Testing question

Well, what you are describing is a curve on a test and the mean is the class average. Your son wasn’t that far behind the mean infact he is within the first standard deviation.

Even in college we have curves like this that range from a 58 to a 100. The spread of the curve depends on how hard the test is. Many times with scores that are low the whole class is curved down as the test may have been too difficult.

It is good that your son wants to know what errors he made so he can learn from them, this shows he is becoming mature and responsible.

At our school the math final is a department-wide test. All classes take the same test at that math level. The test is multiple choice and might be put out by the book publisher. The school does not give the test back to the students because they use it year after year. A student or parent can go in and look over the test and their responce sheet but can not leave the classroom with the material. My guess is with this type of test the students do lower then they do during the school year. The test is a different format then what they normally take and might be harder in content then the tests given by the classroom teacher.

Helen

It’s great he wants to go over the stuff with the teacher. Encourage him *not* to use his mistakes as “proof of his stupidity.” Mathemeticians get a *lot* wrong — but sit there and wrestle with things until they make sense. Believe it or not, people who are good at math weren’t born with it.
For what it’s worth, people confuse me for a math whiz (and I did get a 760 on the GRE Math section). Rarely got more than a 70 on a math test in high school — usually somewhere between 60 & 70. BOy, did I wrestle with it and study…. but I also learned a lot about *how* to study for math, which is a bit differnet than other subjects. Yes, many of the errors were “careless calculation” errors — but no, I wasn’t so brilliant that it came easily; if I hadn’t worked like a dog those grades would have been 30’s. (If it did come easily, I could have just focused on the silly computation details. Focusing on both is a bear — which is behind advocacy for calculators.)
It would be interesting to know what kinds of errors he made. Keep encouraging him to work to understand the stuff — and frankly, to broadcast the attitude that he expects to. It can’t but have an effect on both the teacher and himself.

Is it at all possible for him to believe that people who end up being really good in math struggle with it? It’s *HARD.* STruggling with it doesn’t mean you are stupid — the fact that you have enough brains to wrestle with it means you are very smart. So… please, please, urge him that if he goes in to see the teacher and it is all so much clearer then… tell him that does NOT mean he’s an idiot who should have gotten it. ATtitude is sometimes the difference between success and failure and this is one of those times.
My high school test grades tended to be in the 60’s and 70’s — homework grades saved me, and lots and lots and lots of help from Dad (and very concept-based teaching). Yet I got 760 (out of 800) on the Graduate Record Exam — in the 92%ile of people going to graduate school. It just took a while for it all to sink in — *and* I fought with the stuff ‘til it made some kind of sense.
If you can, have him find out what kind of mistakes he made…. but don’t call ‘em “stupid mistakes” whatever they are. Math gets crammed in awfully quickly and it takes most of us a bit logner than the time between tests to put it all together.
If he’s stupid and senile… so are most of his classmates, eh? It’s up to him whether or not to let this beat him. Inflating the grade won’t make the math any easier. Learning not to let an arbitrary number make you cave in… that’s worth learning.

(1) Average grade on a test can be anything you darned well want it to be. Grading always involves a degree of subjectivity, and grading standards vary by state, by district, by school, by department, by teacher. In the system I grew up in — a system with extremely high standards, by the way, where our Grade 10 program included classic Euclideam geometry and logic, and our English included poetic diction; subjects which now seem to be mostly in colleges — in that system a pass mark was 50 and an A was 80. It was very, very rare indeed for anyone to get over 90. Then we met visitors from the US who got snooty because they had 95 averages and their systems had such “high” standards that the pass mark was 65 — and they couldn’t write a simple sentence. The grades are *entirely* dependent on local standards.

(2) Sue is absolutely right. People who do math work very very hard at it all the time. I had to leave the math grad program because my thyroid messed up and I simply couldn’t keep up with the level of work which requires several hours a day of wrestling with problems, often chewing over the same problem for days or weeks or even months.
It is unfortunate that the extemely mistaken idea has gotten into the public mind tht you should get the answer to a math question instantly by magic; worse that this false idea has gotten into many elementary school classrooms. And the terribly damaging false idea that you are born with a math talent or not and if nort you should just give up. We spend (waste) an awful lot of time in senior high schools and colleges and universities trying to undo the damage this has caused. Look at Sheila Tobias’s “Overcoming Math Anxiety” for some further thoughts on this. Also look at the Third International Math and Science Study for some interesting thoughts on other cultures’ more positive attitudes to math and learning.

Thank you all for your responses. Turned out his errors were careless ones. His teacher felt they were due to his feeling rushed and some misinterupation of the questions. She recommended he get extended time and a test reader next year for his final. He used these accomodations during the school year but not during the final. For his finals requiring extensive reading the school provided extended time and a test reader because for these they felt it necessarry but not for math, math is his strength. We do not know the results of his other finals he is nervously awaiting these results. Thanks again.

Sue makes good points. However, when class averages are really low on certain tests, I think we do have to ask why. Did the teacher race through the unit to complete it before the end of the year? Was if perhaps too challenging? We are seeing incredibly challenging math standards in CA now and I frankly question the wisdom of teaching more faster to all students. I tend to believe, as a special educator, that if we want math competency in our country, we need to teach less, better earlier and lay a strong foundation for higher math later on. We pretty much teach a concept a day.

My district administers a district math test three times per year on grade level standards to date. We have seen some grade levels fail miserably, like 24/30 fail to meet the criteria of 70% to pass. I think this tells us that something is wrong with the test and the curriculum, esp. when teachers are usurping more and more of the day to teach math, and staying after school 2-3 days per week to run intervention programs for their students. This picture is not quite right.

Of course, the question arises whether the extra time needed on math now is necessary to make up for the fact that teachers were trimming the time and effort in previous years. Yes, we know you personally are responsible, Anitya, but an awful lot of people out there are not. A huge number of elementary teachers are math phobic. There are constant instances of teachers telling a class that if they are good, they won’t have to do any math work — a double whammy on time and attitude.

The school system that I attended as a child had extremely high standards, standards that when I tell people about them now I am told I am making things up, but I have copies of the old texts to prove it.

How they succeeded was exactly what Anitya is advocating, but on a system-wide scale. There were criteria set for each grade, clearly understood by all, teachers and students and parents. The number of criteria was kept to a reasonable limit, perhaps three or four major topics a year, the exact opposite of the spiral curriculum of throwing a new concept every day and a new topic every week and hoping some stick.

This was forty-odd years ago, and yes, we had few facilities for LD kids. Funny thing though, the step by step clearly outlined curriculum seemed to work well for a very large number. If you could get this working with modern LD resources, you could have a really good system.