s/o Singapore Conceptual Leaps

[Embassy]

Several Singapore users here have reported that Singapore has conceptual leaps. I've been using it with my boys over a year now and I haven't noticed any conceptual leaps. Maybe I missed something. Can anyone provide some examples and I'll look back in my books. Maybe it was a spot where my ds had some difficulty. I have 1B-4A Standard edition.

 

:bigear:

[Spy Car]

I'll going you in :bigear: because I haven't seen any of these "leaps" either.

 

Bill

[FairProspects]

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Edited November 21, 2012 by FairProspects

[wapiti]

Maybe it would help to rephrase, and identify some instruction as implicit vs. explicit? Or more explicit vs. less explicit?

 

I can't look back right this second (I'm supposed to be making dinner :001_huh: and I only have SM 4B anyway, and all of MM), but it isn't hard to imagine that MM might include more explicit instruction in places, simply because, for one thing, there is no separate teacher manual so all instruction is written out in the text. In contrast, SM involves an additional teacher book, and from what I've seen posted here and there, it sounds like the quality of instructional supports (HIG/TM) for SM might vary amongst grade levels or at least vary between the US/Std editions, so perhaps there might be a weak link in places.

[chepyl]

Maybe it would help to rephrase, and identify some instruction as implicit vs. explicit? Or more explicit vs. less explicit?

 

I can't look back right this second (I'm supposed to be making dinner :001_huh: and I only have SM 4B anyway, and all of MM), but it isn't hard to imagine that MM might include more explicit instruction in places, simply because, for one thing, there is no separate teacher manual so all instruction is written out in the text. In contrast, SM involves an additional teacher book, and from what I've seen posted here and there, it sounds like the quality of instructional supports (HIG/TM) for SM might vary amongst grade levels or at least vary between the US/Std editions, so perhaps there might be a weak link in places.

 

I have also seen people mention only using the text, or only the workbook. If you are strong in math and okay teaching it on your own, I can see bypassing the manual in early levels. I only glance at it and skip a lot of the extra activities. If you only use the workbook, I can see where there would be problems. The text has important information and some of the extra drill kids need. On the other hand, if you just use the text, you miss the practice.

 

I think this may be a reason why some people have problems.

[FairProspects]

.

[Spy Car]

Well, we gave up on 1A because of the leaps. The Standards Edition moves really fast compared to other programs. With math facts and making 10s, MM would have 20-40 pages of problems practicing with each number in 5 different ways or visualizations, and Singapore would have a few examples of a couple of different numbers and move on.

 

That might work for some kids who learn intuitively and apply the principle to other numbers, but for others who need explicit instruction and lots of practice/review to ingrain the concept, it just will not work at all. MM with its constant review and incremental approach is a much better fit for us. I'm glad Singapore works for others, but I definitely see the leaps everyone describes. It may be hard to see though if you don't have a kid who needs very explicit instruction.

 

But what you are describing is a need for additional practice, which is different than having a "conceptual leap." I could easily see a child needing additional practice. For just that reason there is an additional book available in the Standards Edition (called appropriately enough, "Extra Practice" :D) which has more basic level practice with (from what I'm told) additional teaching help for students who need it.

 

Even the Standards Edition, which has more practice and review than the US Edition, is fairly bare-bones in terms of practice. This is why I'm amazed that some people skip whole books in the series, as we could not do that to good effect.

 

We have not used "Extra Practice" (using Intensive Practice instead) but it is what I'd use if I had a child that would benefit from additional work on the basic level of difficulty.

 

Bill

[Alte Veste Academy]

Several Singapore users here have reported that Singapore has conceptual leaps. I've been using it with my boys over a year now and I haven't noticed any conceptual leaps. Maybe I missed something. Can anyone provide some examples and I'll look back in my books. Maybe it was a spot where my ds had some difficulty. I have 1B-4A Standard edition.

 

:bigear:

 

OK, I'm sure this is going to be no help at all but here are my impressions, as someone who has also never had an issue with conceptual leaps in Singapore.

 

I think it has to do with this...

 

MM with its constant review and incremental approach is a much better fit for us. I'm glad Singapore works for others, but I definitely see the leaps everyone describes. It may be hard to see though if you don't have a kid who needs very explicit instruction.

 

If your kid is sailing through Singapore, you're probably not going to notice any conceptual leaps. You know this material (I hope! :lol:), so it's not going to throw you. If it throws your child, however, it will become obvious to you and a search for more explicit instruction will likely follow.

