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> This is definitely a desirable quality in math/physics/chemistry exams. If you make a very long calculation (some of the exam questions require a full sheet o

> This is definitely a desirable quality in math/physics/chemistry exams. If you make a very long calculation (some of the exam questions require a full sheet of paper to calculate) almost perfectly but make a mistake on the second-to-last row, you should get your 4 out of 6 points or so. I question this. (I have worked as a teacher and as a practitioner) First of all, should we ask such long calculations in an exam situation without access to a computer? That's not real anyway. Second of all, if we are asking the long calculation with the expectation that students won't be able to complete it, why are we asking that question? Why don't we ask shorter questions that match the expectations we have? If we are asking the long calculation because we expect students should complete it, why should they get partial credit for failing to meet that expectation? That's what you're testing them on - and they haven't truthfully shown they were better than someone who wrote nothing. They've failed at completing the task, and/or at checking their work. It really shows they were better (or better trained) at gaming the exam - knowing exactly what to write to satisfy the examiner and gain partial credit. This training is very well paid, by the way. >Our tests are standardized too (and same questions nationwide, changing every year). They're just not multiple choice questions. Even if the questions are consistent nationwide, if the pass mark is low enough (or with partial credits), students can arrive at university with wildly different knowledge, having passed via different sections of the course, if not via luck. The university will naturally assume that the student knows all of those sections well, which many students will not. This creates an obvious problem of services being inadequate for first year undergraduates. Where I live this is readily apparent, but few people have noticed and nobody is dealing with it.

krisoft 12y ago
It's not really partial credit for failing to meet expectations. Just an example. A 'complicated' geometry problem. Our expectations is that the student understands the text, draws a draft of the shapes. She then recalls the appropriate two or three equitations. Formulates a plan to solve them (first this eq, which gives that info, with which I can ...), then she executes that plan and writes down the result. Student A does a neat drawing, marks the important measurements, uses those same markings to note the equitations down and sets out to solve them. During a substitution she mistakes one of her 3-s to a 2, therefore the result is completely wrong. She completed 3 of our expectations and failed the last one. Student B draws a happy seal and takes a nap. 0 out of 4 completed goals. I would argue that the first students deserves more credit, and those are full credits not partials.
- learnstats2 12y ago
  This is a fair comment, that a single question can be used test several different aspects of a topic. However, unless you are specifically testing the student's ability to string the different aspects together precisely, I don't believe that to be an optimal exam question. Here, for example, you are seem to be allowing the student a 50% passing grade (2/4 expectations met) if they show they understand the text by drawing it out, and remember the formulas from the syllabus sufficiently to write them down without starting to apply them. That maybe isn't your intent, and maybe your ideal mark scheme would try to avoid over-crediting something like that. But even if that's not what you intended, that has become the reality: setting expectations for partial credit has led to increasingly simplistic expectations of students and this in turn to rampant grade inflation. Grade inflation has been strongly encouraged by institutions' statistical collation, but has been mostly avoided by the SAT. I'm not sure that I want students to have access to good grades even if they consistently give wrong final answers, transposing digits and so on. It shows a lack of precision and a lack of full understanding of the question (not able to do effective sanity checking). Precision is a skill that mathematics can help people to learn, in my opinion. The SAT being multiple choice means you have a fair opportunity to correct this type of mistake - a typographical error typically won't fit with any of the multiple choice answers and you'll have the chance to correct it (costing you only the correction time - and teaching you that precision is of some importance). The wrong multiple choice answers tend to fit deliberately with common conceptual errors. This actually illustrates a useful element of the SAT exam design.
kruczek 12y ago
> Second of all, if we are asking the long calculation with the expectation that students won't be able to complete it, why are we asking that question? Why don't we ask shorter questions that match the expectations we have? We are asking that question, because we want to verify that the student understands the process of solving the problem. Therefore final answer is of lesser importance - what matters is proper procedure that is used to arrive to the answer. And no, shorter questions and shorter answers are not always a way to go, because some problems do require lengthy procedure to be solved. And of course you're right that in real life such calculations would be done by a computer. But that is because in real life the goal is to solve the problem, while at school the goal is to teach the student and verify that knowledge (so that in the future he will be able to create a computer able to solve such problem, metaphorically speaking). > If we are asking the long calculation because we expect students should complete it, why should they get partial credit for failing to meet that expectation? That's what you're testing them on - and they haven't truthfully shown they were better than someone who wrote nothing. They've failed at completing the task, and/or at checking their work. Again it comes down to the expectation - student should be expected to understand the problem and the solution, not to write a single number as an answer. Therefore partial solution (i.e. a procedure where some steps are invalid, but some are still valid) is better than no solution.
hessenwolf 12y ago
Maths practitioner here. Yes, getting the right answer is important. The longer exams give grades for checking your results usually. However, calculations usually take months to set up and implement, and even longer to test, and each calculation needs to be checked and re-checked several times. There is pretty much no time I get the right answer the first time, and I am the go-to person for what I do.
exDM69 12y ago
I respect your opinion but I can't agree with it. What if you make two mistakes that cancel each other out? You get the correct answer but should you get full points? In my opinion: no. > First of all, should we ask such long calculations in an exam situation without access to a computer? That's not real anyway. First of all, students have pretty fancy calculators these days. And one sheet full of equations is not that much for a practical, applied problem. Testing only mundane math skills (simplify, differentiate, solve, etc) doesn't test the ability to apply the skills to any real world problems. There are short problems too, it's not all long problems. If it was only about the correct answer, the grading might as well be 0 to 1 points. Now there are questions worth 1, 2, or 6 points. The first being "simplify this equation" and the last being an applied problem. And learning how to do math without the aid of a computer is a very valuable skill. In practice you have the aid of computers, books and collections of formulae but in my experience, there's no substitute for pen and paper practice. Learning to solve math problems is a skill, not a piece of knowledge. If you don't know some things by heart, and know how to attack a problem, a computer will not help you. > Second of all, If we are asking the long calculation with the expectation that students won't be able to complete it, why are we asking that question? Why don't we ask shorter questions that match the expectations we have? The expectation, of course, is that a student will be able to complete the whole thing. But the longer the calculation, the higher the chance of making a simple stupid mistake. The reviewer will evaluate whether or not the student showed that he understands the problem and the solution. If there's obviously no idea what is going on, it's going to be zero points. Even one point requires a partial solution. > It really shows they were better (or better trained) at gaming the exam - knowing exactly what to write to satisfy the examiner and gain partial credit. This training is very well paid, by the way. No, that's not the case at all. Getting partial credit is completely worthless, you need to have at least 50% of the score to pass. Trying to "game" the exercises won't take you far. For a point of reference, when I did my finals more than a decade ago, you needed 57/60 points (ie 10 problems) to get the highest grade. That means making at most three trivial mistakes during 6 hours.

krisoft 12y ago

It's not really partial credit for failing to meet expectations. Just an example. A 'complicated' geometry problem. Our expectations is that the student understands the text, draws a draft of the shapes. She then recalls the appropriate two or three equitations. Formulates a plan to solve them (first this eq, which gives that info, with which I can ...), then she executes that plan and writes down the result. Student A does a neat drawing, marks the important measurements, uses those same markings to note the equitations down and sets out to solve them. During a substitution she mistakes one of her 3-s to a 2, therefore the result is completely wrong. She completed 3 of our expectations and failed the last one. Student B draws a happy seal and takes a nap. 0 out of 4 completed goals. I would argue that the first students deserves more credit, and those are full credits not partials.

learnstats2 12y ago
This is a fair comment, that a single question can be used test several different aspects of a topic. However, unless you are specifically testing the student's ability to string the different aspects together precisely, I don't believe that to be an optimal exam question. Here, for example, you are seem to be allowing the student a 50% passing grade (2/4 expectations met) if they show they understand the text by drawing it out, and remember the formulas from the syllabus sufficiently to write them down without starting to apply them. That maybe isn't your intent, and maybe your ideal mark scheme would try to avoid over-crediting something like that. But even if that's not what you intended, that has become the reality: setting expectations for partial credit has led to increasingly simplistic expectations of students and this in turn to rampant grade inflation. Grade inflation has been strongly encouraged by institutions' statistical collation, but has been mostly avoided by the SAT. I'm not sure that I want students to have access to good grades even if they consistently give wrong final answers, transposing digits and so on. It shows a lack of precision and a lack of full understanding of the question (not able to do effective sanity checking). Precision is a skill that mathematics can help people to learn, in my opinion. The SAT being multiple choice means you have a fair opportunity to correct this type of mistake - a typographical error typically won't fit with any of the multiple choice answers and you'll have the chance to correct it (costing you only the correction time - and teaching you that precision is of some importance). The wrong multiple choice answers tend to fit deliberately with common conceptual errors. This actually illustrates a useful element of the SAT exam design.

kruczek 12y ago

> Second of all, if we are asking the long calculation with the expectation that students won't be able to complete it, why are we asking that question? Why don't we ask shorter questions that match the expectations we have? We are asking that question, because we want to verify that the student understands the process of solving the problem. Therefore final answer is of lesser importance - what matters is proper procedure that is used to arrive to the answer. And no, shorter questions and shorter answers are not always a way to go, because some problems do require lengthy procedure to be solved. And of course you're right that in real life such calculations would be done by a computer. But that is because in real life the goal is to solve the problem, while at school the goal is to teach the student and verify that knowledge (so that in the future he will be able to create a computer able to solve such problem, metaphorically speaking). > If we are asking the long calculation because we expect students should complete it, why should they get partial credit for failing to meet that expectation? That's what you're testing them on - and they haven't truthfully shown they were better than someone who wrote nothing. They've failed at completing the task, and/or at checking their work. Again it comes down to the expectation - student should be expected to understand the problem and the solution, not to write a single number as an answer. Therefore partial solution (i.e. a procedure where some steps are invalid, but some are still valid) is better than no solution.

hessenwolf 12y ago

Maths practitioner here. Yes, getting the right answer is important. The longer exams give grades for checking your results usually. However, calculations usually take months to set up and implement, and even longer to test, and each calculation needs to be checked and re-checked several times. There is pretty much no time I get the right answer the first time, and I am the go-to person for what I do.

exDM69 12y ago

I respect your opinion but I can't agree with it. What if you make two mistakes that cancel each other out? You get the correct answer but should you get full points? In my opinion: no. > First of all, should we ask such long calculations in an exam situation without access to a computer? That's not real anyway. First of all, students have pretty fancy calculators these days. And one sheet full of equations is not that much for a practical, applied problem. Testing only mundane math skills (simplify, differentiate, solve, etc) doesn't test the ability to apply the skills to any real world problems. There are short problems too, it's not all long problems. If it was only about the correct answer, the grading might as well be 0 to 1 points. Now there are questions worth 1, 2, or 6 points. The first being "simplify this equation" and the last being an applied problem. And learning how to do math without the aid of a computer is a very valuable skill. In practice you have the aid of computers, books and collections of formulae but in my experience, there's no substitute for pen and paper practice. Learning to solve math problems is a skill, not a piece of knowledge. If you don't know some things by heart, and know how to attack a problem, a computer will not help you. > Second of all, If we are asking the long calculation with the expectation that students won't be able to complete it, why are we asking that question? Why don't we ask shorter questions that match the expectations we have? The expectation, of course, is that a student will be able to complete the whole thing. But the longer the calculation, the higher the chance of making a simple stupid mistake. The reviewer will evaluate whether or not the student showed that he understands the problem and the solution. If there's obviously no idea what is going on, it's going to be zero points. Even one point requires a partial solution. > It really shows they were better (or better trained) at gaming the exam - knowing exactly what to write to satisfy the examiner and gain partial credit. This training is very well paid, by the way. No, that's not the case at all. Getting partial credit is completely worthless, you need to have at least 50% of the score to pass. Trying to "game" the exercises won't take you far. For a point of reference, when I did my finals more than a decade ago, you needed 57/60 points (ie 10 problems) to get the highest grade. That means making at most three trivial mistakes during 6 hours.