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Constructing a Computer Algebra System Capable of Generating Pedagogical Step-by-Step Solutions
KTH, School of Computer Science and Communication (CSC).
2016 (English)Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesisAlternative title
Konstruktion av ett datoralgebrasystem kapabelt att generera pedagogiska steg-för-steg-lösningar (Swedish)
Abstract [en]

For the problem of producing pedagogical step-by-step solutions to mathematical problems in education, standard methods and algorithms used in construction of computer algebra systems are often not suitable. A method of using rules to manipulate mathematical expressions in small steps is suggested and implemented. The problem of creating a step-by-step solution by choosing which rule to apply and when to do it is redefined as a graph search problem and variations of the A* algorithm are used to solve it. It is all put together into one prototype solver that was evaluated in a study. The study was a questionnaire distributed among high school students. The results showed that while the solutions were not as good as human-made ones, they were competent. Further improvements of the method are suggested that would probably lead to better solutions.

Abstract [sv]

För problemet att producera pedagogiska steg-för-steg-lösningar till matematiska problem inom utbildning, är vanliga metoder och algoritmer som används i konstruktion av datoralgebrasystem ofta inte lämpliga. En metod som använder regler för att manipulera matematiska uttryck i små steg föreslås och implementeras. Problemet att välja vilka regler som ska appliceras och när de ska göra det för att skapa en steg-för-steg-lösning omdefineras som ett grafsökningsproblem och varianter av algoritmen A* används för att lösa det. Allt sätts ihop till en prototyp av en lösare vilken utvärderas i en studie. Studien var ett frågeformulär som delades ut till gymnasiestudenter. Resultaten visade att även fast lösningar skapade av programmet inte var lika bra som lösningar skapade av människor, så var de anständiga. Fortsatta föbättringar av metoden föreslås, vilka troligtvis skulle leda till bättre lösningar.

Place, publisher, year, edition, pages
2016.
Keyword [en]
computer algebra system, step-by-step solutions, artificial intelligence, pedagogy, high school mathematics
Keyword [sv]
datoralgebrasystem, steg-för-steg-lösningar, artificiell intelligens, pedagogi, gymnasiematematik
National Category
Computer Science
Identifiers
URN: urn:nbn:se:kth:diva-189287OAI: oai:DiVA.org:kth-189287DiVA: diva2:945222
External cooperation
Mathleaks AB
Educational program
Master of Science in Engineering - Computer Science and Technology
Supervisors
Examiners
Available from: 2016-07-04 Created: 2016-06-30 Last updated: 2016-07-04Bibliographically approved

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CiteExportLink to record
Permanent link

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Citation style
  • apa
  • harvard1
  • ieee
  • modern-language-association-8th-edition
  • vancouver
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  • de-DE
  • en-GB
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  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
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