So what do you make of this?

[lazzaroni]

Hi! I am new to homeschooling and to this wonderful resource from which I have received tons of information and advice by lurking around.  Thank you all!  I finally have run into something for which I just don't have an easy answer.  My 9 year old DS has had trouble with his basic math facts (especially timed tests) since 1st grade but he has always scored well in math (mostly A's on every report card since K).   We did do ALOT of after schooling.  My DS has been "labeled" by his former PS gifted program as a visual learner.  From reading here and elsewhere, I understand that VSLs do not appreciate/do well on timed tests.  Yet, our PS continued to require such things even though they themselves know or should know this fact about VSL learners (or am I being too optimistic?).  For many reasons, we decided to begin HSing this year (4th grade).

 

The way math is taught in our district is another HUGE reason we chose to HS.  It is just BAD for us.  It may work for others but not us.  We are using Singapore US now.  I love Singapore.  He seems to like it (ie, no tears or groans).

 

My DS is and has been slow with basic facts but I may have finally gotten him to explain his thought process to me on these questions.  Yesterday, while practicing basic subtraction (we went back to Singapore 2A to rebuild his confidence), he was stopped on 14-6.  Usually, I let him take his time but occasionally I ask what he is thinking just to see if I can help.  Yesterday, he finally told me how he solves these problems.  He deducts 4 from 14 to get to 10.  Then subtracts 6 to get to 4. Then adds 4 to get to 8.  Wow!  I told him he was a genius for being capable of doing that in his head.  But, I am thinking how very exhausting for him.  Now my question is:  is this a product of the multi-step approach that many schools are forced to teach in alignment with Common Core or is this a processing issue/learning disability.  Honestly, it never occurred to me that it could be the latter until I started researching this forum and dyscalculia.  But how on earth does one tell?  He likes math again thanks to homeschooling, revisiting the basics and practicing his math facts daily via games, workbook and Khan Academy.  He is even getting faster at fact recall albeit somewhat inconsistently.  Am I wrong in believing that not enough time was devoted to basic fact mastery in PS and too much time was devoted to developmentally inappropriate conceptual math (like round to the nearest ten, then subtract then add etc...) or are we just an anomaly?  For what it is worth, I am not opposed to Common Core in theory, but the actual implementation of it at least where I am has been less than stellar.

 

Thoughts, please?  And is there anything else I can do to fix this other than what we are doing?  We have had no testing for learning disabilities or ADD because I honestly do not believe that is what is going on here, but I am open to your thoughts.

 

Thank you!

[SarahW]

fwiw, my son fits the description of a VSL to a T, he only went to ps for K, and has a similar circuitous method for doing simple calculations, and can't remember basic facts ("what's 8+8 again? is it 14?") on a consistent basis.

 

Pages of math drill, however, kill him. Last year I had him go through some Hooked on Math books, which are just pages of addition and subtraction, but it didn't help at all. I've simply kept moving forward, knowing that basic calculation will be practiced in more advanced concepts, and that they will just take longer if it's one of the 8+8=14 days. I also add in lots of different work that practices facts. Khan is good for him, though he only likes to do it for a few minutes. I find number-based logic puzzles and have him do a bit of that every day.Sometimes we read Fred. Sometimes we add things up when we are in the car.

 

If your DS likes 2A, that's great. My kid would be whining "this is dumb, I know how to add millions." Yeah, well, maybe you need the practice!

 

Patience is a virtue. And some days I get very virtuous when my kid takes more than a few minutes to figure out 12-4. I tried to teach him tricks when he got stuck, like breaking 4 into two 2's, but that made him "confused" and "forget everything." When I teach him tricks without telling him they are tricks, he sometimes uses them. It gets better over time. I think. I hope.

[lazzaroni]

Thank you both for your thoughts.  Math drill makes my son crazy too so we have tried everything from flashcards to dice to dominoes to practice.  I find if I mix it up like that it does not seem so much like drill.  I can do this so much easier on a daily basis now as a homeschooler than when we were after schooling only.  As for going back to Singapore 2A, my son has no problem with it being "too easy"  - I think it actually has taken so much of the PS pressure off of him and he knows we can move on when we wish.  We have gone through 2A in just a couple of months so he knows we are making progress.  I think that helps as well.  The circuitous route that he let me in on yesterday was just so strange, I had to share it to see if anyone else had experienced it.

 

Thanks again for your comments!

[Elisabet1]

I am definitely a visual learner. And I remember being the last to conquer the timed math fact tests. The teacher had up charts and we got a star when we managed to complete one in the time limit. I was awful at math then.

 

Then one day, around that time, it all clicked. And then I zoomed ahead and became top of my class. I won every math contest that came out from junior high and above..and not by a little. I remember one test where I got double the points of the second place winner. 

 

In college, I was a rare one who tested out of a year of calculus. 

 

I read an article recently that said memorizing math facts during a window of ages (it might have been 7-10, but it was around that) greatly affects math abilities later. IF I had had a choice at 10 years old, I would have definitely have opted out of the tests. They were hard and I was slow to learn! Now, I am glad I never had the option to skip it. I hated it at the time, but am very glad now.

 

I say push your child! He might thank you for it later!

[SarahW]

I really don't mean to harp, but as the OP is a new homeschooler...there is no evidence for learning styles. Trying to figure them out when there's no real evidence for them can be stressful. Of course, the OP should do what works for her, but learning styles - they are not a thing:)

 

 

Here is a recent post of mine describing my kid (and my DH) http://forums.welltrainedmind.com/topic/525869-he-understands-concepts-%E2%80%93-but-wont-do-arithmetic/ .

 

Now, I don't think the whole world is equally split into auditory-sequential and visual-spatial, I just know that my kid isn't "normal."

 

And "learning style" is a bit of a misnomer when it comes to vsl. As far as I can tell it's just a particular approach to view the world. It affects schoolwork, but it affects a lot of things in life as well.

[Sahamamama]

Am I wrong in believing that not enough time was devoted to basic fact mastery in PS and too much time was devoted to developmentally inappropriate conceptual math?

 

I don't know your son's former school, of course, but not enough time devoted to basic fact mastery (in any subject) would be my first guess. Most public schools these days seem to operate on the assumption that all "drill" is also "kill," while ignoring the fact that we end up enjoying what we feel we are good at doing.

 

Anyway, here are some resources:

 

http://www.playkidsgames.com/games/mathfact/mathFact.htm

 

This is a free online math fact practice site that allows you to set up which operation(s) you want him to drill, the amount of time to drill, and the level of difficulty. We usually do about 10 minutes, which leaves my kids begging for more. Nope, tomorrow. Then they are not worn out with it.

 

http://www.mathfactcafe.com/

 

This is a free online math fact drill generator. I like to keep these on hand for "pop drills" before a math lesson.

 

http://sarajordan.com/mathematics.html

 

These are math fact songs on CD that my children have enjoyed. I am okay with them, since the songs are not as annoying as most memory songs. LOL. Your library might have them to borrow. ??

 

http://www.rainbowresource.com/prodlist.php?subject=10&category=2483

 

Daily practice with a complete set of flash cards for every operation (+, -, x, /) -- work on addition, then subtraction, then mixed addition & subtraction, multiplication (by multiplier -- that is, all the "times 9s"), then mixed multiplication (all mastered multipliers), then mixed addition-subtraction-multiplication (quite challenging, actually), and so on.

 

FWIW, my 9.5 year old 4th grader is now "tested out" of addition, subtraction, multiplication, and (most of) division alone, as well as addition & subtraction mixed, but when I mix them up (+, -, x), it's a wild ride. I can see those wheels turning and sometimes grinding, LOL.

 

IMO, there is nothing like sending the child off each morning with a pack of flash cards to study independently. We have these little plastic tote boxes and I keep the week's flash cards in the labelled box. Their daily work assignment includes "Math Fact Practice." Each girl simply gets her box and independently works on her cards. They also listen to the Sara Jordan CDs (on their own while playing) and like to do the Math Fact Practice website at times in place of the drill box. About every three weeks I "surprise" them with a Mom check. Seems to be working here. HTH.

 

Edited to add: I remember now, when my oldest was having difficulty with anything with a 9... either + 9 or - 9, we worked with the Cuisenaire rods to show how the + or - 9 was related to + or - 10. For example, if the fact was 7 + 9 = 16, we made that with rods, then made the same sum with a 10-rod and a 6-rod. She could see how to "make the 9 a 10" by taking one from the other addend (7 becomes 6). It really seemed to help her with those 9 facts. Prior to this, she was saying

 

Another thing we worked on with C-rods was all the facts that "make 10" -- so, 1 + 9, 2 + 8, 3 + 7, and so on. Then we worked with all the fact families from 10 to 20, and that seemed to help something click.

 

I think those two 10s are foundational in some way -- that is, can the child manipulate numbers that add up or subtract down to 10, and can he manipulate up or down to 20? HTH.

 

 

 

 

 

 

 

 

 

 

 

[CaffeineDiary]

Am I wrong in believing that not enough time was devoted to basic fact mastery in PS and too much time was devoted to developmentally inappropriate conceptual math (like round to the nearest ten, then subtract then add etc...) or are we just an anomaly? 

 

More time on basic fact mastery is always good, but I don't think there's anything developmentally inappropriate about what your kid did.  What he's doing is called "regrouping", and it's completely awesome.

 

Imagine instead of "14 - 6" the problem was:

 

1442 - 768

 

Now, you and I - because we're old and slow and not that smart and never learned the concepts - would do this the old fashioned way, by lots of borrowing.  But it's perfectly legitimate to do this instead (I'm sort of exploding the steps super-painfully to try to make it obvious what I'm doing.  In really doing it, you wouldn't do it quite exactly this way):

1442 - 768 =(1000 + 400 + 40 + 2) - (700 + 60 + 8) =  // Dealing with multiples of 10s is always easier, because we are human.(1000 - 700) + (400 + 40 + 2) - (60 + 8) = // How can we group these together to make all the math simpler?(300 + 400 + 40 + 2) - (60 + 8) =(700 + 40 + 2) - (60 + 8) =(700 - 60) + 40 + 2 - 8 =640 + 40 + 2 - 8 =(640 + 40) + 2 - 8 =(680 + 2) - 8 =(670 + 12) - 8 =   // This is "borrowing", but it's borrowing in a way that preserves the number-ness of the numbers!670 + (12 - 8) =  // See?  We still use math facts, just simpler math facts.670 + 4 =674

Here's another, equally valid way to regroup that might be a bit easier to follow.

1442 - 768 = (1000 + 400 + 40 + 2) - (700 + 60 + 8) =(1400 + 40 + 2) - (700 + 60 + 8) =(700 + 40 + 2) - (60 + 8) =(700 + 30 + 12) - (60 + 8) = (700 + 30) - 60 + (12 - 8) =(700 + 30 + 4) - 60 =(600 + 130 + 4) - 60 =(600 + 4) + (130 - 60) =(600 +70 + 4) = 674

Note that this avoids the algorithmic-style insistence that we work from the ones place to higher orders of magnitude (which is safe here because we know the first number is bigger than the second.)

 

This looks ugly and complicated because I'm trying to document every step, but some of the reasons for doing this are:

 

(a) It makes it possible to do certain things in your head that are impossible if you're doing old-school borrowing.

( B) If you work this way, you are less likely to make a mistake that gets you off by a complete order of magnitude or more.  Ever do a subtraction or division problem where you don't just get a slightly wrong answer, but an answer that is, more or less, in a completely different universe?  Regrouping is less likely to get you into that failure mode, and also provides tools for double-checking that your answer is more or less sane. ("Well, 1500 - 750 is 750, so I know my answer should be within 100 of that.")

 

So, in summary:  yes, your kid should practice his math facts, because they're important, but don't think of the conceptual math as some sort of newfangled weird thing that won't help him.  It will give him an incredibly powerful set of tools as he develops and is basically putting him on the right glide-path for pre-algebra and algebra.  Embrace it.

[stripe]

Math games are the way to go rather than pages of worksheets. I also think 5 min a day (or slightly less) makes a big difference. This is built in to most days of MEP, but I add a bit extra.

[Lolly]

Your ds sounds like a very smart boy! He is well on the right track, and he probably figured out his method on his own. My dd invented her own method of subtraction when she was 6. It was amazing. I would try to alter his method just a little. For 14-6, he is starting out correctly, 14-4=10. See if you can get him to move to realizing he only needs to subtract 2 more at this point. He has already taken away 4, so that leaves 2 more to have taken 6 away. 10-2=8. Of course, it may be easier for him to use his method. It is sound mathematical thinking, and actually involves the same number of steps, now that I think about it. (I don't consider figuring in the 6-4=2 a step, but technically it is.) 

[lazzaroni]

Yall are wonderful! Thanks for all the good advice. Math fact cafe is something we just started using. I like it alot. The sing alongs might be worth a try :) We did try xtramath back in the summer, but he hated it. We might give it another go now that we have had lots of practice. Really, thanks for the suggestions and encouragement!

[lazzaroni]

I was posting when others were so I missed some comments. Just for the record, I totally get the regrouping. The problem is that it takes time. Common core strongly suggests no timed activities when learning this method. Yet, at least at our school, they hang on to them. So I guess my thought is choose a path and follow it. Don't try to blend the two because it just left my DS frustrated and exhausted. I do get it and am not opppsed if it is taught well. :) Thanks!

[Lolly]

More time on basic fact mastery is always good, but I don't think there's anything developmentally inappropriate about what your kid did.  What he's doing is called "regrouping", and it's completely awesome.

 

Imagine instead of "14 - 6" the problem was:

 

1442 - 768

 

Now, you and I - because we're old and slow and not that smart and never learned the concepts - would do this the old fashioned way, by lots of borrowing.  But it's perfectly legitimate to do this instead (I'm sort of exploding the steps super-painfully to try to make it obvious what I'm doing.  In really doing it, you wouldn't do it quite exactly this way):

 

1442 - 768 =

(1000 + 400 + 40 + 2) - (700 + 60 + 8) =  // Dealing with multiples of 10s is always easier, because we are human.

(1000 - 700) + (400 + 40 + 2) - (60 + 8) = // How can we group these together to make all the math simpler?

(300 + 400 + 40 + 2) - (60 + 8) =

(700 + 40 + 2) - (60 + 8) =

(700 - 60) + 40 + 2 - 8 =

640 + 40 + 2 - 8 =

(640 + 40) + 2 - 8 =

(680 + 2) - 8 =

(670 + 12) - 8 =   // This is "borrowing", but it's borrowing in a way that preserves the number-ness of the numbers!

670 + (12 - 8) =  // See?  We still use math facts, just simpler math facts.

670 + 4 =

674

 

This looks ugly and complicated because I'm trying to document every step, but some of the reasons for doing this are:

 

(a) It makes it possible to do certain things in your head that are impossible if you're doing old-school borrowing.

( B) If you work this way, you are less likely to make a mistake that gets you off by a complete order of magnitude or more.  Ever do a subtraction or division problem where you don't just get a slightly wrong answer, but an answer that is, more or less, in a completely different universe?  Regrouping is less likely to get you into that failure mode, and also provides tools for double-checking that your answer is more or less sane. ("Well, 1500 - 750 is 750, so I know my answer should be within 100 of that.")

 

So, in summary:  yes, your kid should practice his math facts, because they're important, but don't think of the conceptual math as some sort of newfangled weird thing that won't help him.  It will give him an incredibly powerful set of tools as he develops and is basically putting him on the right glide-path for pre-algebra and algebra.  Embrace it.

 

As mentioned above, my dd devised her own subtraction method when she was about 6. She would have approached your example like this:

 

1442-768

1400-700=700

40-60=owes 20 (her way of processing -20 because she had never heard of negative numbers)

700-20=680

2-8=owes 6

680-6=674

 

She wrote it out under the answer bar as 700-20-6=674(doing those operations in her head). It was actually a much better method, and one that is used in mental math from the old days. Me, I couldn't figure out what the heck she was doing for a while! But, she was coming up with the correct answer everytime. Benefit for her was that her way was actually faster than the "correct" method.

 

For those who are wondering another sample:

 

390-235=100+60-5=155

Edited October 1, 2014 by Lolly

[fairfarmhand]

Fun4thebrain.com has been our friend.

 

I did find that those clunky ways of solving problems were demonstrated when my dd was in K12 virtual. I think it is related to common core. She'd start a lesson having a fair idea of how to solve a problem and when it was over be totally confused because they expected her to be able to solve the same problem 5 different ways. And yes, she was tested on being able to demonstrate that she could solve it each way.

 

But yeah, he does need to get them memorized.

[Lolly]

I was posting when others were so I missed some comments. Just for the record, I totally get the regrouping. The problem is that it takes time. Common core strongly suggests no timed activities when learning this method. Yet, at least at our school, they hang on to them. So I guess my thought is choose a path and follow it. Don't try to blend the two because it just left my DS frustrated and exhausted. I do get it and am not opppsed if it is taught well. :) Thanks!

 

I think it is more that some people get frustrated with timed tests. I have a couple of dc who just get too worked up by them for any benefit. Any timed test lead them to frustration. Actually, I strongly dislike them on principle. They can be a diagnostic tool, but they do not teach the basic facts. The student is not getting immediate feedback on wrong answers. A computer program that gives immediate feedback is a much better choice. (And, less pressure!) 

[Space station]

I think the math games at bigbrainz.com would help a visual learner if they like video games.