Different ways to teach Math (SM vs CLE, etc)?

[LAmom]

I know that there are spiral and mastery programs. But, if you take the approach of Singapore and compare it with the approach of CLE Math, for example, what is the difference? Or even Saxon, etc. Singapore is supposed to be so different from all the others out there. I have only used it for 1A and some of 1B but don't quite understand what is so different about what I am teaching. You know? Lots of manipulatives and pictures....so what do Saxon, CLE, others do? I am assuming they use manipulatives, etc.

 

Make sense? Just ignorant about the difference in approach. :confused:

[Devotional Soul]

I've used CLE 1 and Singapore 1A and 1B. The biggest difference IMO is that Singapore is very colorful and cartoony. CLE has only one color and no cartoons and few pictures (they only relate to the math concepts, like a flower with 2 petals to count when you learn about 2, or 3 ears of corn to go with the daily story problem). CLE has a lot more drill and practice with math facts and lessons are 2-3 pages. It reviews a lot and covers many concepts in each lesson.

[Wee Pip]

I think the differences become greater later down the road (2nd gr & up?)

Singapore & certain other programs will teach the "whys" of math. The emphasis is on understanding what's going on in the numbers, and once the understanding is there, then teach an algorithm.

Other programs (just guessing here, but CLE & Saxon strike me as this type) emphasize more of the algorithm. Line these numbers up, do the steps in this order, and you'll get an answer out of it.

 

For instance: Singapore might teach a few different ways visually that numbers can make up a difference (large number subtraction with borrowing). Take some blocks and you can add up to the large number, or count down to the smaller number, or move some around, or regroup them...eventually, you'll line up some numbers and perform an algorithm, but you don't have to. The other programs might show some blocks and demonstrate regrouping them (maybe?), but it jumps quickly to the algorithm, because that's how you solve it. You line up your numbers, strike out the top number, put a one in front of it, subtract it, and boom - you have your answer.

[LAmom]

ok--that helps a bit. I probably would need to look at the others and maybe that would help, too.

[Spy Car]

I know that there are spiral and mastery programs. But, if you take the approach of Singapore and compare it with the approach of CLE Math, for example, what is the difference? Or even Saxon, etc. Singapore is supposed to be so different from all the others out there. I have only used it for 1A and some of 1B but don't quite understand what is so different about what I am teaching. You know? Lots of manipulatives and pictures....so what do Saxon, CLE, others do? I am assuming they use manipulatives, etc.

 

Make sense? Just ignorant about the difference in approach. :confused:

 

With Singapore there is a model that may not be fully apparent to you yet, but it involves seeing numbers as wholes and parts, and being able to re-group numbers with facility to perform mental math, and developing a parts/wholes method (bar diagrams) to solve word problems.

 

Those number bonds in 1A/1B are the starting point. A child learns that 8 can be re-grouped as 5 and 3. And by extension, 8 minus 3 is 5, and 8 minus 5 is 3. These are the baby-steps. But they are a vital foundation for what is coming, even if the look is at times "cartoonish."

 

Singapore aims to really have the child have a good grasp of mathematical operations and do not teach math by the mere memorization of "math facts" (although they do expect those skills to be honed as well).

 

The whole and parts strategies (and word problem solving) become increasingly sophisticated as you move up levels, or use supplemental materials like the IP or CWP books. There is great merit in this kind of math education, as one simply can't memorize everything, and the Singapore is designed to allow children to perform pretty complex math in their heads.

 

This is only a partial answer, but that's the gist of it.

 

Bill

[Spy Car]

Let's have an analogy.

 

Your child is learning to read, and they encounter the word "diaper."

 

They can either learn to memorize the way this word sounds, or they can (after doing the grunt work it takes to learn the lessons) be able to explain that diaper contains the digraph "ia" which makes for a long-vowel "i" sound.

 

Or you could just have them memorize the sound the word makes.

 

Math is little different. A child can memorize 8 plus 7 is 15. Or they can be able to tell you that in order to make the 8 into a ten they have re-composed the 7 into a 2 (that will be used to make 8 into 10) and 5. Re-grouped we get 1-Ten and 5-Units. 15.

 

The question we have to answer is which type of education we aspire to bring to our children? Then decide.

