DISSOLVE: A system for the generation of human oriented solutions to algebraic equations

Jonathan Oliver; Ingrid Zukerman

doi:10.1007/3-540-52062-7_73

DISSOLVE: A system for the generation of human oriented solutions to algebraic equations

Jonathan Oliver, Ingrid Zukerman

Department of Data Science & AI

Research output: Chapter in Book/Report/Conference proceeding › Conference Paper › Research › peer-review

1 Citation (Scopus)

Abstract

In general, competent algebraists can easily recognize expressions which hold high potential for the successful application of commonly applied algebraic transformations, such as transferring terms to the other side of an equation and factoring out common factors. Novice students, however, have difficulty identifying these expressions and assessing the promise of the application of particular transformations. In order to teach these skills, an Intelligent Tutoring System must be able to reason about algebraic expressions in a way which is accessible to a student. In this paper, we describe a mechanism for the representation and manipulation of algebraic expressions which is able to characterize algebraic transformations commonly performed by algebraists. This mechanism has been implemented in a system called DISSOLVE which generates explainable and intuitively appealing solutions to algebraic equations at the high-school level.

Original language	English
Title of host publication	AI 1988 - 2nd Australian Joint Artificial Intelligence Conference, Proceedings
Publisher	Springer-Verlag London Ltd.
Pages	92-107
Number of pages	16
ISBN (Print)	9783540520627
DOIs	https://doi.org/10.1007/3-540-52062-7_73
Publication status	Published - 1 Jan 1990
Event	Australasian Joint Conference on Artificial Intelligence 1988 - Adelaide, Australia Duration: 15 Nov 1988 → 18 Nov 1988 Conference number: 2nd https://link.springer.com/book/10.1007/3-540-52062-7 (Proceedings)

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	406 LNAI
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	Australasian Joint Conference on Artificial Intelligence 1988
Abbreviated title	AI 1988
Country/Territory	Australia
City	Adelaide
Period	15/11/88 → 18/11/88
Internet address	https://link.springer.com/book/10.1007/3-540-52062-7 (Proceedings)

Keywords

AI and education
Symbolic manipulation

Access to Document

10.1007/3-540-52062-7_73

Cite this

Oliver, J., & Zukerman, I. (1990). DISSOLVE: A system for the generation of human oriented solutions to algebraic equations. In AI 1988 - 2nd Australian Joint Artificial Intelligence Conference, Proceedings (pp. 92-107). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 406 LNAI). Springer-Verlag London Ltd.. https://doi.org/10.1007/3-540-52062-7_73

Oliver, Jonathan ; Zukerman, Ingrid. / DISSOLVE : A system for the generation of human oriented solutions to algebraic equations. AI 1988 - 2nd Australian Joint Artificial Intelligence Conference, Proceedings. Springer-Verlag London Ltd., 1990. pp. 92-107 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

@inproceedings{7a90e5f314634794831fda46ef90db26,

title = "DISSOLVE: A system for the generation of human oriented solutions to algebraic equations",

abstract = "In general, competent algebraists can easily recognize expressions which hold high potential for the successful application of commonly applied algebraic transformations, such as transferring terms to the other side of an equation and factoring out common factors. Novice students, however, have difficulty identifying these expressions and assessing the promise of the application of particular transformations. In order to teach these skills, an Intelligent Tutoring System must be able to reason about algebraic expressions in a way which is accessible to a student. In this paper, we describe a mechanism for the representation and manipulation of algebraic expressions which is able to characterize algebraic transformations commonly performed by algebraists. This mechanism has been implemented in a system called DISSOLVE which generates explainable and intuitively appealing solutions to algebraic equations at the high-school level.",

keywords = "AI and education, Symbolic manipulation",

author = "Jonathan Oliver and Ingrid Zukerman",

year = "1990",

month = jan,

day = "1",

doi = "10.1007/3-540-52062-7_73",

language = "English",

isbn = "9783540520627",

series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",

publisher = "Springer-Verlag London Ltd.",

pages = "92--107",

booktitle = "AI 1988 - 2nd Australian Joint Artificial Intelligence Conference, Proceedings",

address = "Germany",

note = "Australasian Joint Conference on Artificial Intelligence 1988, AI 1988 ; Conference date: 15-11-1988 Through 18-11-1988",

url = "https://link.springer.com/book/10.1007/3-540-52062-7",

}

Oliver, J & Zukerman, I 1990, DISSOLVE: A system for the generation of human oriented solutions to algebraic equations. in AI 1988 - 2nd Australian Joint Artificial Intelligence Conference, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 406 LNAI, Springer-Verlag London Ltd., pp. 92-107, Australasian Joint Conference on Artificial Intelligence 1988, Adelaide, South Australia, Australia, 15/11/88. https://doi.org/10.1007/3-540-52062-7_73

DISSOLVE: A system for the generation of human oriented solutions to algebraic equations. / Oliver, Jonathan; Zukerman, Ingrid.
AI 1988 - 2nd Australian Joint Artificial Intelligence Conference, Proceedings. Springer-Verlag London Ltd., 1990. p. 92-107 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 406 LNAI).

Research output: Chapter in Book/Report/Conference proceeding › Conference Paper › Research › peer-review

TY - GEN

T1 - DISSOLVE

T2 - Australasian Joint Conference on Artificial Intelligence 1988

AU - Oliver, Jonathan

AU - Zukerman, Ingrid

N1 - Conference code: 2nd

PY - 1990/1/1

Y1 - 1990/1/1

N2 - In general, competent algebraists can easily recognize expressions which hold high potential for the successful application of commonly applied algebraic transformations, such as transferring terms to the other side of an equation and factoring out common factors. Novice students, however, have difficulty identifying these expressions and assessing the promise of the application of particular transformations. In order to teach these skills, an Intelligent Tutoring System must be able to reason about algebraic expressions in a way which is accessible to a student. In this paper, we describe a mechanism for the representation and manipulation of algebraic expressions which is able to characterize algebraic transformations commonly performed by algebraists. This mechanism has been implemented in a system called DISSOLVE which generates explainable and intuitively appealing solutions to algebraic equations at the high-school level.

AB - In general, competent algebraists can easily recognize expressions which hold high potential for the successful application of commonly applied algebraic transformations, such as transferring terms to the other side of an equation and factoring out common factors. Novice students, however, have difficulty identifying these expressions and assessing the promise of the application of particular transformations. In order to teach these skills, an Intelligent Tutoring System must be able to reason about algebraic expressions in a way which is accessible to a student. In this paper, we describe a mechanism for the representation and manipulation of algebraic expressions which is able to characterize algebraic transformations commonly performed by algebraists. This mechanism has been implemented in a system called DISSOLVE which generates explainable and intuitively appealing solutions to algebraic equations at the high-school level.

KW - AI and education

KW - Symbolic manipulation

UR - http://www.scopus.com/inward/record.url?scp=70349882498&partnerID=8YFLogxK

U2 - 10.1007/3-540-52062-7_73

DO - 10.1007/3-540-52062-7_73

M3 - Conference Paper

AN - SCOPUS:70349882498

SN - 9783540520627

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 92

EP - 107

BT - AI 1988 - 2nd Australian Joint Artificial Intelligence Conference, Proceedings

PB - Springer-Verlag London Ltd.

Y2 - 15 November 1988 through 18 November 1988

ER -

Oliver J, Zukerman I. DISSOLVE: A system for the generation of human oriented solutions to algebraic equations. In AI 1988 - 2nd Australian Joint Artificial Intelligence Conference, Proceedings. Springer-Verlag London Ltd. 1990. p. 92-107. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/3-540-52062-7_73

DISSOLVE: A system for the generation of human oriented solutions to algebraic equations

Abstract

Publication series

Conference

Keywords

Access to Document

Other files and links

Cite this