algebra issues

This girl’s very high verbal IQ may allow her to compensate for a vision problem when reading (able to establish patterns and fill in gaps from context), but the problem could show up in math as difficulty copying problems accurately, poor attention to visual detail (especially when there is no context, such as whether a sign is - or +), poor visual-motor coordination that slows down her writing, inability to simultaneously process mental tasks and visual-motor tasks, etc. If she were my child, I would want to at least rule out this possibility by getting a developmental vision evaluation. See http://www.childrensvision.com for information, and http://www.covd.org for developmental optometrists who specialize in this type of evaluation.

If visual efficiency problems are either ruled out or remediated, then a program such as PACE (Processing and Cognitive Enhancement) is likely to be helpful for this girl. PACE helps develop underlying skills such as attention to detail, visual processing speed, sequential processing speed, simultaneous processing skills, etc.

Nancy

Have you tried having her do her math problems on graph paper (nor more than four squares/inch) instead of lined paper? Using this simple accomodation for my ds results in a signficant increase in speed and decrease in “careless” errors. Agree with Nancy it may be a vision issue.

This was also a problem for my formerly mixed handed son. He also has a vision issue. With some remediation ( we are 7 weeks into vision therapy) it is only a slight problem. He still has some trouble with missing details but it is much better and he doesn’t make the math sign errors anymore.

Your post does not have a specific question but it may be that this child has an underlying issue. Testing her would be one way to approach this problem.

If formal testing is the only way she can obtain the extra time that clearly she needs and will benefit from, then testing should be done. If though her math teacher would be amenable to giving her extra time without formal testing and a diagnosis, I’d go that route. Some of her anxiety might alleviate as she consistently experiences success on her math tests with the extended time.

The kind of errors you are describing is very very common. Also, the pattern of falling apart suddenly in math is far too common. Certainly look at visual issues. Please, please try to keep her from the “well, you’ll nnever be good at math so do arts” dead-end!! A self-fulfilling prophecy if there ever was one.

When I meet new students like this, I talk them through a problem. I write, and I ask them “what do you do next?” and “why?” and “what is missing here?”

Very very often, the “sudden” falling apart is actually the culmination of a developing weakness over a hole in the foundation skills — a straw that breaks the camel’s back, to mix metaphors. The student has been coping over a weakness and has a number of ways of working around it — but as the work gets more and more demanding, the available time and energy for the coping skills runs out.

Nine times out of ten, the student is weak on fractions. The American curriculum is a disaster on fractions, so most students have a big foundation crack here. A large number of students, at least half, are weak on basic number facts, addition and multiplication. I have a student now, Grade 10 in a top private school, who reaches for a calcultor to do 5 X 7. Many people say this is no problem; but it slows him down tremendously, and the constant breaking off of his work to calculate and then come back to the paper leaves immense room for errors.
If you talk the student through several problems, you will see what skills are missing or slow. Sometimes just being alert to the weak spots allows self-correction.
Some students will accept re-teaching of fractions, and that often really helps. If math facts are a problem, go back over them using logic to rebuild the facts in the mind.

Victoria,
You’ve given me an opening for my current whine—my non-LD dd’s fourth grade math. Kids are divided into two groups—advanced and regular. She’s in advanced. (This is a small school—there is no gifted program.) The teacher appears to believe that advanced means accelerated with no teaching. (By this logic college students would not need professors.)

He copies off workbook pages which have a brief explanation at the top of a topic related to an area followed by 35 or 40 problems. Teaching is comprised solely of going over the problems the next day; there is no pre-teaching—kids are supposed to figure it all out (and relate it to the other math they know) from the brief explanation.

In the last ten days, the kids have zipped through the section on fractions, hitherto not touched upon this year. Topics covered included prime and composite numbers, factoring, greatest common factor, least common multiple, fraction equivalents, improper fractions, mixed fractions, and, finally, application (word problems). Thursday night they were given the 35 problems in application to do for homework, together with 75 more problems of review for the whole fraction area for a test on Friday. This week apparently will be devoted to a speed drive-by of decimals.

I am ready to scream here. In my life since school, fractions, decimals and algebra have been totally invaluable. I really am amazed by people can who think they can live a modern life without these basics. This is just so fundamental that I don’t see how anyone could think devoting just ten days to this subject is nearly adequate for kids to fully absorb and integrate this topic into their thought process. I now have a kid with a 99%ile on the SAT-9 getting Cs in math but, much worse, not really learning this fundamental knowledge. Racing through these topics is just another example of dysteachia. And probably why so many kids fall apart in algebra.

Well, the sort of good news is that in this horrendous spiral curriculum she will be run through fractions again in Grade 5 and again in Grade 6 and probably again in Grade 7, in hopes that some of the drive-by’s will hit.

I would recommend getting some good materials on fractions, and by good I mean with oodles and oodles of visual and concrete work, and working *with* her (what she has obviously missed in school) 15 minutes a day through the summer.
I’ll photocopy out-of print materials and send you copies at cost if you’re interested.

I tutored my child in these areas over the summer of 6th grade, because the teacher basically gave up on teaching math (he was teaching aliens) and threw it to the student teacher to teach this stuff in 4 weeks. Some how, giving a kid 40 problems is more of a solution that actually teaching the methods of math.
Now, in high school, my son tutors other kids in his class on the geometry, but is getting an F—it is the stupid, social group—social think math. No formulas, few proofs—sit around and talk math and you will “discover the principles” the teacher teaches about 20% of the time—and my son feels the teacher is out to nick-pick everything. He is totally frustrated and disgusted with the whole thing.
I refuse to have my child with a disability in this math and the head of the math dept did agree the math curriculum is terrible—but there is no money for new books, so tough luck. How about the teachers just teaching the subject? how about throwing in some direct instruction?
he will have to take math all over again when he gets to college.

I tutor students who are weak with fractions. Reaching for a calculator as a sort of conditioned reflex is also common. Although as I’m thinking about it, I have one students who has recently abandoned the calculator. I’m not sure why that is.

Sara McName.

My son’s principal insists that if we gave all children calculators from Gr. 1 forward, they would do just as well at learning their math facts…he insists research backs this up…

The stuff that passes as “research” in the education field is often a joke. 90% of it consists of someone referring back to someone else who refers back to someone else … and in the end it’s wishful thinking and unfounded opinion. The big NIH reading study and the TIMSS (third international math and science study) skirted around this and developed a few excellent euphemisms (“developing concepts” for actually teaching math rather than paper shuffling, for example). The NIH reading study gently mentioned that after they sorted out the “research” that was actually scientifically sound, they had only 10% of the original mass.

It isn’t usually worth starting a fight, but if you want to burn your bridges, press him to tell you WHAT research. I will bet you dollars to doughnuts that he doesn’t have a clue. He is just repeating a party line that he has been taught.

Calculators *can* be useful, but most teachers don’t have a clue how to use them. And as most elementary teachers are math challenged themselves (Think — how do people make the career choice of going into elementary ed?) the teachers use the calculators as a crutch and model negative behaviours for their students.

I have had a whole class of students failing algebra because of four years of previous bad teaching — one incompetent teacher in Grades 6 and 7, and another totally unqualified one in Grades 7 and 8, small system with only two classes per grade so there was no leavening from outside influences — and when I tried to review fractions they all told me I was crazy, nobody would ever have to do fractions ever again because the calculator did everything. Of course 1/x and x/5 and x/y were a lost cause, and *at least* 40% of the kids in that system proceeded to fail the provincial graduation exams, not counting those who dropped out before exams.

I had a student in adult ed who was unable to pass his algebra tests because an unqualified history teacher was marking them from an answer sheet, and his answers had to match exactly to the letter — if he wrote .5 instead of 1/2 or vice versa, he was marked wrong. His teacher also told him that it was absolutely impossible to find a square root without a calculator (hmm, wonder what Isaac Newton did? First invent a time machine to get the claculator? And where to get fresh batteries?)

Stick to your guns and teach your kid some number sense. The calculator can help with detaill work and long calculations and repetitive stuff, but first you have to have a road map of where you are going.
I have a student right now, in Grade 10 in a prestigious private school in Montreal, all the advantages, and he has been dropped out of the college-prep level and is not getting such hot grades in the general level either. He’s good at getting concepts, but simply doesn’t know how to work through the details of a multi-step problem — never learned how. Everything was always one-step punch it in, and he was fine to Grade 9 when multi-step problems hit, and even with his nice graphic calculator in hand he has no number sense and no systematic problem-solving approach and no attention to detail, and he lost it. This is the one who grabs the calculator to do 5 x 7. He has too much calculation load distracting him from learning anything else about math.

I knew an MBA student who grabbed her calculator to multiply and divide by ten. She would have failed statistics and finance and probably accounting too had she not been able to rely on the group projects to pass. She was pretty aggressive on the marketing end of things, though, so in the end she did find a job, but probably not nearly as good a one as she could have had she had automaticity in her math facts.

Math Educators—
If I may ask for some assistance please!
I am a 43 yr old college student—second time through—ADHD—and am close to graduating—finally—the 22 year plan—and am presently in a “Problem Solving with Math” course—which I think you could say is a math survey course—with a practical flavor—We have just gone through the algebra section—quadratic equations, factoring, polynomials, order of operations, integers, etc. —I hit —slammed into a wall on the last take home test—the amount of time I spent was embarrasing —and still did not complete everything (I did include my scratch paper when I handed in my test—so I could at least get partial credit) —at times I felt as if I were looking at Chinese characters—it just did not register—when I attempted to use the book, many times it just confused me more—as one gets confused when reading legal documents, I spoke to my professor about this, he did not have any solutions come to his immediate mind, but, I believe that he will ponder it over the next week. So, I figure that I too need to delve into a solution, so I went back to this fantastic site, which has been such a help to me in the past–
I wonder if any of you might have some tricks/mechanisms that I might be able to use to help make this more accessable—
I am a History major, and will be going into teaching, having taught on the ski slopes for over 20 years—so causal thinking is a strong point of mine, but I can’t find a bridge to make the connection with math—any suggestions are appreciated—thank you!!
Jon Wallace

It’s too much to give you the whole book right now, but here’s a place to start:

When you are skiing, if someone shows you anew technique, you visualize it, you try out the various moves, etc.; you mentally put yourself into the move before you do it.

Do the same thing in math. **Put yourself into the problem**.
When you get the problem of two guys in rowboats, picture yourself in a rowboat rowing downstream, and then in a rowboat rowing upstream. What’s the difference in how you feel? Why?
When you get the parabola and the maximum/minimum, picture it as a half-pipe and ski down the valley and up the other side. What happens at the bottom? Why? Slope is an obvious concept for skiing — how does the number relate to the steepness?
When you get the problem about the guy trying to maximize his profits, stop thinking about some imaginary ghost — put yourself behind the counter in the ski shop. How much money is coming into your hands? How much is going out? How much is left in your pocket? Are you in trouble?

*Most* students who lack confidence in math try to distance themselves from it. But how can you do well at something that you keep at arm’s length and treat as if it had a bad smell? You have to face down the slope and let yourself go into it — work with it, not against it.

(I also ski, you may guess)

Earlier, maybe a week a go, I posted a detailed outline of problem-solving techniques in seven steps. Use the search button with my name to find it. Most of my students find this extremely helpful.

I don’t know any history teachers that no anything about math. And math teachers tend to be weak in history. I wonder if learning about the history of math might help.

For instance, the Roman symbol for ten is and X. The Chinese symbol for ten is a plus. An X and a plus are basically the same thing. Could they have a common origin?

The Roman symbol for five is a V. It looks like a cuneiform symbol for five that has been rotated 90 degrees counterclockwise. The same goes for the cuneiform symbols for one, two, and three. They look like the Roman one, two and three turned 90 degress.

The cuneiform one, two, and three look like the printed form of Chinese one, two, and three. The cursive form of Chinese one, two and three look like Arabic one, two and three.

I’ve never seen any of this sort of thing in a history course. Maybe because history teachers have so much trouble with math.

Sara McName

how do i do long divbison

This girl’s very high verbal IQ may allow her to compensate for a vision problem when reading (able to establish patterns and fill in gaps from context), but the problem could show up in math as difficulty copying problems accurately, poor attention to visual detail (especially when there is no context, such as whether a sign is - or +), poor visual-motor coordination that slows down her writing, inability to simultaneously process mental tasks and visual-motor tasks, etc. If she were my child, I would want to at least rule out this possibility by getting a developmental vision evaluation. See http://www.childrensvision.com for information, and http://www.covd.org for developmental optometrists who specialize in this type of evaluation.

If visual efficiency problems are either ruled out or remediated, then a program such as PACE (Processing and Cognitive Enhancement) is likely to be helpful for this girl. PACE helps develop underlying skills such as attention to detail, visual processing speed, sequential processing speed, simultaneous processing skills, etc.

Nancy

Have you tried having her do her math problems on graph paper (nor more than four squares/inch) instead of lined paper? Using this simple accomodation for my ds results in a signficant increase in speed and decrease in “careless” errors. Agree with Nancy it may be a vision issue.

This was also a problem for my formerly mixed handed son. He also has a vision issue. With some remediation ( we are 7 weeks into vision therapy) it is only a slight problem. He still has some trouble with missing details but it is much better and he doesn’t make the math sign errors anymore.

Your post does not have a specific question but it may be that this child has an underlying issue. Testing her would be one way to approach this problem.

If formal testing is the only way she can obtain the extra time that clearly she needs and will benefit from, then testing should be done. If though her math teacher would be amenable to giving her extra time without formal testing and a diagnosis, I’d go that route. Some of her anxiety might alleviate as she consistently experiences success on her math tests with the extended time.

The kind of errors you are describing is very very common. Also, the pattern of falling apart suddenly in math is far too common. Certainly look at visual issues. Please, please try to keep her from the “well, you’ll nnever be good at math so do arts” dead-end!! A self-fulfilling prophecy if there ever was one.

When I meet new students like this, I talk them through a problem. I write, and I ask them “what do you do next?” and “why?” and “what is missing here?”

Very very often, the “sudden” falling apart is actually the culmination of a developing weakness over a hole in the foundation skills — a straw that breaks the camel’s back, to mix metaphors. The student has been coping over a weakness and has a number of ways of working around it — but as the work gets more and more demanding, the available time and energy for the coping skills runs out.

Nine times out of ten, the student is weak on fractions. The American curriculum is a disaster on fractions, so most students have a big foundation crack here. A large number of students, at least half, are weak on basic number facts, addition and multiplication. I have a student now, Grade 10 in a top private school, who reaches for a calcultor to do 5 X 7. Many people say this is no problem; but it slows him down tremendously, and the constant breaking off of his work to calculate and then come back to the paper leaves immense room for errors.
If you talk the student through several problems, you will see what skills are missing or slow. Sometimes just being alert to the weak spots allows self-correction.
Some students will accept re-teaching of fractions, and that often really helps. If math facts are a problem, go back over them using logic to rebuild the facts in the mind.

Victoria,
You’ve given me an opening for my current whine—my non-LD dd’s fourth grade math. Kids are divided into two groups—advanced and regular. She’s in advanced. (This is a small school—there is no gifted program.) The teacher appears to believe that advanced means accelerated with no teaching. (By this logic college students would not need professors.)

He copies off workbook pages which have a brief explanation at the top of a topic related to an area followed by 35 or 40 problems. Teaching is comprised solely of going over the problems the next day; there is no pre-teaching—kids are supposed to figure it all out (and relate it to the other math they know) from the brief explanation.

In the last ten days, the kids have zipped through the section on fractions, hitherto not touched upon this year. Topics covered included prime and composite numbers, factoring, greatest common factor, least common multiple, fraction equivalents, improper fractions, mixed fractions, and, finally, application (word problems). Thursday night they were given the 35 problems in application to do for homework, together with 75 more problems of review for the whole fraction area for a test on Friday. This week apparently will be devoted to a speed drive-by of decimals.

I am ready to scream here. In my life since school, fractions, decimals and algebra have been totally invaluable. I really am amazed by people can who think they can live a modern life without these basics. This is just so fundamental that I don’t see how anyone could think devoting just ten days to this subject is nearly adequate for kids to fully absorb and integrate this topic into their thought process. I now have a kid with a 99%ile on the SAT-9 getting Cs in math but, much worse, not really learning this fundamental knowledge. Racing through these topics is just another example of dysteachia. And probably why so many kids fall apart in algebra.

Well, the sort of good news is that in this horrendous spiral curriculum she will be run through fractions again in Grade 5 and again in Grade 6 and probably again in Grade 7, in hopes that some of the drive-by’s will hit.

I would recommend getting some good materials on fractions, and by good I mean with oodles and oodles of visual and concrete work, and working *with* her (what she has obviously missed in school) 15 minutes a day through the summer.
I’ll photocopy out-of print materials and send you copies at cost if you’re interested.

I tutored my child in these areas over the summer of 6th grade, because the teacher basically gave up on teaching math (he was teaching aliens) and threw it to the student teacher to teach this stuff in 4 weeks. Some how, giving a kid 40 problems is more of a solution that actually teaching the methods of math.
Now, in high school, my son tutors other kids in his class on the geometry, but is getting an F—it is the stupid, social group—social think math. No formulas, few proofs—sit around and talk math and you will “discover the principles” the teacher teaches about 20% of the time—and my son feels the teacher is out to nick-pick everything. He is totally frustrated and disgusted with the whole thing.
I refuse to have my child with a disability in this math and the head of the math dept did agree the math curriculum is terrible—but there is no money for new books, so tough luck. How about the teachers just teaching the subject? how about throwing in some direct instruction?
he will have to take math all over again when he gets to college.

I tutor students who are weak with fractions. Reaching for a calculator as a sort of conditioned reflex is also common. Although as I’m thinking about it, I have one students who has recently abandoned the calculator. I’m not sure why that is.

Sara McName.

My son’s principal insists that if we gave all children calculators from Gr. 1 forward, they would do just as well at learning their math facts…he insists research backs this up…

The stuff that passes as “research” in the education field is often a joke. 90% of it consists of someone referring back to someone else who refers back to someone else … and in the end it’s wishful thinking and unfounded opinion. The big NIH reading study and the TIMSS (third international math and science study) skirted around this and developed a few excellent euphemisms (“developing concepts” for actually teaching math rather than paper shuffling, for example). The NIH reading study gently mentioned that after they sorted out the “research” that was actually scientifically sound, they had only 10% of the original mass.

It isn’t usually worth starting a fight, but if you want to burn your bridges, press him to tell you WHAT research. I will bet you dollars to doughnuts that he doesn’t have a clue. He is just repeating a party line that he has been taught.

Calculators *can* be useful, but most teachers don’t have a clue how to use them. And as most elementary teachers are math challenged themselves (Think — how do people make the career choice of going into elementary ed?) the teachers use the calculators as a crutch and model negative behaviours for their students.

I have had a whole class of students failing algebra because of four years of previous bad teaching — one incompetent teacher in Grades 6 and 7, and another totally unqualified one in Grades 7 and 8, small system with only two classes per grade so there was no leavening from outside influences — and when I tried to review fractions they all told me I was crazy, nobody would ever have to do fractions ever again because the calculator did everything. Of course 1/x and x/5 and x/y were a lost cause, and *at least* 40% of the kids in that system proceeded to fail the provincial graduation exams, not counting those who dropped out before exams.

I had a student in adult ed who was unable to pass his algebra tests because an unqualified history teacher was marking them from an answer sheet, and his answers had to match exactly to the letter — if he wrote .5 instead of 1/2 or vice versa, he was marked wrong. His teacher also told him that it was absolutely impossible to find a square root without a calculator (hmm, wonder what Isaac Newton did? First invent a time machine to get the claculator? And where to get fresh batteries?)

Stick to your guns and teach your kid some number sense. The calculator can help with detaill work and long calculations and repetitive stuff, but first you have to have a road map of where you are going.
I have a student right now, in Grade 10 in a prestigious private school in Montreal, all the advantages, and he has been dropped out of the college-prep level and is not getting such hot grades in the general level either. He’s good at getting concepts, but simply doesn’t know how to work through the details of a multi-step problem — never learned how. Everything was always one-step punch it in, and he was fine to Grade 9 when multi-step problems hit, and even with his nice graphic calculator in hand he has no number sense and no systematic problem-solving approach and no attention to detail, and he lost it. This is the one who grabs the calculator to do 5 x 7. He has too much calculation load distracting him from learning anything else about math.

I knew an MBA student who grabbed her calculator to multiply and divide by ten. She would have failed statistics and finance and probably accounting too had she not been able to rely on the group projects to pass. She was pretty aggressive on the marketing end of things, though, so in the end she did find a job, but probably not nearly as good a one as she could have had she had automaticity in her math facts.

Math Educators—
If I may ask for some assistance please!
I am a 43 yr old college student—second time through—ADHD—and am close to graduating—finally—the 22 year plan—and am presently in a “Problem Solving with Math” course—which I think you could say is a math survey course—with a practical flavor—We have just gone through the algebra section—quadratic equations, factoring, polynomials, order of operations, integers, etc. —I hit —slammed into a wall on the last take home test—the amount of time I spent was embarrasing —and still did not complete everything (I did include my scratch paper when I handed in my test—so I could at least get partial credit) —at times I felt as if I were looking at Chinese characters—it just did not register—when I attempted to use the book, many times it just confused me more—as one gets confused when reading legal documents, I spoke to my professor about this, he did not have any solutions come to his immediate mind, but, I believe that he will ponder it over the next week. So, I figure that I too need to delve into a solution, so I went back to this fantastic site, which has been such a help to me in the past–
I wonder if any of you might have some tricks/mechanisms that I might be able to use to help make this more accessable—
I am a History major, and will be going into teaching, having taught on the ski slopes for over 20 years—so causal thinking is a strong point of mine, but I can’t find a bridge to make the connection with math—any suggestions are appreciated—thank you!!
Jon Wallace

It’s too much to give you the whole book right now, but here’s a place to start:

When you are skiing, if someone shows you anew technique, you visualize it, you try out the various moves, etc.; you mentally put yourself into the move before you do it.

Do the same thing in math. **Put yourself into the problem**.
When you get the problem of two guys in rowboats, picture yourself in a rowboat rowing downstream, and then in a rowboat rowing upstream. What’s the difference in how you feel? Why?
When you get the parabola and the maximum/minimum, picture it as a half-pipe and ski down the valley and up the other side. What happens at the bottom? Why? Slope is an obvious concept for skiing — how does the number relate to the steepness?
When you get the problem about the guy trying to maximize his profits, stop thinking about some imaginary ghost — put yourself behind the counter in the ski shop. How much money is coming into your hands? How much is going out? How much is left in your pocket? Are you in trouble?

*Most* students who lack confidence in math try to distance themselves from it. But how can you do well at something that you keep at arm’s length and treat as if it had a bad smell? You have to face down the slope and let yourself go into it — work with it, not against it.

(I also ski, you may guess)

Earlier, maybe a week a go, I posted a detailed outline of problem-solving techniques in seven steps. Use the search button with my name to find it. Most of my students find this extremely helpful.

I don’t know any history teachers that no anything about math. And math teachers tend to be weak in history. I wonder if learning about the history of math might help.

For instance, the Roman symbol for ten is and X. The Chinese symbol for ten is a plus. An X and a plus are basically the same thing. Could they have a common origin?

The Roman symbol for five is a V. It looks like a cuneiform symbol for five that has been rotated 90 degrees counterclockwise. The same goes for the cuneiform symbols for one, two, and three. They look like the Roman one, two and three turned 90 degress.

The cuneiform one, two, and three look like the printed form of Chinese one, two, and three. The cursive form of Chinese one, two and three look like Arabic one, two and three.

I’ve never seen any of this sort of thing in a history course. Maybe because history teachers have so much trouble with math.

Sara McName

how do i do long divbison