s\o Conceptual math thread. Can I get some input here?

[5LittleMonkeys]

I can't tell you the range of emotions I have gone through reading the McDonald's\conceptual math thread. From flat out panic to serene peace of mind. Right now I'm somewhere in the middle and have a few questions.

 

I don't want this to turn into another debate about conceptual vs. procedural. I get conceptual math and it is something I want my dc to get. Over the last two years I have been solidifying my thoughts on how to teach math and I find myself moving in that direction. Right now I am using a combo of MUS and MEP with my dd7 in addition to math games. She is math intuitive, it all comes very easily to her. My oldest, dd12 is also math intuitive and seems to understand how numbers work together and their relationships and has it all figured out before I even get to the lesson.

 

As any of you who have read any of my posts know, my dd11 is the child that keeps me on my toes. I had almost resolved myself to just letting her be and getting her through highschool math as painlessly as possible but recently I've had a change of heart. I think she has more potential than just getting by. She was failing 4th grade math in ps 2 years ago. I did some remedial work with her (amid much crying) and now she is doing MUS Epsilon. She is doing well with it although it is slow going. She resists math at every turn especially when she knows its above and beyond her regular MUS math lesson. She does understand what we are trying to accomplish when we add, subtract, multiply or divide, and she can do the problems but does get hung up on all the 'steps'. She knows that 3+5 is the same as 5+3, and if pressed could tell you that 3+5 is the same as 4+4, or 2+2+2+2 but I don't think that thinking that way is natural to her and it's not automatic because she wasn't taught that way in ps. She has a hard time doing even simple math in her head, in fact, as soon as I mention numbers\math she turns pale and gets nervous. I've stopped trying to get her to memorize her math facts because it was detrimental to her confidence. She has started to remember more of them through repetition of use but still doesn't have instantaneous recall. ...I'm rambling... All of this to ask, how do I go about teaching conceptual math to this child? I truly believe that if she were to back up and learn math the way many in the other thread were talking about doing it she wouldn't be so phobic about it. But when I think about Bill's reference to making his ds's brains hurt (or it was something to that effect) I just can't see this child being able to deal with that. Not that I think that is a bad thing, my dd7's brain seems to be smoking some days but the confidence she gains when she finally gets it is amazing to witness.

 

I want to continue with MUS because, even though she doesn't like math, she really has gotten the concepts with fractions this year thanks to the overlays. She can explain to me and show me with the overlays what the act of dividing a fraction by a fraction is actually doing. I have considered starting her with MEP maybe 2 levels below her grade level, but I'm just not sure if Yr4 in MEP is far enough back or if MEP is even going to give her what she needs. How do I measure her conceptual understanding? I don't even know how to gauge whether or not I need to back up and do remedial work on +-x\. As I said, she can do the functions, she's just slow about it.

 

I wish two years ago I knew what I know now. I feel like she is struggling and phobic of math still because I didn't actually fix the underlying problem when I pulled her out of ps; I just patched it. Any advice you can give would be greatly appreciated. Oh, and if you got this far without hitting the back button...thanks.:D

[Dana]

I'm not sure this will be much help - hopefully others will post!

 

One thing I'm doing with my son is when we start with an algorithm (most recently for division), we work some problems with the base 10 blocks (or whatever manipulatives are most appropriate). Only after he's done work with the manipulatives for a few problems do I show him the standard algorithm.

 

He can then use the algorithm but if he makes mistakes, he has to go back to the blocks.

 

At any point he can use the blocks if he needs them.

 

As time passes, he gets faster with the algorithm than with counting out blocks, so he prefers using the algorithm.

 

I know some developmental math teachers at the community college who will have students who don't know their times tables (yup... it happens) draw a representation of it - so for 8*7 they'd draw a rectangle made up of 8 squares on one side, 7 on the other, and then count the squares. They pick up speed with time.

 

So what I'd be doing would be going back to the concrete meanings of what your daughter's doing and have her demonstrate an understanding of what is actually happening before using standard algorithms.

[siloam]

I really don't have any words of genius here.

 

She is may be extremely resistant to new ideas, she may need to understand while at the same time hating math on principle or you could have an underlying LD you are fighting. For example my dh struggles to pass college math courses, not because he is unable to do math, but because he insists on thoroughly understanding it before doing it. By the time he figures out the first topic the class has already moved on. It snowballs on him.

 

In his case I think he is mildly dyscalculic combined with a personality that just must understand why. Despite that he is a super smart guy who has written patents and is a computer programmer who can count in basic, hex, and several other number systems. These he has mastered because he was given the time to understand them.

 

It sounds a little like your dd.

 

I would back up. With what I don't know, because I suspect she will fight you with anything. My suggestion is Ma Liping's book.

 

I would also as if she can see quantities and numbers in her mind. If she can't I would look at buying the On Cloud Nine manual to develop that ability (Right Start also has visualizing work, but not as extensive).

 

My top recommendation for that would be Right Start becuase that is what worked here (Miquon and Singapore didn't get my oldest two there), but I am sure there are other ways to get to the same goal. You just have to find what works for her.

 

BTW none of my kids do well with being pushed, especially in math. In fact there are whole sections of the Singapore IP and CWP books I have to do with the kids. It is just beyond their frustration level. I do it with them because they still learn from it, but it is a lot of work for me.

 

Heather

[MeganW]

Have you considered adding the RightStart games - so she is getting more math, but since it is fun, maybe it would help her develop more positive feelings about the subject.

[Corraleno]

As any of you who have read any of my posts know, my dd11 is the child that keeps me on my toes. I had almost resolved myself to just letting her be and getting her through highschool math as painlessly as possible but recently I've had a change of heart. I think she has more potential than just getting by. She was failing 4th grade math in ps 2 years ago. I did some remedial work with her (amid much crying) and now she is doing MUS Epsilon. She is doing well with it although it is slow going. She resists math at every turn especially when she knows its above and beyond her regular MUS math lesson. She does understand what we are trying to accomplish when we add, subtract, multiply or divide, and she can do the problems but does get hung up on all the 'steps'. She knows that 3+5 is the same as 5+3, and if pressed could tell you that 3+5 is the same as 4+4, or 2+2+2+2 but I don't think that thinking that way is natural to her and it's not automatic because she wasn't taught that way in ps. She has a hard time doing even simple math in her head, in fact, as soon as I mention numbers\math she turns pale and gets nervous. I've stopped trying to get her to memorize her math facts because it was detrimental to her confidence. She has started to remember more of them through repetition of use but still doesn't have instantaneous recall. ...I'm rambling... All of this to ask, how do I go about teaching conceptual math to this child? I truly believe that if she were to back up and learn math the way many in the other thread were talking about doing it she wouldn't be so phobic about it. But when I think about Bill's reference to making his ds's brains hurt (or it was something to that effect) I just can't see this child being able to deal with that.

Perhaps her problem is not so much with conceptual understanding, as with working memory and processing speed? In other words, it's hard for her to hold all the "steps" in her mind, and quickly retrieve the math facts, and understand the new concepts all at once. My DS12 has those same issues, and I was told (by the person who did the testing that diagnosed the memory/processing speed issues) to separate the two components (math facts & concepts) and allow him to use a facts chart while he continued to learn new concepts. Otherwise, it's kind of like taking a physics class in a foreign language, where half your brain is frantically trying to remember the grammar & vocabulary while the other half tries to make sense of the concepts. Over the course of the last year, DS has needed the chart less and less, as the facts become more automatic and require less brain power to retrieve.

 

When you think about your DD doing problems that make her brain hurt, you're probably thinking of the pain that comes from trying to hold all those facts and concepts and steps in her head at once, because that's the thing that is painful for her. But that's not the kind of "making his head hurt" that Bill's talking about. WHat Bill's talking about is more like exercise — pushing yourself to run a little farther even though your legs hurt. For kids like your DD and my DS, the kind of "brain pain" that we see is more like stress and frustration because they're trying to do too many things at once and they just don't have the bandwidth for it.

 

With my son, what has worked is to (1) separate out the facts recall part of it, and then (2) break down the concepts into very small steps and take them one at a time. This is what Math Mammoth does, which is why it's worked so well for him. MM also illustrates things really well, either graphically or by describing concepts in a way that lets DS picture it in his mind, and he can hold a lot more pictures in his head than he can words. This is a kid who was a year (or more) behind in PS math and just totally not getting it — there were tears of frustration and literal headaches from his "brain hurting." Two years ago he couldn't even explain what multiplication was (and he hadn't even started division); now he can explain and illustrate division of a fraction by a fraction. He understands that a decimal is a fraction, and a fraction is a division problem, and that when you're dividing by a decimal and you move the decimal point in the divisor you're really creating equivalent fractions. His math facts are still not "down cold," his processing speed is still comparatively slow (which is just how his brain works, not a failure of math instruction), but he totally gets the concepts.

 

Jackie

[5LittleMonkeys]

Perhaps her problem is not so much with conceptual understanding, as with working memory and processing speed? In other words, it's hard for her to hold all the "steps" in her mind, and quickly retrieve the math facts, and understand the new concepts all at once. My DS12 has those same issues, and I was told (by the person who did the testing that diagnosed the memory/processing speed issues) to separate the two components (math facts & concepts) and allow him to use a facts chart while he continued to learn new concepts. Otherwise, it's kind of like taking a physics class in a foreign language, where half your brain is frantically trying to remember the grammar & vocabulary while the other half tries to make sense of the concepts. Over the course of the last year, DS has needed the chart less and less, as the facts become more automatic and require less brain power to retrieve. Yes, I'm finding this is the case with dd. I gave her a chart towards the end of last year. At least I'm doing something right for her.:tongue_smilie:

 

When you think about your DD doing problems that make her brain hurt, you're probably thinking of the pain that comes from trying to hold all those facts and concepts and steps in her head at once, because that's the thing that is painful for her. But that's not the kind of "making his head hurt" that Bill's talking about. WHat Bill's talking about is more like exercise — pushing yourself to run a little farther even though your legs hurt. For kids like your DD and my DS, the kind of "brain pain" that we see is more like stress and frustration because they're trying to do too many things at once and they just don't have the bandwidth for it. Yes, yes, yes. I understand the difference, you explained it perfectly.

 

With my son, what has worked is to (1) separate out the facts recall part of it, and then (2) break down the concepts into very small steps and take them one at a time. This is what Math Mammoth does, which is why it's worked so well for him. MM also illustrates things really well, either graphically or by describing concepts in a way that lets DS picture it in his mind, and he can hold a lot more pictures in his head than he can words. This is a kid who was a year (or more) behind in PS math and just totally not getting it — there were tears of frustration and literal headaches from his "brain hurting." I am so glad to hear this...not that your son had headaches but that my dd isn't the only child that this actually happens to. Pretty much everytime we do math she will complain of her head hurting by the end of the lesson. I began to wonder if she needed glasses but she doesn't complain during any other subjects. Two years ago he couldn't even explain what multiplication was (and he hadn't even started division); now he can explain and illustrate division of a fraction by a fraction. He understands that a decimal is a fraction, and a fraction is a division problem, and that when you're dividing by a decimal and you move the decimal point in the divisor you're really creating equivalent fractions. His math facts are still not "down cold," his processing speed is still comparatively slow (which is just how his brain works, not a failure of math instruction), but he totally gets the concepts.

 

Jackie

 

I will look into the RS games...she loves games. She has the most trouble with long division and large multiplication problems so I could look at the MM that focuses on those concepts.

 

So, as far as the MEP would any of you suggest introducing some of those concepts or should I wait until she feels more confident in working through basic math functions? I don't even know if she will be able to handle working through the MM and the MUS at the same time so I may have to do one curriculum at a time. Just thinking out loud there...guess I answered my own question.

 

Thanks for all the responses so far. I can always depend on all of you to help me think things through.:D

[Spy Car]

The RS games really are a fun way to cement recall of math facts. And since you can all play as a family (and older sister likes games) the younger sister can benefit too.

 

I'm not total sure what it means that the 11 year ols is a "math intuitive" and behind at the same time.

 

As to "make their brains hurt" this was playing off a comment in an old thread there one of our posters mentioned her son loved MEP because it made his "brain hurt." What I meant to suggest was some math problems make a child reallly think and begin to do logical reasoning to get the solution. This is different than either memory/recall or working a known strategy or formula.

 

A very simple example sticks in my mind from page 4 in MEP 1A. Children are presented with 6 identical sailboats. Each sailboat has 3 parts: a hull, a sail and a flag. The children are asked to take 3 colors (Green, Yellow, and Red) and to color each ship differently using all 3 colors each time. When my son got this "problem" at 4 I was quite uncertain if he could do it. But he bore down (and it was almost like you could hear the gears of his mind turning) and was able to do it!

 

I fell in love with MEP then.

 

Bill

[Homemama2]

Math mammoth is something that you could easily use with MUS if you are wanting to stick w/ that. You can buy individual topics (addition, clocks, multiplication etc) or by grade level. I bought this to go along w/ Rightstart because my ds needed more practice in a couple areas this summer. All the teaching is right in the student book (no separate teachers manual) and it gives the "why". I love this because even though I've taken up through Calc., I often didn't know why it worked. MEP is another option (free!), but MM makes the explanations crystal clear.