Math strugglers - how they struggle, and how you've helped them?

[Another Lynn]

If you have a math struggler (or maybe a student who is just not math intuitive) would you share in what way they have struggled (particular topics, skills, methods, comprehension?) and what you did that is helping?  Could be a particular curricula? or method? or supplement? or math manipulative? etc.

 

 

 

[mom2bee]

Depends a lot on the level of math that the student is struggling with. You have a wide span of kids so I don't know which tips to give but I have some that I'll share, I just need to find my notebook. BRB.

[Another Lynn]

I'm referring to my 11yo (almost 12yo) dd finishing 6th grade, though I'm glad to hear the stories, experiences of others at any level.

[kateingr]

As a teacher and tutor, the main reason I've seen kids struggle is because they stop believing that math makes sense. They start to see it as a magical set of recipes that gets you the right answer, but not as an interconnected set of ideas that all have a reason for existing. When I taught fifth-grade, I would even make one of my strugglers write "Math makes sense!" at the top of every page to remind her not to start panicking and wildly guessing but to use her brain and THINK! There's no easy way to undo this, but the main approach is to teach concepts (not recipes),  assign fewer problems and encourage your child to think about them carefully.

 

A lack of number sense also can be a huge hindrance. This year, I'm tutoring a wonderful upper elementary student who was taught in public school to count every addition and subtraction problem (with a program called touchmath) instead of mastering the addition and subtraction facts (to the point that she didn't even know right away what 3+6 is). As a result, she could perform the steps of multi-digit addition and subtraction (with counting) but had no sense of what numbers meant and how they related to each other. She hit an absolute wall once she started on multiplication. She and I went back to the very beginning, using the Math Mammoth Blue series along with the AL Abacus, and worked through the addition and subtraction worktexts. Since September, she's mastered all the addition and subtraction facts and can do two-digit mental math with ease, and now is cruising through the multiplication tables. Her entire attitude about math has changed, too. She now believes that she can actually do it, because she's not just wandering in a dark room hoping someone will tell her how to get the answer. 

 

 

 

[Another Lynn]

Kate, I'm so glad you replied.  I've enjoyed your blog.  I really think you've hit the nail on the head.  She has used Saxon the last two years (eta:  completing 6/5 now) and it has given her confidence because of the repetition, but when she has to apply something she has learned to a slightly new situation she struggles.  Our pattern the last two years is to think we're doing well, then towards the end of the book all of a sudden she's out of her league.  She really resists anything that makes her think beyond "I've seen this problem before, I know to do 'this.'"  And I would agree that number sense is lacking too.  With a problem like 38 + 4, she would be most comfortable stacking the numbers and carrying the one, etc. rather than working it mentally.  I would dare say her multiplication facts might be more sure than her addition, except for maybe her "2s" - it particularly takes her an unusual amount of time to divide by 2. 

 

I confess I have mixed feelings about MM.  Every time I look at it, the visual layout of the pages looks overwhelming to me (and I really like math!).  Off to look at it again.... 

[Clear Creek]

My math struggler still had zero number sense in 3rd grade. I switched her to Math-u-see and began at Alpha (1st grade). She is now finishing up Delta (4th grade) at the end of 5th grade and while some things take extra time to learn (I'm talking about you, long division!), she understands numbers and how they relate to each other and how they work together. The way Mr. Demme explains concepts is the opposite of the way that I think and that I teach the concepts. I don't know how long we will stick with MUS (my daughter wants to switch to R&S after she finishes Delta, though I am not sure that will work for her), but it saved our homeschool.

[Farrar]

Both my kids have, at times, struggled with math. Ds, when he was really young, spent a year really unhappy with math and the best thing I did was drop it for awhile and try new things. He ended up being my more math-loving kid. He's doing pre-algebra this year and is so happy. Other ds has more recently been struggling with math and we've jumped around curricula a little for him. It's been hard to find the sweet spot where something isn't too easy or too hard. I feel like for both of them, the best thing I've done is not define them as math strugglers. I really felt like for both it's just a phase and we just have to do a balancing act of waiting it out and trying new things and gently continuing to work at it.

[Farrar]

Kate, I'm so glad you replied.  I've enjoyed your blog.  I really think you've hit the nail on the head.  She has used Saxon the last two years (eta:  completing 6/5 now) and it has given her confidence because of the repetition, but when she has to apply something she has learned to a slightly new situation she struggles.  Our pattern the last two years is to think we're doing well, then towards the end of the book all of a sudden she's out of her league.  She really resists anything that makes her think beyond "I've seen this problem before, I know to do 'this.'"  And I would agree that number sense is lacking too.  With a problem like 38 + 4, she would be most comfortable stacking the numbers and carrying the one, etc. rather than working it mentally.  I would dare say her multiplication facts might be more sure than her addition, except for maybe her "2s" - it particularly takes her an unusual amount of time to divide by 2. 

 

I confess I have mixed feelings about MM.  Every time I look at it, the visual layout of the pages looks overwhelming to me (and I really like math!).  Off to look at it again.... 

 

For this mental math issue, the thing that I found most useful when I was teaching remedial middle school math back in my school career was just playing 24 constantly. We probably played for fifteen to twenty minutes every single day. And some of the kids - who started out not knowing their times tables - got so good that they asked that we hold a schoolwide 24 tournament on Pi Day and they knocked out a bunch of the 8th grade algebra students in the first round. Anyway, just to say, I think games are a good way to sweep up mental math. Muggins is another one that's good for practicing lots of small number mental math with lots of operations.

[mom2bee]

***Understanding the concept alone is not enough.
***Knowing the algorithm is not enough.
***Conceptual understanding + computational fluency is better

***Conceptual understanding + computational fluency + long term retention is best

***Speak Math by using and requiring the correct terminology from the beginning. I have found that many times students can not read their math books with fluency simply because they don't know what the terms mean. When you are unfamiliar with the terms and wording used in math then you get left out of the lessons when a teacher is explaining things and the math book is essentially "talking over the students head."
***Basics should be solid. Math facts must be internalized through practice, repetition, drill, copywork, what-have-you. There are 100 ways to learn your math facts, find the ways that work for you and use them. Regularly. At some point, kids shouldn't be "counting out" their addition/multiplication facts. They shouldn't ever commit the subtraction and division facts to memory and they should understand why they don't have to memorize them.
 

Some students will need to gain computational fluency BEFORE they can master the concept. Others will need to build conceptual understanding BEFORE the computational skills can be mastered. Ideally all students will eventually master both and will get sufficient practice at doing them both so that long term retention is gained.

In the ideal world all students would learn well by first understanding the concept. They would use that conceptual understanding to develop or study several approaches or algorithms and then they would develop fluency in the algorithms by practicing computing a nice sample of problems on the daily basis.

 

 

Think about this: By the 2nd term of first grade virtually all the students in all the English speaking countries of the world know that "letters make sounds and each sound is blended together to read a word" and by the 2nd term of first grade, all students know some letter sounds. Yet, tens of millions of those 1st grade children are still not reading. Why? because the concept isn't enough to get them reading. The "algorithm" of blending alone isn't enough.

 

It is the ability to link the phonics-concept, the blending algorithm and fluent application of the facts (letter sounds) that allow a child to decode with fluency. Its a similar situation in mathematics. Its easier to recognize when a child struggles with reading because we can hear plain and clearly that they are stumbling to decode words. Its hard to hear them do their math, so since you have an older child struggling, I would talk directly with the student as much as possible, to try and understand what they don't understand or why they think they are having difficulties in math. I take a "help me, help you" approach.

 

If they say...

• it takes too long to do the problems--well, they are saying they lack conceptual certainty and probably computational fluency as well.
• they have to stop to count out the answers--well they need to work more on the math facts and until then make use a table for +/*
• they don't know how to solve word problems--they are saying they need more lessons, guidance or support extracting math from English.
• they make a lot of mistakes--they need more guidance and support on being neat.

 

Many times it helps to do FEWER problems with more discussion of the concepts at work, more discussion of the algorithm  and more attention to detail than it does to do DOZENS of problems with out.

As the students build understanding with concept and fluency with the computation they can do a more problems with greater accuracy and speed and when they are at this level, it really helps to do those types of problems as review. NEVER under-estimate the power and the effect that gradual but constant review can have on a learner.

[Paige]

My struggler was much like how Kate described. It didn't make sense, seemed like magical nonsense, and she had a lack of number sense. She also had a lack of confidence and a fear of failure. She's doing much better now that we've switched to CLE and I took her back to a level that I knew she would find success with. 

 

She was in 5th grade and I took her back to the beginning of 3rd grade in CLE even though she had been hobbling along in MM at almost grade level. I may have taken her back a bit too far, but I don't regret it. She has improved so much because she's been able to learn the language of math and what the questions really mean, and how to look at problems without having to stress about difficult calculations. All of the actual math has been easy for her, but she never understood what the words really meant. She still struggles with the language sometimes, but CLE's repetition has helped her remember and learn what key words mean and what to do. It's also helped me to find out the areas where she has been confused. I never could understand what she didn't understand in the past. By switching to a level that was easy for her, I was able to separate out the math from the language. The more I find out which words and phrases she didn't understand, the more I am able to clear those issues up for good! It was like she was doing math with the directions in a foreign language and she was guessing what the directions meant with some success. Neither of us knew which words she had assigned an incorrect meaning to because she had such mixed success. 

 

We've also been able to accelerate it so that she's already on 4th grade CLE and we only switched from MM in Nov or Dec last year. I think we may be able to get her close to grade level by next fall.

 

My DD's problem was always with the easy stuff- place value, counting, more and less, etc. We had thought she had a math problem but it was really a language and vocabulary problem which is apparent in other subjects and areas. MM had too many words- too many ways of saying the same thing. CLE says the same thing over and over which is ideal, IMO, for a child with language difficulties. 

[Another Lynn]

Both my kids have, at times, struggled with math. Ds, when he was really young, spent a year really unhappy with math and the best thing I did was drop it for awhile and try new things. He ended up being my more math-loving kid. He's doing pre-algebra this year and is so happy. Other ds has more recently been struggling with math and we've jumped around curricula a little for him. It's been hard to find the sweet spot where something isn't too easy or too hard. I feel like for both of them, the best thing I've done is not define them as math strugglers. I really felt like for both it's just a phase and we just have to do a balancing act of waiting it out and trying new things and gently continuing to work at it.

Thank you for this encouragement! 

 

For this mental math issue, the thing that I found most useful when I was teaching remedial middle school math back in my school career was just playing 24 constantly. We probably played for fifteen to twenty minutes every single day. And some of the kids - who started out not knowing their times tables - got so good that they asked that we hold a schoolwide 24 tournament on Pi Day and they knocked out a bunch of the 8th grade algebra students in the first round. Anyway, just to say, I think games are a good way to sweep up mental math. Muggins is another one that's good for practicing lots of small number mental math with lots of operations.

I have never heard of 24.  I just looked it up and ordered it - it looks great!  Thank you so much for recommending it!

[Another Lynn]

***Understanding the concept alone is not enough.

***Knowing the algorithm is not enough.

***Conceptual understanding + computational fluency is better

***Conceptual understanding + computational fluency + long term retention is best

***Speak Math by using and requiring the correct terminology from the beginning. I have found that many times students can not read their math books with fluency simply because they don't know what the terms mean. When you are unfamiliar with the terms and wording used in math then you get left out of the lessons when a teacher is explaining things and the math book is essentially "talking over the students head."

***Basics should be solid. Math facts must be internalized through practice, repetition, drill, copywork, what-have-you. There are 100 ways to learn your math facts, find the ways that work for you and use them. Regularly. At some point, kids shouldn't be "counting out" their addition/multiplication facts. They shouldn't ever commit the subtraction and division facts to memory and they should understand why they don't have to memorize them.

 

Some students will need to gain computational fluency BEFORE they can master the concept. Others will need to build conceptual understanding BEFORE the computational skills can be mastered. Ideally all students will eventually master both and will get sufficient practice at doing them both so that long term retention is gained.

 

In the ideal world all students would learn well by first understanding the concept. They would use that conceptual understanding to develop or study several approaches or algorithms and then they would develop fluency in the algorithms by practicing computing a nice sample of problems on the daily basis.

 

 

Think about this: By the 2nd term of first grade virtually all the students in all the English speaking countries of the world know that "letters make sounds and each sound is blended together to read a word" and by the 2nd term of first grade, all students know some letter sounds. Yet, tens of millions of those 1st grade children are still not reading. Why? because the concept isn't enough to get them reading. The "algorithm" of blending alone isn't enough.

 

It is the ability to link the phonics-concept, the blending algorithm and fluent application of the facts (letter sounds) that allow a child to decode with fluency. Its a similar situation in mathematics. Its easier to recognize when a child struggles with reading because we can hear plain and clearly that they are stumbling to decode words. Its hard to hear them do their math, so since you have an older child struggling, I would talk directly with the student as much as possible, to try and understand what they don't understand or why they think they are having difficulties in math. I take a "help me, help you" approach.

 

If they say...

• it takes too long to do the problems--well, they are saying they lack conceptual certainty and probably computational fluency as well.
• they have to stop to count out the answers--well they need to work more on the math facts and until then make use a table for +/*
• they don't know how to solve word problems--they are saying they need more lessons, guidance or support extracting math from English.
• they make a lot of mistakes--they need more guidance and support on being neat.

 

Many times it helps to do FEWER problems with more discussion of the concepts at work, more discussion of the algorithm  and more attention to detail than it does to do DOZENS of problems with out.

As the students build understanding with concept and fluency with the computation they can do a more problems with greater accuracy and speed and when they are at this level, it really helps to do those types of problems as review. NEVER under-estimate the power and the effect that gradual but constant review can have on a learner.

 

Thank you - this is so helpful!  Both lists are so helpful for thinking through where a student needs help.  It has seemed to me that she is one who needs computational fluency before conceptual understanding comes - so I understand what you're saying about that.  *I* need to stay aware of how we are working towards both rather than blindly trust the curriculum to do it for me. 

[Another Lynn]

My struggler was much like how Kate described. It didn't make sense, seemed like magical nonsense, and she had a lack of number sense. She also had a lack of confidence and a fear of failure. She's doing much better now that we've switched to CLE and I took her back to a level that I knew she would find success with. 

 

She was in 5th grade and I took her back to the beginning of 3rd grade in CLE even though she had been hobbling along in MM at almost grade level. I may have taken her back a bit too far, but I don't regret it. She has improved so much because she's been able to learn the language of math and what the questions really mean, and how to look at problems without having to stress about difficult calculations. All of the actual math has been easy for her, but she never understood what the words really meant. She still struggles with the language sometimes, but CLE's repetition has helped her remember and learn what key words mean and what to do. It's also helped me to find out the areas where she has been confused. I never could understand what she didn't understand in the past. By switching to a level that was easy for her, I was able to separate out the math from the language. The more I find out which words and phrases she didn't understand, the more I am able to clear those issues up for good! It was like she was doing math with the directions in a foreign language and she was guessing what the directions meant with some success. Neither of us knew which words she had assigned an incorrect meaning to because she had such mixed success. 

 

We've also been able to accelerate it so that she's already on 4th grade CLE and we only switched from MM in Nov or Dec last year. I think we may be able to get her close to grade level by next fall.

 

My DD's problem was always with the easy stuff- place value, counting, more and less, etc. We had thought she had a math problem but it was really a language and vocabulary problem which is apparent in other subjects and areas. MM had too many words- too many ways of saying the same thing. CLE says the same thing over and over which is ideal, IMO, for a child with language difficulties. 

 

Your description is helpful too.  I do think understanding the language and vocabulary is a factor with my dd as well.  Thank you for mentioning that aspect. 

 

[Minerva]

***Understanding the concept alone is not enough.

***Knowing the algorithm is not enough.

***Conceptual understanding + computational fluency is better

***Conceptual understanding + computational fluency + long term retention is best

***Speak Math by using and requiring the correct terminology from the beginning. I have found that many times students can not read their math books with fluency simply because they don't know what the terms mean. When you are unfamiliar with the terms and wording used in math then you get left out of the lessons when a teacher is explaining things and the math book is essentially "talking over the students head."

***Basics should be solid. Math facts must be internalized through practice, repetition, drill, copywork, what-have-you. There are 100 ways to learn your math facts, find the ways that work for you and use them. Regularly. At some point, kids shouldn't be "counting out" their addition/multiplication facts. They shouldn't ever commit the subtraction and division facts to memory and they should understand why they don't have to memorize them.

 

Some students will need to gain computational fluency BEFORE they can master the concept. Others will need to build conceptual understanding BEFORE the computational skills can be mastered. Ideally all students will eventually master both and will get sufficient practice at doing them both so that long term retention is gained.

 

In the ideal world all students would learn well by first understanding the concept. They would use that conceptual understanding to develop or study several approaches or algorithms and then they would develop fluency in the algorithms by practicing computing a nice sample of problems on the daily basis.

 

 

Think about this: By the 2nd term of first grade virtually all the students in all the English speaking countries of the world know that "letters make sounds and each sound is blended together to read a word" and by the 2nd term of first grade, all students know some letter sounds. Yet, tens of millions of those 1st grade children are still not reading. Why? because the concept isn't enough to get them reading. The "algorithm" of blending alone isn't enough.

 

It is the ability to link the phonics-concept, the blending algorithm and fluent application of the facts (letter sounds) that allow a child to decode with fluency. Its a similar situation in mathematics. Its easier to recognize when a child struggles with reading because we can hear plain and clearly that they are stumbling to decode words. Its hard to hear them do their math, so since you have an older child struggling, I would talk directly with the student as much as possible, to try and understand what they don't understand or why they think they are having difficulties in math. I take a "help me, help you" approach.

 

If they say...

• it takes too long to do the problems--well, they are saying they lack conceptual certainty and probably computational fluency as well.
• they have to stop to count out the answers--well they need to work more on the math facts and until then make use a table for +/*
• they don't know how to solve word problems--they are saying they need more lessons, guidance or support extracting math from English.
• they make a lot of mistakes--they need more guidance and support on being neat.

 

Many times it helps to do FEWER problems with more discussion of the concepts at work, more discussion of the algorithm  and more attention to detail than it does to do DOZENS of problems with out.

As the students build understanding with concept and fluency with the computation they can do a more problems with greater accuracy and speed and when they are at this level, it really helps to do those types of problems as review. NEVER under-estimate the power and the effect that gradual but constant review can have on a learner.

 

[mellifera33]

We have recently started using the games in Ronit Bird's ebooks for building number sense, and I can see the "click" when my 7 y/o internalizes a new concept. The books are inexpensive, and the games are fun. They start at the very beginning, which is what my 1st grader needed. He has been doing well with R&S 1st grade math, but he used a combination of rote memory and counting to figure out his facts. The Ronit Bird games are helping him to see " 3 + 4 = 7" rather than "(1+1+1) + (1+1+1+1) = 7".

[Hunter]

***Speak Math by using and requiring the correct terminology from the beginning. I have found that many times students can not read their math books with fluency simply because they don't know what the terms mean. When you are unfamiliar with the terms and wording used in math then you get left out of the lessons when a teacher is explaining things and the math book is essentially "talking over the students head."

 

Others here can talk about everything else better than I can, but being able to read and write and talk about math is just not discussed enough. I find this to be a really big deal. Only in very rare circumstances will I place a student in a math book that they cannot read.

[OneStepAtATime]

Lack of understanding, solid understanding, of math vocabulary turned out to be one of the huge hidden issues we were facing here. Computation and conceptual mastery were hit or miss, too, but the vocabulary really was a biggie.

 

As mentioned upthread, what has really helped here is CLE math. It works on computation, vocabulary and some conceptual understanding in a very student friendly way (the kids both like CLE and one used to loathe math). I wish with all my heart I had had this program when I was in school.

 

No program is perfect, though. I think CLE is terrific for working on math vocabulary. I think it is weak on conceptual and specifically on more robust word problems. They aren't terrible word probelms at all. I just think there need to be some additional, more conceptual problems. And CLE can get a bit tedious if you don't break it up a bit sometimes.

 

Therefore, we combine it with periodic math games, Beast Academy, and some math word problems from Math In Focus to make the conceptual side stronger. Having a few things rotated in periodically keeps the kids' interest up, helps them see math fron different approaches and helps me to see if they really are retaining and applying what they learned outside the box of a CLE lesson.

 

Love CLE! It has turned math around here. And Beast and Math In Focus word problems are also great.

 

Good luck, OP. You've had some great responses here. I hope they help you and your child.

 

Best wishes.

[Targhee]

I had one who struggled with math when we pulled her from school at the end of third. She constantly made computational errors, and froze at timed math facts quizzes. She hated math! We started working on concepts (she had RighStartA in K then was in public school three years). We went back to third grade SIngapore, and really worked on concrete-pictorial-abstract sequence and emphasized mental math skills. I gave her partial credit when I could see she had the idea but made a computational error. I gave her a multiplication chart to refer to whenever she wanted. She actually made herself a different one with her own color scheme. She continued to use it until about half way through 6th grade. Once I dropped the pressure of facts testing and retrieval she was able to dig into the concepts. She was catching onto those quickly, and her hate of math soon turned to love. I thank heavens we did RS A in the beginning! That, and going back a grade level with Singapore to cover concepts, made math meaningful and relevant, which translated into interest and willingness to persevere. This was definitely one who needed concepts first and fact fluency later. She's in online AoPS Algebra 1 now and loving the challenge! Her computation skills are solid, because they were practiced in the context of meaningful ideas.

 

That's not to say everyone will learn like she does, or come to excel in and love math, but that taking a different approach to math may make the difference. Best wishes!

[OneStepAtATime]

Oh and I agree Ronit Bird ebooks are great and much easier to implement than her printed books (although those are also excellent). I highly recommend them for any math struggler. Don't be fooled by how basic the lessons start out.

[Hunter]

Sometimes, students are just not ready to read and write about certain topics in math, yet, but the scope and sequences say those topics must be covered. Publishers and teachers are forced to look for quick fixes. I'm not sure those quick fixes work long-term.

 

Any publisher that actually hold students back to their reading level is going to get slammed.

 

I don't have the answers. I have freedoms that others here don't have. I'm just not placing students in books they cannot read, anymore. I'm just not.

[mom2bee]

Others here can talk about everything else better than I can, but being able to read and write and talk about math is just not discussed enough. I find this to be a really big deal. Only in very rare circumstances will I place a student in a math book that they cannot read.

 

 

Sometimes, students are just not ready to read and write about certain topics in math, yet, but the scope and sequences say those topics must be covered. Publishers and teachers are forced to look for quick fixes. I'm not sure those quick fixes work long-term.

 

Any publisher that actually hold students back to their reading level is going to get slammed.

 

I don't have the answers. I have freedoms that others here don't have. I'm just not placing students in books they cannot read, anymore. I'm just not.

 

Just to be clear, I'm talking reading reading. As in reading with comprehension. If a student is hearing and reading words that they don't really understand in an explanation of a concept then are you really explaining anything to them?

 

What I mean is many times the child cant keep up in a conversation (either with a book or with a person) that uses proper mathematical terminology and that is a problem. When you go looking for a supplement or alternative explanation, those explanations will invariably use the exact same mathematical terminology and you will always be on the cusp between not fully understanding but "getting the gist of" and "vague understanding" of the topic at hand. When you are confused about a thing, you usually only know that you are confused it is much harder to articulate WHAT you are confused about.

 

Its also a problem in phonics, but I find that there are fewer special terms to know for phonics instruction and discussion, but I also explicitly teach those terms to the best of my ability and I do my best to use the phonics terms and I require my students to use the term.

[mom2bee]

"Today, we are going to learn and practice the algorithm for multiplying rational numbers. Last time we discussed the meaning of multiplying rational numbers and today we're going to find the most efficient and reliable way to calculate the product of rational numbers, then we are going practice it so that we all get the hang of it, okay? Okay, lets begin."

 

"When we are multiplying rational numbers we multiply the numerators of each rational number, and we multiply the denominators of each rational number."

 

Many kids here this in school and don't understand because they don't know those bolded words.

 

I can't tell you how many times a 5th-9th grader has asked "Multiply? You mean timesing the things together?--Oh, okay..."

Or my personal favorite: "Thats not the way we do it in class. We timesd the tops by the tops and the bottoms by the bottoms"

(Yes, the poor dears say timesd)

Most of the people I've tutored in HS and college do not instantly recognize rational number as a synonym for "fraction" the way that they recognize "chilly" or "icy" as a synonym for "cold", but they should. They will get there in a few minutes or if I prompt them to see the word "ratio" within the word rational, but in my experience, they think of fractions and rational numbers as two distinct things that might be vaguely related.

 

Most people think  "fraction" and envision a slice of cake when they should be envisioning a point on a number line or something in the form of "a/b, given that b is not zero.".

 

Likewise many of those same HS and college students can NOT tell me what a numerator or denominator is.They muddle through thinking of them as "something to do with fractions" or "I know one of them is the top/bottom number in a fraction..." but saying to them "don't forget that the denominator of a rational polynomial can never be zero" doesn't TELL them anything because they don't know the words polynomial, or denominator.

 

Its like getting into Freshman Comp or beyond without readily knowing what a "sentence", "punctuation mark" or "clause" is. It makes it exceedingly difficult to have a discussion with them about their writing because if you prompt them about an error "Oh, what punctuation mark goes at the end of a sentence?" they didn't understand the question even though its difficult to ask a student in any plainer terms.

[kateingr]

***Understanding the concept alone is not enough.

***Knowing the algorithm is not enough.

***Conceptual understanding + computational fluency is better

***Conceptual understanding + computational fluency + long term retention is best

 

 

Many times it helps to do FEWER problems with more discussion of the concepts at work, more discussion of the algorithm  and more attention to detail than it does to do DOZENS of problems with out.

 

 

Amen and amen! Thanks for your thoughts on vocabulary, too. 

[Paige]

"Today, we are going to learn and practice the algorithm for multiplying rational numbers. Last time we discussed the meaning of multiplying rational numbers and today we're going to find the most efficient and reliable way to calculate the product of rational numbers, then we are going practice it so that we all get the hang of it, okay? Okay, lets begin."

 

"When we are multiplying rational numbers we multiply the numerators of each rational number, and we multiply the denominators of each rational number."

 

 

 

This type of vocabulary is important to have and students definitely need to understand these terms, but for the OP, I want to clarify that this is not the type of vocab problem my DD was having. I spent way too much time thinking it was these types of terms I needed to explain when DD really had no problem with those because I'd explained endlessly.

 

What may be hidden with some kids with language problems may be problems with basic, simple, everyday words. DD had trouble understanding what the antecedents to the pronouns in the directions were. She had trouble connecting which picture on the page went with which problem, and that maybe it would go with more than one problem, or which ones were just decorations. If there was a puppy on the page, she might convince herself that it needed to have meaning and somehow be connected to a problem! She had trouble understanding that some word problems were isolated and some followed from previous word problems. She struggled with concepts of before, after, next to, etc. She knew what the words meant, but she struggled with where to place them. For instance, with "before" when not used in relation to time, she doesn't intuitively get that everything is and should be left to right. 

 

I don't think my DD's language difficulties are a common cause of math problems, but for me and her previous teachers, they were problems that were difficult to discover. 

[mom2bee]

This type of vocabulary is important to have and students definitely need to understand these terms, but for the OP, I want to clarify that this is not the type of vocab problem my DD was having. I spent way too much time thinking it was these types of terms I needed to explain when DD really had no problem with those because I'd explained endlessly.

 

What may be hidden with some kids with language problems may be problems with basic, simple, everyday words. DD had trouble understanding what the antecedents to the pronouns in the directions were. She had trouble connecting which picture on the page went with which problem, and that maybe it would go with more than one problem, or which ones were just decorations. If there was a puppy on the page, she might convince herself that it needed to have meaning and somehow be connected to a problem! She had trouble understanding that some word problems were isolated and some followed from previous word problems. She struggled with concepts of before, after, next to, etc. She knew what the words meant, but she struggled with where to place them. For instance, with "before" when not used in relation to time, she doesn't intuitively get that everything is and should be left to right. 

 

I don't think my DD's language difficulties are a common cause of math problems, but for me and her previous teachers, they were problems that were difficult to discover. 

Excellent point, mine was a narrow example, but I picked it because of the age of the child in question (11 going on 12) and I was trying to illustrate what I meant about a students inability to "read read" a math book or actually participate in a math discussion due to a lacking vocabulary. If you don't understand those words, you're going to have a hard time with the math because you are constantly reading about them or discussing them or having them mentioned to you as part of the explanation given. We tend to "tune out" the words that we don't understand and focus on the "gist" of what a speaker is saying based on context and body language.

 

But yes, this is also a foundational problem that students have and one that I hinted at in my 2nd post when I said a student who says

that they don't know how to solve word problems could be telling you that they need more lessons, guidance or support extracting math from English.

[Doodlebug]

This is my fourth year homeschooling my now 3rd grader, so we're not at your level yet... 

 

But, keeping math fresh would be my do-over.

 

I would do that by block scheduling math (I think that's what I'm recommending).  About four weeks on a spine curriculum followed by two weeks on a fun supplement (LOF, BA, etc).  And for youngers, a rotation of daily math fact work -- mostly games, some flash card work, and the occasional traditional drill (my kid finally likes these) to coincide with the lighter supplement weeks.

 

Why?  

 

Because my kid struggles mightily with redundant tasks even when he's capable of the work.  Getting him to engage with material he's done over and over and over is, quite literally, impossible.  With my 20/20 hindsight, I think I used to categorize this as a behavior problem. But then, I considered that I didn't have this problem in other subjects -- DS loves history and would read for hours, loves science and would read for hours, tolerates spelling and likes our review changed up daily, dislikes writing but easily and willingly gives me three sentences on a subject he likes. 

 

I've also realized that games make better "real life math" teachers than any traditional drill.  I love Zeus on the Loose because it got my DS thinking about sums of ten, adding single digit numbers to a larger number, holding numbers in his head, etc.  

 

Fresh = engaged.  And if my kid is engaged, he's learning.  

 

 

 

   

 

 

[kateingr]

 

 

Because my kid struggles mightily with redundant tasks even when he's capable of the work.  Getting him to engage with material he's done over and over and over is, quite literally, impossible.  

 

I shudder to think how many people have grown up hating math simply for this reason. Not too many people get a lot of joy out of doing the same thing over and over without anything new to think about. 

[Another Lynn]

This type of vocabulary is important to have and students definitely need to understand these terms, but for the OP, I want to clarify that this is not the type of vocab problem my DD was having. I spent way too much time thinking it was these types of terms I needed to explain when DD really had no problem with those because I'd explained endlessly.

 

What may be hidden with some kids with language problems may be problems with basic, simple, everyday words. DD had trouble understanding what the antecedents to the pronouns in the directions were. She had trouble connecting which picture on the page went with which problem, and that maybe it would go with more than one problem, or which ones were just decorations. If there was a puppy on the page, she might convince herself that it needed to have meaning and somehow be connected to a problem! She had trouble understanding that some word problems were isolated and some followed from previous word problems. She struggled with concepts of before, after, next to, etc. She knew what the words meant, but she struggled with where to place them. For instance, with "before" when not used in relation to time, she doesn't intuitively get that everything is and should be left to right. 

 

I don't think my DD's language difficulties are a common cause of math problems, but for me and her previous teachers, they were problems that were difficult to discover. 

 

Thank you.  I understand what you're saying.  My dd also gets confused sometimes with relational words - at least more than I would expect of an 11 yo.  Additionally, I don't think my dd is as likely to understand the meaning of words (in any subject) from context as others typically would.  

 

[Hunter]

Sometimes it's not even the exact math vocabulary, but just a lack of readiness for the TYPE of vocabulary.

 

A student that cannot take multi-step verbal instruction to make a snack or get ready for bed can't take multi-step instruction to do a math algorithm.

 

A student that isn't ready for science vocabulary that isn't rooted in every day things they are experiencing isn't ready for math vocabulary that is totally removed from anything she experiences.

 

There are 2E geniuses who think in pictures and have the right to receive instruction in their primary language. But for kids that think in words, I don't think we accomplish much long term by trying to move ahead of their verbal abilities.

 

So often it's not a math problem, but a language problem, getting in the way of some students making progress in math. If a child cannot understand multi stepped problems, Mommy having a baby and taking a break from math to have the child do multi-stepped chores can sometimes fix the math problem. Lucky the child who got a baby brother instead of a new math curriculum in this situation.

[Hunter]

Thank you. I understand what you're saying. My dd also gets confused sometimes with relational words - at least more than I would expect of an 11 yo. Additionally, I don't think my dd is as likely to understand the meaning of words (in any subject) from context as others typically would.

 

This is what I am talking about. I have students that struggle with "and" vs "therefore" and "because", in situations like, "I ate pizza; I threw up because I ate pizza." There is a running joke around here when people throw up to use the words "and" and "after" and not "because".

[Lori D.]

Don't know your student to know what is the cause of struggle, but I can share from our math struggler's experiences, and what we did. DS#2 is an extremely Visual Spatial Learner, with mild LDs in spelling, writing, and abstract math concepts. What he needed:

 

1. patience -- allow lots of extra time for brain development

So introduce a topic; if really not getting it, set it aside for a few months, come back and try again -- and it may take several rounds of this before the student has matured the brain areas needed to process the topic. For example,  it took 2 years and 4 rounds of introducing and working with long division for our DS#2 before it finally "clicked" (end of 3rd grade; start of 4th grade; halfway through 4th garde; start of 5th grade). Often, somewhere between 10-14yo is when students with LDs, or "late bloomers", start to

 

2. concrete, tangible, visual, methods for showing and explaining 

DS#2 is great with geometry and 3-D types of math concepts that are naturally very visual and tangible. But most math is abstract to a lesser or greater degree, so manipulatives are really needed. Resources that helped here:

- manipulatives with go-along booklets

- Math-U-See has visual videos AND manipulatives, which made it a winner here.

- Hands-On Equations is great for visualizing the abstract algebra concept of "solving for x"

- Miquon in the early elementary years was very helpful with cuisenaire rods and

- Keys To … workbooks

- visual "bar" method for problem-solving from Singapore Primary (introduced starting in 3A/B)

Along with this idea is making abstract concepts real -- what is the point, or how is this used in real-life? VS learners need to see a connection for concrete real usage of the math.

 

3. whole to parts curriculum

VSL students are big picture (intuit the overall "pattern" or concept) and work down into the specific details (steps of computation, etc.). Often they do better with a mastery program, rather than spiral-based, which allows them to fully absorb a concept before moving on. Spiral programs that present multiple concepts, all in the half-way stage can be very confusing to these students. Or if the program is too incremental and starts with small "parts" and takes too long to build up to the big overall concept. "Discovery"-based can also be a good fit, as VS learners are global thinkers and often "intuitively" or quickly see an overall pattern; from there you can work with them to see how the "parts" (the equations and algorithms) fit into the pattern.

 

4. try, set-aside, return to "struggle concepts"

Of hitting the wall with a concept, set it aside for a week or a month, go to a completely other math program and other math topic and let the "struggle" topic simmer on the back burner of the brain. When you come back to that topic, you might also try coming at it from a different perspective with a totally different type of explanation, which might also "click".

 

 

I'm a big believer in using a spine math AND a lot of a second math program (from a very different perspective and way of explaining) as supplement, all the way through Pre-Algebra. It REALLY helps students see math connections, gives them multiple strategies for thinking about math and adding new concepts to their understanding, and helps develop strong problem-solving and math-thinking skills. I really saw how this helped our math struggler, especially in grades 5-8, once he had "clicked a notch" and was beginning to "get" math a bit more.

 

Perhaps branching out, using some visual manipulatives and doing some "discovery" types of math will help your DD to start seeing connections and "owning" some of the concepts… "Playing" with math might help her move away from the fear of getting off of the safe Saxon script. Even though she is older and at a level above it, what about setting aside Saxon for the rest of the year (the "formal" math that is "right or wrong", and just play together with Beast Academy, or a lower level of Life of Fred, or Zaccaro Math?

 

Just a thought! BEST of luck in finding what helps best! Warmest regards, Lori D.

 

[Upennmama]

My oldest is 12, and never has really gotten math. She went to PS for elementary and did fine. When I brought her home in 5th grade, she was beginning to struggle, and as I worked with her I saw that she had no real conceptual understanding. She just did a bunch of formulas or knew the "way" to do a problem, but it didn't make sense to her. She did saxon for two years and did okay, but was still not understanding. I tried moving her to Teaching Textbooks pre-algebra last year (6th), and it was terrible. I don't know if it's the program or my dd, but it seemed to be making the problem worse. Finally, this year I decided to do something crazy and try Art of Problem Solving. It's really hard, so I chose pre-algebra. In theory, this should be material which she's somewhat comfortable with, as she finished pre-alg already in TT, but it's still incredibly hard. Honestly, I am an adult with a good college degree, and I find it hard much of the time. She's finally getting it, it's amazing. She's no great math scholar, but I see her working through the problems and getting a CONCEPTUAL understanding. Amazing. I was scared this would just confuse her more, and it is confusing, but we struggle though the problems together. It's really good to do it together, because sometimes I don't understand the solutions manual, and we have to work together and then she gets it and has to explain it to me! We have to go pretty slow, but I'd rather go slowly and let her really have it sink in and give her a stronger foundation than move her onto TT Algebra, where I think she could skate by with no understanding. 

[kateingr]

We have to go pretty slow, but I'd rather go slowly and let her really have it sink in and give her a stronger foundation than move her onto TT Algebra, where I think she could skate by with no understanding.

That is awesome! Good for you for trying something so much more difficult! I'm so glad it's working so well.

[swainsonshawk]

I've dealt with a lot of different types of math learners in my homeschool.  My first was a very VSL learner.  The second two were intuitive.  The fourth is math phobic.  I keep using a math curriculum that I like (Singapore--it speaks to me) and I keep tweaking it to fit the different learners.  Two of my kids have required a lot of help to get through the word problems (lots and lots of repetition--we do the really hard ones together and I don't even worry about it).  I've slowed down, stopped math for a season, made my own worksheets, required memorization of math facts to move on added extra reviews, skipped reviews, handed over the multiplication facts chart to struggling students, etc, etc.  

 

Some of my kids are very parts to whole, others are the opposite.

 

I think what really helped my kids was emotional support.  If they feel supported and that "we're in this together" they can continue to work on it.  Keep trying different things.  Something will eventually click.  Try to have your child focus on what they are good at and tell him that everyone struggles with something.  Math is just his "thing."  If you can get him to believe you and believe that you will help him and that he can help himself and that he will be able to do it, eventually, you will make it through.  There really is no secret formula.

 

Okay, so the secret sauce for me is:

 

the al-abacus from Right Start.  I taught that program to my kids for a few seasons (too time consuming for me) and I fell in love with it.  It really makes math visual when they are having trouble visualizing it.

 

math on the white board is more fun than on paper

 

math where mom writes and tells you what to write gets you through those hard days.

 

base 10 blocks demonstrate numbers very easily, too.  

 

Fraction circles help me teach fractions in the beginning, but I don't use them very much

 

Multiplication facts should be memorized at some point. We are still working on this with my 6th grader (for automaticity--he skip counts the big ones over and over), 4th and 2nd graders.  Right now we are using xtramath.org  We have also used flash cards, calculadders, sidewalk chalk, copywork, skip counting songs. . . 

 

[Heathermomster]

My DS is a diagnosed 2e dyslexic/maths disabled/dysgraphic.  We use materials by Ronit Bird, James Tanton, manipulatives, 1/2" grid paper, and math mnemonics.  DH and I are both BSEEs.  The majority of our family friends are scientists, and we use math language.  DS can handle only one topic at a time, and he requires constant review.  DS requires everything that LoriD stated, and we use multiple math source materials with Algebra.  Overall, Ronit Bird teaching math methods have benefited DS the most while How the Brain Learns Mathematics by David Sousa has helped me the most,

[Ausmumof3]

My struggling learner lacks good math fact recall. We take time off every now and then just to work on facts. I am actually considering taking a month or so off Singapore and conceptual work just to focus on getting quicker with maths facts. Part of this is him but part of it is that because he is slow we often don't get the drill done by the time we've done worksheets etc and it just becomes a compounding problem.

[LoveMyBeautifulGift]

What Kate said above could describe my DD, down to the Touch Math learned at PS undermining her math facts. On top of not understanding math, she had convinced herself she was "stupid" at math. Our first year of HS (last year, 3rd grade) I backed off of math as she knew it. We read Life of Fred, which she was very hesitant to do at first, because it was math. But she found herself enjoying it (she's always been a voracious reader) and I didn't press her to do anything else math-wise. Mid-year, I pulled out some math games, Beast Academy and some cheap math workbooks (do the problems and get the answer to a riddle types). She enjoyed Beast Academy, and we worked through a couple of those slowly until about mid-year this year. She hit a wall with multiplication, so we've pulled out Life of Fred again, along with Murderous Maths and games, and are currently taking it easy again. I did have her take an ADAM test this spring. I found it very useful to pinpoint where we need to shore up (for example, I knew she needed to work on multiplication facts, but didn't realize she was also struggling with place value in numbers over 1,000). My plan for the summer is to get those multiplication facts down and then take the ADAM again, so I can map out a plan for next year using Math Mammoth blue series (supplementing with a lot of the fun math she enjoys).

[Another Lynn]

So, a couple questions I'm pondering based on the variety of replies here.....

 

1)  How would you decide whether to back way up vs. adding more conceptual teaching to existing curricula?

 

2)  If you back way up, how do you know how far back to go?  (placement test, or other determination)?

 

3)  Either way, how would you work on number sense with a 6th/7th grader?

[kateingr]

So, a couple questions I'm pondering based on the variety of replies here.....

 

1)  How would you decide whether to back way up vs. adding more conceptual teaching to existing curricula?

 

2)  If you back way up, how do you know how far back to go?  (placement test, or other determination)?

 

3)  Either way, how would you work on number sense with a 6th/7th grader?

 

These are such good questions, Lynn. 

 

My first step would be to check out how well your daughter's doing on the essential basics. Without these, all of math will be difficult and frustrating.  

 

-Addition and subtraction facts

-Fluent multi-digit addition and subtraction, with understanding of regrouping

-Multiplication facts and division facts

-Fluent multi-digit multiplication and long division, with at least a strong understanding of the ideas of multiplication and division, but not necessarily a full understanding of how the algorithms work.

 

To check these, you could just make up some multi-digit problems with different operations and go through the facts with her. 

 

(My kids' rest time is over, so I have to go, but I'll add more later.) 

[kateingr]

Continuing...I'm afraid I'm not answering your questions in order, though. 

 

Beyond the basics of the facts and the standard procedures is that nebulous area of number sense. Based on what you said about your daughter having trouble adding 38 + 4 without stacking the numbers, I'd guess this is an area where she could use some backing up. 

 

Number sense is absolutely vital, but I've had so much trouble finding quality, stand-alone resources. (If anyone knows of any, I'd love to hear about them!) Two options to consider are:

 

1. RightStart's Activities for the AL Abacus (with the corresponding worksheets and an AL abacus). The abacus is an awesome resource for helping kids develop number sense, and I think the streamlined format of the activities guide would allow you to go through it pretty quickly. (I have articles on the AL abacus here and here if you're not familiar with it.) 

 

2. MM Blue series, with the AL Abacus or base-ten blocks for visualizing the concepts. 

 

Both of these include facts work and practice with the standard algorithms, but you could either include it or skip it depending on your daughter's needs. There have been a lot of good suggestions on this thread, too, but I expect one of these might be your quickest route to helping your daughter master these topics. 

 

You can either add this work to your child's regular curriculum (perhaps as a warm-up each day) or you can stop entirely and focus just on mastering the basics. In my opinion, these basics are so important that they're well worth your full attention for a while. Plus, an older child will likely pick them up quickly, so it's not like you'll be spending the next four years on getting through division. But either is fine. :) 

 

Once your daughter's number sense is improved and these basic skills are mastered, then I'd expect you could move back into the grade-level curriculum with additional conceptual teaching without a problem. Fractions, percents, and decimals require careful concept development, too, but most programs start from scratch with these each year in middle school, so you'd probably be okay. But if she started to flounder with any of these topics, I'd make sure to back up again and to get the basic understandings of those concepts solid. (And the "Keys to..." series is one of the cheapest and easiest ways to do this, in case you need it.) 

 

 

 

 

[PeterPan]

Thank you.  I understand what you're saying.  My dd also gets confused sometimes with relational words - at least more than I would expect of an 11 yo.  Additionally, I don't think my dd is as likely to understand the meaning of words (in any subject) from context as others typically would.  

 

Lynn, that would be enough for me to suggest considering some evals.  It would be good to know if there is an SLD, a language processing problem, APD, or something else going on.   I don't recall where you live, but in Ohio we have the Jon Peterson disability scholarship, which is a terrific fit for homeschoolers and anyone willing to give up their FAPE.  You get evals through the ps, an IEP, and then the scholarship gives you funds to get services through providers.  You could use it to get a tutor for her, to get some speech therapy if she needs it for that language comprehension issue you're describing, etc.  

 

It's just nice to know the option is there.

 

So, a couple questions I'm pondering based on the variety of replies here.....

 

1)  How would you decide whether to back way up vs. adding more conceptual teaching to existing curricula?

 

2)  If you back way up, how do you know how far back to go?  (placement test, or other determination)?

 

3)  Either way, how would you work on number sense with a 6th/7th grader?

Have you given her a standardized test?  How far behind actually is she?  When people are saying number sense, that's the core of SLD math.  In other words, I go back to my point that if she's actually struggling that much, this is a dc who would get an SLD math label.  But I really don't know how much struggle we're talking here, kwim?  You could give her a placement test or standardized test and see what happens.  The ps or private psych eval will include achievement testing.

 

And the answer for how to back up is you back up as far as you need to.  Ronit Bird has ebooks (on iTunes) that go all the way back to basic number sense.  (this is the number 3, can you see the 1 inside the 3, etc.)  Her c-rods ebook goes through basic addition facts and place value.  Then she has a multiplication ebook.  After that you have her printed books, which go through more elementary math. With an older student who *has* the foundation of the content from dots, c-rods, and multiplication (those ebooks), you could go right into her Overcoming book.  Overcoming Difficulties with Number: Supporting Dyscalculia and Students who Struggle with Maths  Hey look, she's selling it as a kindle book now!  That's fabulous.  People were frustrated because her ebooks (which are AWESOME, btw) were only available through iTunes.  I'm glad the printed books are now available other ways to work on other devices.

[Another Lynn]

Oh E, thanks for your reply.  I might check out the Overcoming book; it sounds interesting.  (We're not in OH, by the way, but that's helpful info for folks who are.)  Her last year 5th grade SAT10 scores for math:  (Which I might come back and delete at some future date)  Total Math 29 percentile rank, 4.9 grade equiv., Math Prob. Solv. 41 percentile rank, 5.4 grade equiv., Math procedures 19 percentile rank and 3.9 grade equiv.  She's been 1 year behind in curricula from the beginning, so I attributed that to the less than stellar scores.  I did not have her do any standardized testing this year, though I still could online.  And, it just occurs to me now that maybe it would be useful to have her test now as a 5th grader and see what the math scores look like since that would eliminate the issue of whether she's been exposed to so-called "5th grade" topics.  (Inspite of what I said earlier about comprehension and vocab/word meanings, her SAT 10 vocab score was 92 (PR) and comprehension 82 (PR).  Ironic.)

 

 

 

 

[Another Lynn]

Kate, thank you so much for your additional help.  I think she's in decent shape on the basics though some facts are not as automatic as they could be.  She has improved a lot this year with multi-digit multiplication and long division, though I wouldn't call it complete mastery.  I'm leaning toward the Key to books with supplements on the side - abacus, games, problem solving, and some kind of daily review book to review whatever we're not working on in the Key to books.  And a big dose of reminding myself that I'm teaching her, not the curriculum, and to reinforce concepts as often as needed.    

[Heathermomster]

Join us over on the learning challenges boards.. :D

[PeterPan]

Lynn, if there are 2 standard deviations of discrepancy between achievement and IQ, a ps will diagnose SLD (specific learning disability) in that area.  It might be you're there.  That's a discussion you have with a psych or with the ps, however you want to fund it.  I'm all for evals.  Evals give you the right words.  Just the fact that she's (unexpectedly) functioning a full grade behind is significant.  Don't blow off your mother gut.  Evals are good.  :)

 

And yes, join us on LC!  It's the hippest place on the boards.  Only there do I dispense the sacred peanut butter cake recipe.   :drool5: