Math musings...is there value in doing all of the problems on the page.

[5LittleMonkeys]

I have a question and I'm going to try to word it as susinctly as possible...I'm on pain meds for my wrists so bare with me.

 

I have read many times in math threads the advice to just do enough problems to make sure the dc has the concept down and then move on. My question is ... isn't there value in doing more problems than just those that show they understand how to do the problem?

 

I've not used a lot of different math programs so I can't say that there may be some out there that do indeed have a ridiculous amount of practice problems. I'm using MM right now with dd8, and while I'll admit that there are a lot of problems on the page I usually make dd do all of them in one way, shape or form. Orally, written, me as the scribe, on the white board, etc. Especially in the early years, isn't practicing over and over and over again what cements these number bonds and facts into their minds? I believe that if I had only had her do half the problems she would not be as good at math as she is now, but is that just my dc or is that probably true for most dc? (I'm not talking about those exceptions who are superbly gifted.)

 

I'm having to go back with dd13 right now and review rounding of all things! I sat and tried to think back from the last two years on when we have gone over rounding and I realized that we always just discussed it whenever it came up in her work, I'd show her a few examples, she'd do a couple (maybe 5) problems and then we would move on. I thought it was a pretty simple concept and she seems to have a head for math so why bother with pages of practice? Well, since I'm having to go over it again, I have to wonder if a couple pages of practice might not have cemented it into her mind and I wouldn't have to be teaching it to her again.

 

Anyway, I'm not saying I'm right...I'm just musing about it and wondering what others may think.

Edited April 1, 2011 by 5LittleMonkeys

[Wee Pip]

I fell into the "homeschoolers don't have to do every problem" trap. I also fell into the "just knowing how to do the math conceptually is good enough" trap:) Now my kids are behind! I read the Math chapter from The Core (Leigh Bortins), and that's what changed my mind. I also heard the word "Overlearning" quite a bit, and it sounds like a good idea. It doesn't hurt to get really good at something, to the point that it is easy and automatic. Ultimately, I'd like math to be easy for my kids (not painfully difficult, slow, and confusing like it is now). The only way to get there is practice. I still think conceptual learning is really important. But add practice and automaticity, and then you'll have a student that understands his math, and can work problems without difficulty. We are doing math radically different now.

[ElaineJ]

I think it depends on your student and your math curriculum. When I was homeschooled from 3rd through 5th grade, my parents were using A Beka (one of the few available materials back in the pioneer days of home education) and the number of problems per page was....well, it felt infinite! I decided I hated math, and when I had my own children promised not to do the same thing to them. (My parents are wonderful people and excellent teachers, by the way. This is not intended as a slam on them). At the same time, you don't want to fall into the opposite trap of giving too little practice of core skills. I assign my daughter all of the problems in her Math U See and my son all of the problems in his Singapore math and give extra practice and add in one minute math drills to speed computation skills. That seems to work for us and they don't feel like they are spending all day doing math.

 

ElaineJ

[johnandtinagilbert]

I've learned it depends on the "page," but more than that, on the child's speed and need for practice. If the Ax Man has scored 100% on the last 5 pages of addition of 4 digit numbers and suddenly there are 20 problems of....4 digit numbers, no, I don't think he needs to do all 20 problems (he's in 3rd grade); if however, he's been scoring 80's over the past 5 pages, then yes, he's doing all 20.

 

In the older years, I'm finding math is about an allotted time more than a number of problems. Some weeks of Alg. 2 that means 4 problems per day.

 

So, I prefer to stay out of traps and stick with, "What best serves THIS child?"

 

If I were working through a program that had 40+ problems on one page, then I would surely say, "Do the evens."

 

Your point about your dd has been observed here, too. A little practice is always in order, well mostly always. That general "stick it in but don't practice" hasn't proven a good idea over here at all.

[jennynd]

I don't know if I will agree that do 5 problem and move on approach. but I also don't agree do pages and pages worksheet each topic. because it is just gonna become robotic at the end, I don't know how much of the proficient will be truly from understanding

DS is one of those fly though math kid. I still have a half page review sheet right now consist 1 multiple (three digit by 2 with decimals), 1 division (4 digit divided by 2 digit with decimal) and about 4 faction question (mix fraction operation +,_,x,/), and 2 words problem. those are the standard question, even he knew the concept, I feel he need to be "fluent" on it. I also have maybe 4 question from topic he just went through. it usually take him 10 mins to go through all. I feel it works better especially he is on a fast track program already.

[Joyofsixreboot]

Depends on the kid. My 15 yo and now my 7 yo seemed to be born knowing math facts. They look at the page, rattle them off and so I see no reason to subject them to pages of practice. The 10 yo still can't remember his address half the time. He practices and practices and practices his math facts.