 

When MM was all the rage, I bought it and used it for a short time. Incremental is the name of the game with MM. The program takes a child by the hand and makes teeny-tiny baby steps through a progression of many sets of problems for each lesson. It's not just about extra practice. It is about tiny, incremental differences through the sets of problems that provide that extra practice, leading from concrete to algorithms (with much more minute changes than you will find in SM's progression from concrete to algorithms).

 

If you don't see conceptual leaps in SM, go look at MM samples. You will observe that the program provides a 100% solid footpath through math (picture a solid surface with no potholes to stumble over, handrails, lights along the path, a pleasant guide providing some humor... :D). You will see how SM (and probably most other programs) provide a stepping stone path by comparison. It's a great path and we like the little hops, but stepping stones aren't for everyone. On a rainy day, it can be a bummer to misstep land in the mud between them. :lol:

 

I'm feeling lazy so I'm not really interested in looking up examples. Sorry. :tongue_smilie: But these were my impressions having used both. My kids didn't need the solid path and we all prefer SM so that's what I use. It's like anything else though. You work with your child. You will discover what your child needs are and naturally prefer the program that fills those needs...and sometimes berate the one that didn't. :tongue_smilie:

Edited November 6, 2011 by Alte Veste Academy

[Embassy]

 

If your kid is sailing through Singapore, you're probably not going to notice any conceptual leaps.

 

I haven't noticed conceptual leaps, but I wouldn't say my kid is sailing through Singapore either. There have been easier spots and spots where we needed to spend more time. There was also a time where we set aside Singapore for a few weeks and worked on a difficult area. I thought this was a common occurrence with all math programs though:tongue_smilie:

 

Maybe I need to adjust my perspective. As an adult who understands 2nd and 4th grade math I see lots of baby steps in Singapore. I guess if I compared it side by side to something else I might think differently.

[shukriyya]

We only used Singapore for 1/2 a year so I don't have the scope with it that other longtime users have but I didn't notice any conceptual leaps for the portion we used, 2A. Dc moved through it steadily but got bogged down with all the drill.

Edited November 6, 2011 by shukriyya

[TKDmom]

I'm one of the ones who has complained about conceptual leaps. I tend to get math easily, so I never really noticed any problems with conceptual leaps, but my non-mathy dd hit a wall when we got to long division, which appears in 3A. Let me see if I can illustrate how SM approaches division...

 

In 2B, division is taught as the inverse of multiplication. So students have easy division problems that they can solve by knowing their multiplication facts: 80/10=8, 20/5=4, etc. (sorry I'm making these look like fractions, but I don't think I can type division symbols here). It also introduces the concept of a remainder, but still with very simple, concrete examples: 18 tomatoes divided into groups of 4 equals 4 groups, with 2 tomatoes left over. All these problems are written horizontally--never with the symbol that looks similar to a square root. (I can't type this division symbol either, but hopefully you understand what I mean).

 

In 3A, division reappears (this is on p. 94 of the Standards text if you're following along). Quotient and remainder are taught. Initially the problems are very similar to those in 2B, but the new terminology is used. They start to use the standard division algorithm (with the square-root-like symbol). Turn the page and we're now doing long division with more difficult numbers like 80 / 3= 26 R2. And on the next lesson we are now dividing 3-digit numbers.

 

Looking at this as an adult who never had a problem learning division it doesn't look too bad. But when I taught these lessons to my dd who has very little confidence in her math abilities, she flipped out. It was too much for her to learn new terminology, new symbols and a completely new algorithm in 3 days' time. Her brain shut down, and she decided that she would never be able to understand division, so she wouldn't try. It took me a month of backtracking and teaching her pre-division skills with another math program to get her back to the point where she was ready to continue and finish the rest of the 3A books. Next week we will start MM4B, where long division is taught. I'm optimistic that she will have a thorough understanding of division by the time she finishes the 23 lessons that MM spends on this concept.

 

I don't like being critical of SM. I truly love the curriculum, but we must be honest that it won't work with every child. Some children need a more incremental approach. They need to have every step spelled out, and maybe go back over it from a few different angles. A good teacher can probably anticipate and correct the kind of problems that my dd had with SM. But for the rest of us overworked, exhausted parents who forget to read their TM ahead of time...another program might work better.

[Haiku]

expects the students to extrapolate techniques to different types of problems

 

That's what I mean when I say leaps. I think Singapore takes a "Do this with these types of problems. Ok, here's a different type of problem ... how can you take what we just taught you and tweak it to work this problem out?" For my dd-now-17, that didn't work. At all. For my ds8, it would be a disaster. I think my very mathy dd9 would be fine with it, but she also likes MM so I see no reason to worry about Singapore.

