My concerns with Singapore...can you help?

[momto3innc]

Let me start by saying I love singapore. Love the method, love how it is training my kids to think, love the results of that. So I am for sure sticking with it...just am struggling with a couple thoughts I want to think through.

 

So far with my kids we have done this for math:

For K-2, we have done both Singapore and Horizons.

 

I did this because I liked both programs. As we progressed, I realized how much I like Singapore for the reasons mentioned above. From 1st grade on, I used Singapore for primary teaching and Horizons was great for review.

 

In third grade (this year) I switched to only Singapore because I really feel it is superior and wanted to do more of the program (we had not done the IP or very much of the CWP before). So this year for third, my oldest has done 3A/3B textbook, workbook, IP, plus activities from the HIG and some CWP. It has been a good year. He has learned well...no issues. However...and here is my problem finally...I borrowed my friend's Horizons 3 teacher's guide just to see what we would have done this year if I had stuck with using both programs.

 

Honestly I was surprised at how many things were in the Horizons book that are not covered in Singapore. Now obviously, the reverse is true too. Singapore was vastly superior in mental math, problem solving, more difficult division problems, and more challenging measurement problems (maybe more...just the ones I noticed first and are coming to mind as I type). These are super important and I appreciate them and want that to continue.

 

But here are things Horizons covered that Singapore did not (may have missed things or added one I should not have but I think this is fairly accurate):

--solving for an unknown (in an algebraic equation)

--mixed numbers

--Roman numbers

--Plotting number pairs on a graph

--Lines of symmetry, congruent figures

--finding 1/5 of a number, 1/4 of a number, etc...

--names of shapes/solids

--learning the various names of items in a problem (minuend, difference, etc...)

--Fraction to equivalent decimals (3/10=.3, etc...)

--rounding numbers, estimation

--temperature

--learned the various properties (distributive, etc...)

--Volume

--learning about points, lines, line segments

--ratios

--adding/subtraction fractions with like denominations

 

Now I can obviously go back and go over these (and am) but it's a LOT, way more than I would have expected. We live in a state where we need to test at the end of a year. These (the Horizons items) are absolutely the type of things that are on those sorts of tests. I don't want to choose a curriculum to "teach to the test" but I also would like these sorts of things to be covered at least a little so there is recognition of them. I do want the core of what we learn to be teaching the "singapore way" but I'm just a bit disheartened right now and am thinking that next year we will go back to a singapore/horizons combo. Probably teaching from the HIG and do the 4A/4B textbook/workbook and then use various parts of Horizon for teaching the above types of things. I would love to keep the IP/CWP books but we'll have to see what all we can fit in.

 

Sorry, that was a long post. I don't know exactly what I'm asking. I guess...has anyone else noticed this? Any thoughts? Ideas? Help?

 

Thanks!!

[wapiti]

I would look ahead in the scope and sequence for SM. It may be that for a given year, Horizons scope is broader while SM's scope is deeper. It is not as though that list of items never gets covered in SM.

 

Eta, I think your real concern is your annual testing. What test is it, and can you just look up the list of applicable standards? I would be surprised if there were more than a couple little topics that would be on the testing that aren't covered by SM.

[Crimson Wife]

Many of those topics will be covered in Singapore 4 or 5. The one exception I can think of off the top of my head is Roman numerals, and that topic is easy to teach.

[Five More Minutes]

Here's the Singapore S&S. (Not sure which edition you're using, so I'm just linking to the general page.) At least a few of the topics on your list seem to be coming up in 4.

[myfunnybunch]

We have gone through level 6 in Singapore, and almost all of those topics have been covered, and covered thoroughly. As a matter of fact, many of the "missing" things on your list have been covered by my ds who is in the middle of level 5. :)

[momto3innc]

Thanks all. I'm just about to get my Singapore 4 stuff so I will definitely look through it and through the S and S link. I guess I was just surprised when I initially saw the difference between the two. I knew it existed, but had not really seen it before...and did not expect there to be so much I guess. I'll look through the link and process it all.

[jmc1970]

I had the same exact thoughts. I was doing Saxon and Singapore with my 7 year old and thought Singapore had a much better way of computing problems, but when I looked through Singapore 2 and 3, I saw that Saxon still had components that Singapore was missing. As other posters have mentioned, it is definitely on a broader sense, but at least introduced. My solution has been to keep Singapore as our main math program, but sometimes it gets pretty intense to the point that she needs a mental break, which is when we go back to Saxon. She finds it much easier so enjoys the "break". When I feel she has grasped a concept from Saxon that Singapore has not introduced, we go back to Singapore and I find that things have had a chance to sink in more and it's a smoother ride, ...until the next bump. Then we break at Saxon again. Seems to be working and I feel like we are covering more things than just 1 math curriculum could do.

[boscopup]

--solving for an unknown (in an algebraic equation)

 

Singapore has done this since 1A, but without letters. Your child would probably figure it out. If you give your child a problem like: x + 2 = 5 and ask them what x is, I'll bet he can solve it. ;)

 

--mixed numbers

 

I don't think this is on a grade 3 standardized test? This is typically taught in 4th grade. Even with Common Core, it's not in the grade 3 standards.

 

--Roman numbers

 

easy to teach yourself (my dad has my oldest tell him what year the Looney Tunes they're watching was made in ;) )

 

--Plotting number pairs on a graph

 

This is in 4B, and again, CCS doesn't have it in grade 3. Not sure a standardized test would either.

 

--Lines of symmetry, congruent figures

 

Congruent is in 4A, symmetry in 4B. Again, I don't think these are on a grade 3 test normally.

 

--finding 1/5 of a number, 1/4 of a number, etc...

 

This is taught in 3B, chapter 10.

 

--names of shapes/solids

 

2D shapes are done in 1st and 2nd grade. Solids are done in 2B, 3B, and 4A.

 

--learning the various names of items in a problem (minuend, difference, etc...)

 

Not sure when this is taught, but I seem to recall the words being used in word problems...

 

--Fraction to equivalent decimals (3/10=.3, etc...)

 

Decimals aren't taught until 4B. CCS also introduces this in grade 4.

 

--rounding numbers, estimation

 

These are in 3A

 

--temperature

 

Surely you've talked about this in real life. :)

 

--learned the various properties (distributive, etc...)

 

They probably haven't learned the names of the properties (that isn't typically taught until prealgebra, I believe), but they have certainly worked with the distributive property via mental math and via learning multiplication.

 

--Volume

 

This is in 3B

 

--learning about points, lines, line segments

 

I think this is typically not done until 4th grade.

 

--ratios

 

These are in 5A, and I highly doubt they'll be on a 3rd grade standardized test (though if they were, they're simple to teach).

 

--adding/subtraction fractions with like denominations

 

This is in 3B.

 

Honestly, I wouldn't worry one bit. I'm sure your child can pass a grade 3 standardized test if he's successfully completed Singapore 3B. Remember that just because Horizons teaches something, it doesn't mean that that item will be on a standardized test. Horizons is more advanced in scope and sequence than a vast majority of the public schools across this country. :tongue_smilie:

[Arcadia]

We live in a state where we need to test at the end of a year. These (the Horizons items) are absolutely the type of things that are on those sorts of tests.

 

We use the standards edition and my kids could do every question on the equivalent sampler for California's standardized tests. I would just get a sample of those sort of tests that your child would be taking and cover the topics that are not already covered.

 

Roman numerals is never tested but fun to learn. Temperature is covered in science and easy to teach in less than a day.

For 2nd grade math standardized test my kid just had to remember commutative property of addition and associative property of addition.

[momto3innc]

First, yes, I have no doubt he'll pass the test. Honestly not worried that he won't. I think it just threw me a bit I guess? I always knew Singapore's S and S were different, but I guess I hadn't personally encountered it. Trying to process through it I guess. I answered in blue below. I'm very curious to the items in your 3B that I don't see in mine. How big is the difference in things taught in US and Standards? Again, we use it all--textbooks, workbooks, IP, and an occasional CWP.

 

--solving for an unknown (in an algebraic equation)

 

Singapore has done this since 1A, but without letters. Your child would probably figure it out. If you give your child a problem like: x + 2 = 5 and ask them what x is, I'll bet he can solve it. ;)

Absolutely yes! He could definitely solve it. They did it a little more detailed...say...X + 5 = (2 + 4) + 8 Again, he still could probably solve in his head (thank you Singapore!) but I guess I'd like him to see these a little so he's familiar. He's the type who would freak out a bit because he had never seen it before...even though he would eventually figure it out.

 

--mixed numbers

 

I don't think this is on a grade 3 standardized test? This is typically taught in 4th grade. Even with Common Core, it's not in the grade 3 standards.

 

--Roman numbers

 

easy to teach yourself (my dad has my oldest tell him what year the Looney Tunes they're watching was made in ;) )

And he actually did them in second grade Horizons. We just review them periodically. This actually was what made me check the guide. It occurred to me that Singapore didn't teach them (not that I minded...) and made me wonder what else was different...which led to this post :)

 

--Plotting number pairs on a graph

 

This is in 4B, and again, CCS doesn't have it in grade 3. Not sure a standardized test would either.

 

--Lines of symmetry, congruent figures

 

Congruent is in 4A, symmetry in 4B. Again, I don't think these are on a grade 3 test normally.

 

--finding 1/5 of a number, 1/4 of a number, etc...

 

This is taught in 3B, chapter 10.

Hmmm...my Singapore 3B only goes through chapter 9. I have the US edition. What one are you looking at?

 

--names of shapes/solids

 

2D shapes are done in 1st and 2nd grade. Solids are done in 2B, 3B, and 4A.

I do remember them in 2B. They are not in my 3B book.

 

--learning the various names of items in a problem (minuend, difference, etc...)

 

Not sure when this is taught, but I seem to recall the words being used in word problems...

 

--Fraction to equivalent decimals (3/10=.3, etc...)

 

Decimals aren't taught until 4B. CCS also introduces this in grade 4.

 

--rounding numbers, estimation

 

These are in 3A

 

--temperature

 

Surely you've talked about this in real life. :) Definitely! I actually almost didn't write it here since it is such a real life thing...but I thought I would be thorough :) with my list.

 

--learned the various properties (distributive, etc...)

 

They probably haven't learned the names of the properties (that isn't typically taught until prealgebra, I believe), but they have certainly worked with the distributive property via mental math and via learning multiplication.

 

They use the actual names in Horizons but just show very basic examples of them and have them demonstrate how they work.

 

--Volume

 

This is in 3B I don't see this in my 3B. In Horizons they are using the formula...V = L X W X H.

 

--learning about points, lines, line segments

 

I think this is typically not done until 4th grade.

 

--ratios

 

These are in 5A, and I highly doubt they'll be on a 3rd grade standardized test (though if they were, they're simple to teach).

 

--adding/subtraction fractions with like denominations

 

This is in 3B. So...this also isn't in my 3B. Is it because it's US edition? Are the US/Standard that different in introducing concepts? We just finished the fraction chapter. We did equivalent fractions, worked on reducing and making common denominators, but no adding. I showed him myself, but it wasn't in the book. I'm beginning to wonder if something fell out of my 3B book!!

 

Honestly, I wouldn't worry one bit. I'm sure your child can pass a grade 3 standardized test if he's successfully completed Singapore 3B. Remember that just because Horizons teaches something, it doesn't mean that that item will be on a standardized test. Horizons is more advanced in scope and sequence than a vast majority of the public schools across this country. :tongue_smilie:

 

[Susan of Croton]

We've done Singapore since K. Now I have DD(7th) and DS(8th) and we've moved into New Elementary Math by Singapore. In the early years, less is more in my opinion. A lot of programs throw a bunch of stuff at the kids which can be learned in 15 minutes when they are older, but valuable grammar-stage brain time is used for it when they should be focusing on living and breathing arithmetical operations. When you get to algebra, you want a kid that can multiply, divide, etc., and handle fractions, ration, and percentages in his sleep, You don't care if your kid has been exposed to everything there is to know about math. Go deep not wide, is my advice for the primary years. I guess that adds up to "don't worry, you're doing ok"

[Candid]

First, yes, I have no doubt he'll pass the test. Honestly not worried that he won't. I think it just threw me a bit I guess? I always knew Singapore's S and S were different, but I guess I hadn't personally encountered it. Trying to process through it I guess. I answered in blue below. I'm very curious to the items in your 3B that I don't see in mine. How big is the difference in things taught in US and Standards? Again, we use it all--textbooks, workbooks, IP, and an occasional CWP.

 

 

There's an old expression about being a mile wide an and inch deep. I think the problem with many programs is this. I continue to be leery about SM's slow transformation to American standards because of this.

 

I also think doing some topics too early is a mistake, too. It makes children confused and it makes it harder for them to learn to concept when they are ready for it. Much better to steadily build the base and then when the time is right add new concepts.

[Sarah CB]

There's an old expression about being a mile wide an and inch deep. I think the problem with many programs is this. I continue to be leery about SM's slow transformation to American standards because of this.

 

I also think doing some topics too early is a mistake, too. It makes children confused and it makes it harder for them to learn to concept when they are ready for it. Much better to steadily build the base and then when the time is right add new concepts.

 

 

Absolutely! I really think that Singapore teaches thoroughly and that any kid who uses it will come out the end with a thorough understanding of math. I think there are lots of concepts that are typically taught too early, or not taught deeply enough for them to stick.

 

My daughter used Singapore pretty much exclusively from K through grade 10. She went into pre-calculus 11 in high school and was well prepared. She's doing Calculus 12 this semester and will be majoring in engineering in the fall. I'm very happy with how well Singapore prepared her for higher math.

[boscopup]

First, yes, I have no doubt he'll pass the test. Honestly not worried that he won't. I think it just threw me a bit I guess? I always knew Singapore's S and S were different, but I guess I hadn't personally encountered it. Trying to process through it I guess. I answered in blue below. I'm very curious to the items in your 3B that I don't see in mine. How big is the difference in things taught in US and Standards? Again, we use it all--textbooks, workbooks, IP, and an occasional CWP.

 

 

Oh, you're using US Edition! Well, that might be a bit off then (though I still wouldn't be concerned about test taking). My comments were all based on the Standards Edition scope and sequence. They have added some topics to Standards that weren't in US, and they've moved some topics around.

 

Rest assured, the important stuff IS covered, and if you continue with US Edition, your child is getting a fine math education.

[Candid]

Oh, you're using US Edition! Well, that might be a bit off then (though I still wouldn't be concerned about test taking). My comments were all based on the Standards Edition scope and sequence. They have added some topics to Standards that weren't in US, and they've moved some topics around.

 

Rest assured, the important stuff IS covered, and if you continue with US Edition, your child is getting a fine math education.

 

The US edition is actually the version that is what was used in Singapore when they scored higher than the rest of the world. Its only addition is to add imperial measurements and change some names around to be more US.

[Candid]

My daughter used Singapore pretty much exclusively from K through grade 10. She went into pre-calculus 11 in high school and was well prepared. She's doing Calculus 12 this semester and will be majoring in engineering in the fall. I'm very happy with how well Singapore prepared her for higher math.

 

Ditto this for us. I switched my son switched to AoPS Pre-Calculus when the SM materials ran out, this year. He is doing great in it. He is in the 10th grade. My only dilemma is what to do his last year since he is not really a math guy. Think about what that last sentence says about the power of SM.

[Spy Car]

 

 

--learned the various properties (distributive, etc...)

 

They probably haven't learned the names of the properties (that isn't typically taught until prealgebra, I believe), but they have certainly worked with the distributive property via mental math and via learning multiplication.

 

 

 

Great post.

 

I'm snipping this one point as an area of discontent I have with Primary Mathematics (and not with you :D). While students do get implicit understandings of math axioms through practice, I really wish the properties were taught explicitly.

 

In part taking the teaching materials in Miquon as my guide, we've included explicit understanding of mathematical laws (by name) as a fundamental part of the math education since we started the journey. I think the explicit understanding is valuable, and that is is a mistake to wait in giving children the vocabulary of the discipline.

 

Rant over.

 

Bill

 

[TracyP]

I agree with everyone who said that your kids are getting a great education, will pass the test, yada, yada. BUT I understand being leery and I am keeping a toe in more traditional math for this reason. My dd9 uses MM and CLE. My ds7 uses BA and after getting back this year's test scores (we are in a testing state, too) he will be getting CLE with it. His math score was good (85% I think), but it did not reflect how well he is actually doing. My dd scored 99% and he could have, too. I don't say that to compare, btw. I looked at the test and thought again and again, he would know this if we were still using CLE. The couple days we have done CLE so far, have added about 15 min for a lesson and drill sheet. I think it will be well worth it.

[8filltheheart]

I am one that really appreciates the foundation provided by Horizons. When students progress through all 7 books, they really do end up with an excellent foundation for higher math.

 

That said, SM is far more challenging and mental math oriented. Students using SM and understanding it......I think this is a pt that needs to be stressed b/c if a child is struggling with its abstractions and complex problems, they may not be getting the proper foundation they need......are getting a great problem-solving oriented education.

 

My 5th grader has been using a combo of Horizons and Math in Focus for the last 2 yrs. I like the way Horizons teaches some concepts better. She likes the challenge of the word problems in MiF. She only does partial lessons in each, so it has been a good blend of both for her.

 

FWIW, my older kids did not using anything other than Horizons and did not suffer any lack of problem solving ability. However, my 11th grader has said that he would have really enjoyed the challenge of the word problems back then if he had had the opportunity to both like dd.

[Susan in KY]

Singapore covers things later than traditional US programs so they can build a better foundation for mathematical thought. The only disconnects I have found so far are in year 3 (cover symmetry for standardized testing) and year 4 (cover probability). Everything else is accessible for a person who has a deep foundation such as taught in Singapore math. IP and CWP are your best friends for learning how to think and building problem solvers.

 

I totally agree with a pp who said that Algebraic thought has been taught since grade 1. That is what the bar model is all about. There are plenty of bar model problems that are solveable through algebra, but are 3rd and 4th grade problems made accessible via the bar model.

[KarenNC]

What sort of testing are you doing? Is it a state created thing or something like the ITBS?

 

If ITBS or other national standardized test: we did Singapore (US edition) in the early years and had no issue with testing on grade level in math for either the ITBS or the Woodcock Johnson III. I switched to Standards in 3rd grade when it came out, then to Saxon after 4a. FWIW, my child struggled with Singapore and for whom math is the weakest skill area, so I would think it wouldn't be a problem for kids who work well with it. If you are concerned, look through or pick up a test prep book for a test at your child's grade level and see the topics covered. If there are holes, try Khan Academy's website.

 

If state created: unless your local school system is using Horizons, their scope and sequence may be no more predictive of the content of the actual test than Singapore. In that case, I'd definitely go to the scope and sequence of the appropriate grade on your school system's website to see if there are any areas to touch on prior to the test.

 

For Roman numerals, we really enjoyed Arthur Geisert's "Roman Numerals I to MM" --a cute paperback.

[Crimson Wife]

Great post.

 

I'm snipping this one point as an area of discontent I have with Primary Mathematics (and not with you :D). While students do get implicit understandings of math axioms through practice, I really wish the properties were taught explicitly.

 

 

They do get taught formally in the 7th grade books. I teach them as I go along in PM, but for whatever reason, Singapore waits until DM 7 to do it.

[Susan in KY]

They do get taught formally in the 7th grade books. I teach them as I go along in PM, but for whatever reason, Singapore waits until DM 7 to do it.

 

Yup. They want the students to build their own understanding so that they OWN it, not be told all about it and not construct it for themselves.

 

I'll never forget the Singaporean teacher who commented sort of off-handedly, "Perhaps students here forget so easily because they learned by remembering." Hits the nail on the head!

[Spy Car]

 

 

Yup. They want the students to build their own understanding so that they OWN it, not be told all about it and not construct it for themselves.

 

I'll never forget the Singaporean teacher who commented sort of off-handedly, "Perhaps students here forget so easily because they learned by remembering." Hits the nail on the head!

 

I'm not understanding the point you are making in your post. My fault I'm sure, but do you care to clarify?

 

Bill

[Susan in KY]

I'm not understanding the point you are making in your post. My fault I'm sure, but do you care to clarify?

 

Bill

 

The idea is for students to generate their own understanding of the math, in their own words. Once you put the academic language on to it for them, it becomes just another thing to remember. For example, my daughter generated the difference of squares for herself in 6th grade (far beyond the scope of the curriculum) and decided to write a paper about it and get published. lol. She was sad that she hadn't been the one to "discover" it when she learned it had a name. But, she did discover it. It is hers and belongs to her for good. She can explain and apply it. She didn't need a formal name for it. In some cases, naming concepts with academic language takes it out of kids' hands.

 

I know there are many who disagree with the principle, that is obvious. However, when a child discovers something and names it, s/he owns it. If you take some time to read the Singaporean philosophy as it has evolved (look on page 6 of the attached document*), it is clear that the intent is to grow very flexible math thinkers who have the attitudes to tackle unique problems in unique ways. That's why it's a world class curriculum. I think the vast majority of users totally overlook the elegance and intentionality that went into producing it in the first place, and the goal behind it.

 

After all that, they do come back around and give them academic definitions in middle school, but by that time the children have already internalized the principles and heuristics.

 

*ETA: If you send me a PM, I can send you the PDF. It didn't attach for me.

[Spy Car]

 

 

The idea is for students to generate their own understanding of the math, in their own words. Once you put the academic language on to it for them, it becomes just another thing to remember. For example, my daughter generated the difference of squares for herself in 6th grade (far beyond the scope of the curriculum) and decided to write a paper about it and get published. lol. She was sad that she hadn't been the one to "discover" it when she learned it had a name. But, she did discover it. It is hers and belongs to her for good. She can explain and apply it. She didn't need a formal name for it. In some cases, naming concepts with academic language takes it out of kids' hands.

 

I know there are many who disagree with the principle, that is obvious. However, when a child discovers something and names it, s/he owns it. If you take some time to read the Singaporean philosophy as it has evolved (look on page 6 of the attached document*), it is clear that the intent is to grow very flexible math thinkers who have the attitudes to tackle unique problems in unique ways. That's why it's a world class curriculum. I think the vast majority of users totally overlook the elegance and intentionality that went into producing it in the first place, and the goal behind it.

 

After all that, they do come back around and give them academic definitions in middle school, but by that time the children have already internalized the principles and heuristics.

 

*ETA: If you send me a PM, I can send you the PDF. It didn't attach for me.

 

 

I also thInk it is valuable for children to make "discoveries." I remember when my son (4 years old at the time) came to me in a very excited state. He'd been playing with C Rods and "discovered that a 4 Rod and a 5 Rod was the same as a 5 Rod and a 4 Rod.

 

I made a big deal. Shouting out that he'd made a very important discovery, and it was called the "Commutative Law." He was so happy. He "owned" the discovery, and having a name for this property made that discovery a lesson he never forgot.

 

Bill

[Susan in KY]

I also thnk it is valuable for children to make "discoveries." I remember when my son (4 years old at the time) came to me in a very excited state. He'd been playing with C Rods and "discovered that a 4 Rod and a 5 Rod was the same as a 5 Rod and a 4 Rod.

 

I made a big deal. Shouting out that he'd made a very important discovery, and it was called the "Commutative Law." He was so happy. He "owned" the discovery, and having a name for this property made that discovery a lesson he never forgot.

 

Bill

 

Granted, Bill, it most certainly is all in how the teacher handles it. I think you will agree, however, that by and large in the typical schools in which textbooks are used, there is neither time for such free play and discovery nor do teachers (in general) have the freedom or leeway to do much more than say, "this is the commutative property, memorize it." What the Singaporeans have done is slow down the process for schools and create an atmosphere in which bright kids can go as deep as they need to and slower kids can build a steady foundation even though it takes a day or two. The reality on the ground isn't my 11-year-old or your 4-year-old in free discovery, but guided classroom learning that is pushed, pulled, and pressed by any number of other things, many of which—here in the US, at least—have precious little to do with actual learning.

[Chelli]

Great post.

 

I'm snipping this one point as an area of discontent I have with Primary Mathematics (and not with you :D). While students do get implicit understandings of math axioms through practice, I really wish the properties were taught explicitly.

 

In part taking the teaching materials in Miquon as my guide, we've included explicit understanding of mathematical laws (by name) as a fundamental part of the math education since we started the journey. I think the explicit understanding is valuable, and that is is a mistake to wait in giving children the vocabulary of the discipline.

 

Rant over.

 

Bill

 

The properties are taught in MIF by name starting in 3A. I didn't realize that PM didn't teach them until Pre-Algebra. Interesting.

[Susan in KY]

 

The properties are taught in MIF by name starting in 3A. I didn't realize that PM didn't teach them until Pre-Algebra. Interesting.

Even in MIF they introduce them before they name them. Usually they name them the following year.

[Spy Car]

 

 

Granted, Bill, it most certainly is all in how the teacher handles it. I think you will agree, however, that by and large in the typical schools in which textbooks are used, there is neither time for such free play and discovery nor do teachers (in general) have the freedom or leeway to do much more than say, "this is the commutative property, memorize it." What the Singaporeans have done is slow down the process for schools and create an atmosphere in which bright kids can go as deep as they need to and slower kids can build a steady foundation even though it takes a day or two. The reality on the ground isn't my 11-year-old or your 4-year-old in free discovery, but guided classroom learning that is pushed, pulled, and pressed by any number of other things, many of which—here in the US, at least—have precious little to do with actual learning.

 

Here is the thing—and I'd sincerely doubt we'd disagree on this—there is a Third Way between avoiding the teaching mathematical laws as something to be memorized (absent real understanding) and not prescribing a name to concepts that are intrinsically understood (but lack a name to describe them).

 

Likewise there are ways to have both " true discovery" (as in the example of my son's learning of the Commutative Law of Addition) and what I'd call "guided discovery" which is the way Miquon-like methods gave us a way to explore the Distributive Property as it related to multiplication in a hands on way that also lead to "owning it."

 

Either way I think kids should "own it," I just think they should have an explicit understanding of mathematical laws/properties earlier than what I've encountered in the otherwise fine Primary Mathematics. And it it a big part of why I value Miquon so much as part of the math mix.

 

I think kids can have both discovery/ownership and an explicit understanding prior to post-adolescence when words often become 'blah, blah, blah."

 

I'd rather implant both the concepts and the vocabulary to describe them early. Rather than waiting until "pre-algebra." Having names for things that you understand is a good thing, methinks.

 

Bill

 

 

[Aubrey]

 

Oh, you're using US Edition! Well, that might be a bit off then (though I still wouldn't be concerned about test taking). My comments were all based on the Standards Edition scope and sequence. They have added some topics to Standards that weren't in US, and they've moved some topics around.

 

Rest assured, the important stuff IS covered, and if you continue with US Edition, your child is getting a fine math education.

 

 

We've used the US Ed from the beginning to 6B, & although I can't tell you any more what's where, I think everything on your list except Roman numerals is covered. My kids learned those in Latin, lol.

 

Really, though...the *way* that Singapore teaches kids to think about math is so great that...if there's something that isn't covered...well...like phonics, they've been taught HOW to think mathematically. They'll figure it out. Which is better than being taught how to do that one thing & then forgetting, kwim?

[mathwonk]

One advantage to knowing words like "minuend", is you can one - up your college math professor, at least if it is me. I can only guess at that one by analogy with "dividend" which is also barely accessible (well it's not the divisor or the quotient so it must be the other one). (Wait a minute, the analogy may be with subtrahend. It seems an analogous sequence would be subtractor, subtrahend, difference?)

 

One of my most brilliant graduate algebra professors could not remember what numerator and denominator meant so always called them tops and bottoms. That was the great Maurice Auslander:

 

http://en.wikipedia....urice_Auslander

 

 

So there is hope for a child who misses some of these topics early.

[J-rap]

Many of those topics will be covered in Singapore 4 or 5. The one exception I can think of off the top of my head is Roman numerals, and that topic is easy to teach.

 

This. We loved Singapore. We used their science too.

[KarenNC]

I could never remember numerator and denominator so I came up with "no duh" to help me remember. No comes before duh so it's numerator on top and denominator on the bottom. Now I never forget!

 

:laugh:

 

 

Fabulous! My daughter gives it :thumbup:

[Ali in OR]

Back to OP, we continue to use Singapore for primary math instruction and Horizons as continual review/test prep all through 6th grade. I do find Horizons useful--my dds keep circling back to previously learned topics and they cover those "stray" topics that they may not see in Singapore. I choose what I want them to do in Horizons to keep the workload manageable--they only need to do a few long division problems to keep their skills sharp for instance, not all 8 in a particular lesson. As a former math teacher, I'm also a little annoyed with how early Horizons will throw out some topics. Kids do not need to do algebraic manipulation in 2nd or 3rd grade--their time is better spent elsewhere. I hated that Horizons introduced cross products in 5th grade before the kids have the algebraic skills to understand why it works. It became a magic trick instead of a skill based on knowledge of equations. But Horizons does have its place in our home school (always secondary to Singapore).

[mathwonk]

we can't use "no duh" because our grand daughter calls her grand ma "duh", so its confusing to us. :hat: