Math programs listed in order of "mental math" teaching.

[mystika1]

Hi,

I want to make a list of math programs in order of their conceptual teaching. I think most people place Singapore Math on top as far as conceptual teaching(mental math) goes followed by Math Mammoth. Can you guys help me by putting the following programs in order of most conceptual to least?

I am thinking it would be something on the lines of...

MEP

Singapore Math

Miquon

Math Mammoth

BJU

CLE

Horizons Math

Rod and Staff

Saxon

 

If I am forgetting something please add to it. I am thinking of making a switch once my dd completes her MM books. She really needs something more spiral and although I have been doing a rotation of the topical books to make it spiral... I feel that I am covering some topics more than others. I would like something better organized. I may end up doing MM and something else because I like the mental math work.

 

Thanks,

Penny

Edited November 21, 2011 by mystika1

[Missouri Okie]

Don't forget about RightStart. I can't answer your question as RS and Miquon are all I have used, but I would think that RS what rank high up on the mental math spectrum.

[mystika1]

I don't know how I could have forgotten Right Start....

 

MEP

Singapore Math

Right Start

Miquon

Math Mammoth

BJU

CLE

Horizons Math

Rod and Staff

Saxon

[Crimson Wife]

Math in Focus would need to go on your list of conceptual math programs.

 

Art of Problem Solving for higher-level (pre-algebra & up)

[mystika1]

Hi,

Yes...I forgot about Math in Focus. I don't think I explained myself well. I am trying to list the curriculum from most conceptual to least conceptual. I feel kinda stupid cause I didn't just say that....I will edit my original post if I can.

[mystika1]

MEP

Singapore Math

Right Start

Miquon

Math in Focus

Math Mammoth

BJU

CLE

Horizons Math

Rod and Staff

Saxon

[sbgrace]

I would think Math in Focus would be at the same point as Singapore. I'm not at all sure RightStart belongs below Singapore. RSB is almost exclusively mental math.

Edited November 21, 2011 by sbgrace

[mystika1]

OK...thanks!

 

MEP

Right Start

Singapore Math

Math in Focus

Miquon

Math Mammoth

BJU

CLE

Horizons Math

Rod and Staff

Saxon

[Spy Car]

I see two different things being mixed together. One is teaching "mental math" strategies and another is teaching towards conceptual understanding. While they may be inter-related and there might be some over-lap, I don't see them as synonymous terms.

 

Bill

[serendipitous journey]

I see two different things being mixed together. One is teaching "mental math" strategies and another is teaching towards conceptual understanding. While they may be inter-related and there might be some over-lap, I don't see them as synonymous terms.

 

Bill

 

:iagree:

Speaking of which: MathUSee. We use this as our primary math. It is seriously non-optimal on the mental math front. Conceptually I think we're doing well, but Button's a naturally conceptual guy.

[grace'smom]

:iagree:

Speaking of which: MathUSee. We use this as our primary math. It is seriously non-optimal on the mental math front. Conceptually I think we're doing well, but Button's a naturally conceptual guy.

 

Can you explain what you mean by it being non-optimal on mental math? We are doing Alpha in MUS and Math Mammoth 1a/b this year. My dd does mental math very well, but it might be because of the combination or perhaps because she did Rightstart last year...

[Mrs Twain]

If you want more mental math or other resources to help with conceptual understanding, you could add in math supplements rather than changing your entire math program. This is the route I prefer so as to keep consistency in the math program.

 

Supplements I like are Singapore's Mental Math and Challenging Word Problems workbooks, as well as MEP worksheets

[Beth in SW WA]

Supplements I like are Singapore's Mental Math and Challenging Word Problems workbooks,

 

:iagree:

[MeganW]

I see two different things being mixed together. One is teaching "mental math" strategies and another is teaching towards conceptual understanding. While they may be inter-related and there might be some over-lap, I don't see them as synonymous terms.

 

Bill

 

Can you expand on this thought?

[Spy Car]

Can you expand on this thought?

 

Well to give an example, in Singapore math mental math strategies are taught explicitly and supplement like the Fan Math Math Express books (and others) pile on more.

 

Because Singapore also aims to teach the conceptual understandings behind the re-groupings involved in these mental math strategies (although sometimes the math is more implicit than explicit) one can't call these "math tricks" but without some of the associated teaching being present they might qualify as "tricks" if the conceptual understand was not present.

 

Other math programs might teach the "conceptual" basis in a deeper fashion (Miquon for example gets into explicitly teaching the mathematical laws behind the operations much earlier than Singapore) but does not develop the same explicit teaching of "math strategies." this is not to say a child using Miquon might not intuitively develop his or her own mental math strategies (that may very well be the case, as they understand the mathematical reason that makes it possible) they are just not taught as explicit strategies.

 

I hope I'm being clear. No coffee yet :D

 

Bill

[TracyP]

In the same vein as Bill's post, I have a question. I don't think there is anybody who would argue that conceptual understanding is not important. OTOH, I really wonder about mental math strategies. I am pretty good at mental math so my POV may be skewed, but I wonder if kids shouldn't be allowed to learn their own strategies. My dh is also good at mental math but when we compare how we got our answers, his "strategy" was usually very different than mine. It has actually cause a couple arguments because we get frustrated trying to explain/understand how we came up with our answers. The gloves come off, the calculator comes out...:lol: Anyway, it makes me wonder if explicitly teaching a strategy is a good thing or could perhaps just cause frustration. Anyone have thoughts on this?

[Annic]

You can learn "mental math" by rote, and even memorize the strategies or steps and simply follow them.

 

Some programs that say they are conceptual give all the steps, and end up being procedural; the student does not have to do much conceptualizing. A lot of US programs or US-adapted programs seem to do this - lay out all the steps for the student, tell them or show them exactly what comes next, and then practice until they can do follow those steps. Programs that are online or "digital" tend to be like that, I think. Here's the problems, here is how to solve it, go forth and do some more. Though good math students will make the conceptual connection with most any math program. It is whether the student can solve problems he has not seen the same type and steps but cover the same principles or combine concepts in new ways that would determine if there is a conceptual understanding, I think. And whether he can make the next step on his own, maybe with a little help, if the next step really builds on previous understanding. That won't happen if he is immediately given it.

 

So what is a "conceptual" math program? Is it one that tells the student everything? Or one that makes him think for himself, building carefully on earlier ideas? A program that teaches mental math does not necessarily do that, or even just any program now that teaches how to use bar models, because they have become popular. Even those things can be reduced to steps, like some of the steps by step model drawing books I have seen. Possibly it is how a student responds, or how it is taught (by a parent or teacher, not by a book or online program) so maybe there is not a particular program.

[Spy Car]

In the same vein as Bill's post, I have a question. I don't think there is anybody who would argue that conceptual understanding is not important. OTOH, I really wonder about mental math strategies. I am pretty good at mental math so my POV may be skewed, but I wonder if kids shouldn't be allowed to learn their own strategies. My dh is also good at mental math but when we compare how we got our answers, his "strategy" was usually very different than mine. It has actually cause a couple arguments because we get frustrated trying to explain/understand how we came up with our answers. The gloves come off, the calculator comes out...:lol: Anyway, it makes me wonder if explicitly teaching a strategy is a good thing or could perhaps just cause frustration. Anyone have thoughts on this?

 

I think this is one of those areas where there are many valid answers, and will be somewhat a matter of individual responses.

 

For my part, I like teaching additional mental math strategies as a form of "play." The Math Express has been good for this. Some appeal more than other to me and my child. But it can be fun to look at "other ways" to solve mental math problems. We usually discuss what method were are using when doing mental math. I generally (unless we are working on an exercise to learn a particular strategy) leave the math strategy employed to my child's choice, although on occasion I will offer up an explanation for the way I would have solved the problem.

 

I guess that puts me in the camp that is in favor of teaching mental math strategies, at least with the child I've been given. If I had a child who was a "math-intuitive" I might take another approach.

 

Bill

[Spy Car]

You can learn "mental math" by rote, and even memorize the strategies or steps and simply follow them.

 

Some programs that say they are conceptual give all the steps, and end up being procedural; the student does not have to do much conceptualizing. A lot of US programs or US-adapted programs seem to do this - lay out all the steps for the student, tell them or show them exactly what comes next, and then practice until they can do follow those steps. Programs that are online or "digital" tend to be like that, I think. Here's the problems, here is how to solve it, go forth and do some more. Though good math students will make the conceptual connection with most any math program. It is whether the student can solve problems he has not seen the same type and steps but cover the same principles or combine concepts in new ways that would determine if there is a conceptual understanding, I think. And whether he can make the next step on his own, maybe with a little help, if the next step really builds on previous understanding. That won't happen if he is immediately given it.

 

So what is a "conceptual" math program? Is it one that tells the student everything? Or one that makes him think for himself, building carefully on earlier ideas? A program that teaches mental math does not necessarily do that, or even just any program now that teaches how to use bar models, because they have become popular. Even those things can be reduced to steps, like some of the steps by step model drawing books I have seen. Possibly it is how a student responds, or how it is taught (by a parent or teacher, not by a book or online program) so maybe there is not a particular program.

 

Right. It would be hypothetically possible to teach "mental math strategies" as almost simply procedural exercises. As "tricks" if you will. This is not the case, in my estimation, of the way Singapore teaches mental math, as the strategies are interwoven with teaching the concepts, but part of mental math is procedure.

 

There are reasonable grounds for debate methinks for how much connecting of the dots is best for any given child. I know in recent weeks I've read reasonable criticism of Singapore for being both "too spoon-fed" and being full of "conceptual leap" (not being incremental enough). For myself I find it is in a pretty good middle ground (but leaning towards the "spoon-fed") which is OK as I find it easier to add "challenge" than it would to replace the strong scaffolding of a math model of the sort Singapore builds.

 

There are always some trade-offs and we have to appreciate that children (and parent/child combos) that will have different styles and needs. It is pretty awesome how many great math recourses we have to close between.

 

Bill

[Annic]

http://oilf.blogspot.com/2011/11/on-edworld-double-speak.html

[boscopup]

In the same vein as Bill's post, I have a question. I don't think there is anybody who would argue that conceptual understanding is not important. OTOH, I really wonder about mental math strategies. I am pretty good at mental math so my POV may be skewed, but I wonder if kids shouldn't be allowed to learn their own strategies. My dh is also good at mental math but when we compare how we got our answers, his "strategy" was usually very different than mine. It has actually cause a couple arguments because we get frustrated trying to explain/understand how we came up with our answers. The gloves come off, the calculator comes out...:lol: Anyway, it makes me wonder if explicitly teaching a strategy is a good thing or could perhaps just cause frustration. Anyone have thoughts on this?

 

I posted a thread on this a while back. :)

 

Now that I have Singapore in my hands (level 4A), I can see how it encourages, at least at this level, to have kids tell you what strategy to do, and then suggest other strategies that would also work. I think that would have been better for my son than the MM route where it tells you which strategies to use for a set of exercises, practicing the various strategies. Singapore may also do that somewhat also in the early grades (I think I recall some IP work with specific strategies). I haven't seen the HIGs in the early grades.

 

So basically, I think some kids NEED to be taught strategies. They don't figure them out on their own. Others think of their own, but maybe could use some better strategies or alternate ones to think about. For my own son, I think more practice of mental math without specific strategies mentioned would be a good idea. I just scanned in the mental math pages from the appendix of my 4A HIG, and I'll plan to use those periodically to work on mental math. We'll also discuss how he gets the answer, how I got the answer, other methods we could use to get the answer. I think the way it was done in MM ended up being a bit more procedural, and that hampered my son's mental math abilities. That won't happen with every kid though. :) I think it's a bit like the kid with great artistic ability being hampered by an art program like Draw Write Now (which is an excellent program) because of the step-by-step explanations. They sometimes lose their natural ability by going step-by-step that way. Most kids aren't going to lose their artistic ability by using DWN, and most kids aren't going to lose their mental math ability by using MM. In fact, for both programs, many kids will probably gain abilities using those programs (DWN certainly increased my son's artistic ability... I need to pull it out again as he's reverting back to stick figures).

[Spy Car]

http://oilf.blogspot.com/2011/11/on-edworld-double-speak.html

 

This is a very shallow and reactionary way of looking at education. While I will admit to sharing a disdain for "educational theories" that remove a sound grounding in the subjects of study in the name of airy-fairy buzz-words, the alternative should not be a retreat to "procedure only" education.

 

There is an alternative to both these bad choices, and the author of this blog post (as happens so often) completely misses that truth. One can teach for deep understanding and a mastery of computational skill. These things are not inherent antagonists. There is a Third Way between to very bad alternatives.

 

Bill

[anabelneri]

http://oilf.blogspot.com/2011/11/on-edworld-double-speak.html

 

I think this might apply to some degree, but I see a big difference in a group of parents discussing curricula that they've actually used and the labeling used by the professional educators. I agree with that post in particular when I'm trying to choose material marketed for the school folks, but discussions on the Hive are different.

 

I see a difference between mental-math and conceptual understanding, and I think it's useful to have a ranked list of both of those groups. When Sweetie was struggling with subtraction with regrouping, I had to look far and wide to find mental-math options. Our primary curriculum was MEP, which only teaches mental 2-digit subtraction in Year 2. Most other programs that I looked at, including the regular Singapore books and Math Mammoth, taught the written algorithm first. Also, most "living math books" that I was able to find which taught 2-digit subtraction were written-algorithm focused. Right Start taught the mental version, and the Fan Math books from Singapore were helpful.

 

So, of all those, Singapore, Math Mammoth, and Right Start are all talked about as being conceptual, Asian-style math. But they're still different from one another in their emphasis on mental math.

 

I would love to see some of the other math programs added to the list. Teaching Textbooks? Professor B? CIMT?

 

:)

[TracyP]

I posted a thread on this a while back. :)

 

 

Thanks, I missed that one. I found this quote by you on that thread

Perhaps I shouldn't have focused much on strategies, but just practiced using mental math without giving him a strategy unless he was stuck. :confused:

This is exactly what I was thinking. This and just letting it be more conversational. It is a really interesting window into their little brains to talk to them about how they came up with the answer. I guess it is something that just needs to be tailored to the kid...like everything.:D

[Spy Car]

Thanks, I missed that one. I found this quote by you on that thread

 

This is exactly what I was thinking. This and just letting it be more conversational. It is a really interesting window into their little brains to talk to them about how they came up with the answer. I guess it is something that just needs to be tailored to the kid...like everything.:D

 

Talking the mental problem solving through is the key. Listening to how the child is reasoning is indeed "a really interesting window into their little brains."

 

It makes all the difference in the world in making you aware of your child's understanding and it keeps these exercises fun and conversational. And you can see what kind of quirky methods they come up with. There were moments when my child started re-grouping to "Elevens" instead of "Tens," which was a good clue for me that he was ready to move on from "making Tens" practice (:D) and other times where he tried out a making "negative numbers" strategy.

 

In any case "discussion" gives one a window into the child's understanding.

 

Bill

[Crimson Wife]

Some programs that say they are conceptual give all the steps, and end up being procedural; the student does not have to do much conceptualizing. A lot of US programs or US-adapted programs seem to do this - lay out all the steps for the student, tell them or show them exactly what comes next, and then practice until they can do follow those steps. Programs that are online or "digital" tend to be like that, I think. Here's the problems, here is how to solve it, go forth and do some more. Though good math students will make the conceptual connection with most any math program. It is whether the student can solve problems he has not seen the same type and steps but cover the same principles or combine concepts in new ways that would determine if there is a conceptual understanding, I think. And whether he can make the next step on his own, maybe with a little help, if the next step really builds on previous understanding. That won't happen if he is immediately given it.

 

An incremental program isn't necessarily procedural. Conceptual programs teach the "why" rather than just the "how". Some kids are intuitively "mathy" and can make the leap from point A to point D without being explicitly being told about points B & C along the way. Other kids need a more step-by-step-by-step explanation. That doesn't mean that that those kids will wind up with a lesser conceptual understanding in the end.

 

Frankly, it strikes me as a bit of intellectual snobbery to say that the kids who don't intuitively make those leaps have a lesser conceptual understanding as a result. If anything, they may be BETTER able to explain the why's in math than an intuitively "mathy" kid because they don't just "get" it. I get so frustrated when my DH (who is mathy) tells me the answer to a tricky Singapore Intensive Practice problem but can't explain why it is correct. "It just is" isn't very helpful :glare:

[justLisa]

I posted a thread on this a while back. :)

 

Now that I have Singapore in my hands (level 4A), I can see how it encourages, at least at this level, to have kids tell you what strategy to do, and then suggest other strategies that would also work. I think that would have been better for my son than the MM route where it tells you which strategies to use for a set of exercises, practicing the various strategies. Singapore may also do that somewhat also in the early grades (I think I recall some IP work with specific strategies). I haven't seen the HIGs in the early grades.

 

So basically, I think some kids NEED to be taught strategies. They don't figure them out on their own. Others think of their own, but maybe could use some better strategies or alternate ones to think about. For my own son, I think more practice of mental math without specific strategies mentioned would be a good idea. I just scanned in the mental math pages from the appendix of my 4A HIG, and I'll plan to use those periodically to work on mental math. We'll also discuss how he gets the answer, how I got the answer, other methods we could use to get the answer. I think the way it was done in MM ended up being a bit more procedural, and that hampered my son's mental math abilities. That won't happen with every kid though. :) I think it's a bit like the kid with great artistic ability being hampered by an art program like Draw Write Now (which is an excellent program) because of the step-by-step explanations. They sometimes lose their natural ability by going step-by-step that way. Most kids aren't going to lose their artistic ability by using DWN, and most kids aren't going to lose their mental math ability by using MM. In fact, for both programs, many kids will probably gain abilities using those programs (DWN certainly increased my son's artistic ability... I need to pull it out again as he's reverting back to stick figures).

 

DS LOVES Ed Emberley's drawing books. he likes to draw stick figures because he does not wish to draw creative/life like, just wants to get the point across!

 

*I* prefer SM, however DS cannot get past the character like quality of it, and DH is the same way. Those silly boys! It drives him nuts to have birthday cakes around problems, or any picture that is not specifically aligned with the work. MM has too many steps to things but we skip some things. I also use the worksheet maker sometimes instead if the page is too busy. We like to teach one way of doing it, until it is very solidified, THEN teach additional strategies. This seems to work better for DS than giving him 3 ways to do something at once.

[MeganW]

I sort of understand the difference, thanks for explaining.

 

I am naturally mathy, and mental math strategies are something that I came up with as a child. I assumed everyone did that, until it started being discussed on this forum and I asked my DH, and he acted like I was crazy when I started describing some of my shortcuts.

 

My brain is tired from trying to follow you intellectual types! Would I be a total loser to just throw my hands up on really understanding what makes different programs better or worse, and follow the leaders' curriculum choices (as I know they have fully researched & tried out all this stuff)? :) At the moment, we have RS & Miquon going, and MEP every now and then. I think I am giving up on reading every math thread and trying to wrap my brain around it all, and just moving forward using the curriculum as intended and calling it good enough!

[ondreeuh]

You're putting Saxon at the bottom?

 

I was surprised at the amount of mental math that Saxon includes. My son is doing 54, and there is a box with mental math strategies and practice at the beginning of each lesson. Things like "When subtracting change, it's helpful to break down $1.00 into 9 dimes and 10 pennies. So to subtract $0.37, take 3 dimes away from 9, and 7 pennies away from 10. Then you have $0.63 as your answer."

 

I can't judge the whole Saxon program because my son has only done a bit of it, but I'm not sure it deserves the reputation it has as solely drill & kill. I see a lot of mental math and explanation of concepts.

[mystika1]

You're putting Saxon at the bottom?

 

 

Hi,

I just want to say that I am not cutting down any curriculum. The order that I put these in was based on reading many..many...many math threads here over the last couple of years. I have wanted to make a list of curriculum choices in order from most to least mental math teaching for a long time as it would help me when I need to change things up a bit. Saxon has been around for a long time and works wonderfully for the families that use it. I put the list here so that others could help me place everything in order correctly. It's certainly not my intention to cause problems.

 

Sincerely,

 

Penny

Edited November 22, 2011 by mystika1

[serendipitous journey]

Can you explain what you mean by it being non-optimal on mental math? We are doing Alpha in MUS and Math Mammoth 1a/b this year. My dd does mental math very well' date=' but it might be because of the combination or perhaps because she did Rightstart last year...[/quote']

 

I only just saw this ...

 

Button did mental math very well indeed until we hit the need for regrouping. He could solve many regrouping (addition) problems very well mentally, but we worked on regrouping techniques (carrying, etc; what I think of as "accounting") in order to master the numerically larger examples and he just switched skills, and started mentally adding in the same way as he adds for regrouping. This killed his quick facility with numbers. Partly this is because he's accelerated, and hit regrouping when he was four or five. There are many reasons we were doing MUS in an accelerated way: this is a child who went stir-crazy without structured activity, loves numbers and symbols, wouldn't do arts & crafts w/o being forced to, and didn't like being read to (who knows why?). Singapore wasn't an option b/c he was distracted by complicated pages.

 

Naturally I should have done this differently :). If I go this route with Bot-bot, I'll drill him in the mental stuff each day in a separate session. And for Button I've explicitly re-taught techniques for dealing with big numbers in one's head as opposed to on paper.

 

But there's nothing in MUS that has Button recouping those skills. Singapore, on the other hand, calls for increasing levels of mental computation and (from what I've seen) really works to consistently up their mental math skills. I tried supplementing MUS with Singapore, but he started hating math; maybe 'cause I got the level too low. We've added in Primary Grade Challenge Math (Zaccaro), Life of Fred, and some living math books; and I plan to incorporate more verbal mental math into his days to build skills, and maybe try a higher level of Singapore.

 

hope this helps! For many reasons MUS is a good fit for us overall, but there are bits that need tweaking. Imagine that ... ;)

[letsplaymath]

... When Sweetie was struggling with subtraction with regrouping, I had to look far and wide to find mental-math options. Our primary curriculum was MEP, which only teaches mental 2-digit subtraction in Year 2. Most other programs that I looked at, including the regular Singapore books and Math Mammoth, taught the written algorithm first. ...

 

Actually, the entire 1st grade year of Singapore Primary Math is mental math, including subtraction within 100. The written algorithms aren't taught until second grade, and my son was very resistant to learning them, because he was so comfortable with the mental math. He didn't see any point in writing things down.

 

I think the distinction between mental math and conceptual understanding is important. Mental math can be taught by rote, as a "performing monkey" trick. But it can also be used to deepen the child's understanding of place value and other patterns built into our number system -- it depends on your approach. If you keep in mind the goal of knowing HOW to do math and also knowing WHY it works, then you will move toward a conceptual understanding no matter which math program you use. You won't be satisfied with just learning tricks.

 

One of my favorite things to do is to compare mental math techniques, as Spy Car and others have mentioned. I think, when we do that, I learn even more than the student, because I get to see things from a direction I would never have thought of myself. I wrote a blog post giving examples. It was one of my favorite blog posts, and I keep thinking I should write some more like it:

Mental Math: Addition

[Spy Car]

Actually, the entire 1st grade year of Singapore Primary Math is mental math, including subtraction within 100. The written algorithms aren't taught until second grade, and my son was very resistant to learning them, because he was so comfortable with the mental math. He didn't see any point in writing things down.

 

Right. The mental math is taught thoroughly first. My son was also initially resistant to the written standard algorithms (since the mental math skills were so strong) but when you throw-in a few extra digits into the problems they take the point that learning both is necessary.

 

I think the distinction between mental math and conceptual understanding is important. Mental math can be taught by rote, as a "performing monkey" trick. But it can also be used to deepen the child's understanding of place value and other patterns built into our number system -- it depends on your approach. If you keep in mind the goal of knowing HOW to do math and also knowing WHY it works, then you will move toward a conceptual understanding no matter which math program you use. You won't be satisfied with just learning tricks.

 

:iagree:

 

Very well said!

 

One of my favorite things to do is to compare mental math techniques, as Spy Car and others have mentioned. I think, when we do that, I learn even more than the student, because I get to see things from a direction I would never have thought of myself. I wrote a blog post giving examples. It was one of my favorite blog posts, and I keep thinking I should write some more like it:

Mental Math: Addition

 

I am really enjoying your contributions to this forum and your great blog!

 

Bill

[anabelneri]

Actually, the entire 1st grade year of Singapore Primary Math is mental math, including subtraction within 100. The written algorithms aren't taught until second grade, and my son was very resistant to learning them, because he was so comfortable with the mental math. He didn't see any point in writing things down.

 

Huh. That's interesting. Because we did do the 1st grade Singapore books, and that's when Sweetie started counting on her fingers or making tallies on her pages to count up or down. Which is why we switched to Right Start, and then to MEP. I see that they were teaching mental math, but somehow Singapore's style didn't do the same thing for her the way the others did. Now I'm curious to go back and look at how it was being taught and see if I can glean more info about my dd's learning style...

 

Thanks!

:)

[jenbrdsly]

Hi,

I want to make a list of math programs in order of their conceptual teaching. I think most people place Singapore Math on top as far as conceptual teaching(mental math) goes followed by Math Mammoth. Can you guys help me by putting the following programs in order of most conceptual to least?

I am thinking it would be something on the lines of...

MEP

Singapore Math

Miquon

Math Mammoth

BJU

CLE

Horizons Math

Rod and Staff

Saxon

 

If I am forgetting something please add to it. I am thinking of making a switch once my dd completes her MM books. She really needs something more spiral and although I have been doing a rotation of the topical books to make it spiral... I feel that I am covering some topics more than others. I would like something better organized. I may end up doing MM and something else because I like the mental math work.

 

Thanks,

Penny

 

 

I think it would also good to add in some public school curriculum into the list. Where would Everyday Math go, for example? I think that Dale Seymour Investigations would go near the top, and Houghton Mifflin Math Expressions would go in the middle. Can anyone help?

[nmoira]

Actually, the entire 1st grade year of Singapore Primary Math is mental math, including subtraction within 100. The written algorithms aren't taught until second grade, and my son was very resistant to learning them, because he was so comfortable with the mental math. He didn't see any point in writing things down.

MEP doesn't introduce pen-and-paper algorithms until Y3 (technically second grade in the UK, but comparable to third grade math in North America).

 

I think the distinction between mental math and conceptual understanding is important. Mental math can be taught by rote, as a "performing monkey" trick. But it can also be used to deepen the child's understanding of place value and other patterns built into our number system -- it depends on your approach. If you keep in mind the goal of knowing HOW to do math and also knowing WHY it works, then you will move toward a conceptual understanding no matter which math program you use. You won't be satisfied with just learning tricks.

Yes, it's the difference between using "add the 10s then add the units" and "making 10" techniques by rote (and they will work *every* time) and applying the same underlying techniques to other situations; for example, seeing that 48+37 is the same as 50+35 and 81-38 is the same as 80-37.