How would you have graded this simple test?

[Alex Franke]

I like my wife's answer best so far: "I would have stopped marking them wrong when I noticed the pattern, and written 'see me' without a grade. Depending on what kind of kid you were, you might have gotten a do-over or partial credit."

-13, F

Yes, you understood the concept but had the symbols reversed. You still got it wrong. I've never liked 1/2 credits, do overs etc. I think it teaches kids that there is always a second chance and you can get by with just trying. The harsher lesson of failing should make one not want to repeat it again.

I think what makes this example interesting is that I don't see it so black and white. Math is a combination of concepts and (to a much lesser extent) symbols. Of course the answers were wrong, but if the goal is to teach mathematical concepts as opposed to mathematical symbolism, then the grade misses the mark.

Say you were teaching elementary music and asked a kid, "what are the first four measures of the allegro from Eine kleine Nachtmusik" and he wrote or played all the notes correctly, except in the key of C (as opposed to G). Still an "F"?

[jking]

Other than the one the teacher missed, I would have graded it the same. Was the "U" considered a failing grade? Was it below an "F"? I don't see a reason to give something lower than a failing letter grade. You either fail or you don't.

I agree with others that this test should have been a red flag to the teacher that you probably had the greater than/less than concept switched around. A perfect opportunity for correction especially since you aced the rest of the test. If this was the first test after covering the material, it doesn't necessarily indicate poor teaching. People learn at different rates & in different ways. A follow-up test would have been very important here. If the result was the same after the teacher reviewing the concept again, then the teaching may be inadequate.

[dkerfoot]

You all have it wrong - the symbol is a big fish. He turns his tail on the small number so he can eat the big one!

The teacher might not have taught it well - OR the student may not have listened. To know if the teacher failed you have to see the rest of the student's grades.


Interestingly, studies show that students retain knowledge the longest when they THINK they got an answer right and then are surprised to find they got it wrong. If it is then explained to them, they retain the knowledge longer than if they got it right in the first place.

[jking]

I like my wife's answer best so far: "I would have stopped marking them wrong when I noticed the pattern, and written 'see me' without a grade. Depending on what kind of kid you were, you might have gotten a do-over or partial credit."

Certainly the teacher's judgement to that. I wouldn't argue with it.

I think what makes this example interesting is that I don't see it so black and white. Math is a combination of concepts and (to a much lesser extent) symbols. Of course the answers were wrong, but if the goal is to teach mathematical concepts as opposed to mathematical symbolism, then the grade misses the mark.

Say you were teaching elementary music and asked a kid, "what are the first four measures of the allegro from Eine kleine Nachtmusik" and he wrote or played all the notes correctly, except in the key of C (as opposed to G). Still an "F"?

Math is black & white, though. What if half of the questions were addition & half were subtraction? 9+3 = 12 & you answer 6. 12-6 = 6 & you answer 18. If you do this clear through, it's still an F. However, it's still an indication you are confused about the concept. Your music analogy would work had there been reason to believe you answered the questions based on another numerical system (binary, for example).

In the case of Eine lkeine Nachtmusik, it may depend on what key it was originally written in & what key was reviewed in class? However, if I had an elementary music student capable of transposing music on the fly correctly, I might wonder about advancing the student. Is transposition normal for elementary school?

[Alex Franke]

BTW, I had no history of dyslexia, and I always got very good grades in math (with this exception -- probably part of the reason I beat myself up over it.)

What if half of the questions were addition & half were subtraction? 9+3 = 12 & you answer 6. 12-6 = 6 & you answer 18. If you do this clear through, it's still an F. However, it's still an indication you are confused about the concept.

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.

In the case of Eine lkeine Nachtmusik, it may depend on what key it was originally written in [snip] Is transposition normal for elementary school?

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...

[dkerfoot]

Say you were teaching elementary music and asked a kid, "what are the first four measures of the allegro from Eine kleine Nachtmusik" and he wrote or played all the notes correctly, except in the key of C (as opposed to G). Still an "F"?

So if I answer the question: "Who shot Abraham Lincoln" with "Lee Harvey Oswald" should I get partial credit?

Seeing where a student got confused is helpful for correcting their wrong answers, but it doesn't make the answer right or partially right. Wrong is wrong. It will always be wrong.

Here is a quick sample why it is important: I provide free shipping to customers who order more than $65 worth of product:
(order > $65 = Free Shipping)

If I use the <> signs incorrectly, I'd charge my customers who buy more than $65 worth of product, while providing free shipping to those who spend less than $65. The result would be unhappy customers, wasted time issuing refunds to the bigger spenders and lost revenue on the small orders.

What should the grade be? I can assure you I would find this result extremely Unsatisfactory! Wrong is wrong and very nearly right is still wrong.

.

[Alex Franke]

Other than the one the teacher missed, I would have graded it the same. Was the "U" considered a failing grade? Was it below an "F"? I don't see a reason to give something lower than a failing letter grade. You either fail or you don't.