[ChrissySC]

Someone mentioned "robotic" to describe completing numerous problems sets. I would have to say that is exactly what you want. Early on in math, understanding is limited to those things that can be touched. The how and why are not really confirmed until logic stage, IMO. I focus on basic operations heavily. At times, it may seem like overlearning. I am certainly a supporter of overlearning and mastery. The two are necessary. Imagine approaching the distribution property and not having any concept or forgetting how you regrouped. :( You will not have mastery because you did not cement (or overlearn) the skill of addition regrouping. Some things must be committed to memory or mastered and become robotic to the point that they are natural.

 

Every problem is something I find necessary even to the extent that I use two different math programs now. Dd is exceptional with math, but I fear moving too fast and thus we overlearn. Yes, she groans that she did 3-digit multiplication yesterday in Saxon while completing worksheets from MM. :) Oh well, not all school is without verbal discontent.

[boscopup]

I agree with Tina. It depends on the page. I use Math Mammoth also, and the author says it's ok to use half the problems if it's a page full of drill. Leigh Bortins may recommend doing all problems, but she's also talking about Saxon, isn't she? The authors of Saxon suggest doing all the problems, probably because of the incremental nature of that program.

 

For MM, if there are a TON of problems on the page, I'll assign half of them. If there are not a lot of problems about a concept, I'll assign all of them. It just depends on the page and also how much overall practice there is on that topic. There is so much practice of addition/subtraction facts that even when assigning half the problems, my son has still been memorizing the facts easily.

 

If you want to "overlearn" a math topic, doing so via games might be more conducive to preserving a child's interest in math, rather than pages and pages of endless drill.

[Haiku]

isn't there value in doing more problems than just those that show they understand how to do the problem?

 

I think so. I read a book called Why Children Don't Like School by Daniel Willingham, a cognitive scientist, and it changed the way I thought about certain things regarding educating my kids.

 

He talks about the importance of overlearning and sustained practice and learning a skill to automaticity.

 

We use Math Mammoth and I never let my kids skip problems. They do them all for every lesson, and sometimes they do supplemental problems. I have heard tell that Maria Miller, creator of MM, claims that kids can skip problems on the pages if they know what they are doing. I have heard people claim that MM has too many problems per page. I heartily disagree with both.

 

Tara

[RootAnn]

I agree it depends on your kid & your program.

 

We've used Abeka & CLE - both spiral programs. There is a lot of review. If there are six problems of one type that the kid has just had introduced within the last few lessons, I'll have her do all of them. If there are three problems of an "older" type and she's been getting them correct lately, I might cross off two of them. If she hasn't been doing them correctly, I'll leave all three on there.

 

My oldest is "mathy." She needs review but less repetition to "get" something. My 2nd child needs every bit of practice she can get. I can compare Abeka 2 math books and show you entire lessons my oldest was able to skip since they were entirely review. My second one can't skip review lessons. She needs them to cement the concepts and practice, practice, practice.

 

We do math for a certain amount of set time. If we aren't done, it either goes onto the next day's work or it is homework (depending on their level of work ethic that day & which kid we are speaking of).

[kchara]

I fell into the "homeschoolers don't have to do every problem" trap. I also fell into the "just knowing how to do the math conceptually is good enough" trap:) Now my kids are behind! I read the Math chapter from The Core (Leigh Bortins), and that's what changed my mind. I also heard the word "Overlearning" quite a bit, and it sounds like a good idea. It doesn't hurt to get really good at something, to the point that it is easy and automatic. Ultimately, I'd like math to be easy for my kids (not painfully difficult, slow, and confusing like it is now). The only way to get there is practice. I still think conceptual learning is really important. But add practice and automaticity, and then you'll have a student that understands his math, and can work problems without difficulty. We are doing math radically different now.

 

:iagree: I had the same problem, and found the same solution. My kids do a LOT of problems every day. In addition to their MUS, or whatever lesson they're doing that day (we're waiting for our new MUS to come in), they also do one timed drill of 100 addition problems, and another of 100 subtraction problems. It might seem like serious overkill to some, but having a daughter who *should* be closer to 5th grade than 1st grade, and just finished MUS Alpha, I want it to become robotic and automatic. Overlearning definitely has its benefits, especially in regards to math, IMO.

[Ray]

I think so. I read a book called Why Children Don't Like School by Daniel Willingham, a cognitive scientist, and it changed the way I thought about certain things regarding educating my kids.

 

He talks about the importance of overlearning and sustained practice and learning a skill to automaticity.

 

<sniped>

 

Tara

 

You know, I think that's a great book and I refer to it often. What I wanted to expand on, was it helps explain the plusses and minuses of repetition, to include how it can also hinder learning. For potential readers of Willinghams book please note that it lays out both sides to the cognitive topics in it. So even if one is not a fan of excess repetition this book might also tell why the method was a flop.

 

:)

[Chez J]

Put me in the "aiming for robotic" camp. Singapore was a failure for us. We are much better off with Horizons because they have review, and review, and review. I found it actually takes a long time to truly "own" what they are practicing.

[Ellie]

Saxon's Math 54 and up--YES!

 

Other math publishers: Most dc will need to do more than 5 or so. They have to do enough not just so that the concepts are "cemented," but so that the whole process becomes second nature.

[In2why]

Based on my son's personality I have him complete all the problems on the page. If I didn't, it woud become an power struggle on which problems he had to do when, with him insisting that he knew the work so why should he do it. Instead I skip pages if he has them down, BUT we also start every math day with a page of math facts that should take 3-5 minutes to complete and he plays beat the clock. I print those out making sure that they are problems that he can hopefully do automatically.

[wapiti]

As far as MM goes, Maria Miller does say in the User Guide that:

When you have a page or two filled with lots of similar practice problems ("drill") or large sets of problems, feel free to only assign 1/2 or 2/3 of those problems. If your child "gets it" with less amount of exercises, then that is perfect! If not, you can always assign him/her the rest of the problems some other day. In fact, you could even use these unassigned problems the next week or next month for some additional review.

In general, 1st-2nd graders might spend 25-40 minutes a day on math. 3rd-4th graders might spend 30-60 minutes a day. 5th - 6th graders might spend 45-75 minutes a day. If your child finds math enjoyable, he/she can of course spend more time with it! However, it is not good to drag out the lessons on a regular basis, because that can then affect the child's attitude towards math.

(her emphasis)

 

When we started hs-ing, we backed up quite a bit to fill random holes in my dd's learning (some of which have to do with word problems, which are aplenty in MM), and for the topics we were covering at that time, I only assigned half to two-thirds, depending on the page. Now that we finally arrived at the right place in the curriculum for dd, I find I'm assigning almost all the problems.

 

I'm also having to switch things up a bit - word problems are something we need to spend more time on, but where there are several days in a row of word problems, dd can be daunted, so I save those pages to use in between lessons that don't have many.

[SilverMoon]

So, I prefer to stay out of traps and stick with, "What best serves THIS child?"

 

This. Exactly.

 

I have one who really needs to do every single problem on every single lesson, and the entire review section too. Sometimes we have to back up and review the odds or evens before going to the chapter review. For this kid, reducing problem sets in new material is a recipe for disaster.

 

I also have one who can do odds of two lessons every day and excel. Anything slower would bore this one to tears.

 

It really depends on the kid.

[Embassy]

I use Singapore and I don't have my children do all the problems. I typically have them do ones in the textbook orally until I am confident that they can complete the workbook practice independently. Sometimes it is all of the problems in the textbook and sometimes it is only a couple. I don't let them skip any of the mental math practice from the HIG though.

[ondreeuh]

Well, different kids need different amounts of practice. Some math programs, like Math Mammoth, include enough problems for the kids who need the most, and the rest of the kids can cross some off. Other programs, like Singapore, have just enough problems for kids who need the least, and the rest of the kids have to do more from a supplemental book or program.

 

I have a problem with "mastery" programs (Singapore, MM, etc.) that don't include daily review. A) it's boring to do just one thing for each day, and b) what is learned can be easily lost if it's not refreshed regularly. I do not want to have to decide how much review to do and print it all out myself. For those reasons I think programs that include some amount of daily review are superior. We have been using CLE the last two years, and like Saxon it is 90% review, which for us is too much. Next year we are switching to Holt (the source for Thinkwell 6). This is more of a mastery-type program as far as its progression of skills goes, but each lesson has a section of spiral review. The best of both worlds.

[boscopup]

When we started hs-ing, we backed up quite a bit to fill random holes in my dd's learning (some of which have to do with word problems, which are aplenty in MM), and for the topics we were covering at that time, I only assigned half to two-thirds, depending on the page. Now that we finally arrived at the right place in the curriculum for dd, I find I'm assigning almost all the problems.

 

This has been the case for us as well. As we get more "new" topics in, we do more problems. Sometimes I'll have him do a section orally while I scribe. He couldn't possibly write ALL of that. His brain is way ahead of his hand strength!

 

I've looked at some other programs, and MM has more problems than many of them. So since the author says it's ok to cut down the problems if you need to, I think that's fine. We're still doing at least as many problems as we would do in many other programs. But if he completely understands a topic and that's really super clear to me, I see no need to keep drilling it and drilling it and drilling it. If it's a new topic, I'm more likely to assign all the problems. Or if it doesn't require much writing, I might assign all of them. Today, he had a bunch of problems like "1/2 of 20 ___ 13", and you filled in <, >, or =. Those require so little writing, and the fractions are a fairly new topic, so I felt it'd be good for him to do all of them. He had no trouble at all with it, so he probably would have been fine not doing all of them, but since it was just mental work, I'm ok with that. Writing endless numbers would have worn his hand out. He's not ready to do a page of 100 math facts.

 

So basically, I gear the work to his abilities and needs. Some kids need more practice than others. Just because one kid needs pages and pages of fact drill, doesn't mean that every kid needs that. And just because one kid never needs fact drill at all, doesn't mean that every kid doesn't need it. Remember that schools are trying to meet the needs of the most struggling student, so they'll do things that the less-struggling students don't necessarily need. But if you have that struggling student, you shouldn't skimp on the work that that child needs!

[foxbridgeacademy]

Depends on the kid. My 15 yo and now my 7 yo seemed to be born knowing math facts. They look at the page, rattle them off and so I see no reason to subject them to pages of practice. The 10 yo still can't remember his address half the time. He practices and practices and practices his math facts.

Similar situation here, DS is a natural at Math. He was doing 5+ digit addition/subtraction 1/2 way through 1st grade. But he could barely read (dyslexia), DD now at almost 8 (2nd grade) is still working on 3 digit add/sub, but reads at least 2 grade levels higher. Every child is different. DS (current 4th grader) is doing 5th grade math, and will move into 6th grade math by Christmas. We do not do every problem, there's no need, he "gets it". DD also does not do every problem, I sit with her and we spend long amounts of time working it together.

[5LittleMonkeys]

It seems everyone agrees that it depends a lot on the dc. I think I lean toward the overlearning trend although I would never keep pushing if my dc had a complete melt down about it or anything. I do have one dc who can not sit and do math for long periods of time so I break it into two sessions...but she still does all of the problems. So far they all do math without any arguing and (only a minimum of) whining (one dd would whine regardless of how many problems I give her) so I guess we are good.

 

I remember in grade school doing a 100 problem page everyday and I have to say that I got really good at it and attribute that to being able to do mental math really quickly.

 

Thanks for sharing your thoughts!

[EJCMom]

My kids are still little, so I haven't really run into this yet. However, I'm going to be applying something I learned in court reporting school to how much I have my kids practice any new skill. When you learn a new skill, whether it be court reporting or math facts or whatever, you create a literal groove in your brain called a neuropathway. The more you practice that skill, the deeper the neuropathway becomes. So, if you only practice that skill, or math fact, a little bit, you may recall how to do that math problem right then. But, because the neuropathway that you've created isn't very deep, you're less likely to remember how to do that math problem six months from now. The deeper the neuropathway, the longer you remember the concept. The only way to make that neuropathway deeper is to practice. So, I'll be having my kids do all the problems on the MM page, for sure.

[momto3innc]

Even though we are early on in the hs journey, I've been realizing more and more how true this is for my son. We use a combination of Singapore and Horizons which have been a good combination. The variety in the Horizons lessons really provides continual review. We rarely skip, but neither of these programs gives an overwhelming amount of problems most of the time. What we may skip are the additional Horizons worksheets as he usually does not need that much extra practice.

[ChrissySC]

I don't want to be the "downer" but I would like to toss in an opinion/thought. It is more or less how I approach the subject.

 

As math progresses, the difficulty increases, the skill (not just operational but logical too) required to complete a problem increases, and the length of time it takes to find a solution increases. For example, one trig problem took 45 minutes in high school! Well, you say that this is high school, but how does this student learn to sit 45 minutes and finish the one problem?

 

Keep math's future in mind. :)

 

I believe that the number of problems now are strength builders for later, when one problem takes as long as those 25 from days gone past. Perhaps not communicated as effectively as I would have liked, but I hope you get the general idea. It is afternoon, and my day is wearing me out.

 

Again, keep the idea and focus on where your student is going with math. How far do you want to go? I know many of us will be starting Algebra in the logic stage. I ask myself what type of disservice would I be doing if I did not teach my daughter to "sit" with math and make her responses to solving a problem/equation autonomic. I only want you to look past the lesson and look at the subject as a whole. :)

 

Edit: This is not considering drill work. Although, I am a firm believer that basic add, sub, div, and mult should be committed to memory.

[5LittleMonkeys]

As math progresses, the difficulty increases, the skill (not just operational but logical too) required to complete a problem increases, and the length of time it takes to find a solution increases. For example, one trig problem took 45 minutes in high school! Well, you say that this is high school, but how does this student learn to sit 45 minutes and finish the one problem?

 

Keep math's future in mind. :)

 

 

Very good point!