Grading essays

Plagiarism detection and similarity comparisons

Analysis of English word forms and sentence reduction

Checking spelling

with(EssayTools);

$\left[\mathrm{AppendToWordList}\,\mathrm{BinaryCosineCoefficient}\,\mathrm{BinaryDiceCoefficient}\,\mathrm{BinaryJaccardCoefficient}\,\mathrm{BuildScoreModel}\,\mathrm{CosineCoefficient}\,\mathrm{CountMisspellings}\,\mathrm{CountUseOfAllWords}\,\mathrm{CountUseOfEachWord}\,\mathrm{DetectPlagiarism}\,\mathrm{DiceCoefficient}\,\mathrm{IsAdjective}\,\mathrm{IsAdverb}\,\mathrm{IsConjunction}\,\mathrm{IsDefiniteArticle}\,\mathrm{IsIndefiniteArticle}\,\mathrm{IsInterjection}\,\mathrm{IsIntransitiveVerb}\,\mathrm{IsNominative}\,\mathrm{IsNoun}\,\mathrm{IsNounPhrase}\,\mathrm{IsPlural}\,\mathrm{IsPreposition}\,\mathrm{IsPronoun}\,\mathrm{IsTransitiveVerb}\,\mathrm{IsUsuallyParticipleVerb}\,\mathrm{IsVerb}\,\mathrm{JaccardCoefficient}\,\mathrm{Lemma}\,\mathrm{Misspellings}\,\mathrm{PartOfSpeech}\,\mathrm{QuadraticWeightedKappa}\,\mathrm{Reduce}\,\mathrm{Score}\,\mathrm{SetWordList}\,\mathrm{SimilarityScore}\,\mathrm{SpellCorrectWord}\,\mathrm{WordUse}\right]$

Question := "Why is the sky blue?":

Answers := Array(): Scores := Array():

Answers(1) :=
"The blue color of the sky is due to Rayleigh scattering. As light moves through the atmosphere, most of the longer wavelengths pass straight through. Little of the red, orange and yellow light is affected by the air. However, much of the shorter wavelength light is absorbed by the gas molecules. The absorbed blue light is then radiated in different directions. It gets scattered all around the sky. Whichever direction you look, some of this scattered blue light reaches you. Since you see the blue light from everywhere overhead, the sky looks blue. ":

Scores(1) := 10: #www.sciencemadesimple.com/sky_blue.html

Answers(2) :=
"Sunlight reaches Earth's atmosphere and is scattered in all directions by all the gases and particles in the air. Blue light is scattered in all directions by the tiny molecules of air in Earth's atmosphere. Blue is scattered more than other colors because it travels as shorter, smaller waves. This is why we see a blue sky most of the time.":

Scores(2) := 10: #spaceplace.nasa.gov/blue-sky

Answers(3) :=
"A clear cloudless day-time sky is blue because molecules in the air scatter blue light from the sun more than they scatter red light.":

Scores(3) := 8: #math.ucr.edu/home/baez/physics/General/BlueSky/blue_sky.html

Answers(4) :=
"The blue color of the sky is due to Rayleigh scattering. As light moves through the atmosphere, most of the longer wavelengths pass straight through. Little of the red, orange and yellow light is affected by the air.  However, much of the shorter wavelength light is absorbed by the gas molecules. The absorbed blue light is then radiated in different directions. It gets scattered all around the sky. Whichever direction you look, some of this scattered blue light reaches you. Since you see the blue light from everywhere overhead, the sky looks blue.":

Scores(4) := 10: #www.sciencemadesimple.com/sky_blue.html

Answers(5) :=
"Sunlight is a mix of all the colours of the rainbow. Light is a spectrum of light of different wavelengths, from the shorter blue to the longer red  wavelengths.  When sunlight enters the atmosphere, the molecules in the air are the right size to scatter the blue wavelengths of the sunlight, which sort of paints the sky blue.":

Scores(5) := 7: #answers.yahoo.com/question/index?qid=20071031201452AAwbqie

Answers(6) :=
"Blue light is scattered by the air molecules in the atmosphere (referred to as Rayleigh scattering). The blue wavelength is scattered more, because the scatteing effect increases with the inverse of the fourth power of the incident wavelength. ":

Scores(6) := 7: #answers.yahoo.com/question/index?qid=20071031201452AAwbqie

Answers(7) := "The sky is blue because of a reflection of the sea.":

Scores(7) := 0:

Answers(8) := "The sky is blue because the sun is yellow and the grass is green. Yellow and green make blue.":

Scores(8) := 0:

Answers(9) := "These days, the atmosphere is mostly nitrogen and oxygen. Sunlight is made up of all the colors of the rainbow (as well as many wavelengths we can't see); as it jostles through air molecules, blue light is most efficiently reflected, so our eyes end up experiencing a beautiful azure shade":

Scores(9) := 10: #news.discovery.com/earth/no-seriously-why-is-the-sky-blue.html

model := BuildScoreModel(Answers, Scores, questionText = Question);

$\mathrm{model}:=\left[\begin{array}{c}\mathrm{Scoring\; Model}\\ \mathrm{9\; Responses}\end{array}\right]$

NewResponse :=
"Blue and violet wavelengths, on the other hand, are absorbed by the gas molecules and scattered across the sky. Your eye sees these reflected wavelengths as blue.":
#wonderopolis.org/wonder/why-is-the-sky-blue/

Score(NewResponse,model);

$7$

WordUse(Answers, showcount, mincount = 3);

$\left[''the''\=56\,''of''\=24\,''blue''\=24\,''is''\=24\,''light''\=19\,''sky''\=11\,''in''\=9\,''scattered''\=9\,''air''\=8\,''as''\=7\,''atmosphere''\=7\,''all''\=7\,''and''\=7\,''molecules''\=7\,''by''\=7\,''wavelengths''\=6\,''a''\=6\,''you''\=6\,''through''\=5\,''sunlight''\=5\,''because''\=5\,''to''\=5\,''see''\=4\,''it''\=4\,''shorter''\=4\,''from''\=4\,''most''\=4\,''wavelength''\=4\,''yellow''\=4\,''absorbed''\=4\,''directions''\=4\,''red''\=4\,''reaches''\=3\,''scattering''\=3\,''this''\=3\,''longer''\=3\,''more''\=3\,''scatter''\=3\,''rayleigh''\=3\,''different''\=3\right]$

Score("The is of blue light sky in scattered air.", model);

$5$

Score("Blue light sky scattered air molecules.", model);

$6$

ModifiedResponse := Reduce(NewResponse);

$\mathrm{ModifiedResponse}:=\left[''blue\; violet\; wavelength\; hand\; be\; absorbed\; gas\; molecule\; scatter\; sky''\,''eye\; see\; reflected\; wavelength\; blue''\right]$

Lemma("is");

$''be''$

Lemma("are");

$''be''$

Lemma("flew");

$''fly''$

Lemma("flies");

$''fly''$

TwoIdeas := "the sky is blue because it scatters sunlight.";

$\mathrm{TwoIdeas}:=''the\; sky\; is\; blue\; because\; it\; scatters\; sunlight.''$

map(PartOfSpeech, StringTools:-Words(TwoIdeas));

$\left[\left[''Definite\; Article''\,''Adverb''\right]\,\left[''Noun''\,''Verb\; (usually\; participle)''\right]\,\left[''Verb\; (usually\; participle)''\right]\,\left[''Noun''\,''Adjective''\,''Verb\; (usually\; participle)''\right]\,\left[''Conjunction''\right]\,\left[''Pronoun''\,''Noun''\right]\,\mathrm{FAIL}\,\left[''Noun''\right]\right]$

Lemma("scatters");

$''scatter''$

PartOfSpeech(%);

$\left[''Verb\; (transitive)''\,''Noun''\,''Verb\; (usually\; participle)''\right]$

Reduce(TwoIdeas);

$\left[''sky\; be\; blue''\,''sky\; scatter\; sunlight''\right]$

SimilarityScore(NewResponse, Answers);

SimilarityScore(NewResponse, Answers, methods = [CosineCoefficient]);

SimilarityScore(NewResponse, Answers, methods = [DiceCoefficient]);

DetectPlagiarism(Answers);

$\left[\left[1\,4\,1.\right]\,\left[7\,8\,0.3529411765\right]\right]$