I think this was maybe first or second grade, and as I recall we would get grades like "VG", "G", "A" (acceptable/average), something like "needs work" for below average, and then the "U" for unacceptable.

[phi1l]

BTW, I had no history of dyslexia, and I always got very good grades in math (with this exception -- probably part of the reason I beat myself up over it.)

DO you remember why you had all the answer the opposite of right?

[LarryG]

... just that he has the glyphs that symbolize those concepts reversed..

Yes. Exactly. Which is why your grade was fair. You were being tested on two things: did you understand the relative values of the various numbers; did you understand the meaning of the three relationship symbols? Yes to the first; No to the second. The fact it was a simple error of reversal doesn't make it any less wrong.

In the first half of your test, all of the problems involved addition. Suppose you had subtracted instead ... and subtracted correctly ... would you then argue that you actually got all the questions right, you just performed the wrong operation?

Or consider this ... suppose this had been a True/False test, and you answered all the true questions False and all the false questions True. Again, would you make the same argument -- that you understood the concept, but you got your answers reversed?

[Alex Franke]

So if I answer the question: "Who shot Abraham Lincoln" with "Lee Harvey Oswald" should I get partial credit?

Seeing where a student got confused is helpful for correcting their wrong answers, but it doesn't make the answer right or partially right. Wrong is wrong. It will always be wrong.

Here is a quick sample why it is important:

Okay, so it sounds like you would have given the music student an "F" too.

I don't see how the Lincoln/Oswald example fits in with the point I was trying to make about concept and symbolism, so no, I wouldn't see a reason to argue that case.

I completely understand the "why it matters in real life" part, but I don't necessarily think that's the goal when you're introducing a new mathematical concept to a child. It seems to me that you should get the mechanics and concepts down first, then maybe talk about how awful it would be to get it wrong out in the real world.

[Alex Franke]

DO you remember why you had all the answer the opposite of right?

Yes, because I beat myself up over it -- "stupid, stupid mistake!". I was probably thinking "greater than" as I was writing the "less than" symbol.

Yes. Exactly. Which is why your grade was fair. You were being tested on two things: did you understand the relative values of the various numbers; did you understand the meaning of the three relationship symbols? Yes to the first; No to the second. The fact it was a simple error of reversal doesn't make it any less wrong.

To be clear, I'm not suggesting that those answers were not wrong -- or even "less wrong than normal," or "almost right." They were clearly wrong. I'm arguing that the grade "U" is not appropriate in this case.

Or consider this ... suppose this had been a True/False test, and you answered all the true questions False and all the false questions True. Again, would you make the same argument -- that you understood the concept, but you got your answers reversed?

Almost certainly. Especially if I was so consistently wrong. The concept of how to tell the difference between one type of answer and the other would be clear. But the concept that the "T" means true and "F" means false, obviously not clear at all.

[dkerfoot]

Okay, so it sounds like you would have given the music student an "F" too.

I don't see how the Lincoln/Oswald example fits in with the point I was trying to make about concept and symbolism, so no, I wouldn't see a reason to argue that case.

I completely understand the "why it matters in real life" part, but I don't necessarily think that's the goal when you're introducing a new mathematical concept to a child. It seems to me that you should get the mechanics and concepts down first, then maybe talk about how awful it would be to get it wrong out in the real world.

I didn't engage the musical question because I see no relevancy to the math question. But the answer would be "Was playing it in the correct key one of the learning objectives?"

Not having access to the curriculum, I can't say for certain, but it seems reasonable to conclude that a key objective was: "Properly identify and use the symbols for greater than, less than and equals." You did not do this.

It is obvious that you really, really want to hear that this teacher was hard-hearted and unreasonable. You will not hear that from me. Quite honestly, if I found a teacher had given a passing grade to one of my children for the answers you provided, I would be very angry.

Wrong is wrong.

And that's all I have to say about that...

[cgallery]

Wow, we have a lot of tough graders here.

Once I noticed the pattern I would have provided a little more instruction and given you a chance to fix it.

I probably would have provided a nominal mark-down (maybe a couple of points) rather than let you earn a 100% on the work.

[Shep]

I was a child of the 80's so my teacher used the packman analogy. Pacman would always eat the larger number. She would even draw a circle around the > sign to make the pacman complete.

[Alex Franke]

It is obvious that you really, really want to hear that this teacher was hard-hearted and unreasonable. You will not hear that from me.

No, you have this wrong. Do I believe that? Yes. Do I want to hear that from everyone else? No, of course not.

The reason I posted it is to start a conversation on how a child should be graded on a new math concept when he has the mechanics correct but the symbolism incorrect. I personally don't see this as a black and white issue, which is why I think it's interesting to talk about. I'm also curious to know (if there are any early math teachers out there): What is the goal/curriculum at this level?

You obviously see it as black and white. You've made that perfectly clear, and I don't expect you to change your mind or try to make me feel good by telling me that the teacher was evil. :lol: