He does not understand fractions at all

[Janeway]

He has completed all of Singapore Math through 6B. He has completed all of Keys to Fractions. But as soon as he is done with fractions, he does not comprehend it. We started Jacob's Algebra, after having done the first few Keys to Algebra. He could not do it. We spent October to early April on chapter 1 and some of chapter 2. Finally, we switched to Foerster's Algebra. We got through the first chapter with no problem. Now we are on 2-7. The problem is -1/3 X +6 = something. Don't recall right now. Anyway, he could not do it at all. I sat with him to try to do it. I even wrote it out. I tried nudging him along. I has -1/3 times 3 and then -1/3 times 3/1 written out. STILL could not get it. I reminded him this is the same as -1 times 3 over 3 times 1...but written out nicely and in nice big numbers. Nope. He could not get it. He had no idea how to turn -(1 times 3)/(3 times 1) in to an answer. 

 

Since we have already done fractions so many times, already used all of Keys to, all I can think of that is left is maybe get the Epsilon level of MUS. I am not sure. But I do feel like now he is going to be way behind in math. We will spend a year on a level of MUS and then return and start algebra from the beginning. 

 

I do NOT get this!!!!!!! HOW can we spend an entire school year on two chapters of a math book?????????? How can we do fractions as much as we have and he still cannot comprehend?????

[Monica_in_Switzerland]

Can you reframe fractions as division problems?  

 

Sorry, that does not sound like fun for either of you.  

 

There are a couple of good apps out there on simplifying equations/finding unknowns, which includes fraction work.  The best are the Dragonbox apps.  

[Janeway]

Can you reframe fractions as division problems?  

 

Sorry, that does not sound like fun for either of you.  

 

There are a couple of good apps out there on simplifying equations/finding unknowns, which includes fraction work.  The best are the Dragonbox apps.  

Does not comprehend it that way either. Tried manipulatives, tried every day objects and foods, tried using the dry erase board, tried writing with chalk on the drive way, nothing. Nothing works. 

[Janeway]

Can you reframe fractions as division problems?  

 

Sorry, that does not sound like fun for either of you.  

 

There are a couple of good apps out there on simplifying equations/finding unknowns, which includes fraction work.  The best are the Dragonbox apps.  

Would that be the Dragonbox Algebra app? It lists as being for ages 9-11 yr olds..does that sound right?

 

https://itunes.apple.com/us/app/dragonbox-algebra-12-the-award-winning-math-learning-game/id634444186?mt=8

[OneStepAtATime]

Have you looked into the possibility of dyscalculia?

[OneStepAtATime]

You might post this on the Learning Challenges board.

[Arcadia]

This free fractions game might help. We didn't try it.

 

"Salimpoor has helped design a videogame focused on adding, subtracting, multiplying and dividing fractions — the skills any student should have mastered by the end of sixth grade — that puts all her neuroscience expertise for learning into the game mechanics. Called Fog Stone Island and produced by Cignition, the game is free and available online to teachers and students. Salimpoor said the game tracks the intangible information like working memory ability and executive functioning that a teacher would have a hard time identifying." From What Neuroscience Can Tell Us About Making Fractions Stick https://ww2.kqed.org/mindshift/2016/11/21/what-neuroscience-can-tell-us-about-making-fractions-stick/

[Janeway]

Have you looked into the possibility of dyscalculia?

I figured this years ago but the public school refused to test him. FINALLY, after years on waiting lists, he has an evaluation tomorrow.

[EKS]

Neither of my children really got fractions (I mean really, truly, deeply understood them) until after they learned about algebraic fractions.  In fact, there were a lot of things like this in math--true mastery happened over a period of *years*.

 

You don't mention you son's age/grade.  Perhaps taking a year to let things gel by doing a solid prealgebra program would be helpful?  

[forty-two]

Would that be the Dragonbox Algebra app? It lists as being for ages 9-11 yr olds..does that sound right?

 

https://itunes.apple.com/us/app/dragonbox-algebra-12-the-award-winning-math-learning-game/id634444186?mt=8

 

Yes, that's the one. 

[OneStepAtATime]

I figured this years ago but the public school refused to test him. FINALLY, after years on waiting lists, he has an evaluation tomorrow.

Are you testing through the school system or through a neuropsychologist or...?

 

I feel I should mention that the research into dyscalculia is about 20 years behind that of dyslexia and there is still a ton of misinformation out there, as well as no very clear, cut and dried way of assessing.  Different people use different criteria.  Frequently evaluators through school systems are not actually qualified to determine if a child has true dyscalculia.  Also, the causes are not clear, either.  That makes it much harder to get a definitive answer and a clear path to follow.

 

With that much explicit instruction into fractions and still no real comprehension there is obviously a rather profound disconnect somewhere along the way.  Hopefully the evaluation will help you find options for progressing forward.

 

FWIW, DD is dyscalculic. Fractions is one of her hardest subjects.  

[Monica_in_Switzerland]

I hope your evaluation is helpful.  

 

 

Would that be the Dragonbox Algebra app? It lists as being for ages 9-11 yr olds..does that sound right?

 

https://itunes.apple.com/us/app/dragonbox-algebra-12-the-award-winning-math-learning-game/id634444186?mt=8

 

Yes, but they actually have two levels.  There is Algebra 5+ and Algebra 12+.  I'd start on the easier one regardless of age.  They overlap a bit, but both are wonderful.

 

 

[Melissa in Australia]

As a child I only got basic fractions, I could not do complex fraction problems, but quickly worked out to change them all into decimals, work out the problem then change them back into fractions ( if fraction answer was required) - time consuming but it worked. it was only when I was well into algebra that it twigged for me. 

 

I have dyslexia

[Rosie_0801]

My dd has/had dyscalculia and got to understand fractions as being pieces of one the same way that ones are pieces of ten. We'd spent a LOT of time with the CSMP Minicomputers, breaking numbers apart and putting them back together again, so that made sense to her. We didn't get much further than adding and subtracting fractions with common denominators before we had to stop, so maybe this is too basic for your situation.

[Guest]

We had a similar problem. MUS Epsilon has been extremely helpful. I'm having dd use that simultaneously with slowly going back with MUS Algebra I. She did make it through CLE Algebra I this year, but I could tell it wasn't clicking (even though her grades were high) so decided to give it a second go with MUS.

 

When we started at the beginning of MUS Algebra I, it was like deer in the head lights with fractions. I posted on the HS board and received the advice for MUS. It's been invaluable. I can tell a huge difference. She's 3/4 of the way done with Epsilon and we've just started back on Algebra I. It's completely different experience so far. I truly do think some of it is a maturity thing and some was that she needed the way Mr Demme explains it. It's finally clicking.

[Guest]

We had a similar problem. MUS Epsilon has been extremely helpful. I'm having dd use that simultaneously with slowly going back with MUS Algebra I. She did make it through CLE Algebra I this year, but I could tell it wasn't clicking (even though her grades were high) so decided to give it a second go with MUS.

 

When we started at the beginning of MUS Algebra I, it was like deer in the head lights with fractions. I posted on the HS board and received the advice for MUS. It's been invaluable. I can tell a huge difference. She's 3/4 of the way done with Epsilon and we've just started back on Algebra I. It's completely different experience so far. I truly do think some of it is a maturity thing and some was that she needed the way Mr Demme explains it. It's finally clicking.

I was going to recommend this, though MUS has always been our core math program and I have not used it as remediation for one unit that isn't sticking. Even if you spent a year doung MUS before fractions stuck, it is better than trying to move forward with that hole.

 

I didn't really comprehend the processes for working with fractions until I was an adult teaching my own kids and I was hampered in math throughout high school. MUS was what really gave me many "Aha!" moments .

 

I hope your evaluation will be helpful.

[letsplaymath]

How frustrating! I hope the testing will give you some guidance in how to proceed.

 

Fractions are tough for any student. Sometimes, taking a completely different approach to the topic will help it stick. I like the way James Tanton presents things:

• Pamphlet on Fractions

"Fractions are slippery and tricky and, in the end, abstract. It is actually a bit unfair to expect students to have a good grasp of fractions during their middle-school and high-school years." --James Tanton 

[Ellie]

He has completed all of Singapore Math through 6B. He has completed all of Keys to Fractions. But as soon as he is done with fractions, he does not comprehend it. We started Jacob's Algebra, after having done the first few Keys to Algebra. He could not do it. We spent October to early April on chapter 1 and some of chapter 2. Finally, we switched to Foerster's Algebra. We got through the first chapter with no problem. Now we are on 2-7. The problem is -1/3 X +6 = something. Don't recall right now. Anyway, he could not do it at all. I sat with him to try to do it. I even wrote it out. I tried nudging him along. I has -1/3 times 3 and then -1/3 times 3/1 written out. STILL could not get it. I reminded him this is the same as -1 times 3 over 3 times 1...but written out nicely and in nice big numbers. Nope. He could not get it. He had no idea how to turn -(1 times 3)/(3 times 1) in to an answer. 

 

Since we have already done fractions so many times, already used all of Keys to, all I can think of that is left is maybe get the Epsilon level of MUS. I am not sure. But I do feel like now he is going to be way behind in math. We will spend a year on a level of MUS and then return and start algebra from the beginning. 

 

I do NOT get this!!!!!!! HOW can we spend an entire school year on two chapters of a math book?????????? How can we do fractions as much as we have and he still cannot comprehend?????

 

I'm fairly good at fractions, but honestly, that kind of problem would still freak me out, because negative numbers.

[lewelma]

I tutor, and I think it is very very common. There are a couple of ways to help. 

 

1) For algebra, make it algorithmic.  You need a 3 on the top and a 3 on the bottom for them to cancel. 3 over 3 = 1, say that over and over.  Have him drill without deep understanding.  This is ok, because for some kids they gain insight through drill rather than having deep understanding first. In fact, I've taught kids who have gained so much insight with an algorithmic approach to algebra, that then I can explain numerical fractions to them using algebraic fractions.  Think creatively, not all kids learn things in the same way.

 

2) Work on fractions with liquid.  There are kids that just can't understand fractions of objects, but they can understand liquid. I don't get it, but it is true.  Get him in the kitchen doing addition, subtraction (with and without different denominators), multiplication and division of fractions.  Write down the problem on paper, and solve it with liquid first, then solve it with a pencil second. 

 

Ruth in NZ

Edited May 2, 2017 by lewelma

[Ellie]

 

1) For algebra, make it algorithmic.  You need a 3 on the top and a 3 on the bottom for them to cancel. 3 over 3 = 1, say that over and over.  Have him drill without deep understanding.  This is ok, because for some kids they gain insight through drill rather than having deep understanding first. In fact, I've taught kids who have gained so much insight with an algorithmic approach to algebra, that then I can explain numerical fractions to them using algebraic fractions.  Think creatively, not all kids learn things in the same way.

 

 

That would be me. I have to work something over and over until I *own* it, and *then* you can explain the whys to me. :-)

[winterbaby]

Maybe it would help to stop verbally abbreviating the fractional or division relationship as "over." It's not actually "over" anything (except notationally, which he can already see), and he may be losing track of what that means.

[Christy Walters]

I would love to know what you think of the videos on my website:

http://www.aplusses.com/zencart/index.php?main_page=page_3

One of the things that I try to do in these videos is explain WHY the rules work.  I have found that, if students understand why the rules say what they do, they are more likely to apply the correct rule in the correct situation.

 

And Ellie, there's a video on positive and negative numbers that you might find helpful too.  You might also like the chart on page 8 of my Algebra I book (Chapter 1 is online at http://www.aplusses.com/sample/Alg1Ch1_2016.pdf).

 

Please feel free to send me a private message if you think I can help you further.

 

Christy Walters

 

 

[Julie Smith]

I tutor, and I think it is very very common. There are a couple of ways to help. 

 

1) For algebra, make it algorithmic.  You need a 3 on the top and a 3 on the bottom for them to cancel. 3 over 3 = 1, say that over and over.  Have him drill without deep understanding.  This is ok, because for some kids they gain insight through drill rather than having deep understanding first. In fact, I've taught kids who have gained so much insight with an algorithmic approach to algebra, that then I can explain numerical fractions to them using algebraic fractions.  Think creatively, not all kids learn things in the same way.

 

 

What is funny about 1/3 times 3/1 is that you are multiplying a number by it's reciprocal. When Eldest and I dealt with reciprocals and various other fraction things we kept repeating the same sentences out loud. Youngest picked up on it, and I if at any time I started any of the following sentences both boys would finish them: 

 

Any number multiplied by it's reciprocal equals one. 

Division is the same as multiplying by the reciprocal.

When multiplying fractions you don't need a common denominator.

 

Fractions wasn't a problem for Eldest. But he had SO much trouble with negative exponents. Knowing that 3 to the power of 2 equals 1/9 and not -9 was difficult. Everyday we would do a question with negative exponents and when he would forget or get it wrong I would explain the rule, showing in multiply ways why a negative exponent was a fraction and not a negative. We would then do several of those style of questions. Over time I just let the amount of days between doing negative exponent themed questions grow. 

 

It got to the point that if he made any mistake I would lean over and start explaining and he would state, "I know! and be able to go through the explanation all by himself." He then eventually got to the point he would correct himself. Now it's, "So obvious!" He never makes those mistakes. I also know he has full understanding because he usually does things the long way. 

 

With Eldest the first HUGE math road block we hit was long division. It just didn't make any sense to him, and he wasn't content doing the formal without it making sense. We actually had to spend almost a year doing a alternative technique instead of long division. But with Youngest he was happy to just learn the formal. Which was a nice thing for me after banging my head against the wall so often when Eldest was learning it. 

[Hunter]

I think few teens and adults understand the Hindu-Arabic number system. All builds on that. 

 

What is addition?

 

What is multiplication?

 

What is a fraction?

 

These are the three books that most rocked my world.

 

Sam Blumenfeld's How to to Tutor, the arithmetic section.

http://blumenfeld.campconstitution.net/Tutor.htm

 

The arithmetic section in a Guide to American Christian Education.

https://www.christianbook.com/guide-american-christian-education-the-home/0961620110/pd/620110

 

Ray's Practical Arithmetic

https://www.christianbook.com/rays-new-practical-arithmetic/9780880620611/pd/620617?event=CBCER1

Beechick's Parent Teacher Guide

https://www.christianbook.com/rays-new-arithmetics-parent-teacher-guide/ruth-beechick/9780880620710/pd/062071?event=ESRCG

Eclectic Manual of Methods

https://archive.org/details/eclecticmanualof00cincrich

 

Moving onto Algebra. Before the late 1800's, after an arithmetic curriculum strong on definitions, and definitions taught with "object lessons" that were incredibly similar to our manipulatives, and reinforced with lots of oral and written language lessons, the algebra book table of contents mimicked the practical arithmetic. Each algebraic concept was taught after a review of the same concept in the arithmetic.

 

Moderners are in such a rush to get to advanced maths, that we are rushing and compacting the arithmetic phase. We are teaching concepts before the average student is developmentally ready for them. Because we think society NEEDS something, doesn't mean average humans are equipped to accomplish it.

 

Arithmetic is hard for the human brain. That is NORMAL, not a disability. Anything that the hump of the bell curve does is normal. Unless something in the environment damages the majority of people, the majority cannot all be disabled. That is just silly.

 

Things need to be taught over and over when they are taught too early to be understood. I can babble "Mama" at a newborn for 10 hours straight a day, and that newborn is not going to say "Mama" for months. if I have been taught that the only way to get a baby to say "Mama" at a year old is to babble for 10 hours of day month after month, I am going to believe that it is what it takes. If at 10 months, I have switched to only babbling quickly spoken full sentences and never stopping to slowly say a single word, 10 hours of day of quickly spoken full sentences isn't going to teach sentences and probably isn't even going to teach "Mama." And then my kid must be disabled.

 

Again, arithmetic is hard for the average human brain. Some people are gifted at it, like some Olympic gymnasts can do incredible things, but arithmetic is as hard as triple tumbles for average people. Yup, if the average person can't do advanced maths we could end out in like a science fiction movie of too few being able to program the computers. None of that changes the human brain's ability. Yup, without advanced math, the door to a job with decent health insurance is closed. Yup, to all sorts of things that don't make the human brain better at math.

 

When I have tutored adults, and with my own self-education, we went all the way back. What is a number? What is addition? How does our number system work?

 

With Boyden's, Wentworth's, and Ray's old Algebra books, algebraic notation can be taught alongside arithmetic notation, algebraic addition can be taught alongside arithmetic addition, and so on.

 

Gutenberg has retyped the Boyden and Wentworth books and the answers are in the back.

http://www.gutenberg.org/ebooks/subject/3914

 

Ray's Algebra is all over Google Books, with answer keys and some editions even have comprehension questions included.

 

Some of the older Ray's Practical, called the third book, have comprehension questions, too.

 

The Ray's Google pdfs are pretty rough looking and are big files that some devices will choke on, but...I use them anyway, because...there are no modern equivalents.

[Heathermomster]

How old is your DS?

 

Maths disability is irritating and makes absolutely no sense.

 

OP, when I read the problem he was having issues with (-1/3X + 6 = something), my first instinct was to suggest you use Hands-on Equations and practice solving problems such as -2x + 7= -3 first prior to complicating matters by using neg fraction coefficients. If you've done nothing but work on fractions for several months, his problem solving might be rusty. I would also suggest you look at Lial's Beginning Algebra 8th Edition.

 

I love MUS blocks for integer math. I love how you can flip over a rod to the empty side and indicate a negative number. Definitely check out MUS Epsilon. My DS used a TI-15 calculator to verify his answers.