 

Bill

 

ETA: I realize some Southerners (and others) are going to be thrown by the choice of Diaper, but let's assume we are speaking Standard English for the sake of the example :tongue_smilie:

Edited May 19, 2010 by Spy Car

[Corraleno]

Conceptually-focused programs like Singapore (and Math Mammoth & others) teach the "language" of math, not just memorization of facts and formulas. In the earliest levels, the differences won't be as apparent, because the content is quite limited and fairly simple.

 

You can compare it to learning a foreign language. One program might focus on teaching the student to memorize useful phrases and vocabulary, while another may emphasize an understanding of grammar, verb tenses, etc. For the first few lessons, the programs may seem quite similar, because students in both programs are learning to say things like "Where is the post office?" Someone might look at those two programs and think #1 is actually a better choice because it's easier and it teaches them "what they need to know" without unnecessarily "complicating" things with grammar, conjugations, etc.

 

Two years later, however, the student using the first program may have a large stock of memorized phrases and vocabulary they can apply to specific situations, but the student using program 2 will be able to hold meaningful conversations, because they understand the underlying grammar and structure of the language, so they can "decode" words and sentences they've never encountered before.

 

Students who use Singapore or MM or other math curricula with strong conceptual foundations will find that as they move into algebra and above, they already speak the language; the vocabulary and sentence structure may be getting more complex, but the underlying grammar is the same. A student who has only been taught procedurally will be faced with having to memorize a whole new set of "useful phrases" when they hit algebra, because they haven't understood that the phrases they've already memorized are not separate entities but are part of a complete language.

 

Jackie

 

(ETA: I'm not saying that CLE is a purely procedural math program; I've never used it or even seen it other than online samples. I'm just contrasting a hypothetical procedural-type math program with a conceptual one.)

[Spy Car]

Conceptually-focused programs like Singapore (and Math Mammoth & others) teach the "language" of math, not just memorization of facts and formulas. In the earliest levels, the differences won't be as apparent, because the content is quite limited and fairly simple.

 

You can compare it to learning a foreign language. One program might focus on teaching the student to memorize useful phrases and vocabulary, while another may emphasize an understanding of grammar, verb tenses, etc. For the first few lessons, the programs may seem quite similar, because students in both programs are learning to say things like "Where is the post office?" Someone might look at those two programs and think #1 is actually a better choice because it's easier and it teaches them "what they need to know" without unnecessarily "complicating" things with grammar, conjugations, etc.

 

Two years later, however, the student using the first program may have a large stock of memorized phrases and vocabulary they can apply to specific situations, but the student using program 2 will be able to hold meaningful conversations, because they understand the underlying grammar and structure of the language, so they can "decode" words and sentences they've never encountered before.

 

Students who use Singapore or MM or other math curricula with strong conceptual foundations will find that as they move into algebra and above, they already speak the language; the vocabulary and sentence structure may be getting more complex, but the underlying grammar is the same. A student who has only been taught procedurally will be faced with having to memorize a whole new set of "useful phrases" when they hit algebra, because they haven't understood that the phrases they've already memorized are not separate entities but are part of a complete language.

 

Jackie

 

(ETA: I'm not saying that CLE is a purely procedural math program; I've never used it or even seen it other than online samples. I'm just contrasting a hypothetical procedural-type math program with a conceptual one.)

 

 

You explained this better than I did!

 

Very well done Jackie :001_smile:

 

Bill

[nmoira]

 

For instance: Singapore might teach a few different ways visually that numbers can make up a difference (large number subtraction with borrowing). Take some blocks and you can add up to the large number, or count down to the smaller number, or move some around, or regroup them...eventually, you'll line up some numbers and perform an algorithm, but you don't have to.

I'm not sure I agree with the characterization. Singapore teaches the "Singapore Way," which is heavily oriented towards mental math, but progresses without fail to standard algorithms. For example, when learning addition and subtraction, the student are explicitly taught to make 10's. Other methods are not explored, other than very early on when addition and subtraction are themselves being introduced conceptually during which time counting on is encouraged. The why's are certainly covered, but explicitly rather than in a discovery sense (à la Miquon).

[Another Lynn]

ETA: I realize some Southerners (and others) are going to be thrown by the choice of Diaper, but let's assume we are speaking Standard English for the sake of the example :tongue_smilie:

 

Yes, because "i" says I (eye) because it's an open syllable followed by an "a" saying UH... dI uh per :lol: Just kidding!

 

Btw, thanks for your explanation of the regrouping. I know you were oversimplifying, but in all the SM posts that was the best explanation I've read for how it differs from other approaches. Thanks!