 

While I do find MM to be very precise in its explanations of things, I don't really think it's as beat-you-over-the-head-with-it as the above example of the well-lighted path described.

 

Tara

[Farrar]

Full disclosure - we didn't actually end up trying Singapore (though we use the CWP's). After having MEP bomb out, I considered switching to Singapore but saw that many of the things that I saw as problems for my kids with MEP were similar in Singapore.

 

I think it's more than just needing more practice. In MM, what I see is that they'll structure it so that kids are doing the easiest problems first and slowly building up to doing more difficult ones. It's elementary math, so to me, they're not really any harder, but I see that doing the marginally easy ones first helps my kids. Not only that, but they don't just teach a helping step then ask kids use it, they actually spell those problems out and have kids do it separately. So, for example, kids learning to add with 8 don't just get told a strategy of "making 10", they also have the strategy spelled out for them with blanks to fill in. And over a few pages of practice, that crutch is slowly removed so that it's not there any more. Then, once it's done, kids are asked to drill the problems and memorize the math facts. I don't see as much of that extra step in Singapore. For many kids, it's totally unnecessary. Practicing without it is fine. But my kids needed those extra filled in bits to get it. I don't know if it's fair to call it a "conceptual leap" or not, but I do think some kids need those extra steps literally written out for them for awhile as a crutch until they're ready to internalize it.

 

ETA: thinking more... When the comparison is between MM and Singapore, I do think some of it is the fact that Singapore requires you use the IG to really teach the program whereas MM is all just laid out on the page so it's easier to feel those differences. But I think it's also a real difference. As Tara said above, Singapore really wants to challenge kids to make a jump sometimes - especially in the IP and the CWP.

Edited November 6, 2011 by farrarwilliams

[Alte Veste Academy]

While I do find MM to be very precise in its explanations of things, I don't really think it's as beat-you-over-the-head-with-it as the above example of the well-lighted path described.

 

Tara

 

For the record, that was a compliment to MM, not an insult. I wasn't trying to depict the program as beating you over the head, just guiding you easily, step by step. :)

[Embassy]

I'm one of the ones who has complained about conceptual leaps. I tend to get math easily, so I never really noticed any problems with conceptual leaps, but my non-mathy dd hit a wall when we got to long division, which appears in 3A. Let me see if I can illustrate how SM approaches division...

 

In 2B, division is taught as the inverse of multiplication. So students have easy division problems that they can solve by knowing their multiplication facts: 80/10=8, 20/5=4, etc. (sorry I'm making these look like fractions, but I don't think I can type division symbols here). It also introduces the concept of a remainder, but still with very simple, concrete examples: 18 tomatoes divided into groups of 4 equals 4 groups, with 2 tomatoes left over. All these problems are written horizontally--never with the symbol that looks similar to a square root. (I can't type this division symbol either, but hopefully you understand what I mean).

 

In 3A, division reappears (this is on p. 94 of the Standards text if you're following along). Quotient and remainder are taught. Initially the problems are very similar to those in 2B, but the new terminology is used. They start to use the standard division algorithm (with the square-root-like symbol). Turn the page and we're now doing long division with more difficult numbers like 80 / 3= 26 R2. And on the next lesson we are now dividing 3-digit numbers.

 

Looking at this as an adult who never had a problem learning division it doesn't look too bad. But when I taught these lessons to my dd who has very little confidence in her math abilities, she flipped out. It was too much for her to learn new terminology, new symbols and a completely new algorithm in 3 days' time. Her brain shut down, and she decided that she would never be able to understand division, so she wouldn't try. It took me a month of backtracking and teaching her pre-division skills with another math program to get her back to the point where she was ready to continue and finish the rest of the 3A books. Next week we will start MM4B, where long division is taught. I'm optimistic that she will have a thorough understanding of division by the time she finishes the 23 lessons that MM spends on this concept.

 

I don't like being critical of SM. I truly love the curriculum, but we must be honest that it won't work with every child. Some children need a more incremental approach. They need to have every step spelled out, and maybe go back over it from a few different angles. A good teacher can probably anticipate and correct the kind of problems that my dd had with SM. But for the rest of us overworked, exhausted parents who forget to read their TM ahead of time...another program might work better.

