RUcore: Rutgers University Community Repository
Early algebra ideas involving one variable, Clip 1 of 11: Open sentences that can be made True or False with Legal or Illegal substitutions
Descriptive
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MovingImage
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A54A55-ALG-PIB-CLIP001
Genre
(authority = RURes_Genre)
Research data
Genre
(authority = RURes_dataGenre)
Observational data
Genre
(authority = RURes_dataLifecycle)
Edited data
Genre
(authority = RURes_dataLifecycle)
Repurposed data
Genre
(authority = RURes_researchDataType)
Longitudinal data
Genre
(authority = RURes_dataCollectionSetting)
School
Genre
(authority = RURes_researchMethodology)
Qualitative research
Genre
(authority = RURes_qualitativeMethod)
Educational interventions (large group)
Subject
Name
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NamePart
(type = corporate)
Harding Elementary School (Kenilworth, N.J.)
Subject
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(authority = RBDIL_personal)
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(type = personal)
Brian (Kenilworth, student)
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Name
(authority = RBDIL_personal)
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Michael A. (Kenilworth, student)
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(authority = RBDIL_personal)
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Jeff (student)
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(authority = RBDIL_personal)
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Robert (student)
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(authority = RBDIL_personal)
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Matt (student)
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(type = personal)
Romina (student)
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Stephanie (student)
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Amy-Lynn (student)
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Michelle I. (student)
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Michelle R. (student)
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Ankur (student)
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Milin (student)
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Sample of human subjects
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Topic
Mathematics education
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(authority = LCSH)
Topic
Learning, Psychology of--Case studies
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(authority = LCSH)
Topic
Critical thinking in children--New Jersey--Case studies
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(authority = Grade range)
Topic
6-8
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(authority = NCTM Content)
Topic
Algebra
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Topic
Problem solving
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Reasoning and proof
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6
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Algebra
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Topic
Open sentence in one variable
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Topic
Color markers
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(authority = rbdil_forms of reasoning, strategies and heuristics)
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Direct reasoning
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(authority = rbdil_forms of reasoning, strategies and heuristics)
Topic
Substituting numbers for variables
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Equations
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Classroom
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Public school
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Teacher view
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Topic
Generalizing
Subject
(authority = rbdil_representations)
Topic
Truth sets
Subject
(authority = rbdil_representations)
Topic
Box notation for variable
Subject
(authority = rbdil_topic)
Topic
Variables
Subject
(authority = rbdil_district)
Geographic
Kenilworth Public Schools
Abstract
(type = summary)
In the first of eleven clips from the first day of the Early Algebra Ideas sessions, the researcher, Robert B. Davis, introduces ideas about algebraic equations with one variable and truth sets to a class of 6th grade students. Davis begins with the first problem statement printed below to introduce ideas about algebraic sentences or equations with one variable that can be true, false or open. The concept of a variable is introduced by varying the values that can be inserted into a printed ”box” that is a term within the equation. He introduces the idea of a truth set with brackets before demonstrating the mathematical Rule of Substitution, which says that in evaluating any mathematical expression or equation, if a variable appears more than once, for a legal substitution, the same value must be inserted into each “box”. Using the second problem statement below, which has two “boxes” in the equation, Davis asks the students for values to substitute into each “box” in order to create sentences that are legal and false; illegal and false; illegal and true; or legal and true. Observers present included researchers Amy Martino and Alice Alston and Kenilworth mathematics supervisor, Marcia O'Brien.
Problem Statements:
1. True, False or Open?
3 + □ = 5
Is there a number that would make the statement False/True?
Use { } Truth set – rather than “filling in the box and erasing it “.
3. Open sentences with two of the same variable (two “boxes”)
□ + □ = 8
Legal and false? Illegal and false? Illegal and true? Legal and true?
Problem Statements:
1. True, False or Open?
3 + □ = 5
Is there a number that would make the statement False/True?
Use { } Truth set – rather than “filling in the box and erasing it “.
3. Open sentences with two of the same variable (two “boxes”)
□ + □ = 8
Legal and false? Illegal and false? Illegal and true? Legal and true?
PhysicalDescription
Extent
(unit = digital file(s))
1
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video/quicktime
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video/x-flv
TargetAudience
(authority = RURes_discipline)
Social science
TargetAudience
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Mathematics education
Note
(type = supplementary materials)
Transcript and student work are also available.
Note
(type = APA citation)
Robert B. Davis Institute for Learning. (1993). Early algebra ideas involving one variable, Clip 1 of 11: Open sentences that can be made True or False with Legal or Illegal substitutions [video]. Retrieved from
Name
(type = personal)
NamePart
(type = family)
Davis
NamePart
(type = given)
Robert B. (Robert Benjamin)
Affiliation
Rutgers, the State University of New Jersey
Role
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(type = text)
Researcher
NamePart
(type = date)
1926-
Name
(type = personal)
NamePart
(type = family)
Maher
NamePart
(type = given)
Carolyn Alexander
Affiliation
Rutgers, the State University of New Jersey
Role
RoleTerm
(authority = marcrelator);
(type = text)
Researcher
Name
(type = personal)
NamePart
(type = family)
Alston
NamePart
(type = given)
Alice S.
Description
Rutgers, the State University of New Jersey
Role
RoleTerm
(authority = marcrelator);
(type = text)
Researcher
Name
(type = personal)
NamePart
(type = family)
Martino
NamePart
(type = given)
Amy Marie
Affiliation
Rutgers, the State University of New Jersey
Role
RoleTerm
(authority = marcrelator);
(type = text)
Researcher
Name
(type = personal)
NamePart
(type = family)
O'Brien
NamePart
(type = given)
Marcia Joan
Affiliation
Kenilworth (NJ) Public Schools
Role
RoleTerm
(authority = marcrelator);
(type = text)
Teacher
OriginInfo
CopyrightDate
1999-09-30
Place
PlaceTerm
(type = text)
New Brunswick, NJ
Publisher
Robert B. Davis Institute for Learning
RelatedItem
(type = host)
TitleInfo
Title
A54, Early algebra ideas involving one variable (teacher view), Grade 6, September 30, 1993, raw footage.
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A54-19930930-KNWH-TV-CLASS-GR6-ALG-PIB-RAW
RelatedItem
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TitleInfo
Title
A55, Early algebra ideas involving one variable (side view), Grade 6, September 30, 1993, raw footage.
Identifier
A55-19930930-KNWH-SV-CLASS-GR6-ALG-PIB-RAW
RelatedItem
(type = is referenced by)
TitleInfo
Title
Teaching Algebra Ideas to Elementary School Children: Robert B. Davis' Introduction to Early Algebra / by Kathleen E. Spang.
Identifier
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QA.S735 2009
Subject
HierarchicalGeographic
Country
UNITED STATES
State
New Jersey
County
Union County
City
Kenilworth (N.J.)
Extension
DescriptiveEvent
Type
Related publication
Label
Ed.D. dissertation references the video footage that includes Early algebra ideas involving one variable, Clip 1 of 11: Open sentences that can be made True or False with Legal or Illegal substitutions.
Place
Rutgers, the State University of New Jersey, New Brunswick, NJ
DateTime
2009
AssociatedEntity
Role
Author
Name
Spang, Kathleen E.
Affiliation
Rutgers Graduate School of Education
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References
Name
Teaching algebra ideas to elementary school children : Robert B. Davis' introduction to early algebra
Identifier
(type = lccn)
QA.S735 2009
Reference
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QA.S735 2009
Detail
Dissertation is available in hard copy in the Rutgers University Libraries' dissertation collection.
TitleInfo
Title
Early algebra ideas involving one variable, Clip 1 of 11: Open sentences that can be made True or False with Legal or Illegal substitutions
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Robert B. Davis Institute for Learning Mathematics Education Collection
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Identifier
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doi:10.7282/T3XS5T98
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Rights
RightsDeclaration
(AUTHORITY = rbdil1_v1);
(ID = rbdil1_v1)
The video is protected by copyright. It is available for reviewing and use within the Video Mosaic Collaborative (VMC) portal. Please contact the Robert B. Davis Institute for Learning (RBDIL) for further information about the use of this video.
RightsHolder
(type = corporate)
Name
Robert B. Davis Institute for Learning
Role
Copyright holder
Telephone
732-932-8848
Address
Rutgers Graduate School of Education
10 Seminary Place
New Brunswick, NJ 08901-1183
10 Seminary Place
New Brunswick, NJ 08901-1183
ContactInformationDate
2009-11-03
RightsEvent
Type
Permission or license
Label
Non-exclusive license to share the video presentation via RUcore.
DateTime
2009-11-03
Detail
Non-exclusive license to digitize and make openly available the videos and other collection resources of the Institute is on file in the office of the RUcore Collections Manager.
AssociatedEntity
Role
Licensor
Name
Maher, Carolyn A.
Affiliation
Director, Robert B. Davis Institute for Learning, Rutgers Graduate School of Education
Copyright
Status
Copyright protected
Availability
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Open
Reason
Permission or license
Publication
Status
Unpublished
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