How would you have graded this simple test?

[Alex Franke]

Moving on now

Thanks for stopping by! No, not unpopular or "bad guy," but you've already moved on, so I guess you probably won't see this.

[Kristofor]

Clearly the answers were wrong, marking them wrong was the correct thing to do.

Now for me, the issue comes in determining how this grade would play in your grade for the whole course. In most (maybe all?) of my elementary/junior/senior high classes the final grade was just a composite of all of the component grades (homework, quizes, papers, projects, tests, etc.).

In this case you clearly were on the right track and essentially made a single type of mistake repeatedly. If you subsequently had another test that covered this material and aced it I would see little reason to knock your final grade for a skill you had mastered by the end of the class. That is the way several college classes were handled (quizes/homework for assessment, but the grade was all about a couple big projects or and or a midterm/final exam).

At the same time, I see why it would be VERY hard for primary school teachers to grade with that flexibility. Instead of having 6 classes to worry about they would have 150 individuals to assess, and the issues of fairness and objectivity/subjectivity would be harder to deal with in that environment...

PS, I had Honors Physics profs at the U who took exactly the opposite approach for question design as Loring and Twistsol's. I received an A on a 2 hour exam with 19% of the possible points, I believe 3% was a C-... But this was on a crazy Rube Goldberg type question with all sorts of mechanics (massless, frictionless, inextensible, blah blah blah), but also including point charges moving in non-uniform electric and magnetic fields and the like. Poor test design IMO, but that type of approach does make sure you're religious about carrying the correct units of measure from step to step...

[Alex Franke]

BTW, the choice of symbols for G.T. and L.T is surely just as arbitrary as the choice of 2 for Two and 3 for THree, and just as important.
If you had consistently done 2+2 = 6 and 3+3 =4 getting your 2 and 3 reversed, do you think you would have deserved a partial credit or some recognition?

That's interesting. I agree about the arbitrariness of the symbols, but I think that getting opposite relational operators consistently wrong still shows an understanding of their use and the quantities they operate on. So I think "no" on the number example -- the kid would need to go back and learn the numbers before learning the relational operators.

...unless maybe it was discovered that the kid just came in from some obscure culture where "2" meant three and "3" meant two. If that came to light I'd probably set that straight and have then re-take the test.

[sailor55330]

Here's my two cents, which will probably be very unpopular here.

1. The marjority of the items were wrong. Therefore the student should fail. The teacher designed the test to give the student the opportunity to demonstrate the CORRECT understanding of a mathematical symbol and it's correct use. The student did not do this.


2. There is a consistency with the answers. The student seems to have a grasp of the value of numbers, but perhaps not a grasp of the proper use of symbols. A simple verbal test would help to eliminate that. Ask the child which number is bigger and then ask them to express that on the board with the symbols. That could help to determine if the child has a grasp on concept.

3. The "u" vs. A,B,C, etc. I dont' care what designation they use to classify a grade as long as it is understood and practiced among all students. If the student doesn't understand the importance and classifications system, then there is no point of grading in my book.


I probably seem like a bad guy for this, but I am tired of everyone being treated the same and pushed through the system. Not everyone can win, not everyone can get an "a" not everyone has to be right all the time. The teacher is responsible for teaching, but the student is responsible for learning. If everyone in the class made these mistakes, then the teacher didn't do their job, if the majority did not make these mistakes then at least part of the responsibility lies with the student. However, if the teacher sees this, then hopefully they will address with the student--That would be the best thing.

I don't ever remember getting any sympathy grades for math. Basic math at this level is an objective study, not a subjective study. It is commonly understood and accepted that 2+2=4, 5-2=3, etc. Take out all the dyslexic, confused, troubled, stressed, professor error, or any other what-if scenarios and grade the test for what it is---a simple test in basic, accepted mathematics.

Moving on now

[phrog]

Seems to me like there was too much emphasis on one concept. If the idea was to test the student's comprehension of the concept, one or two questions (or maybe 3 at the most) regarding the concept should have sufficed to inform the teacher whether the student "got it." By asking the same question over and over (only using different numbers) the grade got skewed against the student's overall math comprehension. (Obviously, he understood addition and subtraction.) I don't fault the teacher for the grade given but do think the teacher designed a "bad" test.
Richard

[Alex Franke]

Here's an interesting angle for those of you who would record the "U" grade.

Would it ever be fair to grade this differently?

It seems like if most students got it consistently wrong (indicating a teaching error), then maybe a retest would be appropriate at this level. (In college, I had a prof that made a clear error in lecture notes, and that error appeared on many exams. Students that made the error did not get credit restored because they "should have concluded" that the prof was wrong.)

Or what if the kid was dyslexic? Or maybe he missed class on that day and all the kids got together and convinced him that it was the other way around?

What if came out that (obviously purely hypothetically) that the kid came from some obscure culture where the symbols were actually reversed? (The head nod comes to mind -- in northern Greece what looks like "yes" actually means "no.")

Is there any hypothetical case where it should be not-so-black-and-white?

[LCHIEN]

BTW, the choice of symbols for G.T. and L.T is surely just as arbitrary as the choice of 2 for Two and 3 for THree, and just as important.
If you had consistently done 2+2 = 6 and 3+3 =4 getting your 2 and 3 reversed, do you think you would have deserved a partial credit or some recognition?

[Alex Franke]

I used "confusion about the concept" in a general sense. To me, if there's confusion about the symbols (even as simple as reversing them), there is confusion that needs to be corrected. Perhaps my wording isn't as accurate as it could be.

Oh, I see. Yes, I agree that there is confusion that needs to be corrected. We agree on this.

The grade level was part of my point about the music analogy. The analogy is out of place because because of the level of the students involved. Understanding the difference between keys seems like a different level of education that the math question posed.

It was hard to come up with another example that illustrated the concept/symbolism argument. But in any case, I do think kids at that age can understand keys. Music is strange in the sense that it's pretty easy to tell if you have the melody right (regardless of key), but like Loring's example of the trio, it's also pretty easy to tell if you have the key right if it's in context.

It sounds to me like your question really has two parts. Was the test graded fairly? Assuming no malice of the teacher, yes, it was. The answers were wrong & marked as wrong. Could the teacher have handled it differently? Yes, absolutely. The teacher could have recognized the pattern & given you another chance to answer the questions.

I agree, but I would change "graded fairly" to "graded accurately" or "graded equitably." Grading it differently would not be accurate or equitable with respect to the other students (like LarryG's "fair test" example), but I think handling it differently would have been the more fair approach.

At what point does the child get a second chance? The teacher has to us judgement here & may likely err on the side of being "mean" to avoid the appearance of favoritism.

I think this is an excellent point. It's sad, in a way, but I think it's absolutely true.

[twistsol]

IN college (and granted college is a long way from elementary) the professor explained to me, bridges fall, planes crash. Wrong for whatever reason doesn't bring those lives back. (e.g. there was no partial credit for a good intention.)

College physics flashback. I wrote m/s on an intermediate step in a problem rather than m/s squared. The exam had four questions, I got 75% on the exam. Dr. Tsang told me in a heavy Japanese accent "You build a bridge, the bridge fall down, you get not partial credit." I got 100% on every subsequent exam.

The hard lessons are the ones that stick with you the longest. Around the same time our schools graded with O for outstanding, S for satisfactory, and U for unsatisfactory because someone felt that an F was too harsh. We all knew what an F was for and what a U meant as well.

On to your revised question, yes, the teacher should have added a see me or something to make sure you properly understood the concepts, but with the exception of the one answer marked incorrectly, the grade was fair.

[LarryG]

Would you ask (at at least hope) for a warning instead of a ticket?

And if you received a warning, would the lesson of exceeding the speed limit have been lost on you?

Good questions. Fair questions. I expect you already know what my answers are.

Of course I would ask for a warning. And no, the lesson would not be lost on me if I did get off with only a warning. But I'd definitely remember the "lesson" a lot more vividly if I had to open up my checkbook.

[Alex Franke]

IN college (and granted college is a long way from elementary) the professor explained to me, bridges fall, planes crash. Wrong for whatever reason doesn't bring those lives back. (e.g. there was no partial credit for a good intention.)

I had a similar one -- one of those chemistry questions with three pages worth of calculations for the answer. I was off by a factor of ten, shifting the decimal point somewhere along the way. You don't make mistakes like that in chemistry or you could blow yourself up!

So finally, for this to have been such a big deal as to bring it up after all these years it surely made an impression on you.

Well, it's not as if it's been hanging on my wall all this time. I came across it when cleaning house just before I left home for college. I remembered it at the time and stuck it in a "memories" box, where it remained until this weekend. I came across it again and thought, "Hmm... I would have handled this differently. I wonder what the fine folks as BT3Central would say..."

I also realized how many of my "memories" I've completely forgotten over the years!

[cgallery]

I wouldn't be happy about the ticket, I would grumble that the cop was just being a hardass and surely had better things to do with his time than write me up for being one MPH over the limit, I might even scream about selective law enforcement ... but I would never try to argue that, strictly speaking, I was not in violation of the law. Because if I was doing 31 in a 30 zone, I was violating the law.

Would you ask (at at least hope) for a warning instead of a ticket?

And if you received a warning, would the lesson of exceeding the speed limit have been lost on you?

[jking]

This is where I disagree. To me this would not at all indicate that the student is confused about the concept. In fact, it would show me that the student is quite clear on the concept of adding and subtracting one quantity from another -- just that he has the glyphs that symbolize those concepts reversed.

I used "confusion about the concept" in a general sense. To me, if there's confusion about the symbols (even as simple as reversing them), there is confusion that needs to be corrected. Perhaps my wording isn't as accurate as it could be.

If someone asked me to play it, I would probably recognize it as major and play it in C. I'm pretty sure it was originally written in G. I don't think I (or a kid) would be actively and consciously transposing it unless they were truly advanced (and then they'd be a smartass for doing it!)

But in the music example (like I would argue for the math examples), the student is showing, "I get the concept and the mechanics of this -- the intervals, how long the notes are, the rests, etc., even if I don't know the key it's in."

It would be interesting to know if (at this grade level) teachers are trying to teach the concepts or just the symbols...

The grade level was part of my point about the music analogy. The analogy is out of place because because of the level of the students involved. Understanding the difference between keys seems like a different level of education that the math question posed.

It sounds to me like your question really has two parts. Was the test graded fairly? Assuming no malice of the teacher, yes, it was. The answers were wrong & marked as wrong. Could the teacher have handled it differently? Yes, absolutely. The teacher could have recognized the pattern & given you another chance to answer the questions.

The second chance opens a can of worms about where to draw the line, though. At what point does the child get a second chance? The teacher has to us judgement here & may likely err on the side of being "mean" to avoid the appearance of favoritism.

[LarryG]

How many of you that think this grade is okay would have no problem with being pulled over for doing 31 in a 30-MPH zone.

<= 30 is right, 31 is wrong. Right?

We will have to begin by assuming that the speed-measuring equipment was not faulty, that I was in fact driving at a true 31 mph.

I wouldn't be happy about the ticket, I would grumble that the cop was just being a hardass and surely had better things to do with his time than write me up for being one MPH over the limit, I might even scream about selective law enforcement ... but I would never try to argue that, strictly speaking, I was not in violation of the law. Because if I was doing 31 in a 30 zone, I was violating the law.

So in that sense ... yes, <= 30 is right, 31 is wrong. A lot of the lines we draw in life are somewhat arbitrary but you do have to draw the line somewhere.

[Alex Franke]

For years I was confused by less than and greater than because like you I was not always sure which symbol was which.

I have this vague memory of thinking of the symbol as a shark and then mixing it up -- Was it a shark opening his mouth to gobble the bigger number, or was it the pointy nose of a shark with a closed mouth swimming toward the bigger number? But maybe I just dreamed that... who knows!

Having teachers in the family, I think one has to give a teacher grading 30 test papers in between cooking dinner for her family, preparing lesson plans for the next week, and raising children of her own a break.

I couldn't agree with this more. Teachers (and stay-at-home mothers/fathers) are probably the most undervalued professions in the country. It's a shame that it has to be solely "for the love of the game" for just about every teacher and stay-at-home parent I know. For teachers specifically -- so much work, so few resources, so few hours in the day.