]

Too bad it's not as simple as you think. Many students believe that to add fractions you just add the numerators and add the denominators. Is there any reason why you need a common denominator? Do we need a common denominator to multiply fractions? Do we need one to divide fractions? Would it be helpful? Of course the procedure can be taught in 3 easy steps. Too bad it won't be learned or remembered as easily.

[jelewis2]

The reason you need a common denominator has to do with the distributive property, something that should be emphasized more because it underlies all of the standard algorithms.

It's the fact that (a+b)c=ac+bc, or taking c to equal 1/n, (a+b)*1/n=a*1/n+b*1/n, which when simplified says (a+b)/n=a/n+b/n; this cannot be done with a/m+b/n=a*1/m+b*1/n because there is nothing to factor out, that pattern with the distributive property only works with a common factor.

[juice1133]

i dont like math. it is confusing.

[jhelsdon2478]

These textbooks are also good for integration of mathematics and science skills. Students need the practice in science skills also. There is a whole year textbook available instead of buying the separate workbooks. Just to let you know. Not that you would use it.

[biukucanoe]

I just looked over my 7th grade book on volume - Nowhere is printed formula for anything. You're supposed to get enough dough to make a ball and stuff it in a cylinder, and make a paper cone and fill it with rice - in a classroom? No wonder the teacher didn't do this. And he *ruined* it by just giving kids the formula. Why in the heck doesn't anybody realize there's something wrong where the *method* is saved for the "answer" section in the teacher book????

[jelewis2]

I remember when I was a kid I thought something like that would be great to find pi exactly, like filling a disk 4in high and 8in diam. with water, pouring it into a column with 4inx4in base, measuring water level, dividing by 4in; I thought some advanced use of manipulatives like that was how mathematicians actually found pi.

Then I learned about measurement error and about more sophisticated algorithms to calculate pi and other numbers.

[jelewis2]

As for figuring out the *formula* rather than using it to, say, try to approximate pi with one of those demonstrations, that's absolutely ludicrous.

[jelewis2]

They do need practice in science skills.

This is why they take science classes or have sections when elementary school teachers teach about science.

Then again perhaps science has been de-emphasized in elementary school ever since No Child Left Behind.

[jhelsdon2478]

Sir, I understand your fraction, and possibly your reluctance to change. However, I feel that students learn best by discovering things and working together to create and figure it out on their own. We are teachers of students not empty vessels that teachers pour things into. Which sounds like your issue. I do not use CMP2 or Saxon math. You are not responsible to real mathematicians, you are responsible to students. I am sorry you do not like the CMP2 project.

[biukucanoe]

Every adult that graduates 6th grade has memorized pi r squared, so why in the heck do you have to make them derive it when most ADULTS don't have the faintest idea how it is derived (MIT grad myself included)

[jelewis2]

I'm basically on your side, but I wonder how you got through MIT without taking calculus, in which you learn how to derive the formula for area of a circle.

(Hint: Let the circle be centered at the origin of an xy-plane, then it's the area between the graphs of sqrt(r^2-x^2) and -sqrt(r^2-x^2) where x ranges from -r to r; this comes from x^2+y^2=r^2, which comes from the distance formula, which comes from the Pythagorean theorem, which can be proved rather elegantly with a pair of diagrams.)

[biukucanoe]

To this day, MIT will still teach you freshman calculus, which does not include deriving area of a circle. My jr high just told you pi r squared without a clue as to why it works. Using infinitely narrow pie slices is coverd in some books today (but not CM which uses a completely goofy method) you get rectangle pi*r long by r high, thus pi r squared, but the infinite bit is technically calculus.

[jelewis2]

It takes way too long for students to figure out the standard algorithms by themselves; I believe elementary teachers should explain why these algorithms work however, that's my kind of change.

If the extreme constructivist mindset applied to all of mathematics education, it would take a lifetime to make it to what we now call pre-calculus.

[sleeper2345]

@jelewis2 You are in agreement with reform mathematics in your statement that all algorithms should be explained. However, reform mathematics does not just limit explaining algorithms to the teacher, students are also encouraged to explain algorithms. No one expects students to invent all algorithms for themselves. However, students must be allowed to try to solve problems for themselves and see the advantages and limitations of various algorithms.

[sleeper2345]

@jelewis2 The "extreme constructivist" position that you describe is a fantasy made up by those who want students to continue to memorize rules without understanding (e.g., the author of this video).