# I need a mathematician !

…or just someone good at maths.
So I made an educational software based on multichoice quizzes.
The scoring system that I use is simply calculating the percentage of correct answers among the total answers, so if I answered 100 questions and 50 were wrong I get a score of 50% of accuracy.
The problem with this scoring system is that it doesnt reward quantity of questions answered because I would get the same score for someone who answered 4 questions giving 2 correct answers.

Any ideas for a new formula that also rewards quantity ? thanks

This is not a mathematical question. The two things are  mathematically seen  not related to each other.

Hi Horacio,

You almost got it. Instead of calculating the number of QuestionsCorrect/QuestionsAnswered (2/4 = 0.5 or 50 %), maybe try QuestionsCorrect/TotalQuestions (2/100 = 0.02 or 2%).

or assign a weight to each question…

score=sum(weight of correct answers)/sum(weight of all questions)

So if they answer all the questions correctly the score is still 100% but if they answer only the easy questions and not the hard ones the score is lower etc.

[code]Example:
100 questions
10 answers must be given to get points at all

Formula: Maximum(0, (correct answers - 10) / (total questions - minimum answers))
0 > 0
1 > 0
10 > 0
20 > 0,11
30 > 0,22
50 > 0,44
90 > 0,89
100 > 1,00[/code]

Score = (Accuracy * ok) /100

I’m testing this on an excell sheet with random values to see if it’s proportional since I’m not a very mathematical person but it seems that this formula now rewards both quantity and accuracy

Another thing to consider: If a person can choose to not answer a question, then you should probably include a “correction for guessing” which typically means that if each question has M possible answers (e.g. M=4 means there are 4 choices: A, B, C, and D), then a correct answer is worth one point, and an incorrect answer is worth -(1/M) points. Most big standardized tests use this formula, as it gives equivalent scores so a person who is guessing randomly vs. a person who answers no questions at all.

If I go to the California Department of Motor Vehicles to obtain a driver’s license, I must not leave off more than 4 questions or so, otherwise I kiss the license good bye.

I find it pretty preposterous someone would be able to get away with answering only 4 questions out of 100 and still get a good notation.

I know an educational software is biased towards reward as incentive, and penalization is out of fashion, but there should probably be a motivation to fill as many questions as possible. Or maybe the program could just go “try again, please” if the number of responses is too low.

Or simply don’t use a percentage scale as the final reward.

"You answered 5 questions correctly out of a total of ten for this test!
You earned 21 points on this test!
You have 1,742 points in total for the GeeGaw Education Test System! "

Something along those lines, only better of course. With cool graphics and exploding fireworks perhaps?

Educational material (at least here in the United States) is geared towards not damaging the self-esteem of the student… it is not designed to teach them anything, especially how to “think for themselves”… it teaches learning by rote. “2+2=4”, but not WHY.

This is evidenced by the “No Child left behind” program. Promote everyone, lesson plan be damned.

While I more or less agree with you, at least in some specific cases, why does 2+2=4?

(Actually, that might be considered teasing, and I didn’t mean it that way. The proof for 1+1=2, at least as I remember it from Freshman year, was something like 1800 theorems and darn near 20,000 steps. In other words, it is non-trivial. And you need that to prove 2+2 =4. If I recall correctly. )

Hell is paved with good intentions.

France saw this year a rate of 88% success rate in high school graduations. The result is a significant number of students arriving at University not knowing how to spell or count. Poor clueless losers…

My software with multi choice quizzes is more about self evaluation rather than self esteem.

wasn’t inferring your software was not a postive contribution to the educational system. just observing that as a whole the system is failing its commitment to the student and to society in general

[quote=199867:@Paul Raulerson]While I more or less agree with you, at least in some specific cases, why does 2+2=4?

(Actually, that might be considered teasing, and I didn’t mean it that way. The proof for 1+1=2, at least as I remember it from Freshman year, was something like 1800 theorems and darn near 20,000 steps. In other words, it is non-trivial. And you need that to prove 2+2 =4. If I recall correctly. )[/quote]

This brings the following little story to my mind:

I once asked my little daughter: “What is 6 + 8 ?”

I was puzzled, but asked back: “Okay, this is not the result I get, but maybe you can explain how you get that result?”

“Daddy, don’t you see? In 6 there is one circle and in 8 there are 2 of it! 3 circles! 6 + 8 is 3 circles!”

Conclusion: Once you got educated, it becomes pretty difficult to see the world from other perspectives…

Based on the proof set forth by Olivers daughter… 2+2=1

2 is a curly line, but adding another curly line results in one curly line

Any mathematical opinions of my new formula ?
This formula (Score) now should reward also quantity of questions answered