If you have a learner who just didn't grasp conceptual math, what did you do? What worked?

[ILiveInFlipFlops]

Youngest DD (almost 8) is struggling with math. We started with Singapore, and she liked the workbook approach but wasn't grasping the concepts. We switched back to RightStart, but again, she's having trouble with the concepts and ends up guessing at many responses, then getting increasingly frustrated as I try to slow her down and ask her to think about how to find the correct answers. Something as simple as regrouping to turn 4+3 into 5+2 frustrates her, and she "counts on her fingers" in her head to get answers to simple math (and the answers are often still wrong). We are pursuing evaluations, but that's going to take awhile, and in the meantime, I'd like to see if changing methods might help too.

 

Any thoughts and suggestions are very welcome. Thanks!

[wapiti]

Two random thoughts that may or may not help: (1) on the evaluation angle, I'd consider whether there might be developmental vision issues - check the covd site symptom list and/or go for a regular checkup to a covd optometrist (a full eval for that is something entirely different, but they'll often screen for such issues at a regular vision checkup). (2) If there might be sequential weaknesses, I'd start Miquon from the beginning (to take advantage of spatial strengths), taking time to let things sink in but anticipating/hoping that it might ultimately go quickly. After she is doing well with simple addition in Miquon, I'd probably add in lots of games to help cement addition facts (starting with using the rods and later without the rods).

[Walking-Iris]

Miquon and c-rods. Also question? Your child is 8,(no she's 7). Why does she have to turn 4+3 into 5+2? Why not simply do 4

+3? Also you could work on learning the doubles, and then if she knows 3 and 3 is 6 and 4 is one more than 3, the answer would be 1 more than 6...7. Practicing that seems easier to me than 5 and 2.

 

Also if she's counting on her fingers in her head...then she's practicing mental math and I don't see the problem there either. She's able to see something in her mind and find an answer. She'll get faster with practice. If she's getting most of it wrong, just go back and work with one program, I suggest miquon (I don't like the no counting thing in Right Start, especially since it claims to be Montessori based and I see nothing Montessori about it)

 

Conceptual math IMHO is learning how math works, sounds to me like you're trying to get her to just memorize it. I know lots emphasize memorizing facts, but I feel that is a terrible thing to do at first. You can't memorize what you don't understand.

 

Use of manipulatives is a good thing at young ages. 1st-even 4th grade in some instances. Allow lots of practice and use of hands on materials. c-rods, a number line, even countable objects. Work on learning the doubles and fact families.

[ILiveInFlipFlops]

Thank you both for your thoughts. She's 7, but she's about to turn 8, and she reads very well, and above level. I was worried about her reading for a little while and actually made an appointment with a COVD optometrist, but during the between the day I made the appt and day of the appt, something clicked for her and her reading took off. She's been reading things like the American Girl books for 9 months now (since we started our co-op year). Could there still be a vision issue that relates somehow to math but not reading? She does still write most of letters in capitals and gets very frustrated when trying to write in lower case. When she does write in lower case, she often still writes a good number of letters backwards (more than just Bs and Ds). I don't know what that might mean? But other days she writes just fine :confused1:

 

The regrouping was just one example. She also struggles with things like counting by twos, understanding how to move beads on the abacus to find the answer she's looking for, and so on. I've tried teaching her strategies like the doubles you mentioned (e.g., you know 5+5=10, and 4 is one away from 10...) or something along the lines of 4+5=, knowing that 5+5=10, and 4 is one less that 5, so what is one less that 10? She can't seem to grasp any of it, and always resorts to counting up in her head, often still reaching the wrong answer, then shouting out guesses in growing frustration until there are tears.

 

We have lots of manipulatives, we play lots of card games. Most concepts don't seem to be sticking for longer than the lesson I'm teaching at that time. And the level of frustration she works herself into makes it almost impossible to come back to the concept for the next lesson, because she starts out angry and just gets worse. Does that make sense?

 

I'm completely open to hearing more thoughts. I'd love to find out that this is a learning style thing and we don't need to go for an eval! I'm really not sure what's within the range of normal for her age, because my first learns very quickly and rarely needs to spend much time on a concept to have it down, and I've not taught other kids.

[wapiti]

. 

 

[Crimson Wife]

I would work on getting her addition & subtraction facts mastered so that it frees up her working memory. A couple of books that my DS really liked are Mindware Addition Adventures and Subtraction Secrets. Allow her to use manipulatives like C-rods or the abacus as long as she needs them.

[Farrar]

Yeah, I know we talk a lot about getting the concepts first here, but I think it's fine to go the other way and let her memorize the math facts - as Crimson Wife said, to free up her working memory. Then you can focus on the concepts, which may be easier to see once she doesn't have to take so long to get to the answer. And if the abacus isn't clicking, do try the C-rods.

[TraceyS/FL]

My DD with massive math issues does well with MUS. Despite her issues she is able to recall the rod colors and build problems correctly - all while insisting that 6+6 is 13. When she builds it correctly she can see her problem! LOL!!

 

She has severe working memory issues and extreme processing delays (and tracking problems and double vision). Couple those with a genetic thing that already carries with it reduced math ability..... well, math is a struggle.

 

The thing with her is.... it isn't a race. As you saw with your DDs reading, it can happen. I work at the pace she needs to grasp things (knowing I'm not reaching much past Alg 1 - *maybe* - with her either), I never thought she'd learn to count past 10 (she did at at 8), I never thought she'd get those facts in there, but they are in there - sometimes retrieval is a bit slow and off, but that is her.

 

I have never forced math to be something that I pushed her to frustration. Don't get me wrong, she gets frustrated and thinks it is to hard quite often - but we turn the page, and she can go back to it and finish it just like I knew she could. That is the key - while I'm pushing her to learn, I'm not intentionally pushing her to meltdown. Until you have some answers on your eval - work with what you know she can do.

 

I'm pondering having her try Miquon now, i've started adding in some 1st-2nd grade MM pages - and they are a workout for her. She could not do Singapore, and I haven't looked at RS enough to know if she could or not.

 

i would highly suggest trying the C-rods and Miquon, or something else.

 

Hang in there - it is an adventure!

[Mom0012]

Both RS and Singapore were total flops for my son. After lots of tears and struggling, I moved him into Rod & Staff and what a wonderful relief it was. He was very successful with their program. He needed the drill and kill rote approach first, and then got the concepts later. He actually has a very good understanding of math. I don't know if you could attribute it to what someone said above about working memory? He needs to learn the algorithm first, and then he is able to learn the "whys". He used R&S 1 - 6 (partway through 6) and then switched to CLE 6. For him, I'm glad I didn't switch him any sooner. He's a very concrete thinker, but as he's getting older, I see him more readily able to apply problem solving skills to go deeper conceptually than when he was younger.

[Joker]

My oldest dd's worst year was second grade. She just wasn't where I thought she should be. The next year (for 3rd) we used Abeka and she memorized all her facts. It was the best thing I could have done for her because it gave her so much confidence. She now has no trouble in math (she's an A student in the Honor's program at our local ps). She's even been tutoring because some of the other kids have had trouble with the switch to Common Core and having to explain their answers, but she has no trouble at all understanding it.

[126bugeyes]

It sounds to me like she is not understanding (or remembering) how the manipulatives work. But, it also sounds like they are exactly the thing she needs. If she is counting on her fingers in her head, sounds to me like she's envisioning a "visual". She's still getting the answers wrong, because she's not using an actual manipulative. It's really easy to loose track counting an imaginary visual. It can be a trick to get kids to slow down and actually count each unit for each number- 1 for 1. I am not familiar with the types of manipulatives used in Singapore or Right Start, though. I often find that, especially after we haven't worked with a particular manipulative for a while, we may have to back up and talk about what the pieces represent- usually having to do with place value and the idea that you can't have more than 9. I don't believe that all manipulatives are the same. Many are very similar, some are nonsense to me.

[Ellie]

Rod and Staff.

 

Some children just don't do concepts first. They need to know How To Do It first, and then they have to do it for a long time, and THEN they understand the concepts. There's nothing wrong with that, either.

 

 

Rod and Staff. And I'd start with the second grade materials.

[ChicoryChick]

What Tracy, bugeyes, and Ellie said. I tried many different curricula with my 2nd oldest dd who is VSL, but have learned that just having patience was the most important thing, I would teach her something and the next day she would act like she never saw it before. Eventually by going over it and over it again every. single. day. she will finally get it. But I can't take off for the summer because then we have to start over the next year. So its a coulpe of lessons a week to keep it fresh I wish I had tried R&S with her, but it had been such a flop with my oldest I didn't even consider it with her until 6th grade and then I felt it was to late.

 

ETA: She did thrive in the early years with manipulatives (MUS), it was once math became more abstract (multidigit mupltiplication) that we ran into a wall, and I impatiently jumped ship.

[Hunter]

Most of the conceptual programs are also WIDE. There are programs that are conceptual and more narrow, allowing the student to focus on just the priority strands of math.

 

Professor B is both conceptual and narrower than the Singapore and the other more popular curriculums.

 

Arithmetic Village if now available as a cheap download. It is conceptual and narrow, and too cute for words.

 

Less conceptual, but still using simple household manipulatives, is Simply Charlotte Mason Mathematics

 

For math copywork, I like How to Tutor

 

Lately all I'm using is HTT and SCM for the lowest level students. PB and AV might be "better", buuuut...HTT and SCM seem to get the job done and get done, so....

 

I strongly agree with Ellie, that some kids need to do before understanding. As well as direct lessons, HTT and SCM have a lot of discussion of teaching math to struggling students.

[ktgrok]

I would work on getting her addition & subtraction facts mastered so that it frees up her working memory. A couple of books that my DS really liked are Mindware Addition Adventures and Subtraction Secrets. Allow her to use manipulatives like C-rods or the abacus as long as she needs them.

 

Yup...some kids need that first. Rather than figuring it out for themselves, they want to know they can get the answer right, then they are free to figure out why the answer is that way without the pressure/fear of getting it wrong. No harm. Work on memorizing facts.

[....]

Do you think your daughter could be a VSL? About 1 1/2 yr ago, after using every math program out there, I figured out that my son is extremely VSL. Here is an article that helped me: http://www.gifteddev...e/vsl/v85.pdf��

 

If you google it, there are also several websites about it. I'm also getting ready to buy this book: http://www.amazon.co...IH6GTOUWA6US0�� From the description/sample, it has alot of teaching suggestions (which is what I need).

 

I can't tell you how difficult it's been to teach this kid math. :crying: Especially arithmetic. He can solve this: 2(3X) + 1 = 2X + 21, but he can't add/subtract without fingers and I'm still trying to teach him the steps to long division (he just can't remember them). So far, the only math program that worked for him is Life of Fred (he's at Jellybeans) and Beast Academy (but, there are only so many levels of that available). His sister is using AOPS Pre-Algebra and I have a hunch that AOPS might actually work out for him.

 

I hope you figure out what's going on!

 

 

Edited to say: What you described in your OP, my son also could not do at that age. He would also have a problem like 32+15 (written vertically) and he would write "89" at a completely different problem. It was bizarre. Also, if there is alot of writing on a page, he couldn't focus at ALL. I spend about twice as much time with him every day as I do the other kids on math.

[Clear Creek]

Youngest DD (almost 8) is struggling with math. We started with Singapore, and she liked the workbook approach but wasn't grasping the concepts. We switched back to RightStart, but again, she's having trouble with the concepts and ends up guessing at many responses, then getting increasingly frustrated as I try to slow her down and ask her to think about how to find the correct answers. Something as simple as regrouping to turn 4+3 into 5+2 frustrates her, and she "counts on her fingers" in her head to get answers to simple math (and the answers are often still wrong). We are pursuing evaluations, but that's going to take awhile, and in the meantime, I'd like to see if changing methods might help too.

 

Any thoughts and suggestions are very welcome. Thanks!

Math-U-See. My daughter was at the point your daughter was at the beginning of third grade (after two years of R&S). MUS finally helped her move from counting to adding - and there is a difference, which Mr. Demme explains near the beginning of Alpha. My daughter can now add two digit problems in her head correctly, including regrouping...so she has made a lot of progress! I attribute it 100% to MUS.

 

R&S has the student memorize their math facts by doing flashcards and copying the facts daily. MUS has the student memorize their math facts by doing the problem with the blocks until they can visualize the combined total in their head. For my highly VSL, the MUS method was much more effective. Like I mentioned above, she went through R&S 1 and 2 without learning any math concepts or memorizing any math facts. Having her repeatedly copy or say that 4+3=7 was meaningless to her...like if I told you to say and copy that friggles + terwubbles = plat. It would mean nothing to you, have no frame of reference to hang on in your mind, and you could not apply it to any other situation. This was R&S for my middle child. And don't get me wrong; I love R&S - it worked extremely well for my oldest child.

[sixpence1978]

My DD also doesn't get "conceptual" math. She understands math concepts, but never could understand manipulating the numbers. She is dyslexic and has working memory difficulties. Even getting her to memorize her math facts has been tough.

 

She has jumped nearly 2 grade levels in math this past year after we switched to CLE. She is using it a year behind, but is now testing at nearly grade level. I do teach the lessons to her and add in the concepts, but their focus on repetition and drill has helped her immensely.

 

C-rods didn't work well for her either because she does have some visual processing problems so she doesn't immediately see how the size equals a number. We usually bust out either the base 10 kit or her ladybug counters. It's a much more concrete tool for her.

 

For her math facts, teaching her touch math has worked the best. You might want to look into that. Also, learning skip counting songs was key for her learning multiplication. I'm very pleased with her progress this year. Even the "best" programs (Singapore, MM, RS) aren't necessarily the best if it isn't how your child learns. Now that we have made her facts and procedures more automatic through drill and repetition, she has more working memory left over for developing her problem solving skills.

[....]

Even the "best" programs (Singapore, MM, RS) aren't necessarily the best if it isn't how your child learns.

 

:iagree: Absolutely. I wish I would've realized that 4 years ago.

[Mommy22alyns]

Singapore was a huge mess here. I used RightStart for a few years, but I started to think that some drill would help. I switched to CLE and Rebecca has done SO well with it. She's good at math, and she feels confident. I used Horizons for Sylvia for K and then put her in CLE as well.

[Ellie]

Math-U-See. My daughter was at the point your daughter was at the beginning of third grade (after two years of R&S). MUS finally helped her move from counting to adding - and there is a difference, which Mr. Demme explains near the beginning of Alpha. My daughter can now add two digit problems in her head correctly, including regrouping...so she has made a lot of progress! I attribute it 100% to MUS.

 

R&S has the student memorize their math facts by doing flashcards and copying the facts daily. MUS has the student memorize their math facts by doing the problem with the blocks until they can visualize the combined total in their head. For my highly VSL, the MUS method was much more effective. Like I mentioned above, she went through R&S 1 and 2 without learning any math concepts or memorizing any math facts. Having her repeatedly copy or say that 4+3=7 was meaningless to her...like if I told you to say and copy that friggles + terwubbles = plat. It would mean nothing to you, have no frame of reference to hang on in your mind, and you could not apply it to any other situation. This was R&S for my middle child. And don't get me wrong; I love R&S - it worked extremely well for my oldest child.

 

 

But there's more to the first- and second-grade texts than doing math-fact flashcards and copying facts daily (I don't know which grade levels you used, so this is just for public discussion, lol). The oral classtime, which is mandatory for the first three years, does include drill, but not only with math fact flash cards; it also includes numbers which come before, numbers which come after, numbers which are in the middle, and so on. And you just can't beat the way it teaches fractions. When the concept of 1/2 is introduced, the children learn about 1/2 of an hour, 1/2 of a cup, 1/2 of a dollar, 1/2 inch, and so on--IOW, the *concept* of half of something, then applied to many different real-life situations. The first-grade book includes visuals which show the concepts of addition and subtraction, too.

[Clear Creek]

 

But there's more to the first- and second-grade texts than doing math-fact flashcards and copying facts daily (I don't know which grade levels you used, so this is just for public discussion, lol). The oral classtime, which is mandatory for the first three years, does include drill, but not only with math fact flash cards; it also includes numbers which come before, numbers which come after, numbers which are in the middle, and so on. And you just can't beat the way it teaches fractions. When the concept of 1/2 is introduced, the children learn about 1/2 of an hour, 1/2 of a cup, 1/2 of a dollar, 1/2 inch, and so on--IOW, the *concept* of half of something, then applied to many different real-life situations. The first-grade book includes visuals which show the concepts of addition and subtraction, too.

I know there is much more; I have gone through it twice already (and continued on through the 7th grade book with my oldest). I was just illustrating one of the major differences between the two math programs, one that can make a difference for a VSL. I am a huge fan of R&S Math...so much that I plan on using MUS for the written work and the R&S oral classtime with my youngest until he is ready for the fourth grade book, when I will switch him completely to R&S. I have said before on these boards that the meat of the R&S math program in the first two years is the oral classtime; the workbook is just practice. But for some kids the explanations and teaching doesn't work, and for those kids I would recommend MUS; Mr. Demme's explanations are completely different than the ones in R&S and the the way that I naturally teach math.

[ILiveInFlipFlops]

Thank you all, very much! I appreciate all the input and will start exploring some options other than the ones I'm familiar with. I've had a huge pile of C rods for years now (great score at a rummage sale), and we take them along as compact building sets when we travel! Maybe I'll be able to put them to their intended use now :tongue_smilie:

 

Also, I bought used copies of LOF Apples and Fractions, and the other night, I read a few chapters from each as bedtime reading. When I was done, both girls begged for more and started arguing over whose math book I was going to read :lol: Those books are seriously hilarious. We've been walking around singing "Butter fries are butter!" for days now.

[Critterfixer]

I'm not going to suggest anything in the way of curriculum or evaluations, but I'll just say that a number line made all the difference in the world for my son who didn't find manipulatives helpful. Just being able to see it right there in front of him laid out on a line was helpful. In his case, it eliminated a "fat finger" problem when it came to adding up objects. For some reason, the number line just made sense to him.

[1pageatatime]

On a simpler note, it could be that she needs to mature a bit more. Nothing wrong with that! Even a few months can make a huge difference.