 

Thanks so much for the example. I just hit that point in 2B and not too long ago was in 3A. In 2B I was a little concerned. The division with remainder portion was short and I wondered if my son would get it. He didn't have a problem. My other son did have a some difficulty with the long division in 3A. I agree that it could have been more step by step at that point. I had him go slower. I don't know if it was a conceptual leap though. He understood the concept of division with a remainder. He just needed more practice with the algorithm.

[Dana]

Thanks so much for the example. I just hit that point in 2B and not too long ago was in 3A. In 2B I was a little concerned. The division with remainder portion was short and I wondered if my son would get it. He didn't have a problem. My other son did have a some difficulty with the long division in 3A. I agree that it could have been more step by step at that point. I had him go slower. I don't know if it was a conceptual leap though. He understood the concept of division with a remainder. He just needed more practice with the algorithm.

 

I bought a couple of the Spectrum workbooks and have my son work problems from those when he needs extra practice on a topic (like the long division) :)

 

I got Extra Practice, but I don't feel it has enough practice and I haven't used it much. The Spectrum books work better for getting more practice - or I'm sure you could find practice worksheets online.

 

For division, we did need to spend about 3 days where we used the base 10 blocks to show each step. I think this idea may have also been mentioned in the Home Instructor's Guide.

[Crimson Wife]

Incremental is the name of the game with MM. The program takes a child by the hand and makes teeny-tiny baby steps through a progression of many sets of problems for each lesson. It's not just about extra practice. It is about tiny, incremental differences through the sets of problems that provide that extra practice, leading from concrete to algorithms (with much more minute changes than you will find in SM's progression from concrete to algorithms).

 

If you don't see conceptual leaps in SM, go look at MM samples. You will observe that the program provides a 100% solid footpath through math (picture a solid surface with no potholes to stumble over, handrails, lights along the path, a pleasant guide providing some humor... :D). You will see how SM (and probably most other programs) provide a stepping stone path by comparison. It's a great path and we like the little hops, but stepping stones aren't for everyone. On a rainy day, it can be a bummer to misstep land in the mud between them. :lol:

 

:iagree::iagree::iagree::iagree:

It's not about number of practice problems but rather the TEACHING. MM has the student wade in gradually from the shallow end of the pool. Singapore tosses the kid into the deep end and gives a little bit of guidance in the HIG to the teacher as to how to keep the kid from drowning.

 

The Standards Edition HIG *IS* an improvement over the U.S. Edition HIG and I definitely would've been better off with the SE for 3A/B. But even using the SE HIG for 4A & up, I still ran into a few places where we needed a more incremental approach. Thank goodness for MM "blue" :)

[kalanamak]

T

We had other issues with Singapore too, that had nothing to do with conceptual leaps, but I do think it moves faster than other programs and expects the students to extrapolate techniques to different types of problems (which may be why so many like it) but some kids need a lot of scaffolding or practice to be able to do that.

 

Off the top of my head, I can't remember workbook problem that hadn't had a similar type in the text.

 

I dunno. If I had to say where the conceptual leaps were, it would be for the teacher, not the student, and yes, I've had to think out how to teach this next thing rather than it all being programmed out for me. But, that is what I like about it: thin text, Momma's brain, and a bit of trial and error for figuring out what works to teach kiddo.

[Crimson Wife]

Off the top of my head, I can't remember workbook problem that hadn't had a similar type in the text.

 

In 3B, Chapter 6, Section 2 has the student comparing two fractions with unlike denominators. The examples all show problems where one fraction has a denominator that is a multiple of the other (e.g. 3/4 vs. 5/8).

 

Problem 10c out of the blue has students compare two fractions with unlike denominators (3/5 vs. 4/7). I've since been told by posters here that there is a way to solve this without changing both fractions to a common denominator, but the U.S. edition HIG didn't provide any guidance on this. So when DD encountered this problem, she got all upset and I had to tell her to skip it that day and I would show her the following lesson how to solve that type of problem. She caught on very quickly once I explained how to do it, but she didn't make the conceptual leap herself the way her more "mathy" younger brother likely could.

[Alte Veste Academy]

the U.S. edition HIG didn't provide any guidance on this.

 

I truly believe this is the problem. The Standards HIGs are gold. I have personally never stumbled upon any problems in the TB/WB combo that couldn't have been avoided had I applied the teaching from the HIG. Problems with understanding due to the developmental stages and readiness of my individual kids, sure. Problems with understanding due to instruction, no.

[kalanamak]

In 3B, Chapter 6, Section 2 has the student comparing two fractions with unlike denominators.

 

She caught on very quickly once I explained how to do it, but she didn't make the conceptual leap herself the way her more "mathy" younger brother likely could.

 

Aha. See I saw that as a leap for me, not kiddo, for I do remember seeing it and thinking it over and teaching it before we got to it. Because I have such a wiggly, hand-holdy boy whose eyes wander most when doing math, he never meets anything "alone", and I have looked over what he is going to be facing in advance.

 

I guess I assumed the teachers in Singapore know such a thin book inside out, I have tried to know the books inside out, too. At least weekly I glance through them and think about what is coming up.

 

So, by mentioning the technique to kiddo and asking if he sees why one would be greater than the other, I find that when he hits it in the book, he looks at me with that look like I'm a mind reader and that we are "in this together". And I LOVE those moments.

 

However, I do see if the child is doing the workbooks on their own this might be disconcerting.

[EKS]

I found that the most conceptual leaps in the PM series occurred in the 1A/B books. Since the books are intended to be used in a classroom by highly trained teachers in Singapore, I think the leaps are really places where the teacher teaches.

[Spy Car]

In 3B, Chapter 6, Section 2 has the student comparing two fractions with unlike denominators. The examples all show problems where one fraction has a denominator that is a multiple of the other (e.g. 3/4 vs. 5/8).

 

I believe you mean 3B Chapter 10, Section 2 (unless you are referring to the US Edition?)

 

True enough that they—after extensive and very clear instruction on how to find "equivalent fractions," where a child learns that 3/4 is the same as 6/8—are then asked which is greater 3/4 or 5/8?

 

They have already learned to find the "equivalent fraction" (the whole point of the section) of 3/4, and now they have a purpose for doing so in a problem solving situation. These sorts of questions are a prime example of why I enjoy using Primary Mathematics with my son.

 

Bill

Edited November 6, 2011 by Spy Car

[wapiti]

I have an observation that I'm not sure I've seen yet in the above posts. It seems to me that, for some kids, there may be an inherent difference between receiving portions of a lesson orally from a parent (from the HIG) and receiving the entirety of the lesson presented visually in MM, that the student can read to himself if he chooses (not that reading and listening are all that different for those with language weaknesses, but there's the extra step between what's in the HIG and what the parent actually says, and then there are diagrams).

 

I also wonder whether there's a difference where there are diagrams or number representations showing the individual steps. I don't have time this morning, but it would be interesting to compare visual demonstratives - in particular, whether MM's visuals are more numerous due to representing more discrete steps - for particular topics. I haven't seen SM on fractions, but it's hard to imagine any text having more green pies than MM :lol: (in MM, that would be in 5B).

[Alte Veste Academy]

I believe you mean 3B Chapter 10, Section 2 (unless you are referring to the US Edition?)

 

True enough that they—after extensive and very clear instruction on how to find "equivalent fractions," where a child learns that 3/4 is the same as 6/8—are then asked which is greater 3/4 or 5/8?

 

They have already learned to find the "equivalent fraction" (the whole point of the section) of 3/4, and now they have a purpose for doing so in a problem solving situation. These sort of questions are a prime example of why I enjoy using Primary Mathematics with my son.

 

Bill

 

There's also the part in the 3B HIG that says, "Have your student actually do this task, rather than just look at the pages." Not to mention the corresponding activity having the student shade parts of a rectangle themselves, and label the fractions (then keep folding and unfolding the paper to see how the shaded part does not change but the fraction does). There is also a reinforcement exercise in which the student is to receive a copy of labeled fraction bars (found in the appendix) and cut them apart to play with. :tongue_smilie:

[Spy Car]

I also wonder whether there's a difference where there are diagrams or number representations showing the individual steps. I don't have time this morning, but it would be interesting to compare visual demonstratives - in particular, whether MM's visuals are more numerous due to representing more discrete steps - for particular topics. I haven't seen SM on fractions, but it's hard to imagine any text having more green pies than MM :lol: (in MM, that would be in 5B).

 

I can't compare to MM (not having used it) but Primary Mathematics 3B SE is loaded with pictorial representations of fractions, including a lot of "green pies."

 

Bill

[wapiti]

I can't compare to MM (not having used it) but Primary Mathematics 3B SE is loaded with pictorial representations of fractions, including a lot of "green pies."

 

Bill

 

eek - I'm short on time (impending guests/giant mess) - but later I'd like to try to compare explicit lessons per discrete topic (e.g. division of fractions). Or, perhaps someone could lay out the differences on a topic where they think they've seen a difference (e.g. long division). But truly, the volume of green fraction pies can be overwhelming.

 

FWIW, my dd needs more explicit steps than one of my ds8s. For him, I tend to compact 10 or 20 pages or more of MM at a time on occasion, LOL; he leaps over all that. Or, sometimes he leaps ahead and then goes back to fill in a couple of details.

[Alte Veste Academy]

I have an observation that I'm not sure I've seen yet in the above posts. It seems to me that, for some kids, there may be an inherent difference between receiving portions of a lesson orally from a parent (from the HIG) and receiving the entirety of the lesson presented visually in MM, that the student can read to himself if he chooses (not that reading and listening are all that different for those with language weaknesses, but there's the extra step between what's in the HIG and what the parent actually says, and then there are diagrams).

 

Yes, and I think this is worth noting. And then there is also the issue that with SM, students are not receiving the full lesson if there is no teaching from the HIG. (Maybe they will be fine with that but they will not have received the full lesson.) In MM, the student is bound to receive the full lesson as long as he/she progresses through the worktext without skipping parts.

 

I also wonder whether there's a difference where there are diagrams or number representations showing the individual steps. I don't have time this morning, but it would be interesting to compare visual demonstratives - in particular, whether MM's visuals are more numerous due to representing more discrete steps - for particular topics. I haven't seen SM on fractions, but it's hard to imagine any text having more green pies than MM :lol: (in MM, that would be in 5B).

 

I don't think the visuals are more numerous. SM includes lots of pictorial representations, just like MM does. I truly think it boils down to the teaching from the SM HIGs being included in the MM worktext and is, therefore, not optional and forgotten.

[justLisa]

DS used MM in 1st grade, and we began this year in 2nd. I tried to stick with it and several times came *this* close to purchasing SM and posted about it about a million times here. Well, I finally did and DS actually thanked me one day LOL.

 

I never saw the "self teaching" aspect of MM to be useful, as DS never could just look through it and do it, and he IS mathy. I did let him figure out quite a bit on his own last year and I regret it (with MM). I think it is instinctual to finger count and use that as a crutch and after so long it is very hard to turn your brain around to use mental math strategies FIRST. I'm talking about say, 7 + 6, he would count, not think of making 10 plus 3 more. He could do this when I instructed him to do it this way, but then he always went back to counting. DD on the other hand is 5.5 and less mathy by nature and she has been using SM all the while with my instruction first, and she is already showing signs of using mental math strategies and number bonds rather than counting on fingers. It's interesting to me. DS and I actually when through some of 1B just to rev up those basic facts and he is breezing through 2 now.

 

BTW I know MM give instruction on mental math strategies but for DS he never could pick up on the self teaching aspect. I just don't like the look/format of the pages and neither did DS. We still use it occasionally for review and I love the clock/money pages.

 

I'll be curious to see how it plays out for us when we get to level 3. So far I have not noticed any leaps. One thing about MM is it seemed like it was confusing DS to do something many ways in one lesson time. I think it is very important to be able to do things many ways, but not until one method is solidified. Or at least for my DS that is, and we found MM to be confusing this way.

[Spy Car]

eek - I'm short on time (impending guests/giant mess) - but later I'd like to try to compare explicit lessons per discrete topic (e.g. division of fractions). Or, perhaps someone could lay out the differences on a topic where they think they've seen a difference (e.g. long division). But truly, the volume of green fraction pies can be overwhelming.

 

FWIW, my dd needs more explicit steps than one of my ds8s. For him, I tend to compact 10 or 20 pages or more of MM at a time on occasion, LOL; he leaps over all that. Or, sometimes he leaps ahead and then goes back to fill in a couple of details.

 

I could not compare the "division of fractions" as we are still in 3B and currently working on the precursor skill of subtracting fractions.

 

As to green pies in PM, I find it is just the right amount for us. But we also use physical manipulatives like C Rods and Cuisenaire Fraction circle. When it gets more serious I will probably add "fraction bars" as well. Hmmm...maybe a good Christmas gift? :D

 

Bill

[Crimson Wife]

I believe you mean 3B Chapter 10, Section 2 (unless you are referring to the US Edition?)

 

True enough that they—after extensive and very clear instruction on how to find "equivalent fractions," where a child learns that 3/4 is the same as 6/8—are then asked which is greater 3/4 or 5/8?

 

In the U.S. edition, the student is asked to compare fifths with sevenths. Fourths vs. eighths would be simple given the worked examples earlier in the section. DD was cruising right along until she hit the problem asking her to compare 3/5 with 4/7.

 

The way that I (and probably most adults who have been taught traditional U.S. math) would solve this problem is to change both fractions into the common denominator of thirty-fifths. That makes it obvious that 3/5 = 21/35, which is larger than 4/7 = 20/35. However, Singapore doesn't teach that procedure until 5A.

 

A poster here one time explained a different way of figuring out that 3/5 is larger than 4/7 without changing both fractions into a common denominator. I'm not at all "mathy" and wouldn't have come up with it on my own. I can't even remember now what the trick was. Maybe something about knowing that you need 3/7 to make a whole if you've got 4/7 and that 3/5 is greater than 3/7 so that's how the student should figure out the right answer? :confused: I forget exactly how to do it and the U.S. edition HIG didn't offer any hints. So yes, I saw that as a major "conceptual leap".

[Alte Veste Academy]

When it gets more serious I will probably add "fraction bars" as well. Hmmm...maybe a good Christmas gift? :D

 

Bill

 

Well, if you want to get fancy, you could buy some. You will also find a set to copy on page a9 of your 3B HIG. :D

[Beth in SW WA]

I don't think the visuals are more numerous. SM includes lots of pictorial representations, just like MM does. I truly think it boils down to the teaching from the SM HIGs being included in the MM worktext and is, therefore, not optional and forgotten.

 

Bingo. I constantly forget about the HIG (plus, I'm lazy). MM is monkey-simple for moms like me. I stick w/ SM because I spent a small fortune on levels 1 - 5.

 

And I never bought into the myth that MM is 'independent' as compared to SM. Math w/ youngers requires lots of hand-holding whether it's workbook, worksheet, cd or online.

[Spy Car]

Yes, and I think this is worth noting. And then there is also the issue that with SM, students are not receiving the full lesson if there is no teaching from the HIG. (Maybe they will be fine with that but they will not have received the full lesson.)

 

I do agree that the basic teaching paradigm in Primary Mathematics ought to resemble a 3-legged stool. With "concrete" learning opportunities for students (and teacher education) via the HIGs or other methods, a teacher intensive pass through the Textbooks (reenforced as necessary to ensure understanding, and practice work in the Workbooks to assure mastery.

 

Pull out one (or two) of these critical parts and........

 

Do all the "basic" components and then add the Intensive Practice and Challenging World Problems and you've got a world-class math program.

 

Bill

[Spy Car]

Well, if you want to get fancy, you could buy some. You will also find a set to copy on page a9 of your 3B HIG. :D

 

We are kind of "three-dimensionalists" :D

 

Bill

[wapiti]

And I never bought into the myth that MM is 'independent' as compared to SM. Math w/ youngers requires lots of hand-holding whether it's workbook, worksheet, cd or online.

:iagree: Independence has a lot more to do with age. However, there's that HIG vs. all-in-one aspect again - I'd guess that the upper levels of MM may be more independent than SM, unless that particular student doesn't need the additional instruction contained in the HIG.

 

For dd, it was gradual - the further we went through MM 4 and 5, the more independent she became. I'd leave her lesson on the counter for her to start by herself first thing in the morning (which is not to say that I wasn't involved - I'd check in with her, answer questions, etc., but there were many lessons in MM 5 that I did not have to teach at all).

[Halcyon]

In the U.S. edition, the student is asked to compare fifths with sevenths. Fourths vs. eighths would be simple given the worked examples earlier in the section. DD was cruising right along until she hit the problem asking her to compare 3/5 with 4/7.

 

The way that I (and probably most adults who have been taught traditional U.S. math) would solve this problem is to change both fractions into the common denominator of thirty-fifths. That makes it obvious that 3/5 = 21/35, which is larger than 4/7 = 20/35. However, Singapore doesn't teach that procedure until 5A.

 

A poster here one time explained a different way of figuring out that 3/5 is larger than 4/7 without changing both fractions into a common denominator. I'm not at all "mathy" and wouldn't have come up with it on my own. I can't even remember now what the trick was. Maybe something about knowing that you need 3/7 to make a whole if you've got 4/7 and that 3/5 is greater than 3/7 so that's how the student should figure out the right answer? :confused: I forget exactly how to do it and the U.S. edition HIG didn't offer any hints. So yes, I saw that as a major "conceptual leap".

 

My son "got" these right away (unlike his mom). When I asked him how he did it, he (of course) said "I just did" and when I pushed, he said something along the lines of 3/5 the same as 6/10, and 4 over 7 is equivalent to 6/10.5. So 3/5 is bigger." Soooo not the way I would think about this problem.

[Spy Car]

In the U.S. edition, the student is asked to compare fifths with sevenths. Fourths vs. eighths would be simple given the worked examples earlier in the section. DD was cruising right along until she hit the problem asking her to compare 3/5 with 4/7.

 

The way that I (and probably most adults who have been taught traditional U.S. math) would solve this problem is to change both fractions into the common denominator of thirty-fifths. That makes it obvious that 3/5 = 21/35, which is larger than 4/7 = 20/35. However, Singapore doesn't teach that procedure until 5A.

 

A poster here one time explained a different way of figuring out that 3/5 is larger than 4/7 without changing both fractions into a common denominator. I'm not at all "mathy" and wouldn't have come up with it on my own. I can't even remember now what the trick was. Maybe something about knowing that you need 3/7 to make a whole if you've got 4/7 and that 3/5 is greater than 3/7 so that's how the student should figure out the right answer? :confused: I forget exactly how to do it and the U.S. edition HIG didn't offer any hints. So yes, I saw that as a major "conceptual leap".

 

I have not seen a similar type question in the Standards Edition. I think I'd tend to be with you in giving a "down-check" to this sort of problem without some teaching behind it.

 

I'd probably be running out to get those "fraction bars" if I saw many of these, but even that wouldn't really add a good deal to a child's understanding of the math (other than the ability to get the "correct" answer with the aid of a manipulative). So I would not favor this sort of question (out of context) either.

 

I still wouldn't throw the baby-out-with-the-bathwater over one question.

 

Say, I though you were using the Standards Edition? :confused:

 

Bill

[zoo_keeper]

A poster here one time explained a different way of figuring out that 3/5 is larger than 4/7 without changing both fractions into a common denominator. I'm not at all "mathy" and wouldn't have come up with it on my own. I can't even remember now what the trick was.

 

I remember the explanation since it was the way I thought about it when I learned that we couldn't use common denominators.

 

Essentially, when looking at 3/5 and 4/7 you first consider half of each fraction. I.e., 3/5 is .5/5 bigger than 1/2 (1/2 of 3/5 being 2.5/5) while 4/7 is .5/7 bigger than 1/2 (1/2 of 4/7 being 3.5/7). Since .5/5 is bigger than .5/7, then 3/5 must be larger than 4/7.

[Embassy]

In 3B, Chapter 6, Section 2 has the student comparing two fractions with unlike denominators. The examples all show problems where one fraction has a denominator that is a multiple of the other (e.g. 3/4 vs. 5/8).

 

Problem 10c out of the blue has students compare two fractions with unlike denominators (3/5 vs. 4/7).

 

Is this in the US edition textbook? I can't find the 10c problem.

[Crimson Wife]

Is this in the US edition textbook? I can't find the 10c problem.

 

Yes, it's in the U.S. Edition of 3B. I switched over to the SE at 4A because of the better HIG. My younger student will use the SE all the way through and I'm hoping to have fewer issues teaching it.

[boscopup]

This thread has convinced me that I need to try Singapore 4A with my son as soon as we finish division in MM4B. :lol:

 

He makes those conceptual leaps on his own. I've thought for a while that Singapore would have been a better fit presentation wise and didn't want to change mid-stream, but even if it pushes us back a year (which would probably be more like a semester), we'll still finish grade 6 math no later than 4th grade. :tongue_smilie: And if we don't like it, we can always hop back over to MM. Or just use them together sometimes.

 

We're in a bit of a rut and basically need a change of scenery. I have MM1-6, so I can easily look at S&S and patch in any holes left by the switch. I don't think there would be very many. MM is what I needed when I started homeschooling him, because I had to fly through some grade levels to find where he is. Now that we've found it and settled in, the more fun presentation of SM and the less incremental instruction would be good for him. He likes the IP and CWP books, and I'm sure he'll love the TB! (I'll get the WB too ;) )

 

Happy Bill? You've got me using C-rods AND Singapore! :lol:

[Embassy]

Yes, it's in the U.S. Edition of 3B. I switched over to the SE at 4A because of the better HIG. My younger student will use the SE all the way through and I'm hoping to have fewer issues teaching it.

 

Thanks!

[kalanamak]

Yes, it's in the U.S. Edition of 3B. I switched over to the SE at 4A because of the better HIG. My younger student will use the SE all the way through and I'm hoping to have fewer issues teaching it.

 

:lol: I found I had fewer issues teaching it when I abandoned the HIGs altogether.