How do you know to use spiral or mastery for math?

[LAmom]

There are a lot of posts on spiral vs mastery. Looks like which approach to use depends on learning style for each child. So how can I tell? I have a 3rd grader and should know what may work best. She uses MM but sometimes I think she would do better with CLE. What questions does one ask or what do you evaluate to determine what would work best?

 

DD is easily bored and slow with her math. She kind of gets the mental math part (so different from how I learned math). How do I know she wouldn't be bored and slow with CLE? Trial and error?

 

Thanks.

[imagine.more]

Personally I'm not a super mathy person but I had a few math major friends in college and they all outright mocked the spiral methods, particularly Saxon. They said the spiral methods just didn't prepare students for higher level math. Then I got a job teaching Kinder-First grade in a school that used Saxon and oh dear, it was a mess. None of the 5th-6th graders in that school knew any of their multiplication or addition tables so they were constantly counting on fingers and using 'tricks' to figure things out. And they didn't seem to even have a strong grasp of how math and numbers work either, as in the concepts behind the memorized facts. The test scores proved it too, ouch! The teacher next door and I ended up adding in a lot of extra practice for our students that year to make sure they knew their math facts and 2 years later the school met AYP for the first time in 5 years.

[Veritaserum]

Trial and error. :) Also, there are extremes: extreme spiral (Saxon) and extreme mastery (Math U See). CLE is spiral, but it doesn't review every thing the child has ever learned. The review is more of a way to keep skills/concepts fresh. Math Mammoth is mastery, but it doesn't do the same concept for the whole year. Each chapter has a focused concept/skill. There are also cumulative reviews because periodic review helps you remember what you learned before.

 

I have kids using CLE and another using MM, depending on what suits their needs and learning styles. :)

[Ellie]

I don't think spiral vs mastery is all that important. I just don't.

 

Sometimes you just have to pick something and stick with it.

[Crimson Wife]

Does your child prefer to do a whole chapter (or year in the case of Math-U-See) on a single topic or a mix of topics in each lesson?

[Spy Car]

I think it is (in the main) the wrong question.

 

The better questions are:

 

1) Does the program promote a deep understanding of mathematical reasoning? If so, the inter-relatedness of mathematical operations will be appearent and comprehensible to children.

 

2) Are the topics taught in such a way that the laws of mathematics (either explicity or implicitly) are made comprehensible to children?

 

3) Is the program promoting critical thinking and logical reasoning as part of it's approach?

 

4) Are there problem solving opportunities that provoke thought and interest, or is the learning only procedural and at a low level of cognition?

 

5) Does the program promote multi-step problem solving or just single step problem solving?

 

6) Does the program begin to develop the skills necessary for algebraic thinking early-on and in age appropriate ways?

 

7) Does the program build mental math skills in addition to developing procedural competence via use of the standard algorithms (like column addition, subtraction, multiplication, and long-division).

 

8) Does the program have a sophisticated method for teaching word-problem solving skills?

 

When one answers these types of questions satisfactorily then one can ask about how topics are dealt with on a mastery vs spiral basis.

 

If the math is taught as mathematics (and not just arithmetic) and it is done so on a deep level, much of the mastery vs spiral argument vanishes (since all the basic operations of elementary mathematics are inter-related). Only when math is taught purely as procedures and without understanding does the mastery vs spiral issue become a big deal because then one is concerned about whether or not the child is going to remember the procedures (that if followed will lead to a "right answer" when numbers are plugged into a provided formula, but may not represent genuine understanding vs understanding the actual mathematics and being able to use ones knowledge whether one is dealing with time, or measurement, or capacity, or any other sub-topic.

 

At the end of the day some children may benefit from more review than others. But this question is only one small part of the bigger picture.

 

Bill

Edited September 22, 2011 by Spy Car

[RootAnn]

In the bigger picture, not just dealing with math, I can tell my kids do best with spiral programs because:

1) If I don't repeat something (new) every day for a couple of days at least, they forget it.

2) If I don't repeat something that they "know, but which isn't in their permanent memory yet, at least once per week, they forget.

3) Let's say I've given them weekly review for three months. If they show they can remember it like that, I switch to once per month. If I don't review it once per month, it is GONE.

 

It doesn't matter if it is in history, math, science, poetry, spelling, or something as basic as the colors of the rainbow or which colors mix to make other colors (yellow & blue make green). My kids need the constant review. If they are reviewing it themselves as part of what they are already doing (spelling a word when they are writing, reading a historical fiction book, reciting a poem for fun with their siblings, using paint to mix colors, etc.), they remember (as long as the intervals, above, aren't missed). If it is something that doesn't come up often in what they normally do and I don't review it with them, they lose it.

 

I don't know if it is something they will grow out of or not. I just know that a "mastery" program (math, science, history) doesn't work for my kids at their current ages unless I build the spiral stuff in.

 

For example, each SOTW book is "mastery," in general. If you use the cards in the Activity Guide, you can make it more spiral for kids like mine. Or, you can get the audio & let them listen to the whole thing for review at certain time intervals.

 

I know some kids who would feel completely insulted if you repeated things as often as I do with my kids. "Duh, Mom, I got it the first time!"

[songsparrow]

I know some kids who would feel completely insulted if you repeated things as often as I do with my kids. "Duh, Mom, I got it the first time!"

 

This was my daughter's frustration with the spiraling curriculum she did at her school - she was offended by the review of things they had done a year ago, and would say "it's like my teacher doesn't think I learned it when they taught it last year!". She hates reviewing things she already "knows." That was the primary reason I chose a mastery curriculum. If we come to a concept she's forgotten, she doesn't mind a review.

[justasque]

I think it is (in the main) the wrong question.

The better questions are:...

 

Brilliant post. Yes, yes, yes.

[regentrude]

I agree with SpyCar.

but on the topic of spiral vs mastery:

 

we could tell that spiral was not working because the kid got extremely frustrated when the concept was introduced in tiny increments and the next lessons switched to something completely unrelated. They both prefered to explore ONE topic comprehensively, master it, and only then move on to the next thing. The constant jumping between topics and the never going into depth in one sitting drove them nuts. (We switched to a mastery based program with a discovery approach and they are happy)

 

Now, some other students may prefer a variety of practice problems and may prefer to be introduced to a new concept in very small steps, practice the steps, work on some different topic, and then learn the next little thing.

 

Through observing your DD you should be able to discern her preference.

[LAmom]

Good stuff. Thanks for the help. The bottom line is I can't look at a program and answer half the questions Spy Car mentioned. They are excellent things to ask and look at, but some things are hard to determine with my non-math brain. You know? I also can't tell if Saxon or MM will help my student to excel in high school and onward. Or if CLE and Singapore will do the opposite. Or if it really just depends on the learner. Seems like some people just excel at math, some get through it and are OK and some just are terrible. Does it have to do with the learning only? It seems that it would vary for individuals. I know many who have used Saxon and some are terrible at math and some are excellent. I am sure the same can be said for CLE or MM, etc. I don't think necessarily one program is better than the other. I just think it depends on how your student learns and what method works best. I know that already in using MM that the way my daughter is being taught makes sense and I love learning the methods along with her. Fascinating. But this doesn't convince me that a solid program like CLE would cause one to struggle with math or not do well with math facts, etc.

 

Do I even make sense? I don't really know what I am talking about...:tongue_smilie: Just couldn't figure out how some know that dd 1 needs spiral and dd 2 needs mastery, etc. I can't tell and my daughter is in 3rd grade.

 

Anyways, thanks for the input. :001_smile:

[acurtis75]

I have only used two math programs with my dd6 so I can't really speak to the spiral issue. I can tell you that with mathusee there is an emphasis on being making sure facts are memorized and higher math concepts are introduced in a gentle non-threatening way very early. i.e. when learning addition facts there were "mystery number" problems that were basic algebra like x+5 = 8. You can move as fast or as slow as your child needs and it seems to work well with different learning styles since you have the video, manipulatives & worksheets. I also like the fact that the goal is to make sure the child can do problems on paper or in their head and understand "when" to add/multiply, etc with the use of creative word problems. I've looked at several other programs but I know 5 families using mathusee with different age children and all are happy with it.

[acurtis75]

One additional thought...I was a great math student in school but it's not my daughter's strong suit. One of the things I like best about mathusee (we have completed Alpha & Beta & are almost done with Gamma) is that it teaches students to really think about the problems correctly. I see that she is really "getting it" and understanding why problems are done a certain way. There were things about math that I just understood on my own that I recognized my siblings couldn't get...the mathusee explains things in such a way that even if you're not mathmatically inclined you can still get it.

[smillard00]

We've used Math U See from the beginning and, as a trained math teacher, I really appreciated the mastery approach while still having review of concepts already covered (mastered), mental math, and mathematical thinking in word problems. I also appreciated the use of manipulatives when introducing new concepts before going to the more abstract written methods. A few years ago, my oldest went to a private school for a year and my other two went to the school for two years. We noticed several things. My 3rd grader and 6th grader were studying the same topics in their math classes many times during the year they were both there. This was really disturbing to their little homeschooled minds. :D They both did their homework, studied for tests, made As on their report cards. Success, right? Since they've been back home and have resumed MUS, we've had to go back to the books they would have done during those years they were in school and have had to master those concepts. Some things they remembered from their time in school, but many things they just learned for the test, but didn't have the opportunity to master. We worked very hard and went through the books as fast as we dared to get them back to the level where they would have been had we not had our little "school" adventure.

 

What I got from the experience: I feel more comfortable than ever with the mastery approach that we have through MUS. I appreciate the concrete understanding they get through the manipulatives. I make sure they take the review problems seriously and really learn to think through the word problems. Now that my son is in upper level math, we spend time on the honors problems--great critical thinking opportunities there! I'm not comfortable with a spiral approach for my kids because I think it encouraged them to learn things on a shallow level in order to pass the test, but they weren't forced to master it before moving on. Instead, the curriculum was designed to touch on a topic and move on. Touch on a topic and move on. again and again.

 

I don't think there is as much boredom as one would expect from spending a whole year on an area of math. It isn't like you work the same kind of problem for 180 days. Each lesson is a new aspect of that area or operation. There are little lessons on things like measurement or geometry sprinkled in for variety. He keeps things moving.

 

And I find that this sort of learning finds its way into many of our other subjects too. We spend an entire year on a period of history. It is reviewed when we encounter the time period in other books we read or movies we watch or discussions we have. They are constantly seeing connections. In Latin, we master one verb tense or noun declension at a time before we move on. In spelling we master a spelling rule before moving on. It seems to be working for us.

[kalanamak]

Math is really one of the big points I hs over. Some topics he just "gets" and is very unhappy about drill, drill, drill in it. Others seem to just whiz over his head and I have to spiral back. Still others befuddle him (clocks .... I was getting bug-eyed over clocks) and I tried this approach and that approach, and spiraled back, and la de dah de dah, until one day it just hit.

 

So, this is why I like the lean spine of SM: easy to hoist, and it is clear right away if he isn't getting something. Then you come here and start asking.

 

HTH:001_smile:

[boscopup]

I don't think it matters for MOST kids. There are some kids that need daily review of a topic in order to remember anything about it, but I do wonder if those kids understood the concept in the first place if they're needing to review it so frequently (or if there's a working memory problem for the child, that would explain it also). For example, if you've learned subtraction with regrouping, and then you move on to long division, subtraction shouldn't fall out of the student's head. They are doing it when they do long division. So I don't think you would normally need constant review of that topic. The review is embedded in the math you're doing everyday. Topics like clocks, measurements, geometry - those I can see needing more review, but they're taught every single year, so I imagine it'd probably sink in eventually also.

 

I use MM, which does topic by topic. My son came from a school that used Saxon. The incremental nature of Saxon bored ME to death just looking at the homework pages coming home. They were the same, day to day, except one problem would be slightly changed. It also included concepts for review that should have been mastered before moving on to the other concepts presented. The example I usually use here is that they had a page of addition and subtraction facts come home, but then on the other homework sheet (with the 5-6ish problems on it), they had "Color 6 blocks red. How many blocks are not colored?" If the kids haven't nailed that concept, why are they even doing a fact sheet? Do they really need to review "color 6 blocks red" in 1st grade while doing a whole sheet of math facts? And this was every single day that they'd have a problem like this! Way overkill. The kids that need review of that concept probably shouldn't be doing the math facts sheet yet, because they're just memorizing by rote with no understanding.

 

In MM, we do a whole concept, then we review everything we've learned that year at the end of each chapter. If you want to throw in more review of the non-arithmetic subjects (time, measurement, money, geometry), you can always stick those in anywhere you choose. They are not dependent on the other chapters. You could do a problem a day from each of those chapters if you wanted to. MM also throws review in via the word problems. If you're doing double digit subtraction with regrouping, it may throw in some double digit addition with regrouping in the word problems. They aren't all on the topic just learned. ;)

 

I think my son would do fine with MM or CLE. I use MM because it's easier to accelerate (that's what he needs), though you CAN accelerate CLE. My friend started her 3rd grade daughter mid-year last year in CLE 2 and did 2 lessons a day, crossing out the review problems she knew her daughter didn't need. This year in 4th grade, her daughter has had a jump in math abilities (confidence of using CLE helped a lot!), and they'll probably skip into CLE 4 soon, as she learned long division in a day on the white board (completely shocking her mother, I think :lol: ).

 

Saxon is incremental, so it's an extreme version of spiral. If we had continued with Saxon, I think it would have killed my son's love of math. It was just TOO much review at such a low level that was totally unnecessary.

 

Oh, and the best way that I was able to figure out how my son learns? He learns like ME, so I looked at what I'd like to do. :tongue_smilie: My middle son may learn differently, but he's been fine with Singapore Essential Math K so far, and I'll go ahead and use MM with him also. If I find that he struggles to remember concepts day to day, CLE would be my 2nd choice. I prefer MM for the conceptual teaching. CLE has *some*, but not to the degree that MM does. I like CLE and think it's a solid program. If I used it, I'd probably add in the conceptual stuff myself (from MM).

 

Really though, if your child is doing fine with the math you're using, then it's the right math for that child. If your child isn't in tears over MM or failing every chapter test, I don't see any reason to look at CLE. Use what you have. Switching math programs in 3rd grade can get you behind if you aren't careful. I've looked at Singapore, as my oldest would probably enjoy it more (presentation wise), but we're over halfway through the MM series. We're just going to finish the series and move on to prealgebra in another text. If you have something that works in the elementary years, don't change! Keep going through 6th grade, then you can use something else for the higher levels (where changing books each year doesn't matter).

[Alessandra]

The better questions are....

If the math is taught as mathematics....

Bill

 

Wonderful, wonderful post!

[happycc]

I have one child who might be mastery. Once she gets it she usually gets it.

Another child needs the spiral a bit. I would introduce a concept and that concept would need to be covered for several weeks. Next day I would introduce another concept and the first stay stuff would need to be reviewed as well as the 2nd. The third day would have one or two problems of the first day as well as a new concept. The fourth day would have day1 stuff, day 2 and day 3 as well as day four . Each day I would add another concept and wrapping the older stuff around and around like that. I think it takes that child perhaps a month of a topic before I drop it completely but then again it would need to be addressed again the following review. It would be nice if they could also start applying the old concepts into the newer problems. Now what kind of curriculum is that spiral vs mastery or an intense spiral or what?

 

Is there a spectrum of spiral curriculums?

 

 

Now third child needs review review review review of concepts for everyday for months and years.

 

Any math curriculum like that? I think even Saxon might even go too fast for her. We are using Rightstart and I have had to slow that WAY down and add in more reviews.

 

I feel nuts having to accomodate the different needs of the children and then having to find a curriculum that may not exist and still have to use multiple resources and tweak stuff.

[Hedgehog]

In the bigger picture, not just dealing with math, I can tell my kids do best with spiral programs because:

1) If I don't repeat something (new) every day for a couple of days at least, they forget it.

2) If I don't repeat something that they "know, but which isn't in their permanent memory yet, at least once per week, they forget.

3) Let's say I've given them weekly review for three months. If they show they can remember it like that, I switch to once per month. If I don't review it once per month, it is GONE.

 

It doesn't matter if it is in history, math, science, poetry, spelling, or something as basic as the colors of the rainbow or which colors mix to make other colors (yellow & blue make green). My kids need the constant review. If they are reviewing it themselves as part of what they are already doing (spelling a word when they are writing, reading a historical fiction book, reciting a poem for fun with their siblings, using paint to mix colors, etc.), they remember (as long as the intervals, above, aren't missed). If it is something that doesn't come up often in what they normally do and I don't review it with them, they lose it.

 

I don't know if it is something they will grow out of or not. I just know that a "mastery" program (math, science, history) doesn't work for my kids at their current ages unless I build the spiral stuff in.

 

.

 

This is so my dc. Daily reminders needed.. and not just in schoolwork.. :glare: