careless errors on Algebra 2 tests

I would take him to a developmental optometrist to find out if he has any developmental vision delays. A developmental vision evaluation includes about 20 tests of visual function not included in a regular eye exam. If your son tests as having problems with “visual efficiency” skills (basically focusing, binocularity and tracking), then vision therapy is likely to help. If he has problems with “visual processing” (reversals, short-term visual memory, visual sequencing, visual perception, pattern recognition, field-of-vision), then he would be a good candidate for PACE (Processing and Cognitive Enhancement). Since visual processing skills build on visual efficiency skills, PACE is also a good follow-up to vision therapy.

PACE is expensive (around $2400 for a 12-week program where we are) but is usually extremely effective with the kinds of problems you are describing, and works well with older children. It is an intensive, comprehensive cognitive skills training program that develops visual processing, pattern recognition, attention to detail, speed of processing, auditory processing, logic and reasoning, etc.

The fact that your son makes careless written errors and then cannot find them indicates to me a visual processing problem. The careless writing can result from problems with visual-motor coordination, which is a common side-effect of having a developmental vision delay. The inability to find the written errors indicates difficulty with visual perception — which could be due either to a developmental vision delay or simply to lack of development of visual processing skills. All of these problems are typically correctable with appropriate intervention and therapy.

Basically a teacher has the right to determine how test questions will be graded. I do think partial credit should be given when understanding of the concepts is clearly shown. However, this requires additional time on the part of the teacher. I believe you would have a good chance of getting this accommodation for your son if you could provide documentation of problems with visual processing.

You can find developmental optometrists in your geographic area at http://www.covd.org. Some good websites with information are http://www.visiontherapy.org, http://www.vision3d.com, and http://www.children-special-needs.org.

Website for PACE is http://www.learninginfo.com.

Mary

Peg,

My son did this in Algebra too, it was extremely frustrating for him as well.. Making calculation errors like you have mentioned is very common with people who are ADD. We didn’t figure this out until he was in his first semester of Geometry but he ended up getting a C in Algebra…all because of the careless erros that were caused by inattention…..In Geometry, it got worse but after we tried medication he was able to get an A in Geometry.

Been There done that….on tests myself and I had a lot of anxiety because I KNEW the material and the harder I tried the worse my anxiety got. It was all part of the ADD…..Medication has helped me as well with paying attention so that I don’t make careless errors that cost dearly…..

Pattim, it seems a couple of years ago when I first found these boards, you were one of the first people to answer my questions! I’m still asking them, so here goes.

I am wondering who is the best professional to diagnose ADD. Child psychologist? Psychiatrist? Pediatric neurologist?

I know a lot of educators and physicians use the Connors assessment, but that is so unscientific! Do you know if the TOVA is a fairly definitive way to check for ADD?

Also, I am wondering if, when you were making careless mistakes in math, you had trouble finding them afterwards.

Mary

This is a pattern I work with day in and day out, with regular students in college algebra, with advanced students in calculus and advanced calculus, with remedial students in developmental math; with classroom students and with tutoring students.

I keep coming back to a simple fact: if something happens rarely, to 5% of the student population, then it’s a disability. If it happens regularly, to 80% of the student population, then it’s the *norm* **in that school system**.
If this same thing is NOT the norm in decently-run schools, then the problem is with the *school system*, not the students.

MOST American school systems, and *almost all* math programs/textbook sold here, have deep systemic problems with teaching. Almost all the programs/texts rush through twelve to twenty topics superficially every year, and almost all rely on superficial multiple-choice tests which reward facile copying and which punish taking time to think things through. This fault shows up in senior high school as national math achievement drops through the floor, in college where students are in remedial math and out of technical programs in droves, and in graduate school where there aren’t enough qualified American students (taking American tests) to fill the places.

Before we blame the poor kid, we need to take a second look at what is missing and why. It is so easy to say that kids have vision problems, that they are LD, that the problem is the family, or poverty, or violence, or TV. All *can* be great excuses for not doing the nitty-gritty hard work of actually teaching a subject properly and thoroughly.

SOME kids have serious vision and learning problems that need to be addressed with intensive retraining; but they are a small minority. 90% of students can and will learn high school level work IF they are taught it. The problem, 90% of the time, lies in the program or the teaching methods or both, which skim over the material superficially and leave students stranded without fundamental skills.

Almost all of the students I deal with, from remedial fractions to advanced three-dimensional calculus, have exactly the same problem: they have been coached intensely in formula filling and guessing games, and have no idea at all of thinking in depth or at length. They are sure that school work in general and math in particular consists of yelling out the answer immediately without hesitation, and that they are valued according to the speed at which they can scream out or circle in the most “right” answers.

Therefore, multi-step problems, creative problem-solving, analysis of diagrams, building up a logical proof, and any real world work using math are absolutely foreign to them, and in fact they strongly resist doing anything of this nature because it is clearly and obviously taking up their time and preventing them from getting lots and lots of marks for “right” answers. After all, they can fill in fifty multiple-guess questions or plug numbers in twenty formulas in the time I take to draw a diagram and analyze a problem, and I am nastily preventing them from getting that nice golden glow of achievement they get from taking home a high-scoring machine-graded mark sheet.

Most of the “careless” errors I see in Algebra 2 and up come from the fact that yes, the student does *not* care.
— the student does not know why he has to write out all these steps. After all, he can guess the answer right most of the time on the basic problems, so he must know the material, mustn’t he? (NO, the basic probelems are warmups to the real stuff, and are guessable because they’re supposed to be simple warmups; the trouble is, he’s supposed to be learning a *technique*, and by guessing, he’s undercutting himself, and will fail on the real problems without the technique, but he has ten years of guessing success under his belt, and he doesn’t want to change now)
— the student is angry and frustrated that he isn’t getting the instant payoff that he’s been trained to expect in his earlier math classes. He often makes mistakes almost deliberately, as a way of “getting back” at this mean teacher who is demanding such silly stuff, not what the student considers to be “real” math, i.e. memorize and reply instantly for instant reward.
— the student does not have any goal in math class. He has been trained out of thinking through problems, and trained into memorize-and-shout/check/hurry. To him, the only rewards in math class are external — the teacher gives marks or gold stars or even candy treats. When a teacher tries to teach real math, where the goal is understanding, the student has lost his focus on the treats and pats. He doesn’t care about problems (he’s been told for ten years to forget about why, hurry up and fill in the worksheet this way) and he is upset about the loss of treats, so the errors are his way of showing that he does not care.

Why can’t he go back over and edit and find his own errors? For one thing, he tuned out completely all those nice explanations of purpose and method and how and why this works, and only came halfway into focus when the teacher told him how to do the magic trick to get the answer. Answers and external rewards are the goal that has been trained; the rest, in all his experience, is just time-wasting digression. Since he’s looking for instant magic tricks and one-second one-step answers, this multi-step logical technique is Greek to him. If he doesn’t care and the whole idea has no meaning to him except as a ritual he’s being forced through, a second going-over isn’t going to make it any better.

As far as the teacher’s marking: yes, it is a good general policy to give partial marks for partially correct work. Several problems arise in practice; it takes time; students compare papers and scream at you for hours (literally) because they got one mark less than their friend for what *they* consider the same; parents often join in the screaming at you; and some students calculate exactly how careless they can afford to be and still keep the grade they want. Teachers who want to make a point of getting the techniques clear all the way through, not slacking, may insist on corect answers only. Not always nice, but sometimes necessary to make a point. The real world does not reward an engineer who drops a decimal point and lets a bridge collapse, even if it was a simple calculation error in the last step.

Take some time talking to your kid. Ask him (without leading questions, just casually) what he thinks math is; why he has to do math; what it might be used for later. If he’s like almost all the students I have, you will be shocked and dismayed at the answers.

Take some time actually reading the math book together — the introduction to the teacher and the student, the historical notes in the boxed sections, the statement of problems at the beginning of each chapter — all the stuff that almost always gets ignored in the rush to “cover the material”. (I always ask *who* is covering the material, me or the student; and what “covering” it really means, anyhow — if it’s not understood and not used and not transferred to other classes and not retained even a week, what was our purpose here anyway??) If your student is like almost all I meet, this idea that there is some content in a math book will be totally new to him; he’s most likely used to grabbing at answers before even looking at the problem.

Then review the material he is supposed to be doing, his most recent tests etc., *without telling* him how to do things; *ask* him what he knows and what he can figure out and why he would do a certain thing and where he can find ideas when he draws a blank. At first this will be incredibly slow, and may feel like pulling teeth; you’ll have to break down and give hints now and then, but keep trying to draw it out of him.

Try working out loud doing a model problem; explain every idea you think of, why and how you are doing this operation. Then have him do a sample similar to yours, right there in front of you. Again, slow and like pulling teeth, but this is what wioll make it meaningful to him.

Wonderful… and sadly so true. This is a battle I fight with my own children- one in precalc and one in eighth grade. The older one gets it though- all these years of listening to my explanations before she knew more math than I remembered:) have helped she says. The eighth grader an I are still working on it.
Thanks Victoria.

Robin

Peg,
My son is currently taking Algebra 2 with Keystone National High School, a correspondence course. He is homeschooled, however, many students who go to school take some courses at Keystone, and their h.s. accepts the regional accreditation that Keystone has. (same level of accreditation as your school). I used to teach h.s. math, and many teachers gave partial credit. However, rather than fight this thing tooth and nail, your son could just drop the course, and take it with Keystone. My son understands the concepts, but is quick to make many careless errors, too. Many students do not like to check over their work, but it’s important. He should also keep track of exactly what type of errors he is making. That is more valuable than you might think! It will be a real eye-opener. Catherine

and parents of younger kids should know that getting kids to THINK about problems and EXPLAIN their answers is not that painful when they are younger. It’s still a slow process, but in the long run I think it will be worth the extra effort.

Jean

It’s ironic.. I read all the posts before I read your original one. The thing I kept thinking was of course,about my own kid first. Then me,and then anxiety.
Okay,maybe I am one of those 5 %ers,and so is my son,but Anxiety over Math is big and real in my house. I tried soo hard to make sense of Math in school,that I was blinded by Anxiety. It pretty much paralyzed any chances of me ever getting a decent grade in class. I could SWEAR to you that I knew the material,that I checked and rechecked my problems,and sure as the sun would come up the next day,I had made careless mistakes. When the teach would tell me,”you made a careless mistake” I would often wonder about the meaning behind this. Care Less? Not . Okay,so they might as well have said stupid mistake. Because I did care,it wasn’t a mistake I meant to make,and heck I checked it over and over,and over,I JUST CAN”T GET THIS STUFF! my mind would scream. In comes anxiety. Then comes helplessness.As you grow up, in comes,care less. Then you have a child of your own,you see the same look on his face. You see the “I could scream” expression. You go over the multiplication facts just one more time,he forgets them one more time. The one benefit my kid has over me. He doesn’t have a dad who is a Math genius. He doesn’t have to endure my Dad. My Dad made it his mission after dinner and a hard day at work,to drill a hole in my head and dump the math in. I suppose this should of made me feel fortunate. It didn’t. It should of helped me learn the math,it didn’t. It helped me to feel so helpless to escape the torture of homework. 50 problems,in 4 hours,bed ,only to wake up and sit through another class,get 50 more problems and do it all over again.All I can say,is thank god for business trips,And calculators. My kid? Well it took a whole school year to keep him from getting anxious about doing Math at all. A whole year of,don’t worry about it,it will be okay. I showed him how to use a claculator. And NO MATH homework. Nadda,zippo,nothing. Now he can sit through Math class,he is starting to retain some of it. We’ll see. In the end? Well, I’m a nurse. I use my calculator to figure out medication dosages,and balance my check book. Aside from that? I will NEVER spend four hours doing Math again! Won’t make my kid do it either. Let’s face it. If he was going to be a budding Math Wiz,well he wouldn’t need me to drill and kill him,now would he? It’s not that I am anti Math,I’m just for not strong arming kids into learning it.Bored? So he sits in a class and it’s easier for him. So what! Maybe he get some of his self esteem back.

A psychologist can diagnose ADD but can’t prescribe meds… I would probably go with the psychiatrist because they can prescribe and monitor the progress. We got lucky because our HMO covered a referral to a pediatrician who specialized in ADD who was affliiated with the University which has done lots of research and medication trials on ADD. He told me that a report from a Neuropsyche would be good because they can diagnose the learning problems. The pedicatric specialist also clued me in on the drop in processing speed and sure enough that had happend in all of my daughters IQ testing…to drop from 122 to 80 something was quite a significant drop…that the school psychologist totally ignored me when I asked her about this 3 months prior…why would she drop that much?? It just didn’t add up to me..

Rating scales like the SNAP IV and the Conners, when the patient is on meds and off meds is usually what they do to diagnose because there really aren’t any tests that are specifically geared toward ADD. The TOVA has it’s problems. It is a continuous performance test. They can do it with either the auditory or visual version. I aced the TOVA but I was doing everything I could to stay focused..and according to the TOVA I am not ADD. The Nelson Denny Reading Test is another test the psychologist used to help pinpoint ADD. I messed up on the Denny..because of inattention to details..it is a timed test and you have to work as fast as you can. Which means you have to concentrate, do vocabulary, read passages, do comprehension answers…. When I made the careless mistakes in math as does my daughter we didn’t notice them until we painstakingly went over them to find them when we knew we had the wrong answers… I still make bozo errors now and then but I do know how to balance a checkbook to the penny now…:-)

Well, he did get “drilled and killed” last week (by my math genius husband) and lo and behold, he got a 91 percent on his last test! I don’t quite know what this means yet, but at least he isn’t failing the class now. I spoke with the teacher again and she told us to hang in there and that she had changed how she gave the test so there was less copying involved (some of his mistakes were simply that he copied the problem down wrong). She also said that she usually does give partil credit, but she has been sick and somehow her grading wasn’t consistent with this last time.

We will see how it goes next week with the test. Homework is still painfully slow for him and he has several soccer games on school nights between now and the test. He is thrilled with his grade, though, and more confident that he can do it.

Thank you all for your ideas on this. I’m sure the struggle isn’t over yet.

Peg

Peg,
I am soo glad for your son:-) The fact that the teacher is willing to accomodate his needs will be a big factor in all of this.

Thanks for the info!

Mary

Peg,

Your son may have dyscalculia. Some of the symptoms are listed here: http://www.ld.org/info/indepth/dyscalculia.cfm along with some strategies that might help.

I have dyscalculia and have the same problem when I copy problems down. I transpose numbers when writing phone numbers, taking inventory, or even omit numbers or letters (2x becomes 2 or x by itself).

Hope this information helps,
Bev

Also, here are some related sites and books/study guides to help:

http://www.ldonline.org/ld_indepth/math_skills/math-skills.html

Good Luck,
Bev

I have a weird learning disability — I have very poor sense of time and space, poor vision including weak tracking and inability to see the big picture, poor hearing and cocktail party syndrome, poor social skills which also relate obviously to the above, some form of hyperactivity; and a tendency to reverse letters and especially numbers. I also have four university degrees, one of them an honours degree in pure math. I’ve taught up to and including three-dimensional advanced calculus. I don’t know my left from my right, but I can find the volume under a hyperbolic paraboloid. Just because I reverse numbers doesn’t mean I’m bad at math — it just means I have to triple-check every time I read, write, or dial a telephone. Just because I reverse letters doen’t mean I’m bad at English; it just means I use my hyperactive speed to edit everything three times.

The point being that one symptom doesn’t make a disease, and often things can be worked around. Try to find your strengths and ways to use them.

Victoria,
I LOVED your post. I couldn’t agree more,with your point:-) Let me ask? If you didn’t have the interest in the Math,would you have not put forth so much effort? I too,have a learning disability. Dyslexic,since kindergarten. I would put forth as much effort as was needed,some times it was superhuman,to do something I really wanted to do.And do it well.One of many good benefits of being Ld,I believe:-)

Hard to explain. I can’t say I find math easy, because I don’t, necessarily. Some seems to be obvious and come easily, and some is extremely difficult. But I’ve always been fascinated by patterns and regularities, in math, in art, in music, and in languages. The logic and balance of algebra and the structure of geometry fascinate me; it’s work, but it’s work that I enjoy doing — very similar feeling to rebuilding the bathroom, learning
how to change the head gasket on my car, painting watercolours, and so on.(Wish I’d had the chance to learn a musical instrument).Very hard work, but a lot of fun.

One time in a graduate level combinatorics seminar, the professor had given us a number of problems that were not at all obvious to solve. He asked a few days later who had come up with the solution; three out of the seven of us raised our hands. He gave the class to us to present our work. Each of us had done something so totally different that anyone not a math major wouldn’t believe we were doing the same subject, much less the same problem. The first volunteer at the board was a young hotshot on the fast track to a professorship. He invented his own new algebraic function and symbols, defined his terms, and used it to prove the result. The second was a quiet and unassumaing but very good, hardworking student. He went through a long and complex algebraic proof referring to about six different theorems. Then there was me, the forty-year-old mother and teacher returning to my studies; I got up and drew boxes and put dots in them. No joke — I work concretely and pictorially even in grad-school abstract math.

Interesting points relating to the above—
The professor, an internationally-known leader in the field, was extremely complimentary about my proof and my originality, and in fact offered to be my doctoral advisor before other people in the department convinced me I was in the wrong place. REAL mathematicians, as opposed to pretentious people who know only a dash of the subject, are as concrete and visual as possible; and they value a characteristic of math called “elegance”, which consists partly of doing things smoothly and simply, without wasted effort, and finding a neat and original way to do things.

I once had a student at the community college **apologize** to me for being a visualizer. I tried hard to tell her that this is a very very good thing, not a fault, but could see I was making little headway against twelve years of counter-productive teaching. In fact, this is about on the level of having a student apologize to you for thinking of the words in their head while reading or writing.

Anyway, my point here is that some things that are viewed negatively by the present school system — visualizing, needing a structure and pattern before memorizing, working concretely before verbalizing — are actually positive skills, not faults, and should be encouraged,

My 11 year old has dyscalculia and we were suffering through computating, mean, median and mode. He knows the steps but his lack of proficiency in basic math skills made him extremely frustrated. This is my first time at this site. Your posting gave me hope for his future. I have a question, did you receive a public school education? I am in N.J. and he goes to the resource room for math and language arts. Before today I thought that his Resource Room teacher was doing a good job now I am not so sure. All suggestions welcomed.

Go for those basic skills. You can’t build a house without a foundation. Calculators are good for speeding up multiple tedious calculation, but they can’t do the thinking for you. You need what is called “number sense”; an idea of what kind of number makes sense in a certain location. For example in a correspondence course I was correcting, all the student, not liking decimals, multiplied instead of dividing, and came to the result that the focal length of a camera was ten meters —a distance from lens to film of over thirty feet. A person with number sense will immediately see that something is wrong here and go back over the problem. There is no way to develop number sense except to work with numbers, and to do that work in meaningful ways that are directly attached to the real world.
I use old texts (pre-1955) from used book stores; problem-solving should be the central part of the course, with manipulation being a tedious mechanical fact which is presented once as a tool for getting the meaning we want, less than 10% of the text (opposite of many present texts).
The majority of my students, up to and including university, stalled out on fractions and need to go back to the old Grade 5 level. If you can get your kid motivated to really understand math, it’s worth spending twenty minutes a day getting this kind of thing right. Twenty minutes a day for a couple of years will make all the difference in the world.

As far as myself, yes I did go to public schools, but these were the public schools of Montreal under the old English system, based somewhat on the old British system, and I have discovered since that time that they were not at all typical; also I had very good informal teaching from my parents.